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Cosmic microwave background polarimetry with ABS and ACT: Instrumental design, characterization, and analysis

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C OSMIC M ICROWAVE BACKGROUND P OLARIMETRY
WITH
ABS AND ACT: I NSTRUMENTAL D ESIGN ,
C HARACTERIZATION , AND A NALYSIS
S ARA M ICHELLE S IMON
A D ISSERTATION
P RESENTED TO THE FACULTY
OF
IN
P RINCETON U NIVERSITY
C ANDIDACY FOR THE D EGREE
OF
D OCTOR OF P HILOSOPHY
R ECOMMENDED FOR ACCEPTANCE
BY THE
D EPARTMENT OF
P HYSICS
A DVISER : S UZANNE T. S TAGGS
S EPTEMBER 2016
ProQuest Number: 10167560
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c Copyright by Sara Michelle Simon, 2016.
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Abstract
The ΛCDM model of the universe is supported by an abundance of astronomical observations,
but it does not confirm a period of inflation in the early universe or explain the nature of dark energy
and dark matter. The polarization of the cosmic microwave background (CMB) may hold the key
to addressing these profound questions. If a period of inflation occurred in the early universe, it
could have left a detectable odd-parity pattern called B-modes in the polarization of the CMB on
large angular scales. Additionally, the CMB can be used to probe the structure of the universe on
small angular scales through lensing and the detection of galaxy clusters and their motions via the
Sunyaev-Zel’dovich effect, which can improve our understanding of neutrinos, dark matter, and
dark energy.
The Atacama B-mode Search (ABS) instrument was a cryogenic crossed-Dragone telescope
located at an elevation of 5190 m in the Atacama Desert in Chile that observed from February
2012 until October 2014. ABS searched on degree-angular scales for inflationary B-modes in the
CMB and pioneered the use of a rapidly-rotating half-wave plate (HWP), which modulates the
polarization of incoming light to permit the measurement of celestial polarization on large angular
scales that would otherwise be obscured by 1/ f noise from the atmosphere. Located next to
ABS in the Atacama is the Atacama Cosmology Telescope (ACT), which is an off-axis Gregorian
telescope. Its large 6 m primary mirror facilitates measurements of the CMB on small angular
scales. HWPs are baselined for use with the upgraded polarization-sensitive camera for ACT,
called Advanced ACTPol, to extend observations of the polarized CMB to larger angular scales
while also retaining sensitivity to small angular scales.
The B-mode signal is extremely faint, and measuring it poses an instrumental challenge that requires the development of new technologies and well-characterized instruments. I will discuss the
use of novel instrumentation and methods on the ABS telescope and Advanced ACTPol, the characterization of the ABS instrument, and the first two seasons of ABS data, including an overview
of the data selection process.
iii
Acknowledgements
This work would not have been possible without the exceptional people I have met along the way.
I owe a great deal of thanks to my adviser, Suzanne Staggs, who has been a great guide throughout
my graduate experience. She always gave me the freedom to follow my intellectual curiosity while
pushing me to constantly challenge myself and grow.
I would also like to thank Lyman Page, who has also been a valuable adviser throughout my
graduate career. From helping me and my colleagues study for prelims at midnight to helping
me with my talks, Lyman has always been supportive of my work. The Atacama B-mode Search
(ABS) experiment would be lost without the Herculean efforts of Akito Kusaka. His ingenuity
and commitment have been integral to the ABS project, and he has intellectually challenged me
throughout my years working with him. I have also had the great opportunity of working on
the feedhorn arrays for Advanced ACTPol (AdvACT) with Jeff McMahon. His positivity and
mentorship have encouraged me to take intellectual risks and pushed me to be a better researcher.
I would also like to thank Nils Halverson for giving me the opportunity to work with him while I
was an undergraduate at the University of Colorado where I fell in love with the field.
I have had the great opportunity to work with many colleagues in the ABS collaboration who
have also become good friends. My thanks go to Lucas Parker, Katerina Visnjic, John Appel,
and Tom Essinger-Hileman for their contributions to developing and fielding the ABS instrument
and for their continual support and guidance after ABS was fielded. I also want to acknowledge
Srinivasan Raghunathan who played a key role in keeping ABS running, especially when we were
short staffed, and who is an integral part of the analysis team. I’d like to thank Patty Ho, Kevin
Crowley, Glen Nixon, and Steve Choi for their work both on the analysis team and in the field. I
also want to thank Norm Jarosik, Joe Fowler, Mike Nolta, Jon Sievers, and Toby Marriage for their
contributions to ABS. Extra special thanks also go to the site engineer Masao Uehara for keeping
the ABS and ACT sites running and for always stocking the site with Oreo Cakesters when I was
around.
My work with the ACT collaboration has been immensely rewarding, and I owe a great amount
iv
of thanks to the collaboration, especially Mike Niemack, Ed Wollack, Bob Thornton, Laura Newburgh, Renée Hložek, Shawn Henderson, Maria Salatino, Yaqiong Li, Jon Ward, Patricio Gallardo,
Kevin Coughlin, Charles Munson, and Alec Josaitis. I also want to thank my office mates Emily
Grace and Christine Pappas for being excellent resources and friends. While at Princeton, I also
had the privilege to be a part of the Princeton Gravity Group and benefited from the support and
knowledge of Bill Jones, Paul Steinhardt, David Spergel, Jim Peebles, and Ed Groth.
I also owe a great deal of gratitude to my NASA Space Technology Research Fellowship, which
gave me opportunities to work with the brilliant researchers at the National Institute for Standards
and Technology (NIST) in Boulder and attend conferences each year. I want to thank Kent Irwin for being my fellowship Research Collaborator while he was at NIST and Carl Reintsema for
taking over the role of Research Collaborator in my last years and for many helpful discussions
about multiplexing. While at NIST, I had the great pleasure of working under the guidance of
Hannes Hubmayr, who is an invaluable resource. I am also very thankful to Jim Beall for many
insightful conversations about the feedhorn fabrication process and for fabricating the AdvACT
feedhorns with Jeff Van Lanen. I would also like to thank Gene Hilton, Joel Ullom, Sherry Cho,
Dale Li, Shannon Duff, Doug Bennett, Dan Becker, Dan Schmidt, Randy Doriese, Colin Fitzgerald, and Peter Lowell for always making me feel welcome at NIST. I also owe Jay Austermann
significant thanks for being a great mentor and source of information when I worked with him as
an undergraduate at the University of Colorado and for his continued support and insight while at
NIST.
The staff at Princeton is truly exceptional and were one of the most enjoyable parts of my time
at Princeton. I would like to give special thanks to Angela Lewis for helping make my constant
travel effortless, conquering Concur, and keeping a smile on my face with her kindness. I’d also
like to thank Darryl Johnson for solving many last minute packing emergencies, many wonderful
conversations, and always making me laugh. I want to thank Ted Lewis for his help both in the
stock room and purchasing. His patience and calm under pressure helped avert several crises, and
I enjoyed talking photography and life with him. I owe Regina Savadge a great deal of thanks
v
for helping keep the department running smoothly, organizing the women in physics lunches, and
taking an active role in trying to make the department more inclusive for all. Bert Harrop was an
invaluable resource for my work on ACTPol. I want to thank Elaine Remillard-Bridges, Laura
Deevey, Courtney Kohut, and Stephanie Rumphrey for their help with my fellowship and Jessica
Heslin, Barbara Mooring, Katherine Hare, and Catherine Brosowsky for their work as the Graduate Administrator. I’d also like to thank Geoff Gettelfinger, Lauren Callahan, Julio Lopez, Claude
Champagne, Barbara Grunwerg, and all the other staff who work behind the scenes to make everything in Jadwin run smoothly.
While at Princeton, I was also privileged to be a participant in several groups of hard-working
individuals dedicated to making STEM fields more inclusive. I would like to thank my fellow
members on the graduate student and postdoc women in STEM leadership council, especially
Angelina Sylvain, Colleen Richardson, Chaevia Clendinen, Jenny Schieltz, and Genny Plant. I
would also like to thank my fellow members on the Physics Committee for Climate and Inclusion
for making impactful changes within the department and the women in physics group, including
Merideth Frey, Lauren McGough, Mallika Randeria, and Laura Chang. I owe Emily Shields a
great debt of gratitude for starting the women in physics group, taking the first steps to improve
the department, and for her mentorship.
Over the course of my time at Princeton, I was fortunate enough to work alongside several
brilliant graduate students and postdocs who have also become some of my closest friends. Among
these are my colleagues from the SPIDER collaboration: Ed Young, Anne Gambrel, Sasha Rahlin,
Ziggy Kermish, Stevie Bergman, Jon Gudmundsson, Aurelien Fraisse, and Steve Benton. I’d also
like to acknowledge Shawn Westerdale, Kenan Diab, Guangyong Koh, Katie Spaulding, Peace
Sangtawesin, and Max Hirschberger. I’d especially like to thank Shawn for sharing my enthusiasm
both for puns and for torturing Ed with puns. I would also like to thank Felicity Hills for keeping
it f’real. She has been a constant source of intellect, humor, support, and kindness.
I owe my gratitude to several friends outside of Princeton for their support: Julie Davis, Scott
Nikiel, Victoria Pollard, Darcy Marceau, Katie Mahoney, Cynthia Musante, and Krista Schiff. I
vi
don’t know where I would be without their constant support. I also want to thank my physical
therapist and friend, Melissa Walker, and her team for helping me recover from shoulder surgery.
Her patience and enthusiasm encouraged me to push myself through a difficult recovery.
I want to thank my amazing family for constantly believing in me. I’d especially like to thank
my dad Ronald Simon and my aunt Irene Allen who have loved and supported me throughout my
whole life. I’ve also had the great honor of knowing and loving my brother Luke Simon. From
the first moment I held him, I knew he had a bright future, and even though he recently grew taller
than me, he will always be my favorite little brother.
Finally, I would not have made it this far without the love and support of my fiancé Scott
Murray. Thank you for accepting me as I am, driving me dinner when I was working long hours,
helping me recover from surgery, keeping me company when I was in the field even when the
internet connection was so poor that we could only see frozen images of each other, and reading
every word in this thesis several times over. You enrich my life and encourage me to grow. You
are my best friend and the love of my life.
vii
Relation to Previous Work
Some of the work in this dissertation has been presented at conferences and published. The sections
in this work that contain content from these conferences and publications have been modified
and/or expanded for this dissertation. In all cases, the content in these sections was first presented
at conferences and subsequently published. In the following, I will list these presentations and
publications. I will also describe my contributions to each publication.
Section 3.2.3
Poster Presentation, S. M. Simon, “The In Situ Performance of TRUCE Pixels in the Atacama-BMode Search,” 15th International Workshop on Low Temperature Detectors, June 2013.
S. M. Simon, J. W. Appel, H. M. Cho, T. Essinger-Hileman, K. D. Irwin, A. Kusaka,
M. D. Niemack, M. R. Nolta, L. A. Page, L. P. Parker, S. Raghunathan, J. L. Sievers, S. T. Staggs,
and K. Visnjic. In Situ Time Constant and Optical Efficiency Measurements of TRUCE Pixels in
the Atacama B-Mode Search. Journal of Low Temperature Physics, 176:712718, September 2014.
I wrote the entirety of the above publication. This publication has two major sections. The first
describes a novel technique for measuring time constants that I developed based on a suggestion
from and under the guidance of Akito Kusaka. The second section describes the analysis of optical
efficiency measurements performed by Kat Visnjic. This dissertation section only uses content
from the time constant section of the above publication and contains some verbatim passages.
Sections 3.3.3 and 3.4
Poster Presentation, S. M. Simon, “Characterizing Detectors with a Half-Wave Plate on the Atacama B-mode Search Instrument,” 16th International Workshop on Low Temperature Detectors,
July 2015.
S. M. Simon, J. W. Appel, L. E. Campusano, S. K. Choi, K. T. Crowley, T. Essinger-Hileman,
P. Gallardo, S. P. Ho, A. Kusaka, F. Nati, G. A. Palma, L. A. Page, S. Raghunathan, and
S. T. Staggs. Characterizing Atacama B-mode Search Detectors with a Half-Wave Plate. Journal
of Low Temperature Physics, December 2015.
viii
I produced all of the content for and wrote the entirety of the above publication. These dissertation sections contain some verbatim selections from the above publication.
Section 4.2
Oral Presentation, S. M. Simon, “Characterization of the Atacama B-Mode Search,” SPIE Astronomical Telescopes + Instrumentation, June 2014.
S. M. Simon, S. Raghunathan, J. W. Appel, D. T. Becker, L. E. Campusano, H. M. Cho, T. EssingerHileman, S. P. Ho, K. D. Irwin, N. Jarosik, A. Kusaka, M. D. Niemack, G. W. Nixon, M. R. Nolta,
L. A. Page, G. A. Palma, L. P. Parker, J. L. Sievers, S. T. Staggs, and K. Visnjic. Characterization of the Atacama B-mode Search. In Millimeter, Submillimeter, and Far-Infrared Detectors and
Instrumentation for Astronomy VII, Volume 9153 of SPIE Conference Proceedings, page 91530Y,
July 2014.
This publication has three major sections: a section on the spectral response of the detectors,
a section on the telescope pointing, and a section on the beam. I produced the content for the first
section, while Srinivasan Raghunathan developed the telescope pointing content and Glen Nixon
produced the content in the beam section. I wrote the the majority of the paper, but I used some
excerpts from a summary written by Srinivasan Raghunathan for the pointing section that was
specifically written for this paper. This dissertation section only uses content from the section on
the detector spectral responses from the above publication and contains some verbatim passages.
Chapter 6
Poster Presentation, S. M. Simon, “Wideband Spline-Profiled Feedhorns for Advanced ACTPol,”
16th International Workshop on Low Temperature Detectors, July 2015.
Oral Presentation, S. M. Simon, “The design and characterization of wideband spline-profiled
feedhorns for Advanced ACTPol,” SPIE Astronomical Telescopes + Instrumentation, June 2016.
S. M. Simon, J. Austermann, J. A. Beall, S. K. Choi, K. P. Coughlin, S. M. Duff, P. A. Gallardo,
S. W. Henderson, F. B. Hills, S. P. Ho, J. Hubmayr, A. Josaitis, B. Koopman, J. McMahon, F. Nati,
L. Newburgh, M. D. Niemack, M. Salatino, A. Schillaci, B. L. Schmitt, S. T. Staggs, E. M. Vavaix
giakis, J. T. Ward, and E. J. Wollack. The design and characterization of wideband spline-profiled
feedhorns for Advanced ACTPol. Submitted to Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VII of SPIE Conference Proceedings, June 2016.
I wrote the entirety of the above publication. For this work, Jeff McMahon ran a Markov
chain Monte Carlo (MCMC) estimation of the the feedhorn leakage using far-field beams that I
modeled as input. This contribution is described in the last paragraph of Section 4.3 in the above
publication. With the exception of Jeff McMahon’s MCMC estimation, I produced all of the
content in the publication. This dissertation chapter contains some verbatim passages from the
above publication.
x
Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
Relation to Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
1
Introduction
1
1.1
ΛCDM Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
The Cosmic Microwave Background . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.2.1
Temperature Anisotropies . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.2.2
Galaxy Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.3
Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4
Polarization in the CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.1
1.5
2
Measuring Polarization with the Stokes Parameters . . . . . . . . . . . . . 14
Observational Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Cosmic Microwave Background Instruments
2.1
18
The Atacama B-mode Search Instrument . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1
Telescope Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.2
Observation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.3
Telescope Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
xi
2.2
2.3
3
2.1.4
Focal Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.5
Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.6
Further Instrumental Details . . . . . . . . . . . . . . . . . . . . . . . . . 30
The Atacama Cosmology Telescope Polarimeter . . . . . . . . . . . . . . . . . . . 32
2.2.1
Observation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.2
Telescope Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.3
Focal Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
The Advanced ACTPol Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.1
Observation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.2
Focal Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Half-Wave Plate Formalism and Applications
49
3.1
HWP Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2
Time Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3
3.4
3.2.1
Impact on Beam and Pointing . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.2
Established Methods of Determining Time Constants . . . . . . . . . . . . 57
3.2.3
Phase Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2.4
Modeling the Time Constants for All Observations . . . . . . . . . . . . . 64
3.2.5
Angle Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Responsivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3.1
Absolute Responsivity Calibration . . . . . . . . . . . . . . . . . . . . . . 73
3.3.2
Relative Responsivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.3
Time-Dependent Responsivity . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3.4
Full Responsivity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Data Selection with the HWP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4.1
Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4.2
Determining the Data Selection Parameters . . . . . . . . . . . . . . . . . 81
3.4.3
PWV Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
xii
4
Further Optical Characterization
4.1
Fourier Transform Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2
ABS Bandpass Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3
Preliminary ABS Bandpass Measurements Prior to Deployment . . . . . . . . . . 97
4.4
5
4.3.1
Positional Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.3.2
Spectra Cutting Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Optical Measurements of 220/350 GHz Detectors for AdvACT . . . . . . . . . . . 102
4.4.1
Bandpass Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4.2
Beam Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
ABS Data Selection Pipeline and Analysis
5.1
5.2
6
84
ABS Data Selection Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.1.1
Determining if the Telescope is Operating Nominally . . . . . . . . . . . . 110
5.1.2
Determining if the Detectors are Operating Properly . . . . . . . . . . . . 112
5.1.3
Eliminating Timestreams with Too Many Glitches . . . . . . . . . . . . . 114
5.1.4
Eliminating Timestreams with Excess Scan Synchronous Signal . . . . . . 116
5.1.5
Determining if the Timestream is Stable and Gaussian Distributed . . . . . 117
5.1.6
Determining the Noise Properties of the Timestream . . . . . . . . . . . . 119
5.1.7
Eliminating Detectors Under High Loading Conditions . . . . . . . . . . . 120
5.1.8
Impact of the Data Selection Criteria . . . . . . . . . . . . . . . . . . . . . 122
ABS Analysis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Wideband Spline-Profiled Feedhorns for AdvACT
6.1
109
128
Feedhorn Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.1.1
Electromagnetic Simulation Software . . . . . . . . . . . . . . . . . . . . 131
6.1.2
Random Profile Determination . . . . . . . . . . . . . . . . . . . . . . . . 132
6.1.3
Profile Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.1.4
Method 1: Iteratively Adding Frequencies . . . . . . . . . . . . . . . . . . 136
xiii
6.1.5
6.2
6.3
7
Method 2: Parallel Optimization . . . . . . . . . . . . . . . . . . . . . . . 137
Feedhorn Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.2.1
Modeling Fabrication Tolerances . . . . . . . . . . . . . . . . . . . . . . . 140
6.2.2
Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.2.3
Cross Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.2.4
Beam Coupling Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.2.5
Polarization Leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Feedhorn Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.3.1
Analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.3.2
Sources of Uncertainty in the Measurements . . . . . . . . . . . . . . . . 167
6.3.3
Impact on AdvACT Performance . . . . . . . . . . . . . . . . . . . . . . 169
Future Work
173
A 150/230 GHz Feedhorn Measurements
176
A.1 Beams at All Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
A.1.1 E-plane Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
A.1.2 H-plane Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
A.1.3 Cross-Polarization Beams . . . . . . . . . . . . . . . . . . . . . . . . . . 191
A.2 Beams Truncated at Lyot Stop at All Positions . . . . . . . . . . . . . . . . . . . . 198
A.2.1 E-plane Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
A.2.2 H-plane Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
A.2.3 Cross-Polarization Beams . . . . . . . . . . . . . . . . . . . . . . . . . . 213
A.3 Beams Plotted Together at Each Position . . . . . . . . . . . . . . . . . . . . . . . 220
A.3.1 Position 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
A.3.2 Position 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
A.3.3 Position 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
A.3.4 Position 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
xiv
A.4 Repeated Measurements at Position 7 . . . . . . . . . . . . . . . . . . . . . . . . 249
A.4.1 E-plane Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
A.4.2 H-plane Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
A.4.3 Cross-Polarization Beams . . . . . . . . . . . . . . . . . . . . . . . . . . 258
Bibliography
262
xv
List of Tables
1.1
Most Recent ΛCDM parameters . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
ABS Key Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2
ACTPol Key Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3
AdvACT Key Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4
AdvACT Observation Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1
Impact of 3dB Frequency on Beam and Pointing . . . . . . . . . . . . . . . . . 56
4.1
ABS FTS Measurement Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.2
ABS Bandwidth and Center Frequencies . . . . . . . . . . . . . . . . . . . . . 93
5.1
Data Selection Criteria Applied Individually . . . . . . . . . . . . . . . . . . . 123
5.2
Data Selection Criteria Applied Successively . . . . . . . . . . . . . . . . . . . 124
6.1
Feedhorn Optimization Frequencies . . . . . . . . . . . . . . . . . . . . . . . . 131
6.2
Feedhorn Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.3
Simulated Feedhorn Performance . . . . . . . . . . . . . . . . . . . . . . . . . 146
xvi
8
List of Figures
1.1
CMB Temperature anisotropy measurements . . . . . . . . . . . . . . . . . . . . . 10
1.2
Thomson scattering off an electron in a quadrupolar temperature anisotropy creates
linear polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3
E-mode and B-mode polarization patterns around a local temperature extrema . . . 13
1.4
The Stokes Q and U parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5
Current CMB polarization measurements . . . . . . . . . . . . . . . . . . . . . . 17
2.1
The ACT and ABS telescope site . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2
The ABS observation fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3
A photograph of the ABS telescope . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4
A cross section of the ABS receiver . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5
A ray-tracing diagram of the ABS optics . . . . . . . . . . . . . . . . . . . . . . . 26
2.6
Photograph of an ABS pixel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7
The ABS focal plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.8
A cross section of an ABS feedhorn . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.9
A photograph of a transition-edge sensor . . . . . . . . . . . . . . . . . . . . . . . 28
2.10 The superconducting to normal transition for a TES . . . . . . . . . . . . . . . . . 28
2.11 A diagram of the TES electrical circuit . . . . . . . . . . . . . . . . . . . . . . . . 28
2.12 A diagram of the ABS fabrication wafers . . . . . . . . . . . . . . . . . . . . . . 29
2.13 A schematic of a multiplexing readout system . . . . . . . . . . . . . . . . . . . . 31
2.14 A photograph of the Atacama Cosmology Telescope . . . . . . . . . . . . . . . . 34
xvii
2.15 A ray-tracing diagram of ACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.16 An image of the ACTPol receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.17 A prototype metamaterial Si anti-reflective coating . . . . . . . . . . . . . . . . . 36
2.18 A ray-tracing diagram of the cold ACTPol optics . . . . . . . . . . . . . . . . . . 37
2.19 A cross section of the PA3 ACTPol optics tube . . . . . . . . . . . . . . . . . . . 37
2.20 Photographs of an assembled ACTPol array . . . . . . . . . . . . . . . . . . . . . 38
2.21 PA3 hex and semihex wafers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.22 Photographs of a multichroic PA3 pixel . . . . . . . . . . . . . . . . . . . . . . . 39
2.23 Flexible readout circuitry for ACTPol . . . . . . . . . . . . . . . . . . . . . . . . 41
2.24 Flexible readout circuitry for AdvACT . . . . . . . . . . . . . . . . . . . . . . . . 44
2.25 A picture of the backside of the HF AdvACT array . . . . . . . . . . . . . . . . . 44
2.26 A picture of the HF AdvACT array mid-assembly . . . . . . . . . . . . . . . . . . 45
2.27 The full HF array detector wafer . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.28 A magnified view of the HF array . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.29 A single HF multichroic pixel for AdvACT . . . . . . . . . . . . . . . . . . . . . 48
3.1
A diagram of polarization modulation with a HWP . . . . . . . . . . . . . . . . . 50
3.2
A cross section of the ABS HWP system . . . . . . . . . . . . . . . . . . . . . . . 51
3.3
An average power spectra before and after demodulation with a HWP . . . . . . . 52
3.4
The shift in pointing and beam width resulting from the detector time constants for
a scan in one direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5
The shift in pointing and beam width from time constants for a scan in both directions 58
3.6
A photograph of the ABS time constant measurement setup . . . . . . . . . . . . . 59
3.7
Representative timestreams of the two time constant measurements . . . . . . . . . 60
3.8
Power versus frequency relations of time constant measurements . . . . . . . . . . 61
3.9
Optical 3dB frequency measurements across the array . . . . . . . . . . . . . . . . 61
3.10 Histograms of the 3dB frequencies of the detectors . . . . . . . . . . . . . . . . . 62
xviii
3.11 Distributions of 3dB frequencies for the four ABS wafers for the first phase method
measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.12 Distributions of 3dB frequencies for the four ABS wafers for the second phase
method measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.13 Optical 3dB frequencies from the first phase method measurement plotted across
the array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.14 Optical 3dB frequencies from the second phase method measurement plotted
across the array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.15 Distribution of the thermal 3dB frequencies of the detectors . . . . . . . . . . . . . 70
3.16 The responsivity decay of a batch B detector . . . . . . . . . . . . . . . . . . . . . 78
3.17 The A2c and A2s signals for a single bolometer plotted as a function of PWV . . . . 79
3.18 A detector flagged with zero response . . . . . . . . . . . . . . . . . . . . . . . . 80
3.19 A type 1 detector before and after reprocessing . . . . . . . . . . . . . . . . . . . 81
2
3.20 Histograms of the χCES
distributions for each season . . . . . . . . . . . . . . . . 82
3.21 The PWV from APEX is plotted against the 2 fm PWV . . . . . . . . . . . . . . . 83
4.1
Diagram of a Michelson Interferometer . . . . . . . . . . . . . . . . . . . . . . . 86
4.2
Diagram of a Martin-Puplett Interferometer . . . . . . . . . . . . . . . . . . . . . 88
4.3
Diagram of the FTS setup used on ABS . . . . . . . . . . . . . . . . . . . . . . . 90
4.4
The average bandpass of each ABS wafer . . . . . . . . . . . . . . . . . . . . . . 93
4.5
The average bandpass of each ABS wafer with their errors . . . . . . . . . . . . . 94
4.6
Histograms of the bandwidths for each ABS wafer . . . . . . . . . . . . . . . . . 95
4.7
The CMB center frequency of the ABS detectors plotted across the array . . . . . . 96
4.8
Detectors with measured bandpasses prior to deployment . . . . . . . . . . . . . . 98
4.9
The center frequencies of the detectors measured prior to deployment . . . . . . . 99
4.10 Interferograms and spectra of half of the ABS array measured prior to deployment . 100
4.11 FTS Spectra from subsets of detectors on opposite sides of the array . . . . . . . . 101
xix
4.12 Interferograms and spectra of the eight columns of detectors used in the preliminary analysis prior to deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.13 A single 220/350 GHz prototype pixel for AdvACT . . . . . . . . . . . . . . . . . 103
4.14 Test configuration of two single 220/350 GHz prototype pixels for AdvACT . . . . 104
4.15 Measured FTS spectra for prototype 220/350 GHz pixels with a 1050◦ C source . . 105
4.16 Measured FTS spectra for prototype 220/350 GHz pixels with a 500◦ C source . . . 105
4.17 Measured FTS spectra for prototype 220/350 GHz pixels with a 250◦ C source . . . 106
4.18 Measured FTS spectra for prototype 220/350 GHz pixels with a LN2 source . . . . 106
4.19 Two measured spectra from orthogonal 350 GHz detectors on the same pixel . . . . 107
4.20 Measured beams for 350 GHz and 220 GHz detectors . . . . . . . . . . . . . . . . 108
5.1
Histograms of ABS scan duration, scan width, scan period and HWP rotation frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2
The distribution of 1/ηbin across the first two seasons of ABS data . . . . . . . . . 113
5.3
Histogram of the number of glitches per observation for ABS . . . . . . . . . . . . 115
5.4
Histograms of ABS scan synchronous signal data selection parameters . . . . . . . 117
5.5
Histograms of the demodulated stationarity, raw stationarity, raw skewness, and
raw kurtosis for ABS data selection . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.6
Histograms of the noise data selection criteria for ABS . . . . . . . . . . . . . . . 120
5.7
Histograms of the PWV and 3dB frequencies during ABS observations . . . . . . . 121
5.8
Simulated E-mode measurements for ABS . . . . . . . . . . . . . . . . . . . . . . 126
6.1
Cross section of a 90/150 GHz ACTPol corrugated feedhorn . . . . . . . . . . . . 129
6.2
90/150 GHz AdvACT spline-profiled feedhorn and conical feedhorn designs . . . . 129
6.3
Photograph of the top wafer of the 150/230 GHz feedhorn stack . . . . . . . . . . 132
6.4
Photograph of the fully assembled 150/230 GHz AdvACT feedhorn array . . . . . 133
6.5
A photograph of the detector side of the AdvACT 150/230 GHz feedhorn array . . 138
6.6
The final 150/230 GHz AdvACT feedhorn design . . . . . . . . . . . . . . . . . . 139
xx
6.7
Reflection of 90/150 GHz feedhorn candidates . . . . . . . . . . . . . . . . . . . . 141
6.8
Reflection of 150/230 GHz feedhorn candidates . . . . . . . . . . . . . . . . . . . 142
6.9
Reflection of 150/230 GHz feedhorns with waveguide options . . . . . . . . . . . 143
6.10 Cross polarization of 90/150 GHz feedhorn candidates . . . . . . . . . . . . . . . 145
6.11 Cross polarization of 150/230 GHz feedhorn candidates . . . . . . . . . . . . . . . 145
6.12 Beam coupling efficiency of the 90/150 GHz feedhorn . . . . . . . . . . . . . . . 147
6.13 Beam coupling efficiency of the 150/230 GHz feedhorn . . . . . . . . . . . . . . . 147
6.14 Beam coupling efficiency of a 90/150 GHz conical feedhorn . . . . . . . . . . . . 148
6.15 Beam coupling efficiency of a 150/230 GHz conical feedhorn . . . . . . . . . . . . 148
6.16 Beam coupling efficiency of a 150/230 GHz corrugated feedhorn . . . . . . . . . . 149
6.17 The modeled EE and BB polarization spectra of the 90/150 GHz feedhorn candidates152
6.18 The modeled EE and BB polarization spectra of the 150/230 GHz feedhorn candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.19 The simulated temperature to polarization leakage of the 90/150 GHz feedhorn
candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.20 The simulated temperature to polarization leakage of the 150/230 GHz feedhorn
candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.21 The simulated E-mode to B-mode polarization leakage of the 90/150 GHz feedhorn candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.22 The simulated E-mode to B-mode polarization leakage of the 150/230 GHz feedhorn candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.23 Modeled E-modes and B-modes with the feedhorn leakage set to zero . . . . . . . 155
6.24 Modeled E-modes and simulation leakage B-mode signal with the feedhorn leakage and B-mode signals set to zero . . . . . . . . . . . . . . . . . . . . . . . . . . 156
6.25 Modeled E-modes and simulation leakage B-mode signal with the feedhorn leakage included . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.26 Modeled E-mode and B-mode leakages when the feedhorn leakage is included . . . 158
xxi
6.27 The positions of the holes in the feedhorn mounting plate . . . . . . . . . . . . . . 160
6.28 The VNA beam measuring setup for the 150/230 GHz feedhorn array . . . . . . . 160
6.29 The VNA transmitter and receiver setups for the low band
. . . . . . . . . . . . . 161
6.30 The VNA transmitter and receiver setups for the high band . . . . . . . . . . . . . 161
6.31 Reflections in the peak of the VNA beam measurements . . . . . . . . . . . . . . 162
6.32 Measurements of the H-plane, E-plane, and cross-polarization beams at 150 GHz . 164
6.33 Measurements of the H-plane, E-plane, and cross-polarization beams at 220 GHz . 164
6.34 Measurements of the H-plane beams across the array at 150 GHz . . . . . . . . . . 165
6.35 Measurements of the H-plane beams across the array at 220 GHz . . . . . . . . . . 165
6.36 A narrow bandwidth feature in the E-plane at 270 GHz . . . . . . . . . . . . . . . 166
6.37 E-plane measurements at 269 GHz and 271 GHz . . . . . . . . . . . . . . . . . . 166
6.38 An artifact in the beam due to a motor glitch . . . . . . . . . . . . . . . . . . . . . 168
6.39 Photograph of the Teflon washer that caused a tilt in the VNA system . . . . . . . 168
6.40 The FHWMs as a function of frequency for the simulated and measured E-plane
and H-plane beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
6.41 The beam coupling efficiency as a function of frequency for the simulated and
measured E-plane and H-plane beams . . . . . . . . . . . . . . . . . . . . . . . . 171
6.42 The avaerage beam coupling efficiency as a function of frequency for the simulated
and measured beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
A.1 Measurements of E-plane beams at 130 GHz at each feedhorn position. . . . . . . 177
A.2 Measurements of E-plane beams at 140 GHz at each feedhorn position. . . . . . . 177
A.3 Measurements of E-plane beams at 150 GHz at each feedhorn position. . . . . . . 178
A.4 Measurements of E-plane beams at 160 GHz at each feedhorn position. . . . . . . 178
A.5 Measurements of E-plane beams at 170 GHz at each feedhorn position. . . . . . . 179
A.6 Measurements of E-plane beams at 180 GHz at each feedhorn position. . . . . . . 179
A.7 Measurements of E-plane beams at 200 GHz at each feedhorn position. . . . . . . 180
A.8 Measurements of E-plane beams at 210 GHz at each feedhorn position. . . . . . . 180
xxii
A.9 Measurements of E-plane beams at 220 GHz at each feedhorn position. . . . . . . 181
A.10 Measurements of E-plane beams at 230 GHz at each feedhorn position. . . . . . . 181
A.11 Measurements of E-plane beams at 240 GHz at each feedhorn position. . . . . . . 182
A.12 Measurements of E-plane beams at 250 GHz at each feedhorn position. . . . . . . 182
A.13 Measurements of E-plane beams at 260 GHz at each feedhorn position. . . . . . . 183
A.14 Measurements of E-plane beams at 270 GHz at each feedhorn position. . . . . . . 183
A.15 Measurements of H-plane beams at 130 GHz at each feedhorn position are shown. . 184
A.16 Measurements of H-plane beams at 140 GHz at each feedhorn position are shown. . 184
A.17 Measurements of H-plane beams at 150 GHz at each feedhorn position are shown. . 185
A.18 Measurements of H-plane beams at 160 GHz at each feedhorn position are shown. . 185
A.19 Measurements of H-plane beams at 170 GHz at each feedhorn position. . . . . . . 186
A.20 Measurements of H-plane beams at 180 GHz at each feedhorn position. . . . . . . 186
A.21 Measurements of H-plane beams at 200 GHz at each feedhorn position. . . . . . . 187
A.22 Measurements of H-plane beams at 210 GHz at each feedhorn position. . . . . . . 187
A.23 Measurements of H-plane beams at 220 GHz at each feedhorn position. . . . . . . 188
A.24 Measurements of H-plane beams at 230 GHz at each feedhorn position. . . . . . . 188
A.25 Measurements of H-plane beams at 240 GHz at each feedhorn position. . . . . . . 189
A.26 Measurements of H-plane beams at 250 GHz at each feedhorn position. . . . . . . 189
A.27 Measurements of H-plane beams at 260 GHz at each feedhorn position. . . . . . . 190
A.28 Measurements of H-plane beams at 270 GHz at each feedhorn position. . . . . . . 190
A.29 Measurements of cross-polarization beams at 130 GHz at each feedhorn position. . 191
A.30 Measurements of cross-polarization beams at 140 GHz at each feedhorn position. . 191
A.31 Measurements of cross-polarization beams at 150 GHz at each feedhorn position. . 192
A.32 Measurements of cross-polarization beams at 160 GHz at each feedhorn position. . 192
A.33 Measurements of cross-polarization beams at 170 GHz at each feedhorn position. . 193
A.34 Measurements of cross-polarization beams at 180 GHz at each feedhorn position. . 193
A.35 Measurements of cross-polarization beams at 200 GHz at each feedhorn position. . 194
xxiii
A.36 Measurements of cross-polarization beams at 210 GHz at each feedhorn position. . 194
A.37 Measurements of cross-polarization beams at 220 GHz at each feedhorn position. . 195
A.38 Measurements of cross-polarization beams at 230 GHz at each feedhorn position. . 195
A.39 Measurements of cross-polarization beams at 240 GHz at each feedhorn position. . 196
A.40 Measurements of cross-polarization beams at 250 GHz at each feedhorn position. . 196
A.41 Measurements of cross-polarization beams at 260 GHz at each feedhorn position. . 197
A.42 Measurements of cross-polarization beams at 270 GHz at each feedhorn position. . 197
A.43 Measurements of E-plane beams at 130 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
A.44 Measurements of E-plane beams at 140 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
A.45 Measurements of E-plane beams at 150 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
A.46 Measurements of E-plane beams at 160 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
A.47 Measurements of E-plane beams at 170 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
A.48 Measurements of E-plane beams at 180 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
A.49 Measurements of E-plane beams at 200 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
A.50 Measurements of E-plane beams at 210 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
A.51 Measurements of E-plane beams at 220 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
A.52 Measurements of E-plane beams at 230 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
xxiv
A.53 Measurements of E-plane beams at 240 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
A.54 Measurements of E-plane beams at 250 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
A.55 Measurements of E-plane beams at 260 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
A.56 Measurements of E-plane beams at 270 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
A.57 Measurements of H-plane beams at 130 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
A.58 Measurements of H-plane beams at 140 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
A.59 Measurements of H-plane beams at 150 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
A.60 Measurements of H-plane beams at 160 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
A.61 Measurements of H-plane beams at 170 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
A.62 Measurements of H-plane beams at 180 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
A.63 Measurements of H-plane beams at 200 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
A.64 Measurements of H-plane beams at 210 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
A.65 Measurements of H-plane beams at 220 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
xxv
A.66 Measurements of H-plane beams at 230 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
A.67 Measurements of H-plane beams at 240 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
A.68 Measurements of H-plane beams at 250 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
A.69 Measurements of H-plane beams at 260 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.70 Measurements of H-plane beams at 270 GHz at each feedhorn position truncated
at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.71 Measurements of cross-polarization beams at 130 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
A.72 Measurements of cross-polarization beams at 140 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
A.73 Measurements of cross-polarization beams at 150 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
A.74 Measurements of cross-polarization beams at 160 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
A.75 Measurements of cross-polarization beams at 170 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
A.76 Measurements of cross-polarization beams at 180 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
A.77 Measurements of cross-polarization beams at 200 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
A.78 Measurements of cross-polarization beams at 210 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
xxvi
A.79 Measurements of cross-polarization beams at 220 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
A.80 Measurements of cross-polarization beams at 230 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
A.81 Measurements of cross-polarization beams at 240 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
A.82 Measurements of cross-polarization beams at 250 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
A.83 Measurements of cross-polarization beams at 260 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
A.84 Measurements of cross-polarization beams at 270 GHz at each feedhorn position
truncated at the Lyot stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
A.85 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 130 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
A.86 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 140 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
A.87 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
A.88 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 160 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
A.89 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 170 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
A.90 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 180 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
A.91 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 200 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
xxvii
A.92 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 210 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
A.93 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
A.94 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
A.95 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 240 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
A.96 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 250 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
A.97 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 260 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
A.98 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 270 GHz for Position 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
A.99 Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 130 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
A.100Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 140 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
A.101Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
A.102Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 160 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
A.103Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 170 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
A.104Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 180 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
xxviii
A.105Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 200 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
A.106Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 210 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
A.107Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz for Position 2. The dip in the E-plane at ∼-20◦ is a motor glitch. 232
A.108Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
A.109Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 240 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
A.110Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 250 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
A.111Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 260 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
A.112Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 270 GHz for Position 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
A.113Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 130 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
A.114Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 140 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
A.115Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
A.116Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 160 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
A.117Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 170 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
xxix
A.118Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 180 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
A.119Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 200 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
A.120Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 210 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
A.121Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
A.122Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
A.123Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 240 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
A.124Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 250 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
A.125Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 260 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
A.126Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 270 GHz for Position 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
A.127Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 130 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
A.128Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 140 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
A.129Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
A.130Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 160 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
xxx
A.131Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 170 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
A.132Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 180 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
A.133Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 200 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
A.134Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 210 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
A.135Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
A.136Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz are shown for Position 8. The dip in the H-plane at ∼-30◦ is a
motor glitch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
A.137Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 240 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
A.138Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 250 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
A.139Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 260 GHz for Position 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
A.140Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 270 GHz for Position 8. The peak in the E-plane at ∼20◦ is a motor glitch. 248
A.141The original measurement of the E-plane beam at position 7 at 200 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 249
A.142The original measurement of the E-plane beam at position 7 at 210 GHz is shown
with its simulation and repeated measurements above. . . . . . . . . . . . . . . . . 250
A.143The original measurement of the E-plane beam at position 7 at 220 GHz is shown
with its simulation and repeated measurements above. . . . . . . . . . . . . . . . . 250
xxxi
A.144The original measurement of the E-plane beam at position 7 at 230 GHz is shown
with its simulation and repeated measurements above. . . . . . . . . . . . . . . . . 251
A.145The original measurement of the E-plane beam at position 7 at 240 GHz is shown
with its simulation and repeated measurements above. . . . . . . . . . . . . . . . . 251
A.146The original measurement of the E-plane beam at position 7 at 250 GHz is shown
with its simulation and repeated measurements above. . . . . . . . . . . . . . . . . 252
A.147The original measurement of the E-plane beam at position 7 at 260 GHz is shown
with its simulation and repeated measurements above. . . . . . . . . . . . . . . . . 252
A.148The original measurement of the E-plane beam at position 7 at 270 GHz is shown
with its simulation and repeated measurements above. . . . . . . . . . . . . . . . . 253
A.149The original measurement of the H-plane beam at position 7 at 200 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 254
A.150The original measurement of the H-plane beam at position 7 at 210 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 254
A.151The original measurement of the H-plane beam at position 7 at 220 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 255
A.152The original measurement of the H-plane beam at position 7 at 230 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 255
A.153The original measurement of the H-plane beam at position 7 at 240 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 256
A.154The original measurement of the H-plane beam at position 7 at 250 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 256
A.155The original measurement of the H-plane beam at position 7 at 260 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 257
A.156The original measurement of the H-plane beam at position 7 at 270 GHz is shown
with its simulation and repeated measurement above. . . . . . . . . . . . . . . . . 257
xxxii
A.157The original measurement of the cross-polarization beam at position 7 at 200 GHz
is shown with its simulation and repeated measurement above. . . . . . . . . . . . 258
A.158The original measurement of the cross-polarization beam at position 7 at 210 GHz
is shown with its simulation and repeated measurement above. . . . . . . . . . . . 258
A.159The original measurement of the cross-polarization beam at position 7 at 220 GHz
is shown with its simulation and repeated measurement above. . . . . . . . . . . . 259
A.160The original measurement of the cross-polarization beam at position 7 at 230 GHz
is shown with its simulation and repeated measurement above. . . . . . . . . . . . 259
A.161The original measurement of the cross-polarization beam at position 7 at 240 GHz
is shown with its simulation and repeated measurement above. . . . . . . . . . . . 260
A.162The original measurement of the cross-polarization beam at position 7 at 250 GHz
is shown with its simulation and repeated measurement above. . . . . . . . . . . . 260
A.163The original measurement of the cross-polarization beam at position 7 at 260 GHz
is shown with its simulation and repeated measurement above. . . . . . . . . . . . 261
A.164The original measurement of the cross-polarization beam at position 7 at 270 GHz
is shown with its simulation and repeated measurement above. . . . . . . . . . . . 261
xxxiii
Chapter 1
Introduction
With only six independent parameters, the current ΛCDM paradigm describes an expanding, flat
universe dominated by dark energy and dark matter whose structure is a result of nearly scaleinvariant adiabatic Gaussian perturbations. While this model is supported by an abundance of
astronomical observations, it does not confirm if there was a period of inflation in the early universe, explain the nature of dark energy and dark matter, or describe what caused the perturbations
that seeded the current structure in the universe that we observe today. One of the most precise
tools for probing such cosmological questions is the cosmic microwave background (CMB), which
was formed roughly 400,000 years after the beginning of the universe. Because it was formed so
early in the universe, measurements of the CMB contain a wealth of information about the earliest
moments of the universe that can address these profound questions.
1.1
ΛCDM Cosmology
The standard model of cosmology describes a universe that is expanding at an accelerating rate, flat,
and dominated by dark energy and cold, dark matter that began in a hot, dense state 13.7 billion
years ago. Its structure was seeded by nearly scale-invariant adiabatic Gaussian perturbations
that have evolved into the structure observed in the universe today. This hot, dense beginning is
supported three key observations: the current expansion of the universe, the abundances of light
1
elements in the universe, and remnant blackbody radiation.
The universe is currently expanding.
Edwin Hubble was the first to measure the expansion
of the universe by finding a linear relation between the distances of extra-galactic nebulae (i.e.,
galaxies) and their velocities [1]. To determine the velocities of distant objects, the redshift is
used. The redshift z is defined as
z≡
λobs − λem
,
λem
(1.1)
where λem is the wavelength of the emitted light and λobs is the measured wavelength of the light.
The relativistic Doppler effect defines the velocity along the line of sight v in terms of redshift as
v
1+z = p
1+
,
c
1 − v2 /c2
1
(1.2)
where c is the speed of light. For non-relativistic velocities, this simplifies to z ≈ v/c.
Determining the distances of other galaxies is more difficult than measuring the velocity. Observations of the measured luminosities of standard candles, objects with known luminosities, are
used to measure astrophysical distances. Hubble used the pulsations of Cepheid variable stars and
novae to measure the distances of galaxies [1]. Cepheid variable stars are pulsating stars whose
periods are related to their luminosities. While Hubble underestimated the distances of these objects, he determined in 1929 that galaxies are moving away from the Milky Way at velocities
proportional to their distance, indicating that the universe is expanding [1]. This relation can be
expressed as Hubble’s law:
v = H0 r ,
(1.3)
where r is the distance of the object and H0 is the Hubble constant. The Hubble constant is often
expressed in terms of the dimensionless Hubble parameter h, which is defined as H0 ≡ 100h =
67.74±0.46 km/s/Mpc [2]. If the universe is currently expanding, then extrapolating the expansion
back in time shows that the universe began in a hot, dense state. Additionally, measurements of
Type 1a supernovae have showed that the universe is expanding at an accelerated rate [3, 4].
2
The abundances of light elements in the universe support a hot, dense beginning. If the universe was hotter and denser in the past, then the universe would have been so hot at early times that
there would have been no bound nuclei. As temperatures cooled below the binding energies of elements, light elements formed through fusion in a process called Big Bang Nucleosynthesis (BBN).
Relative abundances of light elements in the universe today agree with the amounts predicted by
BBN [5, 6].
A hot, dense beginning would have left a remnant field of blackbody radiation throughout the
universe. Before the formation of atoms, there were free electrons and protons coupled to each
other through Coulomb scattering and electrons and photons coupled through Thomson scattering.
The interaction rates were larger than the rate of expansion, so the universe was in equilibrium. As
the universe expanded, became more diffuse, and cooled, the reaction rate for Thomson scattering
decreased. When it became cool enough for neutral atoms to form in a period called Recombination, the cross section and thus the reaction rate for Thomson scattering drastically decreased.
Roughly 400,000 years after the beginning of the universe, the reaction rate of Thomson scattering
fell below the expansion rate, and the photons decoupled from matter and free streamed though the
universe, leaving a blackbody radiation field uniform to one part in 105 that permeates the universe
in all directions and currently peaks in the microwave section of the electromagnetic spectrum (e.g.,
reference [7]). This radiation field, called the cosmic microwave background, was first measured
in 1965 by Penzias and Wilson and is the strongest evidence in favor of the current cosmological
paradigm [8]. The CMB contains a wealth of information in both its temperature and polarization,
which will be discussed in Sections 1.2 and 1.4, respectively.
The dynamics of the universe can be described by three equations.
These equations describe
how the curvature of the universe is connected to the energy density ε and pressure P of its contents. The Friedmann equation uses Einstein’s field equations to describe how a homogeneous and
3
isotropic universe expands or contracts [9]. The Friedmann equation is expressed as
ȧ(t)
a(t)
2
=
κc2
8πG
ε(t)
−
,
3c2
R20 a(t)2
(1.4)
where G is the gravitational constant, a(t) is the scale factor, R0 is the radius of curvature at the
present time t0 , and κ is the sign of the curvature. For a flat universe, κ = 0, while κ = +1 for
positive curvature and κ = −1 for negative curvature. The scale factor a(t) describes how distances
in the universe change over time and is equal to one at time t0 . Hubble’s law can be generalized in
time as
v(t) = H(t)r(t) ,
(1.5)
where the Hubble parameter H(t) today (t0 ) is H(t0 ) = H0 . The Hubble parameter can then be
expressed in terms of a(t) as
ȧ(t)
.
a(t)
(1.6)
8πG
εc (t) .
3c2
(1.7)
H(t) =
For a flat universe, Equation 1.4 simplifies to
H(t)2 =
Rearranging this equation, the critical density εc (t) can thus be defined as
εc (t) =
3c2 H(t)2
.
8πG
(1.8)
If ε(t) > εc (t), the universe has positive curvature and is closed. If ε(t) < εc (t), the universe has
negative curvature and is open. The energy density of the universe is often represented in the
normalized form
Ω(t) =
4
ε(t)
,
εc (t)
(1.9)
where Ω(t)=1 is a flat universe. The Friedmann equation can thus be rewritten as
1 − Ω(t) = −
κc2
.
R20 a(t)2 H(t)2
(1.10)
The energy density ε(t) is the sum of the energy densities of all the components in the universe.
Our universe is flat and comprised of matter, radiation, and dark energy. The energy density of both
baryonic and cold dark matter (CDM) in the universe is given by
εm (t) =
εm,0
,
a(t)3
(1.11)
where εm,0 is the present energy density of matter. Similarly, the energy density of radiation is
εγ (t) =
εγ,0
.
a(t)4
(1.12)
Dark energy can take several forms, but the ΛCDM model assumes that dark energy takes the
form of a cosmological constant Λ. In this case, the cosmological constant can be expressed as a
constant energy density in time
εΛ =
c2
Λ.
8πG
(1.13)
Each component of the universe thus evolves differently in time. At early times, a(t) is small
so radiation dominates the energy density of the universe. As time progresses and the universe
expands, matter begins to dominate the energy density of the universe followed by dark energy.
The curvature of the universe from the Friedmann equation goes as a(t)−2 , so any curvature in the
universe would become dominant after the period of matter domination.
The next equation that governs the dynamics of the universe is called the fluid equation and is
derived from thermodynamics:
dQ = dE + PdV ,
(1.14)
where dQ is the heat flow between regions, dE is the change in internal energy, and dV is the
5
change in volume. For a homogeneous universe, dQ = 0, and the expansion of the universe is
adiabatic. The energy equation is then Ė + PV̇ = 0, which gives
ε̇ +
3ȧ
(ε + P) = 0 .
a
(1.15)
The final equation is the acceleration equation, which is derived from Equations 1.4 and 1.15
and describes the acceleration of the universe:
ä
4πG
= − 2 (ε + 3P) .
a
3c
(1.16)
To determine the acceleration, an equation of state relating the energy density to the pressure is
needed. The equation of state is expressed as
P = wε,
(1.17)
where w depends on the component of the universe. To preserve causality w ≤ 1. For photons,
w = 1/3, and w ≈ 0 for non-relativistic matter, which includes both baryonic and cold dark matter.
For relativistic species with mass, 0 < w < 1/3. Thus both matter and radiation slow the expansion
of the universe. However, in the case of dark energy, w < −1/3, so the acceleration of the universe becomes positive. For a cosmological constant, w = −1, so at late times when dark energy
dominates, the universe will expand at an accelerated rate.
The standard model of cosmology can be described by six independent parameters.
The
ΛCDM model assumes a flat (Ω(t)=1) universe that has dark energy in the form of a cosmological
constant (w = −1) and a fixed sum of the neutrino masses, Σ mν , and number of neutrinos, Ne f f .
These assumptions leave six parameters to fit that describe the baryonic and cold dark matter
densities, the initial fluctuations in the plasma of the early universe, and reionization physics. The
most up to date values of these parameters are listed in Table 1.1.
6
The baryonic and cold dark matter energy densities are expressed in terms of the parameters
Ωb h2 and Ωc h2 , respectively. Here Ωb and Ωc are the normalized energy densities as defined in
Equation 1.9.
The slight fluctuations in density in the early universe would have caused baryon acoustic
oscillations (BAO) in the plasma. As gravity pulled matter into overdensities, the baryonic matter
heated and expanded outward from the overdensities as a result of pressure from heat and photons.
In turn, this expansion cooled the matter, which was then pulled into overdense regions again.
Because light was coupled to baryonic matter, the photons oscillated with the baryonic matter and
provided additional pressure. When the photons decoupled from baryonic matter at the formation
of the CMB, information about these oscillations at the time of decoupling was imprinted in the
CMB. The characteristic angular size of the fluctuations frozen into the CMB is parameterized by
the size of the acoustic horizon at decoupling, θ∗ .
The power spectrum of the initial scalar fluctuations in the plasma of the early universe can be
described by a power law as
ns −1
k
,
P(k) = As
ki
(1.18)
where k is the comoving wavenumber, ki is the initial comoving wavenumber, As is the initial
amplitude of the scalar fluctuations, and ns is the scalar spectral index. The physical wavelength
of the comoving wavenumber is given by 2πa(t)/k. After accounting for acoustic oscillations,
the scalar spectral index is measured as the overall slope of the CMB angular power spectrum.
These fluctuations can be further described by the running of the spectral index with wavenumber,
α = dns /dk, which is set to zero in the standard ΛCDM model.
The final parameter in the ΛCDM model is the reionization optical depth τ. After recombination, matter coalesced until the first stars ignited and reionized the universe, which would have
scattered a fraction of CMB photons. The reionization optical depth is the least constrained parameter in the standard model and holds information about the process of star formation and physical
processes that occur at late times in the universe.
7
Table 1.1: Most Recent ΛCDM parameters
Parameter Planck 2015 Release WMAP 9 Year Results
Ωb h2
0.02230 ± 0.00014
0.02264 ± 0.00050
2
Ωc h
0.1188 ± 0.0010
0.1138 ± 0.0045
10
ln(10 As )
3.064 ± 0.023
109 ∆2R = 2.41 ± 0.10
ns
0.9667 ± 0.0040
0.972 ± 0.013
100θ∗
1.04093 ± 0.00030
1.0391 ± 0.0022
τ
0.066 ± 0.012
0.089 ± 0.014
The most recent cosmological parameters as from the 2015 Planck release [2] and the 9 year
Wilkinson Microwave Anisotropy Probe (WMAP) release [10]. The Planck values use the TT,
TE, and EE power spectra likelihoods and the Planck polarization data in the low-` likelihood
(lowP) with lensing reconstruction (lensing) and external data (ext) like the Planck lensing data or
BAO. This Planck model is denoted as TT, TE, EE + lowP + lensing + ext [2]. The WMAP
9 year values use only WMAP data and the curvature fluctuation amplitude ∆2R is used in place of
the initial amplitude of scalar fluctuations As [10].
1.2
The Cosmic Microwave Background
The first measurements of the CMB revealed a highly uniform blackbody with a temperature of
3 K, which we now know to be uniform to one part in 105 . NASAs COsmic Background Explorer
(COBE) satellite made the first full-sky measurements of the CMB, measured the temperature of
the CMB with unprecedented precision (2.726 ± 0.010 K) [11], and also made the first detection
of the CMB temperature anisotropies [12]. The temperature anisotropies have subsequently been
measured by a wide range of CMB experiments with increasing precision and, in combination with
other cosmological probes, have yielded much cosmological information including the curvature,
baryon content, and dark matter content of the universe. Additionally, light from the CMB has
travelled from the surface of last scattering to today and thus carries information about the structure
of the universe through gravitational lensing and inverse Compton scattering off the high-energy
electrons in galaxy clusters.
1.2.1
Temperature Anisotropies
The temperature anisotropies in the CMB are a snapshot of the acoustic oscillations at decoupling.
To calculate the temperature anisotropies, the mean temperature of the CMB is subtracted along
8
with the dipole term from the Doppler shift of Earth’s motion relative to the CMB. The temperature
anisotropy signal can then be decomposed into spherical harmonics Y`,m as
∆T(n̂) = ∑ aT`mY`m .
(1.19)
`,m
The temperature spectrum as a function of multipole moment ` is thus given by
C`T T =
1
|aT`m |2 .
∑
2` + 1 m
(1.20)
The CMB temperature anisotropy spectrum is shown in Figure 1.1. Multipole moments are inversely related to size scales, so the peaks in the spectrum at the lowest ` are on the largest size
scales. Modes begin oscillating when their wavelengths are twice the size of the horizon, so oscillations on small angular scales (large `) entered the horizon earlier. Modes in their extrema of
oscillation will have enhanced fluctuations, which appear as peaks in the temperature anisotropy
power spectrum. The first peak in the temperature anisotropy power spectrum around ` ∼ 100 is
the last mode to enter into the horizon and gives the horizon size at decoupling θ∗ . The mode
in the first acoustic peak has only undergone compression, while the mode in the second peak is
compressed and then expanded. Thus, odd numbered peaks represent maximal compression, while
even numbered peaks represent the maximal expansion. Because it does not interact with photons,
cold dark matter only coalesces about the original overdensities, so it is in phase with the compression peaks, enhancing the amplitudes of the odd numbered peaks, and out of phase with expansion
peaks, decreasing the amplitudes of the even numbered peaks. The amplitudes of the peaks in the
temperature anisotropy spectrum thus hold information about the relative quantities of baryonic
and cold dark matter in the universe.
1.2.2
Galaxy Clusters
Galaxy clusters are the largest structures in our universe and formed relatively recently, making
them highly sensitive to effects of dark energy and dark matter. Galaxy clusters leave an imprint
9
`(` + 1)C`/2π(µK 2)
104
CMB Temperature Power Spectrum
103
Planck (2015)
102
102
Multipole (`)
103
Figure 1.1: Shown above are measurements of the temperature anisotropy spectrum from the
Planck 2015 data release in purple and the modeled temperature spectrum in black [13]. The
temperature anisotropies have been well characterized by a wide range of CMB experiments with
increasing precision.
on the CMB through the thermal Sunyaev-Zeldovich (SZ) effect where low energy photons from
the CMB are inverse Compton scattered by high-energy electrons in galaxy clusters [14, 15]. An
additional effect (the kinetic SZ effect) also results when CMB photons interact with electrons
that have high energies due to their velocities [16]. While the determination of cosmological
parameters is improved by using the exponential sensitivity of the evolution of the cluster mass
function, cluster mass estimates are currently limited to 10-20% by systematics. Cluster masses
can be determined with several physically independent mass measures: the SZ effect from CMB
experiments, CMB lensing, weak lensing shear from optical surveys, and galaxy dynamics from
optical spectroscopy. By cross-correlating these independent methods, an improved understanding
of both the observational and astrophysical systematic uncertainties in the data can be gained.
Cross-correlations between SZ clusters and galaxy shear from optical surveys can determine the
dark matter distribution and trace how luminous galaxies interact with their dark matter halos as
a function of redshift. These measurements and the comparison of the velocity field from the
10
kinematic SZ effect and the cluster mass function (the number of clusters as a function of z and
mass) will tighten constraints on dark energy, dark matter, and the sum of the neutrino masses.
1.3
Inflation
Despite the strong evidence in support of the ΛCDM paradigm, it leaves several questions unanswered. Inflationary models predict that the universe underwent a period of exponential expansion
from 10−36 s until between 10−33 s and 10−32 s [17]. Inflationary theory provides explanations for
the lack of magnetic monopoles and the unusual flatness and homogeneity of the universe.
Grand Unified Theories predict that magnetic monopoles should exist, but none have been measured. Because inflation expands space so drastically, the number density of magnetic monopoles
would be exponentially small, making the likelihood of measuring a magnetic monopole extremely
rare [17].
Additionally, measurements have determined that the universe is flat within a few percent [10].
As the universe expands, curvature decays less slowly than matter and radiation, so any deviation
from flatness in the early history of the universe would be highly divergent from flat today. To
get the value of flatness that is observed today, the early universe would have had to be flat to one
part in 1060 at the Planck time (5 × 10−44 s). However, initial conditions with a flatness fine-tuned
to such a high precision would be highly unlikely. An inflationary period would have drastically
flattened any initial curvature through the vast expansion of space, eliminating the need to fine-tune
the initial curvature of the universe [17].
Finally, the universe is extremely homogenous and isotropic on scales that could not have been
in causal contact if the current expansion of the universe is extrapolated into the past. In inflationary
models, the horizon size before inflation is exponentially increased after inflation, allowing for
large size scales to be in causal contact prior to inflation [17]. While inflationary models address
some of the questions left unanswered by ΛCDM, many cosmological questions including the
nature of dark matter and dark energy as well as a need for more experimental evidence in support
11
of inflation remain (for a review, see Abazajian et al., 2015 [18]).
1.4
Polarization in the CMB
Before decoupling, photons in the early universe were coupled to electrons through Thomson scattering. Quadrupolar temperature variations in unpolarized light led to linearly polarized scattering,
creating polarization anisotropies as shown in Figure 1.2 (for a review, see [19]). These polarization anisotropies can be mathematically decomposed into even parity (E-modes) and odd parity
(B-modes) modes. Figure 1.3 illustrates E-mode and B-mode polarization patterns around a local
temperature extrema. Three types of perturbations to the spacetime metric can create quadrupoles
in temperature: scalar, vector, and tensor perturbations. E-modes are created by scalar, vector,
and tensor perturbations, while odd parity modes, B-modes, are only created by tensor and vector perturbations [20, 21]. In inflationary models, the rapid expansion of the universe converts
quantum fluctuations into perturbations on cosmological scales and thus predicts the presence of
both E-modes and B-modes [22]. Scalar perturbations are sourced by density perturbations, vector
perturbations are sourced by peculiar velocities and vorticity, and tensor perturbations are gravitational waves. Vector perturbations are damped by inflation and are thus negligible, so the only
expected contribution to the primordial B-modes is from the inflationary gravitational wave tensor perturbations [20, 21]. The B-mode polarization (BB) spectrum has two contributions formed
from scattering in the presence of inflationary gravitational waves that can be seen in Figure 1.5:
a primordial peak at large angular scales of ∼ 2◦ formed during recombination and a peak at very
large angular scales (∼ 10◦ ) formed during reionization [20]. Primordial B-modes would provide
the most direct evidence for inflationary models of the universe. The amplitude of the B-mode
peak at ` ≈ 100 is quantified by the tensor-to-scalar ratio r and could give the energy scale of inflation [20, 21, 23]. Due to the gravitational lensing of the E-mode signal by intervening large-scale
structure such as galaxy clusters, an additional peak in the B-mode spectrum exists at small angular
scales [24].
12
Figure 1.2: Thomson scattering off an electron
in a quadrupolar temperature anisotropy creates linear polarization. The red and blue vectors indicate the magnitude and direction of
polarization of a photon. Unpolarized photons
from a hot spot (red) and cold spot (blue) separated by 90◦ scatter off an electron (green),
resulting in a photon with a net polarization.
Figure adapted from [7].
Figure 1.3: Above are E-mode and B-mode
polarization patterns around local temperature extrema. E-modes have even parity, and
B-modes have odd parity. Figure adapted
from [25].
The E-mode polarization (EE) spectrum can further constrain several cosmological parameters. Measurements of E-modes on small angular scales (high-`) would directly constrain ns and
α. Because small angular modes enter the horizon prior to recombination, the EE spectrum is also
a sensitive probe of the primordial helium abundance YHe [26, 27]. Further, the high-` EE spectrum can constrain the sum of the neutrino masses Σ mν through constraining the abundances of
primordial helium and baryonic matter and the effective number of neutrinos Ne f f by measuring
the high-` acoustic peaks of the EE spectrum [28].
The lensed B-mode and temperature signals contain information about the growth of structure
in the universe, Σ mν , dark matter, and dark energy [29]. The lensing in the CMB is sourced by
intervening matter in the universe between decoupling and today. It can thus probe the matter distribution, including both baryonic and dark matter, of the universe across a wide range of redshifts
with its sensitivity peaking between z ∼ 2 and z ∼ 4 [29]. As a relativistic species, neutrinos in
the early universe would have acted as a pressure, suppressing the formation of structure, so measurements of the formation of structure would also provide constraints on Σ mν . When combined
13
with low redshift (z ∼ 1) optical galaxy lensing measurements, the CMB lensing spectra can further constrain dark energy through tracing its effect on the growth of structure. Additionally, if
the lensed B-modes are well characterized, measurements of the primordial BB spectrum could be
improved by removing the lensed B-mode signal, a process called “delensing.”
1.4.1
Measuring Polarization with the Stokes Parameters
When measuring linear polarization, a natural representation is the Stokes Q and U parameters.
The electric field E of a photon propagating in the ẑ direction is given by
E = (Ex x̂ + Ey ŷ)eikz z−ωt ,
(1.21)
where kz is the wavenumber in the ẑ direction, z is the position in the ẑ direction, ω is the angular
frequency, t is time, and Ex and Ey are the magnitudes of the electric field in the x̂ and ŷ directions,
respectively. The Stokes Q and U parameters can then be introduced to describe the polarization:
Q = hEx2 i − hEy2 i ,
U = 2 Re(Ex Ey∗ ) .
(1.22)
The directions associated with the Q and U Stokes parameters are shown in Figure 1.4. These
parameters can then be expressed in terms of the spin-2 spherical harmonic expansion ±2Y`m fields
(Q ± iU) as
(Q ± iU) = ∑ a±2
`m (±2Y`m ) ,
(1.23)
`,m
2
where the coefficients a−2∗
`m = a`m [30]. The Stokes parameters are dependent on the defined axes,
so to express the polarization in a coordinate-independent way, linear combinations of the a±2
`m
14
coefficients can be constructed such that
1 2
−2
= − a`m + a`m ,
2
i
aB`m =
a2`m − a−2
`m .
2
aE`m
(1.24)
The coefficient aE`m has even parity, while aB`m has odd parity. The E-mode and B-mode signals can
thus be written as
E(θ , φ ) = ∑ aE`mY`m (θ , φ ) ,
`,m
B(θ , φ ) = ∑ aB`mY`m (θ , φ ) .
(1.25)
1
haX`m aY`m∗ i ,
∑
2` + 1 m
(1.26)
`,m
The spectra are then given by
C`XY =
where X and Y can be E-mode, B-mode, or temperature. The coefficients aE`m and aB`m in Equation 1.24 thus define the EE (C`EE ) and BB (C`BB ) spectra, respectively.
+Q
-U
+U
-Q
Figure 1.4: The Stokes Q and U parameters are shown above in the International Astronomical
Union (IAU) convention. Positive and negative values of Q and U are orthogonal, and the Q and
U signals are rotated 45◦ with respect to each other. The Stokes parameters are a natural basis for
measuring linearly polarized signals.
15
1.5
Observational Challenges
Figure 1.5 shows the current state of CMB polarization measurements. E-mode polarization and
lensing B-modes have been detected by a number of CMB polarimetry experiments, including
ACTPol [31], POLARBEAR [32], SPTpol [33, 34], and BICEP2 [35]. However, the primordial
B-mode signal has yet to be detected, and the current best upper limits place r < 0.12 at 95%
confidence [35]. At these levels, galactic foregrounds from synchrotron and dust emission are
dominant and must be well characterized and removed to gain sensitivity to primordial B-modes.
The spectra of synchrotron emission scales with frequency ν as ν −2.7 , and dust emission scales as
ν 1.6 , making synchrotron contamination dominant at low frequencies and dust dominant at high
frequencies [36, 37]. Because the primordial B-mode signal is expected to have a root mean square
value of < 100 nK at ` ≈ 100, a large developmental effort is still necessary to precisely measure
the polarization anisotropies in multiple frequency bands to mitigate the effects of foreground
contamination.
In addition to foreground contamination, CMB polarization experiments that seek to measure
the B-mode signal must scan large patches of the sky to probe large angular scales. This can be
problematic for ground-based experiments that must observe through the atmosphere, which can
fluctuate by tens of mK on minute time scales [38]. This 1/ f noise from the atmosphere can
obscure information from the B-mode signal on large angular scales. However, the atmosphere is
unpolarized, so modulating the incoming polarization can separate the faint B-mode signal from
the fluctuations in the unpolarized atmosphere, facilitating the recovery of polarization information
on large angular scales.
To measure the CMB polarization anisotropies, especially the B-mode signal, current and future experiments must deploy large-scale arrays of highly sensitive, uniform detectors with wide
frequency coverage. These detectors and instruments as well as their systematic errors must be
well understood and characterized to reach the level of sensitivity necessary to measure such faint
signals.
This work will describe three CMB polarimetry experiments: the Atacama B-mode Search
16
102
`(` + 1)C`/2π(µK 2)
101
Polarization Power Spectra
Planck (2015)
ACTPol (2014/16)
POLARBEAR (2014)
SPTpol (2015)
BICEP/Keck (2015)
100
10−1
Lensing B + tensors
10−2
r=0
10−3
r=0.01
10−4
101
102
Multipole (`)
103
Figure 1.5: Shown above are measurements of the E-mode and B-mode power spectra from Planck
in purple [13], ACTPol in blue [31], POLARBEAR in cyan [32], SPTpol in red [33, 34] and the
BICEP2, Keck, and Planck joint analysis in green [35]. The solid black lines are the modeled
E-mode and B-mode spectra for an r = 0.01. The B-mode spectrum includes contributions from
the lensed E-mode signal (dashed line) and the primordial signal (dotted line). E-modes and lensed
B-modes have been measured, but the primordial B-modes have yet to be detected.
(ABS), the Atacama Cosmology Telescope Polarimeter (ACTPol), and its upgrade Advanced ACTPol (AdvACT). Chapter 2 will provide an overview of the experiments. One method of polarization
modulation employs a continuously-rotating half-wave plate (HWP) to recover B-mode polarization on large angular scales. This technology was pioneered by the ABS experiment for groundbased experiments, was used in the last season of observation for ACTPol, and is slated for use on
AdvACT. This technology will be described in Chapter 3 along with several novel characterization
and data selection techniques, and Chapter 4 will focus on further methods of optical characterization for CMB instruments. The data selection and analysis process for ABS will be presented in
Chapter 5. The development and testing of feedhorns for AdvACT, which deployed its first array
in June 2016, will be presented in Chapter 6. Chapter 7 will summarize the current state of the
ABS and AdvACT experiments.
17
Chapter 2
Cosmic Microwave Background
Instruments
To measure the CMB polarization anisotropies, especially the B-mode signal, current and future
experiments must deploy large-scale arrays of highly sensitive, uniform, cutting-edge detectors.
Additionally, the detectors and instruments as well as their systematic errors must be well understood and characterized to reach the level of sensitivity necessary to measure the faint CMB polarization signals. The Atacama B-mode Search (ABS), which will be discussed in Section 2.1, was a
pathfinder CMB polarization experiment that observed on degree-angular scales from an elevation
of 5190 m in the Atacama Desert in Chile. ABS fielded new detector technologies and employed
a continuously-rotating half-wave plate (HWP) for polarization modulation, establishing this technology for ground-based CMB experiments. The Atacama Cosmology Telescope (ACT) is a 6 m
telescope with arcminute resolution located at the same site in the Atacama as ABS [39]. ACT’s
high resolution enables measurements of the CMB at small angular scales. The first receiver for
ACT, the Millimeter Bolometer Array Camera (MBAC), observed the temperature of the the CMB
from 2007 to 2010 [40]. To allow for measurements of the CMB polarization anisotropies at small
angular scales, the ACT receiver was upgraded to the ACT Polarimeter (ACTPol), which began
observations in 2013 and is described in Section 2.2 [41]. The next-generation receiver for ACT
18
is Advanced ACTPol (AdvACT) and is described in Section 2.3. AdvACT will have larger frequency coverage than ACTPol to thoroughly characterize and remove foregrounds and will probe
larger angular scales than ACTPol through the use of continuously-rotating HWPs. The first of
four AdvACT arrays was fielded in June 2016.
2.1
The Atacama B-mode Search Instrument
The primary scientific goal of ABS was to measure or limit the B-mode spectrum from multipole
moments of ` ≈ 40 to ` ≈ 500, a range that includes the primordial B-mode peak at ` ≈ 100. The
ABS instrument was a crossed-Dragone telescope located in the Atacama Desert in Chile and observed at 145 GHz between February 2012 and October 2014. The key characteristics of the ABS
instrument are shown in Table 2.1. ABS featured a fully cryogenic telescope and pioneered the
use of a continuously-rotating HWP for ground-based observations, which is described in detail in
√
Chapter 3. ABS has a receiver noise equivalent temperature (NET) of 41 µK s, and a modulation
efficiency at 145 GHz of 99.7% at normal incidence to the HWP. The following section will give
an overview of the ABS instrument, but further details of the instrument can be found in several
theses as outlined in Section 2.1.6.
Table 2.1: ABS Key Characteristics
Parameter
Value
Number of Bolometers
480
Base Temperature
300 mK
Angular Resolution
32.7 ± 0.5 arcmin (FWHM)
Solid Angle
102 ± 6 µsr
Frequency Coverage
127-163 GHz
Sky Coverage
∼3100 deg2†
√
Receiver Noise Equivalent Temperature (Sensitivity) 41 µK s
Detector Time Constants
& 50 Hz
Polarization Modulation
10.2 Hz
Location
Ground (Chile, 5190 m)
†Note that the primary field is ∼ 2400 deg2 .
19
2.1.1
Telescope Site
The ABS instrument was deployed in the Parque Astronómico located in the Atacama Desert in
Chile. The telescope site was situated at an elevation of 5190 m near the peak of Cerro Toco at
67◦ 470 1500 W and 22◦ 570 3100 S. This telescope site was selected because its elevation and arid conditions minimize the contamination to millimeter wave light from atmospheric water vapor. Each
observation season ranges roughly from April through December when there are optimal observing conditions. The remaining period of the year from January to March is used for instrumental
upgrades and repairs. The site’s mid-latitude position allows for access to ∼20,000 deg2 of the
sky, which opens the possibility of overlap with several astronomical surveys across a wide range
of wavelengths including BOSS [42], DES [43], DESI [44], HSC [45], and LSST [46]. The midlatitude position also allows for making cross-linked maps since the same fields can be observed as
they rise in the East and set in the West. Cross-linking is particularly good for isolating instrumental polarization from celestial polarization (though ABS does not fully utilize this strategy). The
ABS site is shared with ACT and is shown in Figure 2.1.
Figure 2.1: The telescope site for ABS and ACT in Chile is shown above. The large structure is the
ACT ground screen, which shields the ACT telescope from ground pickup. The leftmost structure
is the ABS telescope, which was fielded on top of a shipping container to enable rapid deployment.
20
2.1.2
Observation Strategy
The loading from water vapor in the sky is dependent on the elevation angle of the telescope, so
to minimize fluctuations in the loading, the ABS instrument employed constant elevation scans
(CESes). The scanning speed was 0.75◦ /s in azimuth, and each scan in the first two seasons had
an amplitude of 10◦ in azimuth (∼7◦ on the sky). Each CES is roughly 60-90 minutes long, and
the detectors were biased and calibrated before each CES. ABS observed a ∼2400 deg2 , lowforeground CMB patch (Field A) below the Galactic plane centered at (RA, DEC) = (25◦ ,-42◦ ).
Field A was observed at an elevation of θel ∼ 45◦ both as it rose in the east and set in the west.
In addition to the primary field, a smaller (∼700 deg2 ) secondary CMB field (Field B) with low
foregrounds centered at (RA, DEC) = (175◦ ,0◦ ) and an 80 deg2 patch of the Galactic disk (Field G)
centered at (RA, DEC) = (266◦ ,-29◦ ) were also observed. Figure 2.2 shows the ABS fields plotted
with those of several other CMB polarization experiments.
Field A was given the highest priority in the observation schedule. Field B was observed when
Field A was unavailable, and Field G was observed when neither CMB field was available. Occasionally, point source and calibration observations were given priority over the observation fields.
Additionally, the ABS fridge needed to be recycled every 48 hours, a process which took ∼7 hours,
so the fridge recycling was scheduled to minimize interference with Field A observations. ABS
made both daytime and nighttime observations.
In its third season of observations in March 2014, an upgraded azimuth motor system with
higher torque and slower speed was installed. Observations in the first two seasons were performed
with a separate scan motor because the old azimuth motor was not suited for azimuthal scans. The
scan motor was limited to ∼7◦ scans on the sky, but the new azimuth motor system enabled scans
of ∼20◦ , which enabled ABS to probe lower multipole moments. Additionally, the ABS focal
plane is ∼20◦ across, so larger scans also allow pixels on opposite sides of the array to observe
the same sky patches. The new motor used a custom coupling gear shaft so that the same coupling
gear between the motor and the azimuth gear could be used. New electromagnetic shielding for the
motor, cables, controller box, and motor driver was constructed out of GIRON Magnetic Shielding
21
ABS FieldA
ACTD2 ACTD1
ABS FieldB
ACTD5
ACTD6
SPIDER
QCMB-1
QCMB-4
QCMB-2
ABS FieldG
QCMB-3
SPT
-400
BICEP2
K CMB ; HFI : = 143 GHz
1000
Figure 2.2: The ABS observation fields are outlined in black above and overlaid on maps of the
Stokes I parameter at 143 GHz from Planck’s HFI instrument in equatorial coordinates [47]. Also
shown are the ACTPol fields in red [48], the SPIDER field in pink [49], the QUIET fields in yellow [50], the BICEP2 field in purple [51], and the SPTpol field in navy blue [52]. ABS, SPIDER,
QUIET, and BICEP2 are all large angular scale experiments, while ACTPol and SPTpol target
small angular scales. Field A is the primary observation field, while Field B is a smaller patch
above the Galactic disk. A patch of the galaxy, Field G, is also observed when Field A and Field
B are not available. Image courtesy of Srinivasan Raghunathan.
Film to minimize the noise pickup from the motor system in the detector readout. Measurements
of the detector and readout noise properties were used to tune the scan speed and turnarounds of
the scanning to minimize the noise in the signal band around 10.2 Hz.
2.1.3
Telescope Design
The full ABS telescope is shown in Figure 2.3. A ground screen comprised of honeycomb aluminum paneling and a conical baffle machined out of aluminum shields the 30 cm diameter aperture of the telescope from stray radiation from the ground and other structures. The ABS cryostat1 is comprised of four temperature stages enclosed in a vacuum shell: 40 K, 4 K, 1 K, and
1 The
ABS cryostat was built by Precision Cryogenic Systems, Inc. Indianapolis, IN 46214.
22
300 mK [53]. Liquid cryogens are difficult to obtain on a steady basis due to the remote location
of the telescope, so the cryogenic system avoids the use of non-recycled liquid cryogens. A system
of two pulse tube cryorefrigerators from Cryomech2 (a PT407 and a PT410) cools the 40 K and
4 K stages. The measured temperatures of the 40 K and 4 K stages in situ are 42 K and 3.6 K,
respectively, and the cooling powers available at each stage are 41 W and 1 W, respectively. The
pulse tubes are most efficient when vertical, so they are mounted on the outside of the cryostat
at a 45◦ angle so that they are vertical when the telescope is observing at an elevation of 45◦ . A
He adsorption system backed by the pulse tubes provides cooling to the 1 K and 300 mK stages.
The 1 K stage is cooled by a 4 He adsorption refrigerator, while the 300 mK stage is cooled by a
3 He/4 He
adsorption refrigerator system [53, 54, 55, 40].
Figure 2.3: The ABS telescope is shown above. The square panels comprise the ABS ground
screen. The electronic readout equipment and control computers are housed in the container below.
The readout for ABS employs three stages of superconducting quantum interference devices
(SQUIDs), which are extremely sensitive magnetometers, so the cryostat also has several layers
of magnetic shielding. At 300 K, there is a µ-metal magnetic shield, and a cryoperm shell at 4 K
provides additional shielding. The ABS detectors and the first two SQUID stages are encased in
superconducting Al pods, and the final SQUID stage is housed in Nb boxes. Nb foil is also placed
above and below each SQUID multiplexing chip for further magnetic shielding.
2 Cryomech
Inc. Syracuse, NY 13211.
23
An ambient-temperature HWP sits above the 30 cm diameter window into the cryostat. The
HWP is the first optical element on the telescope, which means that any instrumental polarization
is not modulated with the signal. The cryostat window is constructed from 1/8” thick ultra-high
molecular weight polyethylene (UHMWPE) with anti-reflection (AR) coatings of Zitex G-1153
porous polytetrafluoroethylene (PTFE) on both sides [56, 57]. The AR coatings and filters for
ABS are optimized for ∼145 GHz. Inside the cryostat at 300 K, there is a 1.6 THz metal mesh
infrared (IR) blocker [56]. At 40 K, a set of five single-layer, low-pass, metal-mesh IR blockers are
fastened above a 2.5 cm thick PTFE filter that is AR coated on both sides with Zitex G-115. An
additional four IR blockers are mounted below the 40 K PTFE filter. Two metal-mesh IR blockers,
a 1” thick PTFE filter AR coated in Zitex G-115, and a 3/8” thick Nylon filter AR coated with
Zitex G-115 are mounted below the cold stop at 4 K [57]. The thickness of the 4 K filter stack was
minimized to avoid ray-clipping. After passing through the filter stack, the radiation then reflects
off of the 4 K primary and secondary mirrors onto the 300 mK focal plane.
The compact crossed-Dragone configuration of the ABS telescope shown in Figure 2.4 allows
for a large focal plane area and for the 60-cm primary and secondary mirrors to be cooled to
4 K by a system of two pulse-tube coolers, which reduces loading and thus increases sensitivity.
Additionally, the cross-Dragone design is optimized for low cross-polarization and a clean beam
with no need for cryogenic lenses [56, 58, 59, 60, 61]. The ABS primary mirror is a concave
parabolic mirror 57.1 cm in diameter, and the secondary mirror is a 58.5 cm concave hyperbolic
mirror. The ABS optics also employ an aperture stop 25 cm in diameter at 4 K to ensure that
any beam spillover only lands on cold optical elements. The ABS optics were designed using
a ray-tracing software, Code V [62], and further verified using physical optics simulations from
DADRA4 that incorporated the feedhorns and mirrors [56]. A diagram of the optics from Code
V is shown in Figure 2.5. The ABS telescope has an angular resolution of 32.7 ± 0.5 arcmin full
width at half maximum (FWHM), which integrates to a solid angle of 102 ± 6 µsr [63].
3 Norton
Films, http://www.norton-films.com/
Analysis of a Dual Reflector Antenna, Rahmat-Samii, Y., Imbriale, W., & Galindo-Israel, V., YRS
4 Diffraction
Associates.
24
Figure 2.4: Above is a cross section of the ABS receiver. A warm baffle and half-wave plate are
above the cryostat window. Light enters through the window, goes through a series of filters, and
reflects off of the primary and secondary mirrors onto the focal plane. The primary and secondary
mirrors are kept cold at ∼4 K by a pulse tube refrigerator system. A He adsorption system cools
the focal plane to 300 mK. Image from [56].
2.1.4
Focal Plane
The ABS focal plane array is cooled to a base temperature of 300 mK and contains 240 TRUCE5
pixels (480 detectors) that are designed for operation at 145 GHz and fabricated at the National
Institute of Standards and Technology (NIST) in Boulder [64, 65]. The pixels (Figure 2.6) are arranged into 24 triangular pods of ten that make up the hexagonal focal plane shown in Figure 2.7.
Each 5 mm diameter pixel has two transition-edge sensor (TES) bolometers coupled to orthogonal
polarizations from a planar orthomode transducer (OMT). Each ABS pixel has its own individ5 TRUCE
is a collaboration among Princeton University, the University of Colorado, the University of Chicago, the
University of Michigan, National Institute of Standards and Technology, and the NASA Goddard Space Flight Center.
http://casa.colorado.edu/henningjw/TRUCE/TRUCE.html
25
43
Figure 2.5:Figure
Above
a ray-tracing
of the
the final
ABSABS
optics
from
CodeThe
V. sky
Light
on the
3.3:isCodeV
ray tracingdiagram
diagram for
reflector
design.
is toenters
the
in of
thethe
figure.
The focal
planeon
is at
theright,
bottom,
primary
right, and secondary
left, reflectsleftoff
primary
mirror
the
reflects
offreflector
of the at
secondary
mirror on the top,
the top.
the sameThe
color
correspond
raysindicate
coming inthe
at same
the same
and focusesreflector
on theatfocal
planeAllonrays
theofbottom.
colors
of thetorays
angles from
angle from the sky and converge on approximately the same point in the focal plane. Figure
the sky. Silviu
Pufu generated the optical design of the ABS telescope. Image from [56].
courtesy of Silviu Pufu.
ually machined, single-moded, corrugated Al feedhorn (Figure 2.8) coupled to the pixel with a
respectively. CodeV outputs for the final optical design are shown in Figures 3.3 and 3.4.
waveguide [57]. The feedhorn angles are optimized to minimize beam mismatch between the two
3.2.1
Physical Optics Simulations with DADRA
polarizations on each pixel [56].
Once the optical design had been optimized using the CodeV ray-tracing software, it was
Light from the feedhorn is waveguide coupled to a planar OMT that splits the radiation into two
further verified using the DADRA program2 . This code performs a physical optics analysis
linear, orthogonal polarizations [66]. The signals from the OMT pass through a co-planar wavegof the feedhorn, primary reflector, and secondary reflector system of ABS. The radiation
uide to microstrip
transition
to minimize
loss and
sent down
Nb microstrip
pattern from
the feedhorns
was simulated
usingare
CCORHRN
andsuperconducting
then input into DADRA
with the shapes
of the
and
secondary
DADRA generates
complex
lines to thealong
bolometers.
Each of
the primary
Nb lines
has
a seriesreflectors.
of quarter-wave
stub filters
that define the
three-dimensional, electric-field data in the plane of the 4 K aperture stop. With a separate
observation bandpass
[67]. Each TES is suspended on a silicon nitride membrane connected to the
2
Diffraction Analysis of a Dual Reflector Antenna, Rahmat-Samii, Y., Imbriale, W., & Galindo-Israel,
V., YRS Associates
300 mK bath only through a weak thermal link of four thin legs (Figure 2.9). Upon reaching this
TES island, the Nb transmission lines terminate into lossy Au meanders, which deposit the power
from the radiation onto the island as heat and increase the temperature [65]. This temperature increase is measured by the TES located at the center of the island and is a measure of the incident
power on the detector. TES bolometers are biased in the center of their sharp superconducting-tonormal resistance transitions at their critical temperatures (Figure 2.10) and take advantage of the
26
X TES In-line filter OMT Y TES 1.6 mm 5 mm Figure 2.6: A TRUCE pixel designed to measure a
band around 145 GHz is shown above. Each pixel
contains two TES bolometers coupled to orthogonal
polarizations from an OMT.
Figure 2.7: The hexagonal focal
plane has 24 pods with ten pixels
each. The focal plane is roughly
30 cm wide and is cryogenically
cooled to ∼300 mK.
steep dependence on temperature to create a highly sensitive detector [68]. Each ABS TES is a
molybdenum-copper (MoCu) bilayer that is biased at a constant voltage to be on the superconducting transition by being placed in series with a shunt resistor as in Figure 2.11. A small increase
in incident power will increase the TES resistance, causing a change in readout current. An increase in resistance of the TES decreases the electrical power (V 2 /R), which is also dissipated on
the island, compensating for the increase in optical power and thus keeping the TES stable on the
transition via negative electrothermal feedback.
The two halves of the ABS array were fabricated in two batches, batch A and batch B. Each
batch is made up of two separate fabrication wafers. Batch A is made up of wafers 1-4 and 1-11,
and Batch B is made up of wafers 1-14 and 1-15. Figure 2.12 shows the location of each wafer
on the array. Due to unexpected changes in the properties of the deposition materials between
fabrications, batch B has a bandpass shifted up by ∼ 12 GHz. Measurements of the ABS detector
bandpasses are discussed in Section 4.2.
27
Figure 2.8: A single ABS feedhorn with a section cut out so that the corrugations are visible
is shown above. The ABS feedhorns are conical corrugated feedhorns that are individually
machined out of Al.
Figure 2.9: A close-up of a TES island with
Au meanders is shown above. This particular
close-up image is from an ACTPol detector.
The thin silicon nitride legs can be seen in the
four corners, and the molybdenum-copper bilayer TES can be seen in the very center.
Figure 2.10: The transition from superconducting to normal is shown for an ACTPol
bolometer. It can be seen that the transition region is very steep, allowing for increased sensitivity.
Figure 2.11: A TES electrical circuit is shown
above and is inductively coupled to a SQUID
for readout.
28
1-4
1-11
1-15
1-14
Figure 2.12: The ABS focal plane is shown above with colors denoting the four constituent fabrication wafers. Each cross represents the two detectors sensitive to orthogonal polarizations on
each pixel. The top five triangular pods of ten pixels shown in dark blue are from wafer 1-4, and
the second row of seven pods shown in light blue are from wafer 1-11. The yellow pixels shown
in the bottom two rows of the array are from wafer 1-14, while the dark red pixels in the bottom
half of the array are pixels from wafer 1-15.
2.1.5
Readout
The NIST time-domain multiplexing detector readout used by ABS is comprised of a series of
inductors and SQUIDs [69], which are highly sensitive magnetometers that consist of superconducting loops and Josephson junctions. SQUIDs can both detect and amplify small signals. Each
TES detector is inductively coupled to a stage 1 readout SQUID (SQ1) by placing it in series with
an inductor as seen in Figure 2.11. An inductive summing coil couples the signals from a given
number ndet of SQ1s to a common stage 2 SQUID (SQ2). Each SQ2 is in turn inductively coupled
to a stage 3 series array of SQUIDs that serve to further amplify the signal, which is then read out
by the UCB multichannel electronics (MCE) [70]. The MCE also controls the feedback for tuning
the SQ1s and biases the detectors.
Each instance of ndet detectors sharing a SQ2 is called a column, while each of the ndet detectors
in the column are called a row. A schematic of the readout for a 2 column x 2 row time-domain
multiplexed array is shown in Figure 2.13. In each column, ndet detectors share a multiplexing
line, which limits the number of cryogenic wires and thus reduces the thermal loading on the focal
29
plane [71]. Each row of SQ1s are biased one after the other such that one detector at a time is
read out in each column. When the detector is not being read out, the LR circuit integrates the
accumulating signal. The ABS MCE has a sampling rate of 200 Hz. Each ABS column can
readout ndet = 32 detectors, but only 22 rows are multiplexed in each column. Of the rows read
out, two are dark SQUIDs, while twenty are detectors. With this readout scheme, each of the 24
detector pods constitutes a multiplexing column.
2.1.6
Further Instrumental Details
Several other theses describe the ABS project in further detail. The optical design of the telescope,
the design of the focal plane, and the HWP design are all described in [56]. A Mueller matrix
model of the HWP is also presented in [56]. The original design of the ABS filters is described
in [56], but the filter configuration was modified during the ABS deployment, which is outlined
in [57]. Details of the cryogenic system of the telescope are described in [53]. The design and
testing of the ABS feedhorns is presented in [57]. Further details about the ABS detectors, the
array assembly, and the SQUID multiplexing readout can be found in [73]. Dark and optical tests
of the detectors prior to deployment, including superconducting Johnson noise, responsivity, noise
spectra, complex impedance, bandpass, optical efficiency, and beam measurements, are presented
in [73]. The data acquisition system, including the motion control, housekeeping, and MCE, is
described in [53]. Preliminary data processing techniques and data-selection criteria are outlined
in [57]. Finally, details of the telescope pointing can be found in [74], and the characterization of
the telescope beam using Jupiter observations is described in [63].
30
Column
ouputs:
Column 1
Column 2
Each colored block
corresponds to the
components for an
individual pixel.
Row address
currents:
Row 1
Row 2
Figure 2.13: The schematic for a 2 column x 2 row array SQUID time-domain multiplexing readout
is shown
TES detector
is inductively
coupled
to its own SQUID
(SQ1).
Figure
3.3:above.
TwoEach
column
multiplexing
readout
schematic.
The amplifier
large decrease
The colored blocks represent each of the four individual detectors with their SQ1s. Columns of
readout
wiring from multiplexing is due in part to addressing rows of SQUIDs
detectors and their SQ1s are read out sequentially so that the signal from one detector at a time is
seriessent
as todepicted
in a two
column
two
rowinductively
array. coupled
(Figureto acourtesy
the second here
stage SQUID
(SQ2).
The SQ2by
signal
is then
series arrayof
of SQUIDs for amplification and read out with the room temperature MCE electronics. SQUID
Doriese.)
feedback lines from the MCE inductively couple to the SQ1s to keep them biased at a constant
value. Figure from [72].
31
in
in
R.
2.2
The Atacama Cosmology Telescope Polarimeter
Installed in 2013, ACTPol is the first polarization-sensitive receiver for ACT. The ACT telescope
is an off-axis Gregorian telescope with a 6 m primary mirror located at the same site in Chile as
ABS as can be seen in Figure 2.1 [39]. ACTPol observes the polarization of the CMB on small
angular scales from ` ≈ 200 to ` ≈ 3000. Its arcminute resolution enables an abundance of high` physics: measuring the gravitational lensing of the CMB, detecting galaxy clusters via the SZ
effect, and constraining a number of cosmological parameters including the sum of the neutrino
masses, the number of neutrino species, scalar spectral index, the running of the spectral index
with wavenumber, and the primordial He abundance [41]. ACTPol has several similarities to ABS.
It uses an upgraded pixel design from the ABS pixels for its three arrays, which consist of two
148 GHz arrays (PA1 and PA2) and a 97/148 GHz multichroic array (PA3). Additionally, ACTPol
uses the same time-domain multiplexing readout architecture as ABS, but uses a 32 column x 33
row readout for each array with a detector sampling rate of 15.15 kHz that is downsampled to
399 Hz [75]. In its 2015 season, ambient-temperature HWPs were added to the ACTPol receiver
to enable observations at larger scales. The key characteristics of the ACTPol arrays are shown in
Table 2.2 [75].
Table 2.2: ACTPol Key Characteristics
Parameter
PA1
PA2
PA3-148 GHz PA3-97 GHz
Number of Bolometers 1024
1024
510
510
Center Frequency
148
148
148
97
(GHz)
Major Axis FWHM
1.37
1.33
1.58
2.13
(arcmin)
Minor Axis FWHM
1.32
1.31
1.33
2.00
(arcmin)
Solid Angle (arcmin2 )
2.27 ± 0.05 2.12 ± 0.03 3.12 ± 0.13
6.62 ± 0.22
√
Sensitivity† (µK s)
∼16
∼9.5
∼10
∼14
Detector Time
1.9
1.8
1.3
1.3
Constants (ms)
Base Temperature
100 mK
100 mK
100 mK
100 mK
†Sensitivity values are for a precipitable water vapor/sin(elevation)=1 mm.
32
The ACTPol instrument was designed and constructed with the help of a large group of people. The cryogenic receiver work was primarily done at the University of Pennsylvania [76];
the cold optics were designed at Cornell University and constructed at the University of Michigan; the detectors were designed at the University of Michigan [77, 78, 79] and were fabricated by
NIST; detector testing was performed at NIST, Cornell University, the University of Michigan, and
Princeton University [80, 81, 82]; and the arrays were assembled at Princeton University [80, 81].
2.2.1
Observation Strategy
Like ABS, ACTPol scans azimuthally at constant elevation. ACTPol scans with a speed of 1.5◦ /s
and a scan period of 10-20 s, depending on the observation field [75]. In the 2013 season, ACTPol observed four deep fields, each ∼ 70 square degrees, centered near the equator (DEC=0◦ )
with PA1 [48]. These deep fields are plotted in Figure 2.2 and called deep1 (RA=150◦ ), deep2
(RA=175◦ ), deep5 (RA=355◦ ), and deep6 (RA=35◦ ) [48]. In the 2014 season and the first month
of the 2015 season, ACTPol observed two wide fields: a ∼700 deg2 field that includes deep5 and
deep6 called deep56 that was centered at (RA, DEC) = (16◦ ,-2◦ ) and a ∼2000 deg2 field called
BOSS-N that was centered at (RA, DEC) = (180◦ ,8◦ ) and designed to overlap with the northern
BOSS galactic survey [83]. For the remaining 2015 season, ACTPol targeted low-foreground areas
to search for B-mode polarization on larger angular scales by observing a ∼190 deg2 field called
deep8 centered at (RA, DEC) = (2.5◦ ,-42◦ ) and a ∼700 deg2 field called deep9 centered at (RA,
DEC) = (65◦ ,-39◦ ) [83]. ACTPol typically observes at an elevation between 40◦ and 55◦ , and
utilizes the advantages of cross-linking by observing each field both as it rises and sets at several
elevation angles.
2.2.2
Telescope Design
The ACT telescope is shown in Figure 2.14. An outer ground screen encloses the telescope and can
also be seen in Figure 2.1. ACT is further protected from ground emission by a co-moving ground
screen. ACT employs a compact off-axis Gregorian design that is optimized for a wide field of
33
view and fast scanning [39, 40]. ACT consists of primary and secondary mirrors and an enclosed
receiver cabin. The primary mirror is 6 m in diameter and constructed out of 71 individually
adjustable Al panels, while the secondary mirror is 2 m in diameter and constructed from 11 such
panels. Figure 2.15 shows a ray-tracing diagram of the ACT telescope [75].
Figure 2.14: A view of the ACT telescope from the top of its outer ground screen is shown above.
The co-moving inner ground screen further shields the mirrors from stray light. The primary mirror
can be seen on the right side of the telescope. Photograph courtesy of Mark Devlin.
The ACTPol receiver is a large cryostat that consists of three independent optics tubes as can be
seen in Figure 2.16. Each optics tube has its own window and houses three lenses, filters, and a full
detector array. The focus of the off-axis Gregorian optics is positioned between the window and the
first lens in each optics tube to minimize the size of the optics so that they can fit in the cryostat, and
each optics tube has a Lyot stop at 1 K. The lenses in each optics tube are each slightly tilted and
offset to achieve a diffraction-limited design. The lenses are made of Si, and have metamaterial AR
coatings that are comprised of layers of square pillars machined into the lens surfaces with a dicing
saw [84]. PA1 and PA2 both have two layer coatings, but a three layer coating (Figure 2.17) must
be used on the PA3 multichroic array to achieve broadband transmission. A ray-tracing diagram
of the PA1 and PA3 optics tubes with their lenses is shown in Figure 2.18.
The ACTPol cryostat6 is shown in Figure 2.16 and has four temperature stages: 40 K, 4 K,
6 The
ACTPol cryostat was built by Precision Cryogenic Systems, Inc. Indianapolis, IN 46214.
34
ACTPol Instrument
3
,"#-+.)&/'
01&2#12&"'
8&$6)&/'
01&2#12&"'
34"%)1$-+'
5&)6"'
!"#"$%"&'
()*$+'
9'6'
!"#"$%"&'
!"#"$%"&'
0277-&1'01&2#12&"'
Figure 2.15: A ray-tracing diagram of the ACT primary and secondary mirrors into the receiver is
shown above. Light hits the primary, reflects onto the secondary, and is focused into the receiver.
The receiver is protected from the elements by the receiver cabin. Image courtesy of Bob Thornton
filters (Tucker & Ade 2006) at ambient temperature; foldicing saw, creating layers of square pillars. The result(fromby[75]).
lowed
a combination of blocking filters and low pass
ing coating has a coefficient of thermal expansion matchFigure 2. Ray trace of ACT’s primary and secondary mirrors up to the entrance of the receiver. The major components of the telescope
upper structure are shown, except for the inner ground screen and part of the receiver cabin wall, which have been removed for clarity.
The telescope is shown in its service position (where the receiver cabin floor is level), corresponding to a viewing elevation of 60◦ .
edge (LPE) filters (Ade et al. 2006) at 40 K; the first lens
ing that of the rest of the lens. Lenses based on a twoand accompanying filters at 4 K; the Lyot stop, two more
layer design (Figure 4a) are used in both the PA1 and
7 PT410)
lenses,
and additional
low
pass
filters
all (Cryomech
at 1 K; and the
PA2 optics.
Simulations
showed
thatKthe
resulting
coat1
K,
and
100
mK.
A
pulse
tube
refrigerator
cools
the 40
and
4 K stages
final LPE filter and array package at 100 mK. A ray trace
of the cold optics is shown in Figure 3.
3
4 ,334%5670)"+%
ofThe
thesize
cryostat.
Thetube
1 Kisand
100bymK
dilution refrigerator8 (DR)
of each optics
limited
bothstages
the sizeare cooled by a He/ He
834%5670)"+%
84%5670)"+%
of the cryostat (which had to fit in the existing receiver
&)*+%2%
cabin)
as
well
as
the
the
maximum
diameter
of
the
lowbacked with its own Cryomech PT407 pulse tube cooler [85]. The 100 mK &$/0%%
stage&)*+%-%
has 100 µW of
pass edge filters (Section 4.3). To minimize the size of
+0/1%
%%%%%-.%&'(%
the entrance optics, the receiver is positioned such that
cooling
power
has a temperature
between
the
Gregorian
focusand
is located
between the receiver
win- 100 mK and 115 mk in the field with all three arrays
&)*+%,%
dow and first lens. The Gregorian focus is not telecentric,
which
is a requirement
a large,
flat feedhorn-coupled
&'(%
installed
[75]. In itsforfull
configuration,
a cooldown of the cryostat takes about 14 days.
detector array (see Hanany et al. 2013). To achieve a
telecentric design, small offsets and tilts were incorpocross
section
thefinal
PA1
optics
tube is shown in Figure 2.19 with its components labeled.
ratedA
into
the three
lenses.ofThe
design
is diffractionlimited across each focal plane.
Each optics tube has its own 32 cm in diameter (34 cm for PA3) window at 300 K made of 6.4 mm
4.2. Lenses
!""#$%%
SiliconUHMWPE
was chosen for
thecoated
lens material
due to PTFE
its highfollowed by a series of IR blocking filters at 300 K,
thick
AR
in porous
thermal conductivity, high index of refraction (n = 3.4),
and low loss at our wavelengths. The high index of re40 K, necessitates
and 4 K [86].
edge
(LPE)
fraction
the use Low-pass
of AR coatings.
ACT
previ- metal-mesh filters are fastened at 40 K, 4 K, 1 K,
ously used Cirlex coatings (Lau et al. 2006), but they incurred
an estimated
net efficiency
reduction
(Swetz
and 100
mK and15%
define
the upper
edge of
the bandpass for PA1 and PA2, which have no on-chip
Figure 3. Ray trace of the cold optics. The upper trace shows
et al. 2011). For ACTPol, we created “meta material”
the PA3 (multichroic) optical path and the lower trace shows the
AR coatings produced by removing some of the silicon
PA1filter
path. The
PA2 optical
pathsecond
is a mirror
image
to that are
of PA1
filters
[87].depths
The first
is fastened
at 4lens
K after
the
stack,
and the
two
lenses
into
controlled
fromlens
the surfaces
of each
at
and has been removed for clarity. The constituent elements are
sub-wavelength scales using a custom three-axis silicon
described in the text.
7 Cryomech
8 Janis
Inc. Syracuse, NY 13211.
Research Corporation LLC. Woburn, MA 01801.
35
ACTPol Instrument
/2()*+%,(-*.,(
/0+*&0$1(
2,3"04,"'&$"(5/26(
9
!"#$%&'&()*+%,(-*.,(
79(!$>>,"(-$?,"(
)B<(D>&0E%(-*.,(
79(!$+A()+'&,(
:889(ʹ(789(;<8(
=*%>,1%0$1((
@01A$?(
)B:(
)BC(D>&0E%((
-*.,(
789(ʹ(:9(;<8(
=*%>,1%0$1((
F'E**G(=H,++(
)B<(
)BC(
Figure 2.16: The ACTPol receiver is shown above. Three separate optics tubes house the three
Figure 9. Model of the as-built cryostat. For scale, the length of the cryostat is 1.5 m. The PA3 optics tube and most of the radiation
cryostat
is cooled of
byflexible
a system
ofsheets
a pulse
cooler
andused
a dilution
shieldsACTPol
have beenarrays.
removedThe
for clarity.
A combination
copper
andtube
copper
braid are
to reducerefrigerator.
vibrational coupling
between the pulse tubes and internal cryostat components.
Image courtesy of Bob Thornton (from [75]).
4K-1K carbon fiber! 1K-100mK carbon !
fiber suspension
4K cold ! suspension
plate
G10
Lens 3
Lens 2
wedge
300K, 40K, and 4K LPE!
and IR blocking filter stacks
1K radiation !
Array ! shield
module
Lens 1
~ 1 mm
Figure 2.17: A prototype three-layer metamaterial AR coating is shown above. Square pillars are
machined directly into the Si lenses with a dicing saw to engineer the index of refraction of the AR
coating. PA1 and PA2 use a two layer coating, while the multichroic PA3 array uses a three layer
coating. The AR coatings are machined at the University of Michigan.
stalled at 1 K after the Lyot stop. The bottom of each optics tube where the arrays and readout are
4K baffle tube
Central thermal
busshield
tower the SQUIDs and detectors
located has a double layer magnetic shield of Amumetal
4K9 to
40K filter plate
Cryostat front plate
1K! 100 mK!
Double layer of !
contact contact
magnetic
shielding
from magnetic fields. To add an extra layer of shielding to the printed circuit boards (PCBs) that
house the multiplexing chips, an aluminum cover is fastened around the readout boards. Addition-
Figure 10. Cutaway view of the PA1 optics tube showing the internal optics, mechanical structures, magnetic shielding, and cold straps.
critical
andthe
where
aluminum
is superconducting
(resultally,
series
arrays are
housed inside Nb
boxes asconducting
in ABS. aluminum alloys, which is problematic for the
ing in reduced thermal conductivity), oxygen-free highSQUIDs (Section 6.3).
conductivity
copper (OFHC) was generally used. AnThe three optics tube assemblies are of similar design,
9 Amuneal
Manufacturing
Corporation.
Philadelphia,
other reason
for using
mostly copper
below ≈
1 K is po- PA 19124.
yet self-contained to allow each one to be deployed inditential problems with magnetic flux expelled by super- 36 vidually. A cross-section of the PA1 optics tube is shown
except for the inner ground screen and part of the receiver cabin wall, which have been removed for clarity.
s service position (where the receiver cabin floor is level), corresponding to a viewing elevation of 60◦ .
06) at ambient temperature; folof blocking filters and low pass
et al. 2006) at 40 K; the first lens
s at 4 K; the Lyot stop, two more
w pass filters all at 1 K; and the
y package at 100 mK. A ray trace
wn in Figure 3.
s tube is limited by both the size
ad to fit in the existing receiver
e maximum diameter of the lown 4.3). To minimize the size of
receiver is positioned such that
ocated between the receiver winGregorian focus is not telecentric,
or a large, flat feedhorn-coupled
nany et al. 2013). To achieve a
l offsets and tilts were incorpoes. The final design is diffractionl plane.
dicing saw, creating layers of square pillars. The resulting coating has a coefficient of thermal expansion matching that of the rest of the lens. Lenses based on a twolayer design (Figure 4a) are used in both the PA1 and
PA2 optics. Simulations showed that the resulting coat,334%5670)"+%
834%5670)"+%
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the lens material due to its high
igh index of refraction (n = 3.4),
velengths. The high index of reuse of AR coatings. ACT previ)B:(
gs (Lau et al. 2006), but they in)BC(D>&0E%((
% net efficiency reduction
(Swetz
-*.,(
Figure 2.18:
A ray-trace
of the
ACTPol PA1 (bottom) and PA3)B<((top) optics are shown above. The
Figure789(ʹ(:9(;<8(
3. Ray trace of the cold optics. The upper trace shows
Pol, we created “meta material”
)BC(
the
PA3
(multichroic)
and through
the lower the
tracewindow
shows the
PA2
optics
are
the
same
as
those
in PA1.optical
Lightpath
enters
and is re-imaged onto
by removing some of the silicon
=*%>,1%0$1((
PA1 path. The PA2 optical path is a mirror image to that of PA1
ofbeen
three
Si lenses.
ImageThe
courtesy
of Bob
Thornton
(from [75]). The
om the surfacesthe
of focal
each plane
lens atby a series
F'E**G(=H,++(
and has
removed
for clarity.
constituent
elements
are
sing a custom three-axis
silicon
described
in
the
text.
optics design for ACTPol was performed by Mike Niemack.
Figure 9. Model of the as-built cryostat. For scale, the length of the cryostat is 1.5 m. The PA3 optics tube and most of the radiation
shields have been removed for clarity. A combination of flexible copper sheets and copper braid are used to reduce vibrational coupling
between the pulse tubes and internal cryostat components.
300K, 40K, and 4K LPE!
and IR blocking filter stacks
4K-1K carbon fiber! 1K-100mK carbon !
fiber suspension
4K cold ! suspension
plate
G10
Lens 3
Lens 2
wedge
1K radiation !
Array ! shield
module
Lens 1
4K baffle tube
40K filter plate
Cryostat front plate
Central thermal bus tower
1K! 100 mK!
Double layer of !
contact contact
magnetic shielding
FigureFigure
2.19:
crossview
section
ofoptics
the tube
PA1
optics
tube optics,
withmechanical
its filters
and lenses
is shown
above.
10.A
Cutaway
of the PA1
showing
the internal
structures,
magnetic shielding,
and cold
straps. Light
enterscritical
through
the window,
through
a seriesconducting
of IR blockers,
passes
through
the lenses,
and where
aluminum ispasses
superconducting
(resultaluminum alloys,
which
is problematic
for the and
ing in reduced thermal conductivity), oxygen-free highSQUIDs (Section 6.3).
reaches
the focalcopper
plane
at 100
Image
ofThe
Bob
[75]).
conductivity
(OFHC)
wasmK.
generally
used.courtesy
AnthreeThornton
optics tube (from
assemblies
are of similar design,
other reason for using mostly copper below ≈ 1 K is potential problems with magnetic flux expelled by super-
yet self-contained to allow each one to be deployed individually. A cross-section of the PA1 optics tube is shown
37
Figure 2.20: The sky side (left) and back (right) of an ACTPol array are shown above. The detector
array is ∼15 cm in diameter. On the sky side, the detector feedhorn apertures can be seen. On the
backside, the readout and wafer tiling can be seen. In its full configuration the back of the array has
heat clamps for each hex and semihex wafer to heat sink them to the array. Photographs courtesy
of Emily Grace and Benjamin Schmitt.
2.2.3
Focal Plane
The ACTPol focal planes are cooled to 100 mK, which reduces thermal noise and thus increases the
sensitivity of the TES detectors. The ACTPol PA1 and PA2 focal planes each consist of 512 pixels
with 1024 detectors that operate at 148 GHz, and the PA3 focal plane has 255 multichroic pixels
with 510 detectors that have 148 GHz sensitivity and 510 detectors that have 97 GHz sensitivity. Each array is fabricated by NIST and consists of a monolithic corrugated feedhorn array, a
waveguide interface plate (WIP) wafer, a detector wafer, and a detector backshort fabricated out of
two wafers. The detector wafer consists of three hexagonal (hex) wafers and three semi-hexagonal
(semihex) wafers all fabricated on 3” wafers and tiled together. The sky side and backside of an
ACTPol detector array is shown in Figure 2.20. The detector readout is bent behind the focal plane
to maximize the focal plane area. PA3 hex and semihex detector wafers are shown in Figure 2.21.
The ACTPol pixels have a similar design to the ABS pixels. Unlike the ABS pixels, the PA1
and PA2 detectors have no band-defining filters. The PA3 detectors use on-chip bandpass filters to
define the two frequency bands on each chip and are some of the first multichroic CMB pixels to
38
Figure 2.21: Photographs of a PA3 hex detector wafer (left) and semihex detector wafer (right)
are shown above. Three hex and three semihex wafers are tiled together to make each array.
Photographs courtesy of Dan Schmidt
Hybrid-T
Filters
OMT
TES
Figure 2.22: Photographs of a PA3 pixel are shown above. The left image shows the full pixel,
while the right shows a magnified image of the hybrid tee and TES. Light is coupled onto the OMT
by the feedhorns and is split into orthogonal polarizations. The polarization from each OMT fin is
then split between the 97 GHz and 148 GHz bands by a diplexer and on-chip band-defining stub
filters. Signals from each of the fins for each polarization at each frequency are passed through a
hybrid tee and onto a TES bolometer. Some of the wiring bond pads can be seen on the edges of
the left image. Photographs courtesy of Dan Schmidt.
be fielded. The signals from opposite OMT probes for each frequency on the PA3 detectors are fed
into a hybrid tee to reject higher order modes [77]. Like ABS, the detectors use a MoCu bilayer
for the TES, but they also couple the TES to a reservoir of PdAu to increase the heat capacity and
slow the detector time constants in order to achieve higher stability. Images of a multichroic PA3
pixel are shown in Figure 2.22. The feedhorns define the low edge of the bandpass on PA1 and
PA2 with a waveguide cutoff, while the high band cutoff is defined by the LPE filters.
Flexible superconducting cables, which will henceforth be referred to as flex, connect the de39
tector circuitry to the SQUID readout circuitry. The flexibility of the readout cables allows for the
readout circuitry to bend behind the focal plane, maximizing the focal plane detector area. The
flex are wire bonded on both the detector and multiplexing readout sides. For the first arrays,
the flex were commercially manufactured by Tech-Etch10 and consisted of thin lines of aluminum
deposited on Kapton that are superconducting during operation. Because the Tech-Etch flex is
soft, it had to be glued with Stycast 126611 to Si stiffeners on the detector side and Cu stiffeners
on the readout side to enable bonding. Additionally, to achieve the pitch necessary for the detector readout, two flex had to be glued together on the detector side. Originally, a gluing rig that
clamped the flex to the stiffeners while the glue dried was used. This gluing process could leave
an uneven surface and glue often leaked onto the flex bonding area, which made bonding difficult.
Because the alignment achievable with this by-hand method was crude, the automatic wire bonder
could not be used in its full automatic mode, which slowed the bonding process. Additionally,
the clamping method used plexiglass with screws for tightening, which occasionally fractured Si
stiffeners, rendering them unusable. This method was significantly improved by developing a new
gluing method that used a bump-bonder (also known as a flip-chip bonder) to align and glue the
flex onto its Si stiffeners and the two layers of flex onto themselves. The pressure used to press the
flex while gluing is adjustable and even on a bump-bonder, which prevented the Si stiffeners from
fracturing. This method also eliminated glue flowing onto the traces, allowed for fine alignment,
and resulted in an even gluing surface, which increased the yield to ∼ 90%.
However, the Tech-Etch flex is manufactured by rolling aluminum onto Kapton and etching
the traces. The grain size of the aluminum with this method is large, which has low yield, results
in over-etching, and makes bonding difficult. Additionally, Tech-Etch could not consistently reach
the specification of a 100 µm trace with a 200 µm pitch, so ACTPol began fabricating its own
flex [88]. By using a sputtered aluminum film, a 1 µm feature size can be attained with a pitch only
limited by the bond pad size. To fabricate the flex, aluminum traces are deposited on polyamide
that transitions to bare silicon, eliminating the gluing issues, as the aluminum bond pads are on
10 Tech-Etch
11 Emerson
Inc. Plymouth, MA 02360.
and Cuming. Billerica, MA 01821.
40
bare silicon. The first iterations of this flex were successfully tested at Princeton and had a yield
of ∼ 90%. This flex was used for half of the PA3 readout and is also employed in AdvACT.
Figure 2.23 shows the fabricated flex in use on a semi-hex wafer for PA3.
Figure 2.23: The flex connects the detectors to the SQUID readout. The flexibility of the flex allows
for the readout to bend behind the focal plane to leave more room for the detectors. The fabricated
flex is shown connecting a semi-hex wafer. The detector wafer is on the bottom, and the vertical
board is a PCB with readout wiring that the multiplexing readout chips are glued to. The flex is
wire bonded to the detector side and the multiplexing chips on the readout boards. The commercial
flex needs two layers of flex glued on top of each other to achieve the wiring density necessary for
readout, while the wiring pitch of the fabricated flex is small enough to allow a single layer of flex.
The fabricated flex transitions from polyamide to bare Si to increase the bonding efficiency. Image
courtesy of Christine Pappas.
41
2.3
The Advanced ACTPol Instrument
AdvACT is an upgraded receiver for ACT that will replace ACTPol. AdvACT will use the same
cryostat as ACTPol but will modify the optics and detector arrays in each optics tube. With the high
resolution provided by ACT, AdvACT will be able to characterize the CMB polarization on small
angular scales like ACTPol. Additionally, AdvACT will employ continuously-rotating HWPs at
ambient temperature as the first element in each optics tube, which will allow it to probe larger
angular scales with the aim of measuring the primordial B-mode signal from inflation. However,
to be sensitive to primordial B-modes, AdvACT will have to carefully characterize and remove the
foreground contamination from galactic dust. To do this, AdvACT will observe in five frequency
bands by sequentially fielding four feedhorn-coupled arrays of multichroic polarization-coupled
detectors in the three ACTPol optics tubes. A high frequency (HF) array with 150/230 GHz
coverage will be fielded first and then supplemented with two mid-frequency (MF) arrays with
90/150 GHz sensitivity. Next, one MF array will be replaced with a low frequency (LF) array
that has 28/41 GHz coverage [89]. The key characteristics of AdvACT arrays are shown in Table 2.3 [89]. The 150/230 GHz array for AdvACT was installed in June 2016.
Table 2.3: AdvACT Key Characteristics
Parameter
Number of Bolometers
Center Frequency
(GHz)
Angular Resolution
FWHM (arcmin)
Projected Map Noise
(µK-arcmin)
Base Temperature
HF
230 GHz
1006
230
MF/HF
150 GHz
2718
150
MF
90 GHz
1712
90
LF
41 GHz
88
41
LF
28 GHz
88
28
0.9
1.4
2.2
4.8
7.1
25
7
8
70
80
100 mK
100 mK
100 mK 100 mK 100 mK
The AdvACT instrument is the result of the efforts of a large collaboration. The mechanical
design of the arrays was performed at the University of Pennsylvania [90]; the cold optics were
designed at Cornell University and constructed at the University of Michigan [84]; the HWPs were
42
designed and constructed at the University of Michigan; the feedhorns were designed at Princeton
University and fabricated and tested at NIST [91]; the readout layout was designed and tested at
Cornell University [89, 92] and fabricated by NIST; the detectors were designed at the University of
Michigan [79] and were fabricated by NIST [93]; detector testing was performed at NIST, Cornell
University, the University of Michigan, and Princeton University; and the arrays were assembled
at Princeton University [94].
Each AdvACT array will employ a similar optics and filtering scheme as the ACTPol PA3
array, but the filters and optics in each array will be modified to accommodate the observation
bands of the multichroic pixels in each array. The readout of the AdvACT arrays will also be
modified for each array. The HF readout will use 32 columns each with 64 rows to readout 506
pixels (three of which are optically dark) and 24 dark squid channels [89]. The MF array layout
is still in development, but will likely have 431 pixels (three of which will be optically dark) and
36 dark squid channels that employ a 32 column x 55 row readout. The readout channelization of
the LF array has yet to be determined. To achieve the necessary wire density to read out such a
large array, AdvACT employs custom-fabricated flexible readout cables as shown in Figure 2.24.
Unlike ACTPol, AdvACT will use a single custom PCB ring for the readout of each array as shown
in Figure 2.25. With this readout scheme, the readout no longer needs to bend behind the focal
plane to maximize the available focal plane area. Once the array is electrically tested, a large goldplated Cu ring is fastened above it to protect and magnetically shield the readout electronics, and a
gold-plated Cu snaketongue ring is clamped to the back of the array for heat sinking (Figure 2.26).
Finally, a gold-plated Cu cap is fastened over the snaketongue ring to seal the backside of the array.
2.3.1
Observation Strategy
AdvACT will scan azimuthally at constant elevation for observations and observe each field as it
rises and sets like ACTPol. The optimal scan speed and width are still being determined. AdvACT observations are split into day and night strategies. During the night, AdvACT will observe
three wide fields that together cover ∼14,100 deg2 of the ∼20,000 deg2 accessible from the site:
43
Figure 2.24: The HF flex is shown above and connects to the detector array to the readout. The
flex is fabricated at Princeton and uses a sputtered aluminum film to achieve the necessary wiring
density for the readout. Photograph courtesy of Patty Ho.
Figure 2.25: A picture of the backside of the HF AdvACT array is shown above. The PCB is a
ring that goes around the array. Multiplexing chips are glued onto the PCB and wire bonded to
the flex. In turn, the flex is also wire-bonded to the detectors. This readout design maximizes the
focal plane area without bending the readout behind the array, which enables a thin array profile.
Photograph courtesy of Patty Ho.
44
Figure 2.26: A picture of the backside of the HF array is shown mid-assembly. A gold-plated Cu
ring is fastened above the PCB for protection. Additionally, a gold-plated Cu snaketongue ring is
used to clamp the back of the detector array for heat sinking. Photograph courtesy of Patty Ho.
wide 01h n, wide 01h s, and wide 12h n. During the day, AdvACT will make deep observations in
two low-foreground areas to target the large-scale inflationary B-modes: day 02h s and day 14h n.
These observations are performed during the day because larger angular scales are less sensitive
to the beam aberrations that occur during daytime observations [83]. During times when no other
fields are available deep5 will be observed. Table 2.4 summarizes the field centers and sizes for
the AdvACT observation strategy [83].
Table 2.4: AdvACT Observation Fields
Field Name
wide 01h n
wide 01h s
wide 12h n
day 02h s
day 14h n
RA
1◦
1◦
12◦
38◦
210◦
DEC
0◦
-40◦
8◦
-40.5◦
11◦
45
Size (deg2 )
5700
5000
3400
1700
870
2.3.2
Focal Plane
Like ACTPol, each AdvACT array consists of a monolithic feedhorn array, a waveguide interface
plate (WIP) wafer, a detector wafer, and a detector backshort fabricated out of two wafers fabricated by NIST. Unlike ACTPol, the feedhorn arrays for AdvACT use a spline-profiled design
instead of a corrugated design, which is discussed further in Chapter 6. To use the available focal
plane area more efficiently, the AdvACT detector array is fabricated on a single 150 mm diameter
wafer versus the tiled 3” wafers used by ACTPol and uses multichroic detectors [93]. Additionally, the detector layout is further optimized to increase detector density by using a rhombus pixel
design. The AdvACT HF detector array wafer is shown in Figures 2.27 and 2.28.
Figure 2.27: A photograph of the full HF detector wafer is shown above. Each pixel is a rhombus to
maximize the packing density, and the full array is arranged into three large rhombi. The detector
array is encased in protective pink foam in this image. Photograph courtesy of Shannon Duff.
46
Figure 2.28: A magnified photograph of the HF detector wafer is shown above. The detector
wiring outlines each pixel, and the bonding pads can be seen along the wafer edges. Each pixel
has a TES bolometer for each polarization at each frequency for a total of four TES bolometers.
The triangular features in the two pixel corners are test features for measuring step height and for
etch endpoint monitoring during processing. Photograph courtesy of Shannon Duff.
The AdvACT multichroic pixels build off of the ACTPol multichroic pixel technology [78].
As in ACTPol’s PA3 pixels, the signal from each OMT fin is split into two frequency bands by
a diplexer, the bandpasses are defined by the on-chip filters, and a hybrid tee is used to reject
higher order modes. However, the larger wafer format requires stricter fabrication uniformity.
TESes made from metal bilayers like the MoCu ones in ACTPol and ABS require two separate
depositions, and the critical temperature of the TES is highly dependent on the thickness and
geometry of each layer. Thus, to increase TES uniformity across the array, the AdvACT TESes
use a single deposition layer of AlMn. As in ACTPol, the TESes are coupled to PdAu for extra
heat capacity to tune the detector time constants. The 230 GHz detectors use a constant layer of
PdAu, while the 150 GHz detectors use a “swiss” PdAu design, which features a PdAu layer with
an array of holes like swiss cheese. Images of HF multichroic pixels are shown in Figure 2.29.
47
Figure 2.29: Photographs of HF pixels are shown above. On the left is a photograph of an HF pixel
from the HF detector array, while the photograph on the right shows a single HF test pixel. The
150 GHz TES islands have a checkered “swiss” PdAu layer to tune the detector time constants.
The hybrid tee feature is next to each TES, but is easier to see in the right image. The OMT splits
incoming radiation into two orthogonal polarizations. The polarization from each OMT fin is then
split between the 150 GHz and 230 GHz bands by a diplexer and on-chip band-defining stub filters.
Signals from each of the fins for each polarization at each frequency are passed through a hybrid
tee and onto a TES bolometer. Photograph courtesy of Shannon Duff.
48
Chapter 3
Half-Wave Plate Formalism and
Applications
An ideal HWP is made of a birefringent material and flips the polarization of incoming light along
the fast axis of the crystal resulting in a polarization shift of 2χ as shown in Figure 3.1, where χ
is the incoming polarization angle of the light with respect to the fast axis. Thus, a HWP rotating
with frequency fm modulates the incoming polarization at 2 fm , which is detected in the bolometer
timestreams at 4 fm [95]. The modulation is good for controlling systematics, eliminates the need
for differencing timestreams from orthogonal pairs of detectors to gain polarization sensitivity, reduces the sensitivity loss associated with filtering the timestreams, and enables the characterization
of CMB instruments with novel techniques. A continuously rotating HWP modulates incoming
polarization, which allows for the separation of celestial polarization from unpolarized long time
scale fluctuations (1/ f noise). The main source of 1/ f noise for ground-based experiments is
fluctuations in the unpolarized atmosphere, which has a 1/ f knee on the order of ∼1 Hz. This
knee frequency only permits stability in the timestreams on order of a second, which is particularly
detrimental when trying to measure polarization on large angular scales where the primordial Bmode signal is expected to peak. While the 1/ f noise is primarily due to unpolarized atmospheric
fluctuations, it can also have contributions from temperature drifts in the HWP, readout electronics,
49
changes in the detector bath temperature, and changes in detector responsivities.
FIG. 3.
The powe
encoder readout durin
tion. The sharpness o
the stability of the rot
Figure 3.1: Light with polarization χ passes through a HWP (top). Because the HWPpeaks
is birethat are ∼ 0.3 H
fringent, light along the two crystal axes travels at different speeds. The thickness of thetoHWP
is and slow freq
small
selected so thatFIG.
the component
traveling
along
the
fast
axis
completes
an
integer
number
of
periods
cles of the HWP rota
2. Propagation of a wave through the HWP. Incoming
while the component
along
the
slow
axis
completes
a
half
period
less
so
that
it
is
phase
shifted
for thebyexact HWP ro
linear polarization is decomposed into two orthogonal linear
180◦ . This results
in
the
incoming
polarization
of
the
light
flipping
about
the
fast
axis
for
a shiftasinopposed to ass
tion
polarizations along the crystal axes of the sapphire (fast and
polarization of slow
2χ. Figure
Akito
Kusaka
andat
Tom
Essinger-Hileman
(from [95]).
axes).courtesy
These of
two
waves
travel
different
speeds. The
◦
sapphire thickness is chosen to produce a 180 phase shift
between these two waves, which reflects the incoming polarunpolarized sky emi
ABS pioneered the use of a continuously rotating HWP for ground-based applications.1 The
ization about the fast axis of the crystal. As a result, the poicant HWP-synchro
larization
rotates
by
an
angle
of
2χ,
where
the
angle
between
ABS HWP (Figure 3.2) is an ambient-temperature 330 mm diameter α-cut sapphire plate
that is from the
radiation
the fast axis and incoming polarization is χ. The number of
the detectors will b
3.15 mm thick oscillations
with 305 µmand
AR coatings
Rogers RT/Duroid
relative of
wavelengths
for the6002
two fluoropolymer
waves within laminate [56].
fects produce a line
the sapphire as shown are merely illustrative.
HWP optical axis th
The HWP is rotated smoothly and continuously on air bearings at fm = 2.55 Hz, which modulates
This signal can be m
the polarization of the detector timestreams at 10.2 Hz. The ABS HWP is the first opticalby
element
small misalignm
bearing
of the telescope,
which
foraxis
the separation
of instrumental
and signal
polar- or encoder
and
the allows
crystal
of the sapphire
(Fig. polarization
2). ABS operates with f
! 2.5 Hz, where f
denotes the HWP
the AR coating. At
m
ization. The median knee frequency
of the ABS detectorsmafter demodulation is 2.0 mHz,
which
also
produce a small
rotation frequency. This rotates the incident polariza-
at 4fand
m . These signa
tiononattime
2fm
! of
5 Hz,
is dB
detected
bolomeallows for stability
scales
500 swhich
with a 30
rejectionin
of the
atmospheric
fluctuations
ters at 4fm ! 10 Hz. The rotational frequency fm has a
low. To the extent t
thus the recovery
of information
fromof
large
angular
[95].Fig.
Figure
illustrates the reduction
the AR coating uni
small
modulation
order
0.1scales
Hz (see
3);3.3however,
signal are expected
4, we find that this
sume a constant modulation frequency. With only the
1 The balloon-borne telescope MAXIPOL was the first CMB polarization experiment to use a continuously rotating
where A(χ) does no
sky signal taken into account, the HWP-modulated sigHWP [96].
The signal of inte
nal, dm (t), may be represented in terms of the incoming
50
cipally at 4fm as sh
Stokes parameters I(t), Q(t), and U (t), as well as the
age of unpolarized
angle χ(t):
particularly detrime
spheric signal and te
d = I + εRe{(Q + ıU )m(χ)} .
(1)
treatment
in thisover
paper
is general
and doesobservation.
not asin 1/ f noise inthe
the detector
timestreams
a typical
single ∼hour-long
Figure 3.2: A cross section of the ABS HWP in its air bearing housing is shown above. The HWP
is rotated with a system of three graphite air bearings (shown in black) and the angle is read out by
an encoder disk (green). Figure courtesy of Akito Kusaka and Tom Essinger-Hileman (from [95]).
Further, the HWP enables ABS to significantly reduce systematic errors due to the beam. With
the HWP, the ABS instrument has a scalar leakage around 0.01%, which is an order of magnitude
lower than that of other CMB experiments. Additionally, dipole and quadrupole leakages are
estimated to be < 0.06% at 95% confidence. Overall, these combined effects represent a systematic
error of r . 0.01 [97].
HWPs can also be made broadband for use with multichroic pixels by stacking several of them
together [98]. ACTPol is currently using a multichroic 90/150 GHz broadband Si metamaterial
HWP designed and constructed at the University of Michigan by Kevin Coughlin. The Si metamaterial allows one to tune the indices of refraction of the HWP. The high index of refraction of
the Si also means that the HWPs can be thinner, which results in less loading than sapphire. Each
broadband metamaterial HWP consists of three individual HWPs rotated with respect to each other
and sandwiched between broadband AR coatings. Similar broadband HWPs are planned for each
of the AdvACT arrays.
51
We show both the ra
spectrum after the su
that is constant over t
observed at the harm
fm , most of them corr
and disappear after th
traction leads to little
tom panel shows the
timestreams. Here, th
respond to two differe
spectrum of a single T
form each of the real a
them in power, which
spectrum of dd̄ .” In t
the demodulated time
is found by maximizin
noise of the real (ima
aging the power spect
by inverse-variance we
same manner as we do
that the demodulated
two degrees of freedo
and these two corresp
binations of Q and U
defines
the orthogonal
7. power
The power
TES
be- before
Figure 3.3: TheFIG.
average
spectra spectra
of all of of
the the
TESes
for timestreams
a single observation
(top)
the1/eigenmodes
of
foredemodulation
and after the
demodulation.
The data
from the has aare
and after (bottom)
is shown
above. The spectra
beforeare
demodulation
large
f
phase
φ0 is determine
same
CMB-observing
as Fig.
3. out
Each
spectrum
is theFigure
noise component,
while
the demodulatedCES
spectrum
is flat
to mHz
frequencies.
courtesy
inverse-variance
weighted
average
over
∼
300
TESes.
The
TES. We typically fin
of Akito Kusaka and Tom Essinger-Hileman (from [95]).
top panel shows the power spectra of the timestreams before
noise in the two degr
demodulation. The dashed and solid lines correspond to the
timestream, and the
timestreams
and after
the subtraction
of closely
A(χ) that
is the hibit
The demodulation
processbefore
is described
in Section
3.1 and will
follow
formalism
extremely low 1/
constant during this CES, respectively. The bottom panel
of characinverse-variance we
defined in Kusaka
& Essinger-Hileman
et al.,
2014
[95]. Sectionstimestream.
3.2 and 3.3 describe
the
shows
the power spectra
of the
demodulated
For
noise level better than
the dashed line, the spectrum of each TES is a sum of the
terization of ABS with the HWP, and Section 3.4 describes the use of the second harmonic
the tends to sho
eachofTES
power spectra of real and imaginary parts of the demoduever, it tends to show
lated
timestream
HWP for the ABS
data
selection. dd̄ . For the solid line, the spectrum of each
the peak is correlated
TES is obtained as a inverse-variance weighted sum of the
!
ıφ0
the TES is sensitive. T
spectra of the real and imaginary parts of dd̄ ≡ e dd̄ , which
the 1/f noise has optic
is defined in the text. The typical responsivity of a TES is
∼ 100 aW/mK. The scan frequency (fscan ) as well as the
As shown in the top
harmonics of the modulation frequency (fm ) are indicated by
noise component in raw
arrows.
1 Hz and a spectral i
frequencies in the dem
to ∼ 106 reduction in
amplitude) and demon
TES or lower) since inclusion
52 of those may overestimate
to polarization of less
the stability of the timestreams. Typically ∼ 300 TESes
Figure 8 shows the
(out of ∼ 400 functional TESes) pass these criteria and
cies of the demodulat
are used for further evaluation.
tors. The knee freque
3.1
HWP Demodulation
The detector timestream dm is composed of the unpolarized sky intensity I, the modulated polarization signal P(χ), white noise Nw , and spurious modulation signals A(χ) that depend on the HWP
angle χ such that
dm = I + P(χ) + Nw + A(χ).
(3.1)
The modulated polarization signal can be represented in terms of the Stokes Q and U parameters
(Equation 1.22) as
P(χ) = εRe{(Q + iU)m(χ)},
(3.2)
where the modulation is given by m(χ) = exp[−4iχ] and ε is the polarization modulation efficiency
factor, which is close to one. The spurious modulation signals A(χ) consist of components at
every harmonic n of the HWP rotation frequency and can be decomposed into cosine and sine
components as
h
i
nc
ns
ns
A(χ) = ∑ An (χ) = ∑ (Anc
+
λ
I)
cos(nχ)
+
(A
+
λ
I)
sin(nχ)
.
0
0
n
(3.3)
n
Here the A0 terms are stable and independent of the sky intensity and the λ terms are small [95].
The demodulated timestream is then determined by applying a bandpass filter to dm to account for the slight variations in fm , multiplying dm by m∗ (χ), and applying a low-pass filter that
passes f . 2 Hz to eliminate higher order terms and all Anc,s and λ nc,s terms other than the n = 4
components. From [95], the final demodulated timestream dd¯ is then given by
i
1
4c
4c
Re
4s
4s
εQ + A0 + λ I + Nw + εU + A0 + λ I + iNwIm .
dd¯ =
2
2
(3.4)
The dominant component of A(χ) for ABS is the n = 2 component, A2 (χ), which is a sinusoidal
signal at the second harmonic of the HWP rotation frequency and is dominated by systematic
effects of the HWP. This 2 fm signal has a contribution from differential emissivity along the two
53
crystal axes that contribute to the A2c,s
terms. Differential transmission of the unpolarized signal I
0
due to differences in the loss tangents of the two HWP crystal axes contributes to the λ 2c,s I terms
in A2 (χ). An additional contribution to the λ 2c,s I terms results from differential reflection along
the two crystal axes, which has an additional contribution from using an AR coating with a single
index of refraction on the birefringent HWP. An ideal AR coating between the transition of two
√
materials has an index of refraction of n1 n2 and a thickness of a quarter wavelength. In the
case of the ABS HWP, n1 is the index of refraction of air (∼ 1), and n2 is the index of refraction of
sapphire, which is 3.07 along the fast axis and 3.40 along the slow axis. The Duroid AR coating has
a refractive index of 1.71, which is better matched to the fast axis, resulting in more transmission
along the fast axis. From Equation 3.3, the A2 (χ) signal is given by
2c
2s
2s
A2 (χ) = (A2c
0 + λ I) cos(2χ) + (A0 + λ I) sin(2χ).
(3.5)
The loading from unpolarized sky intensity scales linearly with precipitable water vapor (PWV) for
low PWV and constant elevation. The loading from the PWV changes as a function of elevation θel
as 1/ sin (θel ). However, ABS observes in constant elevation scans, and in the ABS observations
of the primary field, the elevation varies by less than 3◦ , corresponding to a change in loading of
< 5%. Thus, we can take the loading from PWV as a constant and express A2 (χ) as:
2c
2s
2s
A2 (χ) = (A2c
0 + λ PWV ) cos(2χ) + (A0 + λ PWV ) sin(2χ).
(3.6)
To characterize the 2 fm signal, the measured PWV values from the nearby Atacama Pathfinder EXperiment (APEX) radiometer, which is located approximately 6 km from the site at an elevation
of 5100 m, are used. The 2 fm signal is clean, simple, and, to a good approximation, statistically
independent of the demodulated timestreams used for CMB analysis since the polarization modulation occurs at 4 fm . This makes the 2 fm signal an ideal calibration source as will be discussed in
Section 3.4.
54
3.2
Time Constants
The time constant of each detector is a key property that describes the stability and time response
of the detector. If the time constant is too large, it must be accounted for in the demodulation of the
signal from the HWP polarization modulation, in setting the scanning frequency of the telescope,
in measuring the telescope beams and pointing, and in determining the polarization angles of the
detectors. This section will describe the time constants of the ABS detectors and their impact on
the instrument calibration. The optical time constant τopt is often expressed in terms of the 3dB
frequency f3dB , which is given by f3dB = 1/(2πτopt ).
3.2.1
Impact on Beam and Pointing
The time constants can both shift the detector pointing and smear the beam, resulting in an increase
in the measured beam width. To estimate these effects the beam is approximated as a Gaussian with
a full width at half maximum (FW HM) of 30 arcmin, which is close to the 33 arcmin truncated
Gaussian that describes the ABS beam. For primary field observations, the ABS instrument scans
at a rate of fscan ≈ 0.75 deg/s at an elevation θel between 46◦ and 48◦ . The scanning speed on the
sky fsky is then given by fsky = fscan cos (θel ) ≈ 0.5 deg/s. The time domain Gaussian beam β (t)
is then defined as
−t 2
β (t) = e 2σ 2 ,
(3.7)
where t is time and
σ=
FW HM
√
.
2 fsky 2 ln 2
(3.8)
Fourier transforming into frequency space, the beam is given by
β ( f ) = e−2π
55
2 f 2σ 2
.
(3.9)
The time constants of the detectors act as a low pass filter, so the beam is convolved with a low
pass filter given by
h( f ) =
1 − i f / f3dB
2
1 + f 2 / f3dB
(3.10)
and then Fourier transformed back into the time domain to determine the impact on the pointing
and beam widths. The low pass filter in Equation 3.10 is a good approximation in the range of
3dB frequencies expected for the detectors as can be seen in Figure 3.8. Figure 3.4 shows the
effect from varying 3dB frequencies on the beam. These calculations give the shift and change in
beam width for scanning in one direction, but the telescope scans in both directions. If there are
an equal number of scans in each direction, the pointing offset averages out, but an odd number of
scans could give a pointing offset. Thus the above calculation gives the maximum pointing offset.
The effect of scanning both ways further broadens the beam because the average measured beam
is the sum of two offset beams as illustrated in Figure 3.5. To account for this, the two beams
from scanning in either direction are approximated as two Gaussian beams and a Gaussian is fit
to their sum. Table 3.1 summarizes the impact of the time constants on the beam for various 3dB
frequencies. The lowest optical f3dB value that passes all of the data selection criteria is greater
than 30 Hz, which results in a negligible impact on the ABS pointing and beam.
Table 3.1: Impact of 3dB Frequency on Beam and Pointing
3dB Frequency (Hz) Pointing Shift (arcmin) ∆ FWHM (arcmin)
0.5
7.353
10.5
1.0
4.313
3.7
5.0
0.950
0.17
10.0
0.477
0.043
20.0
0.239
0.011
30.0
0.159
0.0047
40.0
0.119
0.0026
50.0
0.096
0.0016
100.0
0.048
0.00052
The pointing shift and beam width changes from different 3dB frequencies are shown above. The
typical 3dB frequency of the ABS detectors is ∼100 Hz, and the lowest f3dB that passes the data
selection criteria is greater than 30 Hz.
56
50
0.5 Hz
1.0 Hz
5.0 Hz
10.0 Hz
20.0 Hz
30.0 Hz
40.0 Hz
50.0 Hz
100.0 Hz
No Shift
40
Power
30
20
10
00
10
20
30
40
50
Angle (arcmin)
60
70
80
Figure 3.4: The shift in the pointing and the beam width for a scan in one direction as a result of
several time constants is shown above. Note that 3dB frequencies above 5 Hz have an extremely
small effect. The lowest 3dB frequency in the ABS analysis is above 30 Hz, so these shifts are
negligible. The power is in arbitrary units.
3.2.2
Established Methods of Determining Time Constants
In theory, the beam broadening and pointing offset can be used to characterize the time constant of
a detector by using planet scans, but the signal to noise on an individual planet scan is low, so other
methods of characterization are necessary. Two other methods of determining the time constants
are the bias step and amplitude methods.
The bias step method characterizes the electrical time constant of a detector τel by inputing a
low amplitude square wave through the bias line and fitting the exponential response. The current
I as a function of time t goes as
±t
I(t) ∝ e τel ,
57
(3.11)
0.05
Scan Direction 1
Scan Direction 2
Combined Scan
Gaussian Fit
0.04
Power
0.03
0.02
0.01
0.00100
50
0
Angle (arcmin)
50
100
Figure 3.5: The shift in the beam width from the time constant when scanning in both directions is
estimated with the sum of two Gaussians shifted in pointing and beam width in opposite directions.
This can be approximated and fit as a Gaussian. The shift for an extremely slow detector with an
f3dB = 0.5 Hz is shown above to illustrate this effect. This effect is negligible in the ABS analysis
because the lowest 3dB frequency is above 30 Hz. The power is in arbitrary units.
where the exponential is positive as the voltage is increased and negative as the voltage is decreased. The bias step method is quick and easy to perform before measurements, but τel must be
properly correlated to optical time constant measurements to determine the optical time constant
τopt . The bias step method could not be used on ABS because the firmware on the ABS bias cards
did not allow for targeting individual bias lines in an MCE registry. Instead, the ABS bias cards
could only step all biases in a register at the same time, which would have negated the SQUID
tuning since the TES biases share a register with the SQ2 biases on ABS.
Amplitude method measurements were taken in January 2013 to characterize the optical time
constants of the ABS detectors. The time constants were determined by modulating the infrared
(IR) source from the Fourier transform spectrometer (FTS) with a chopper at various frequencies
and measuring the amplitude of the detector responses with the HWP stationary. Two sets of data
58
were taken with an angled aluminum mirror tilted at slightly different angles to capture different
sets of detectors as can be seen in Figure 3.6. The response in power P of the detectors is given by
P( f ) ∝
1+
1
f
f3dB
2 ,
(3.12)
where f3dB is the optical 3dB frequency and f is the modulation frequency of the source.
Angled Mirror
Chopped IR
Source
Figure 3.6: The time constant measurement setup on the ABS cryostat is shown above. The signal
from a chopped IR source is input into the cryostat via an angled mirror at ambient temperature.
The raw timestreams of the two time constant measurements are shown in Figure 3.7. For each
detector, the filtering effects of the low-pass Butterworth filter, which has a 3dB frequency of 60 Hz
and is applied to the raw data by the MCE firmware, are removed from the raw timestream [73].
Next a Fourier transform is applied to the timestream. The resulting spectrum has a peak in frequency space for every chopper frequency. The timestream spectrum is split into small sections
in frequency space that include the full peak down to its edges. For each section, the frequency
of the chopper is the frequency of the maximum of the peak. Each peak has width, so the power
at each frequency is determined by integrating the power across the entire section. The optical 3dB frequency is then determined by fitting the power versus frequency relation to Equation 3.12. Figure 3.8 shows the power versus frequency measurements of the raw timestreams
59
in Figure 3.7 and their fits. Frequencies that experience significant fluctuations in atmospheric
power, like the first four frequencies in the first file, are excluded from the fits based on the instability of the raw timestreams. Figure 3.9 shows the measured f3dB on the array for each measurement, and Figure 3.10 shows the histograms of each measurement. The weighted average of the
measured 3dB frequency across the array is f3dB = 36.1 ± 0.2 Hz for the first measurement and
f3dB = 33.83 ± 0.12 Hz for the second measurement.
0.360
0.355
Amplitude (pW)
Amplitude (pW)
0.2
0.0
0.2
0.4
0.6
0.80
0.350
0.345
0.340
0.335
50 100 150 200 250 300 350 400
Time (s)
0.3300
50 100 150 200 250 300 350 400
Time (s)
Figure 3.7: The raw timestreams of representative detectors are shown above for the first (left) and
second (right) time constant measurements. The frequency of the source is increased roughly every
30 s, and the amplitude of the signal decreases as the frequency increases. Each time the frequency
of the chopper is changed, it leaves an artifact in the form of a vertical line in the timestream. The
first ∼30 s period in each plot has no frequency modulation so does not contribute to the time
constant measurement. The first measurement suffers from large atmospheric fluctuations in the
first four frequencies, while the second timestream suffers a jump during the last frequency.
The optical time constant of a detector increases with increasing loading. The added loading
from the atmosphere near the horizon behind the IR source was large enough to drastically slow
the detector time constants and, in some cases, fully saturate the detectors, making them nonresponsive. Thus, the time constants measured with this method were not representative of the time
constants under typical loading conditions. Additionally, the measured amplitudes were highly
sensitive to changes in loading correlated to the weather. Each time constant measurement took
∼7 minutes to complete. The atmosphere can change by tens of mK on minute time scales, which,
without the use of the HWP, caused fluctuations in the signals on order of a pW as can be seen in
60
7000000
1.8
6000000
1.6
5000000
Power (aW2)
Power (aW2)
2.0 1e9
1.4
1.2
1.0
0.8
3000000
2000000
1000000
0.6
0.4 −2
10
4000000
10−1
100
Frequency (Hz)
101
102
0
10−2
10−1
100
Frequency (Hz)
101
102
Figure 3.8: The power versus frequency relations are shown above in green for the first (left)
and second (right) time constant measurements for the same detectors as Figure 3.7. The best
fit 3dB frequency curves are shown in black. The large atmospheric fluctuations in the first four
frequencies of the first measurement and in the last frequency of the second measurement cause
the power to fluctuate more than the effect from the time constant. These points must be excluded
from the fits.
Figure 3.9: The optical 3dB frequencies from the chopped time constant measurements are plotted
across the ABS array above for the first measurement (left) and second measurement (right). The
angle of the mirror shown in Figure 3.6 was changed between measurements. Each cross represents
the two detectors sensitive to orthogonal polarizations on each pixel, and the two axes are the
locations of the pixels in degrees across the array when the telescope is pointing at the north
horizon. Detectors that are white were not measured. The majority of the detector 3dB frequencies
could not be measured with this method. Additionally, the extra loading from the IR source slowed
the time constants of the detectors significantly from those during nominal CMB observations.
61
Figure 3.10: Histograms of the 3dB frequencies of the detectors determined with the amplitude
method for the first (left) and second (right) measurements are shown above. The first measurement
only fit 39 detectors, and the second measurement fit 107 detectors. This represents less than a
quarter of the array.
the left panel of Figure 3.7. The power versus frequency plot in the left panel of Figure 3.8 shows
that the fluctuations are larger than the effect from the time constants. Because of these effects, the
first data file yielded fits for only 39 detectors while the second data file only fit 107 detectors.
3.2.3
Phase Method
As an alternative method to the amplitude method, the optical time constants were characterized
using the phase delay of the 4 fm signal as first suggested by Akito Kusaka and described in Simon
et al., 2014 [99]. Because it uses the phase, this novel technique is less susceptible to atmospheric
fluctuations over the course of the measurement than the amplitude method. For each phase method
measurement, data were taken while slowly varying the rotation speed of the HWP with a sparse
polarizing wire grid made of thin (0.005”) and reflective Manganin wires on a 1” pitch positioned
4.8” above the HWP. The wire grid, which was perpendicular to the optical axis and covered
the entire beam, was used to input a polarized signal of ∼ 0.1 pW. This signal adds minimal
loading, so the time constants are closer to those during nominal observation than those measured
with the amplitude method. The phase φ found from demodulating the signal with respect to the
polarization modulation frequency 4 fm is the difference between the physical polarization angle of
62
the grid and the measured polarization angle, which includes the apparent angle rotation due to the
time delay of the detector response. It can be modeled as the phase of a one-pole filter:
φ = arctan
4 fm
f3dB
+C,
(3.13)
where f3dB is the optical 3dB frequency of the detector. Because (4 fm )2 is expected to be much
2 , the phase can be linearly approximated as
less than f3dB
φ ≈ φ0 +
f3dB 4 fm
4 fm
≈
φ
+
,
0
2 + (4 f )2
f3dB
f3dB
m
(3.14)
where φ0 is a constant offset related to the intrinsic polarization angle of the detector [99].
Two sets of phase measurements were taken in April 2013 to characterize the detector time
constants. The first measurement fit 356 detectors, and the second measurement fit 362 detectors, which is a dramatic improvement over the amplitude method. Figures 3.11 and 3.12 show
histograms of the 3dB frequencies determined by linear fits from each single ∼20 minute measurement for each of the four ABS fabrication wafers, and Figures 3.13 and 3.14 show the time
constants from each measurement plotted as a function of location on the ABS focal plane. There
are 18 detectors with f3dB values greater than 200 Hz that have been excluded from the figures for
clarity. The small time constants of these detectors have not been correlated with any effects and
they are sufficiently small that they would not need to be corrected for in the timestreams. The
median values of the f3dB distributions found from all fit detectors on each wafer are 57+101
−8 Hz
+21
+15
for wafer 1-4, 115+40
−24 Hz for wafer 1-11, 120−18 Hz for wafer 1-14, and 92−7 Hz for wafer 1-
15. The upper and lower limits indicate the spread among detectors within each wafer with the
boundaries containing 34.1% of the fit detectors above and below the median. The average percent difference between the f3dB values for each detector between the two sets of measurements
is 6%, which is consistent with changes in loading between measurements. The dominant systematic effect between measurements is the change in atmospheric loading incident on the detectors,
which changes both the detector biases at the beginning of each measurement and the time con63
stants. Even the lowest median f3dB value only causes a 3% signal attenuation from the 10.2 Hz
polarization modulation of the HWP [99].
Figure 3.11: Above are distributions of 3dB frequencies for the four wafers and for individual
detectors in the ABS focal plane for the first phase method measurement. The detectors in wafer 14 are the slowest with a median 3dB frequency value of 57 Hz. It is unknown why the detectors
in wafer 1-4 have slower time constants than the other fabrication wafers. Note that there are 18
detectors with 3dB frequencies above 200 Hz, but the frequency scale has been truncated at 200
Hz for clarity.
3.2.4
Modeling the Time Constants for All Observations
The 3dB frequencies of the detectors are dependent on the loading and bath temperature, so they
must be determined for each observation. Further phase method measurements were made in
May 2014 under various loading conditions to determine if the time constants can be assumed
constant in the data analysis. However, during these measurements, the time constants for half of
64
Figure 3.12: Above are distributions of 3dB frequencies for the four wafers and for individual
detectors in the ABS focal plane for the second phase method measurement. The frequency scale
has again been truncated at 200 Hz for clarity. Image from [99].
the detectors in the array were inadvertently taken between 80% and 100% of the transition-edge
sensor (TES) normal resistance Rn compared to the nominal bias point of 30% Rn due to a biasing
glitch. Specifically, the polarized input signal from the wiregrid modulated by the HWP caused
oscillations in the current versus voltage (IV) curves that are used to determine the proper biasing
point of the detectors. This caused a glitch in the biasing software and resulted in half of the array
being electrically biased high. While this glitch can be corrected for future projects, the optical
time constants above 80% Rn are not the same as those at the nominal bias point and thus could
not be used to determine the dependence of f3dB on measurement conditions.
However, as is described below, the measured optical time constant τe f f is proportional to the
thermal time constant τ by a proportionality factor that can be estimated from the IV curves taken
65
15
3dB Frequencies File 1
10
5
Hz
0
5
10
1515
200
180
160
140
120
100
80
60
40
10
5
5
0
10
15
Figure 3.13: The optical 3dB frequencies from the first phase method measurement are plotted
across the ABS array above using the same convention as Figure 3.9 The frequency scale has
again been truncated at 200 Hz for clarity.
before every observation.2 This allows for the optical 3dB frequency f3dB to be estimated for each
observation. For a Thevenin-equivalent TES circuit in the regime of small signal performance,
Irwin and Hilton [68] defines the transition parameters α and β as well as the loop gain L :
T0 ∂ R α=
R0 ∂ T I0
I0 ∂ R β=
R0 ∂ I T0
PJ α
L = 0 ,
GT0
(3.15)
(3.16)
(3.17)
where the subscript 0 denotes the steady state signal, T denotes the temperature of the TES, R
denotes the TES resistance, I denotes the current through the TES, PJ0 is the Joule power, and
2 This
analysis was suggested and performed by John Appel.
66
15
3dB Frequencies File 2
10
5
Hz
0
5
10
1515
200
180
160
140
120
100
80
60
40
10
5
5
0
10
15
Figure 3.14: The optical 3dB frequencies from the second phase method measurement are plotted
across the ABS array above with the same convention as Figure 3.9. The frequency scale has again
been truncated at 200 Hz for clarity.
G is the thermal conductance of the device. The intrinsic time constant of the detector without
the presence of electrothermal feedback is given by τ = C/G, where C is the capacitance of the
bolometer assembly. Irwin and Hilton solve the coupled electrothermal equations and show that τ
can be related to the effective optical time constant τe f f by
τe f f
η −1 ≡
=
τ
(1 − Rsh /R0 )L
1+
1 + β + Rsh /R0
!−1
,
(3.18)
where Rsh is the shunt resistance of the circuit and the parasitic resistance of the circuit is taken as
negligible compared to Rsh [68]. Irwin and Hilton also solve for the power-to-current responsivity,
sI (ω), where ω is the angular frequency [68]. The DC power-to-current responsivity of the TES
to a low amplitude sine wave sI (ω = 0) is the change in the current through the TES (dI0 ) from a
67
change in optical power (dPopt ) while holding the bias current (Ibias ) constant and is given by
1
dI0 L
Rsh −1
=−
sI (ω = 0) =
+1−
,
dPopt Ibias
I0 R0 τel R0 L
R0
(3.19)
where L is the inductance of the TES circuit and τel is the electrical time constant defined by Irwin
and Hilton [68]:
τel =
L
.
1 + β + Rsh /R0
(3.20)
However, the typical definition of the responsivity S is the ratio of the signal dPopt to the measurement dI0 at constant Ibias :
S=
dPopt = sI (ω = 0)−1 .
dI0 Ibias
(3.21)
Substituting Equations 3.20 and 3.19 into Equation 3.21 and rearranging gives
−
dPopt dI0 I
bias
I0 R0 (1 − Rsh /R0 )
−1 =
1 + β + Rsh /R0
.
(1 − Rsh /R0 )L
(3.22)
Since the total power P is defined as the sum of the electrical power dissipated on the TES and the
optical power, P = PT ES + Popt , the response in power with current can also be written as in [73] as
dPopt dP dPT ES =
−
.
dI0 Ibias dI0 Ibias
dI0 Ibias
(3.23)
Because the circuit is in parallel, the voltage across the TES (VT ES ) and the voltage across the shunt
resistor Vsh are equal, and Ibias = I0 + Ish . The electrical power on the TES is then given by
PT ES = I0VT ES = I0 Rsh Ish = I0 Rsh (Ibias − I0 ).
(3.24)
The second term in Equation 3.23 is then
dPT ES = Rsh (Ibias − 2I0 ).
dI0 Ibias
68
(3.25)
The power flow to the heat bath P is
P = K T0n − Tbn ,
(3.26)
where Tb is bath temperature, T0 is the temperature of the TES, n = 1 + β , and K describes the
thermal heat link to the the bath and is given by G = nKT0n−1 [68]. The temperature of the TES
depends directly on R0 and I0 , so P directly depends on I0 across the transition. While R0 is
dependent on Ibias , T0 is not directly dependent on Ibias , so, as Appel showed in [73], the first term
in Equation 3.23 can be approximated by
0
dP dP dPT ES dPopt
=
=
+
dI0 Ibias dI0
dI0
dI0
dPT ES dIbias
dPT ES =
+
dI0 Ibias dIbias dI0
dIbias
= Rsh (Ibias − 2I0 ) + I0 Rsh
dI0
(3.27)
Equations 3.25 and 3.27 can be used in Equation 3.23 to get
dPopt dIbias
= I0 Rsh
.
dI0 Ibias
dI0
(3.28)
Substituting Equations 3.28 and 3.22 into Equation 3.18 gives
dI0
η −1 = 1 + (R0 /Rsh − 1)
= 1+
dIbias
!
Ibias
dI0
−2
,
I0
dIbias
(3.29)
which can be fit from an IV curve. The optical 3dB frequency f3dB can thus be estimated by
f3dB = η f3dB,thermal ,
(3.30)
where f3dB,thermal = 1/(2πτ). The optical 3dB frequencies from the time constant data sets described in Section 3.2.3, which did not suffer from the biasing glitch, were used to determine the
69
thermal time constants of the detectors, which are assumed constant in time. Figure 3.15 shows
the distribution of the thermal 3dB frequencies of the ABS detectors. Next, η is fit from each IV
curve for each detector in each observation across all seasons. These values are binned to allow
an estimation of η from averaging the results of all similar IV curves over all nominal observations. This method allows a determination of η within ∼ 4% for any saturation power and bias
current combination. The distribution of η −1 across all CMB observations of Field A is shown in
Figure 5.2 with no data selection applied. The nominal range of η −1 is 0 < η −1 < 1, and typical
values are around η −1 = 0.25. Using the thermal 3dB frequencies and binned η values, the optical
3dB frequencies for each detector during each nominal CMB observation are determined using
Equation 3.30. The distribution of the optical 3dB frequencies with no data selection applied is
shown in the right panel of Figure 5.7.
70
Number of Detectors
60
50
40
30
20
10
00
5
10
15
20
25
30
Thermal 3dB Frequency
35
40
Figure 3.15: A histogram of the thermal 3dB frequencies of the ABS detectors is shown above.
The small distribution of detectors with low thermal 3dB frequencies are from wafer 1-4.
70
3.2.5
Angle Shift
Because ABS employs a continuously-rotating HWP, fluctuations in the time constants of the detectors between observations can cause apparent shifts in the polarization angles of the detectors.
This effect is of particular importance when calibrating the polarization angles of the detectors.
The magnitude of the angle shift from the detector time constant is half the offset in phase, which
is given by Equation 3.13. In the case where f3dB is constant throughout all CMB observations,
the angle shift can be neglected, so the primary concern is the secondary effect of fluctuations in
the angle shift between CMB measurements. For a low 3dB frequency of 30 Hz, a 10% shift to a
lower f3dB results in a 0.96◦ shift in polarization angle.
The direction of the angle shift is dependent on the coordinate system of the polarization angle
definition and the rotation direction of the HWP. In all cases, the shift in phase is in the direction
of the HWP rotation. ABS uses the Healpix convention such that the vertical polarization angle is
ψ = 0◦ and the horizontal polarization angle is ψ = 90◦ . The ABS HWP rotates in the positive
direction in the coordinate system. The ABS polarization angles are measured with observations of
Tau A and with a wire grid as described in [100].3 With the wire grid measurement, the measured
angle ψmeas is defined as
ψmeas ≡ 1/2 arctan (U/Q) = 1/2arg(demod) = ψW G − ψdet ,
(3.31)
where Q and U are the Stokes parameters as defined in Equation 1.22, arg(demod) is the phase
argument of the demodulated timestream, ψW G is the angle of the polarized signal from the wire
grid, and ψdet is the polarization angle that the detector is sensitive to when the HWP encoder
value is zero. The phase φ is equal to arg(demod), which gives
1
ψdet = − φ + ψW G .
2
3 The
(3.32)
calculation of the polarization angles from the wire grid measurements without the time constant corrections
was performed by Steve Choi.
71
Expanding the phase into φ = φ0 + 2∆ψ and using Equation 3.13, we can then write the detector
angle as
ψdet = −1/2φ0 − ∆ψ + ψW G = ψdet,0 − ∆ψ + ψW G = ψdet,0 − 1/2 arctan
4 fm
+ ψW G , (3.33)
f3dB
where ψdet,0 is the intrinsic polarization angle of the detector. The angle shift is in the negative
direction, so ∆ψ must be added to the polarization angles of the detectors for all observations
and polarization angle measurements to correct for this effect. For each observation, ∆ψ is determined using the HWP rotation frequency fm from the HWP encoder and f3dB as determined in
Section 3.2.4. The IV curves for the polarization angle measurements were performed before the
wire grid was in place, but it was determined that the extra loading from the wire grid could be neglected in the calculation of η. However, future experiments could further mitigate the uncertainty
on the angle shift by taking the IV curves for wire grid calibrations with the wire grid in place.
3.3
Responsivity
The ABS responsivity model consists of three primary procedures: 1) determining the absolute
responsivity calibration for a reference detector, 2) determining the the relative responsivities of
the detectors with respect to the reference detector, and 3) determining the time-dependence of
the detector responsivities. The time-dependence of the responsivity can be tracked over several
time periods ranging from days to years. However, this analysis uses four epochs in the first two
seasons of data (t1.1 , t1.2 , t2.1 , and t2.2 ) where the responsivity is constant in time as determined by
the 2 fm method in Section 3.3.3. The duration of each epoch is typically a few months, although
the shortest epoch (t1.2 ) is two weeks. It is important to note that changes in responsivity between
epochs only occur in batch B detectors and that there is no evidence of the responsivities of batch
A detectors changing. The reference detector dre f (column 23, row 11) is a batch A detector close
to the center of the array that has a large number of Jupiter observations. These observations show
that dre f has a constant responsivity in time.
72
3.3.1
Absolute Responsivity Calibration
Frequent observations of Jupiter offer an opportunity to calibrate the responsivity of the reference
detector to Rayleigh-Jeans (RJ) temperature units. These observations must then be converted
from RJ temperature units into CMB temperature units by using the average measured bandpasses
of each fabrication wafer to describe the detector responsivities during CMB observations. A final
normalization factor is found by comparing the Planck TE spectrum to the Planck T spectrum ×
the ABS E spectrum.
Jupiter Observations
An absolute calibration measurement of the responsivity of the reference detector RRJ
dre f is made using Jupiter measurements.4 The responsivity of a Jupiter measurement RJ in an individual detector
d is defined as
RJ,d =
A
Tpeak
,
(3.34)
where A is the measured peak of the Jupiter observation in aW. Here Tpeak is the peak amplitude of
Jupiter in mK and is given by
Tpeak = 1000TJ
ΩJ
.
Ωb
(3.35)
The temperature of Jupiter is TJ = 175± ∼ 10 K [101]. From [102], the solid angle of Jupiter ΩJ is
dependent on the distance D (in AU) from Jupiter to the Earth at the time of observation and goes
as
−8
ΩJ = 2.481 × 10
5.2
D
2
sr.
(3.36)
Finally, the solid angle of the beam is determined from characterizing the beam with Jupiter measurements and is Ωb = 104 ± 4 µsr [63].
The statistically averaged responsivity of the reference detector RRJ
dre f is determined by taking
the mean of RJ,d /rdwg for all detectors d in batch A, where rwg is the relative responsivity from
4 Calculations of the responsivity from Jupiter observations were performed by Akito Kusaka, and the solid angle
of the ABS beams was calculated by Glen Nixon
73
wire grid measurements as described in Section 3.3.2. Note that only batch A detectors are used
for this calculation as they have constant responsivity over the three seasons. The uncertainty in
this value from scatter in the Jupiter and wire grid measurements is 3.9%. Using this method
and accounting for uncertainty from the temperature of Jupiter, the beam solid angle, and scatter
amongst measurements, the responsivity of the reference detector is 124 ± 10 aW/mKRJ .
Conversion to Thermal Units
The responsivity from observing Jupiter is specified in RJ temperature units. Thus, the RJ responsivity must be converted to CMB responsivity to describe the responsivity of the detectors
during nominal CMB observations. The Planck blackbody equation of the CMB is a function of
the temperature T of the CMB and is given by
BPlanck
(T ) =
v
2hν 3
1
,
hν
2
c e kb T − 1
(3.37)
where h is Planck’s constant, c is the speed of light in vacuum, kb is the Boltzmann constant, and
ν is the center frequency of the detector. The blackbody curve of a RJ source is
BRJ
v (T ) =
2kb ν 2
T.
c2
(3.38)
RJ between T and T
The conversion factor RCMB
RJ
CMB is determined by
RJ
RCMB
=
∂ BPlanck
(T )
v
∂T
.
∂ BRJ
v (T )
∂T
(3.39)
From 3.37,
hν
∂ BPlanck
(T ) 2h2 ν 4
e kb T
v
.
= 2
∂T
c kb T 2 (e khν
T
2
b − 1)
(3.40)
Equation 3.38 gives
∂ BRJ
2kb ν 2
v (T )
=
.
∂T
c2
74
(3.41)
Substituting Equations 3.40 and 3.41 into Equation 3.39, the conversion factor is
RJ
RCMB
=
hν
kb TCMB
2
hν
e kb TCMB
(e
hν
kb TCMB
− 1)2
mKRJ
,
mKCMB
(3.42)
where T = TCMB = 2.725 K. This factor is calculated separately for each of the four fabrication
wafers on ABS using the CMB wafer center frequencies determined in Section 4.2.
Final Normalization
The final normalization factor rT E is determined by comparing the Planck TE spectrum to the
Planck T spectrum × the ABS E spectrum. This factor is typically close to one but is of particular
importance for ABS because it corrects for the possible case where the polarization modulation
efficiency is less than one.
3.3.2
Relative Responsivity
Several calibration measurements of the relative detector RJ responsivities were performed over the
course of each ABS observation season using a sparse, polarized wire grid as in [100]. The relative
wg
wg
wg
wg
responsivity from wire grid measurements can be expressed as rt,d
= Rt,d
/Rt,d
, where Rt,d
is the
re f
wg
absolute responsivity of a detector d and Rt,d
is the absolute responsivity of the reference detector
re f
wg
dre f . The relative responsivities of the detectors rt,d
are measured by rotating a polarized wire grid
in front of the HWP in discrete steps. The ratio of the demodulated amplitude of a detector d
to the demodulated amplitude of the reference detector dre f is determined for each step and then
averaged. The measured relative responsivity values are then averaged within each epoch t for
each detector.5 Season 2.2 (t2.2 ) has the largest number of wire grid responsivity measurements
(five) and is thus chosen as the reference epoch.
5 The
analysis of the wire grid responsivity measurements was performed by Steve Choi.
75
3.3.3
Time-Dependent Responsivity
Two methods can be used to track the time-dependence of the absolute responsivity: the bias power
fit (BPF) method6 and the amplitude of the 2 fm signal. The BPF method uses the bias power’s
relation to the atmospheric loading to determine the responsivity of the detectors for each ∼hourlong observation. The total power on the detector is the sum of the optical power and the electrical
power from biasing. When the optical power increases, the resistance of the TES increases, which,
since the detectors are voltage biased, decreases the bias power. Changes in optical power will thus
result in changes in the bias power. The optical power on the detectors is approximately linear with
PWV for low PWV, so the bias power Pbias determined from the IV curves before each observation
can be fit by the function
Pbias = A
B
PWV
+
+C,
sin (θel ) sin (θel )
(3.43)
where A, B, and C are constants and θel is the elevation of the telescope. The responsivity for each
BPF .
detector from this model is then given by −A, which is averaged over each epoch to get Rt,d
The amplitude of the second harmonic of the HWP rotation frequency provides a complimentary method to track the time-dependence of the detector responsivities over three seasons of
observation, which was first described in Simon et al., 2015 [103]. The 2 fm signal as defined in
Equation 3.6 can be expressed in terms of a total amplitude linear with PWV and a constant phase.
Each roughly hour long observation contributes a point to both the amplitude and phase distributions. By plotting the amplitude versus the PWV for the full period of observations, trends in the
responsivity over time can be determined. While the responsivities of batch A detectors remain
constant across all seasons of observations, the 2 fm amplitudes of the batch B detectors exhibit
three discrete decays over the course of the first two seasons of observations, defining the four
epochs of constant responsivity as can be seen in Figure 3.16. Seasons 1 and 2 have two stable
epochs each. To determine the responsivity within each epoch, a linear fit of the amplitude versus
PWV is performed. The discrete decays in responsivity of batch B detectors are consistent between
6 The
BPF responsivity values were calculated by Patty Ho.
76
both the slope and y-intercept of the 2 fm amplitude fits. While either the slope or y-intercept can be
used to determine the responsivity, the y-intercept of the 2 fm amplitude for each epoch is used as
2f
a measure of the responsivity of a detector in that epoch Rt,d for the ABS analysis. While the 2 fm
amplitude is only used to track the responsivity between epochs in the ABS responsivity model, it
can also be used to determine the relative responsivity of the detectors with respect to a reference
detector. When this is done, the responsivity decay from the 2 fm amplitude between epochs for
batch B detectors is consistent with that found in relative responsivity measurements performed
with a polarizing wire grid as described in Section 3.3.2. The source of the variability has not yet
been identified, but each epoch of stable batch B responsivity was preceded by a month or longer in
which no observations were made and the cryostat warmed to ambient temperature, after which the
cryostat was re-pumped to reach vacuum and cooled before resuming observations. One possible
candidate for the decay was peeling AR coatings on any of the cryogenic or optical elements that
detectors in batch B would be more sensitive to due to their shifted bandpasses. However, a visual
inspection of all of these elements showed no deterioration in the AR coatings, indicating that this
was not the cause of the decay.
Both of these time-dependent models only use PWV< 2.5 mm for their linear fits. This represents relatively high loading, and under these conditions, the detectors can begin to exhibit nonlinearities in their responses. Additionally, in the full responsivity model the responsivity in each
epoch with these methods is normalized by the responsivity of the reference epoch (t = t2.2 ).
3.3.4
Full Responsivity Model
The primary responsivity model for ABS uses the values from the 2 fm method to track the time
variability of the detector responsivities for both batches of detectors and is given by
2f
wg
RJ
Rd,t = rT E RCMB
RRJ
dre f rt2.2 ,d
77
Rt,d
2f
Rt2.2 ,d
aW
.
mKCMB
(3.44)
Season 1.1
Season 1.2
Season 2.1
Season 2.2
Figure 3.16: The 2 fm amplitude as a function of PWV for Seasons 1 and 2 is plotted above for
a single batch B detector. The points range from early (dark blue) to late (light blue) times. The
responsivity decreases discretely in four distinct epochs. Image from [103].
Two secondary models are also defined. One uses the BPF method for the time-dependence instead
of the 2 f method, and the other assumes no time variability. These models are used in place of the
primary model and are run through the full analysis to quantify the level of systematic error in the
final analysis.
3.4
Data Selection with the HWP
The 2 fm signal can also be used to determine if the detectors are biased and responding properly,
making it a valuable tool for data selection. The following discussion will closely follow Simon
et al., 2015 [103], which first presented this technique. From Equation 3.6, we can define the
amplitudes of the cos (2χ) and sin (2χ) components of the 2 fm signal as A2c and A2s , respectively.
For each bolometer, the A2c and A2s signals are characterized with respect to PWV for each epoch
of data as in Figure 3.17. Each ∼hour-long constant elevation scan (CES) contributes a point to
78
both the A2c and A2s distributions for each detector and must pass a set of loose criteria. If the CES
has fm < 2.5 Hz, fm > 2.6 Hz, no PWV data, or a 2 fm amplitude of zero, that CES is cut. Entire
detectors are cut if they are known to have zero responsivity or if the remaining number CESes is
less than 10% of the total number of CESes. The A2c and A2s distributions are linearly fit for data
with PWV values below 2.5 mm to exclude possible nonlinearities in detector behavior at high
loading. To eliminate the impact of outliers on the fit, a preliminary fit of the data is performed and
only the inner 85% of the residuals are used to determine the optimal fit [103].
Figure 3.17: The A2c (blue) and A2s (red) signals for a single bolometer are plotted above as a
function of PWV with their fits. Each CES contributes a point to both the A2c and A2s distributions.
The vertical dotted line indicates the 2.5 mm PWV fitting cutoff. The slopes of the A2c and A2s
signals depend on the polarization angle of the detector. Image from [103].
After subtracting the fit, the median of the residuals and the limits above and below the median
that contain 34.1% of the data are determined. These limits act as effective positive and negative
standard deviations σ± . The standard deviations of the A2c and A2s distributions for each detector
(σcos and σsin respectively) are then given by the quadratic mean of σ+ and σ− for each distribution
79
2 :
and are used to make a statistical parameter χCES
2
χCES
=
2c − A2c
ACES
f it
σcos
!2
+
2s − A2s
ACES
f it
σsin
!2
,
(3.45)
2c and A2s are the amplitudes of the cosine and sine components for a given CES and
where ACES
CES
2s
A2c
f it and A f it are the amplitudes from the fit at the given PWV of the CES [103].
3.4.1
Special Cases
Detectors with zero response that are not known to have zero response must be caught and cut for
the entire epoch. In a given epoch, there are approximately 20 such detectors. A typical detector
with zero response is shown in Figure 3.18. Most zero responsivity detectors can be identified by
the amplitude of the fit slopes being less than 0.1 mK/mm. The remaining zero response detectors
have non-zero slopes from scatter, which can be caught by testing for a slope less than 50 mK/mm
and a ratio of the standard deviation to the y-intercept of the fit greater than one.
400
cos(2f)
sin(2f)
dT HWP (mK)
200
0
200
400
6001.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
PWV (mm)
Figure 3.18: An example of a detector with zero response that is flagged for removal is shown
above with the same conventions as Figure 3.17. In this particular case, the detector started having
zero response shortly after the beginning of Season 1.
80
Additionally, in each epoch, there are five to seven detectors that do not operate properly at
low PWV due to being improperly biased. To avoid cutting these detectors completely, they are
flagged as “type 1” detectors and reprocessed. Because of their poor behavior at low PWV, type
1 detectors have poor fits and can thus be identified as fits that have standard deviations greater
than 60 mK and a ratio of the standard deviation to the y-intercept of the fit greater than 0.5. To
reprocess these detectors, they are re-fit with the low PWV values excluded. A type 1 detector
before and after reprocessing is shown in Figure 3.19.
Figure 3.19: One of the . 10 type 1 detectors is shown before (le f t) and after (right) reprocessing
with the regions of poor biasing excluded from the fit. Image from [103].
3.4.2
Determining the Data Selection Parameters
2
Using the distributions of χCES
for each detector and the entire detector distribution, the optimal
2
2
χCES
cutting threshold for each epoch is determined. For all seasons, if χCES
> 36.0, the detector
timestream for the given CES is cut. The reprocessed type 1 detectors in the second season require
2
2
tighter χCES
constraints (χCES
> 20.25) than nominal detectors, so all reprocessed detectors remain
flagged so that a separate variable cutting parameter can be applied [103]. Figure 3.20 shows the
2
χCES
distributions of each season with their cuts.
81
Number of CESes
�
χ2CES
2
Figure 3.20: Histograms of the χCES
distributions for each season are shown above. Histograms
for Season 1 are on the left and Season 2 are on the right. The lower panels show the distributions
for type 1 detectors, and the top panels show the distributions for the rest of the detectors. The
2
black lines indicate the cutting threshold, which is χCES
= 36 for all distributions except type 1
2
detectors in Season 2, which require a tighter criteria of χCES
= 20.25.
3.4.3
PWV Recovery
Additionally, the linear A2c and A2s fits from this data selection technique can be used to recover
the PWV for CESes where there are no APEX radiometer measurements (∼ 8% of the total data).
To determine the PWV, the median value of the calculated PWV from a subset of 100 detectors
that are highly sensitive to the variation in PWV, do not exhibit non-linearities, and are consistently
well behaved throughout all seasons is determined. This method allows for a small number of the
100 detectors used to be ill-behaved without affecting the PWV estimation [103]. The PWV values
calculated from the 2 fm signal are calibrated against the APEX PWV values for the data set where
82
APEX values are available as shown in Figure 3.21, and the relation is approximated as a one-toone function. Once calculated, the PWV can then be used in both the 2 fm data selection and the
cut on PWV that is described in Section 5.1.7. Without this technique, CESes without PWV would
be automatically cut. An alternative model where the PWV values for all CESes (not just those
2
missing measurements) are determined from the A2c and A2s fits and used to determine new χCES
values will be run through the full analysis to quantify the uncertainty in this method.
3.0
APEX PWV (mm)
2.5
2.0
1.5
1.0
0.5
0.00.0
0.5
1.0
1.5
2.0
2f PWV (mm)
2.5
3.0
Figure 3.21: The PWV from APEX is plotted against the 2 fm PWV above. The green line indicates
a one-to-one relation.
83
Chapter 4
Further Optical Characterization
To attain the level of sensitivity necessary to measure the faint B-mode signal, CMB instruments
and their detectors must be well characterized. On ABS, routine elevation scans at constant azimuth (sky dips) and observations of the moon, Saturn, Jupiter, Venus, and RCW 38 are used for
calibrating the beam, pointing, and the detector optical efficiencies. Observations of Tau A are used
to measure the detector polarization angles, and wire grid measurements are used to characterize
both the polarization angles of the detectors and their responsivities as described in Sections 3.2.5
and 3.3.2. A Fourier Transform Spectrometer (FTS) is used to measure the frequency response of
the detectors, which is necessary for the removal of systematic errors and foreground sources with
known emission spectra and for absolute calibration as described in Section 3.3.1. Section 4.1 describes how an FTS measures the spectral response of the detectors. Sections 4.2 and 4.3 describe
FTS measurements of the ABS detectors in-situ in the field and prior to deployment, respectively.
Prior to finalizing the observation bands for AdvACT, 220/350 GHz prototype pixels were
fabricated at NIST. The spectral responses of these detectors were measured at NIST, which will
be described in Section 4.4.1. FTS measurements of these multichroic pixels are of particular
importance because they can determine if the on-chip filters are working as expected. Additionally,
cold beam map measurements of these detectors were performed at NIST and will be described in
Section 4.4.2. AdvACT later decided not to use a 350 GHz band.
84
4.1
Fourier Transform Spectrometers
A Fourier Transform Spectrometer (FTS) measures the spectral response, or passband, of a detector
using the interference pattern between two beams of light from a source with a known spectrum.
Experiments without a HWP achieve sensitivity in polarization data by differencing the signal
of the two orthogonal bolometers on each pixel. Thus, any difference in the bandpasses of the
bolometers results in a systematic error in the resulting signal. FTS data can help correct this
systematic error associated with pair-differencing. Because it uses a HWP, ABS does not pairdifference detectors and thus does not suffer from this systematic. On ABS, FTS data is used for
calibration (Section 3.3.1) and the removal of foreground sources. Known foreground sources like
dust and synchrotron radiation have different spectral dependencies than the CMB and can thus be
removed from the observed signal if the spectral response of the detectors is well measured.
Consider first one of the most basic interferometers: the Michelson Interferometer that is shown
in Figure 4.1. Two mirrors are positioned perpendicular to each other and at a 45◦ angle to the
beamsplitter. Collimated light from the source is split into two beams of equal amplitude by a
beamsplitter. One beam hits a fixed mirror, while the other hits an adjustable mirror that can vary
its distance from the beamsplitter. Both beams reflect off the mirrors toward the beamsplitter where
they recombine and are measured by a detector. Another optional collimator can be used between
the beamsplitter and detector to focus the output beam onto the detector. When the two beams
recombine, they interfere such that the magnitude of interference depends on the difference of the
path lengths that the light in the beams has traveled.
Bolometers, like those used in ABS and AdvACT, measure the average power Pav of the recombined beam, which is proportional to the square of the combined electric field. If the beams
are in vacuum, then the proportionality constant is given by α = bcε0 /2, where b is the beam
area, c is the speed of light, and ε0 is the permittivity of free space in SI units. In an ideal system
with a monochromatic source of angular frequency ω, the power measured by the detector is then
85
Detectors
Figure 4.1: A Michelson Interferometer is shown above. A collimated beam of light is split equally
into two branches by the beamsplitter. The light in each branch travels to the mirrors and is reflected
back to the beamsplitter, where it recombines, causing an interference pattern that changes as the
adjustable mirror’s position is varied. The reflected beams are drawn with an offset for clarity, and
the portion of the beam that is reflected back to the source is omitted.
dependent on the difference in path lengths ∆z and goes as
αA20
(1 + cos(k∆z)),
Pav (∆z) =
4
(4.1)
where k and A0 are the wavenumber and amplitude of the input electric field, respectively.
Extending this to a source with a continuous spectrum, the average power is given by the sum
of the power at every angular frequency ω:
Pav (∆z) =
Z ∞
αA(ω)2
−∞
4
(1 + cos(k∆z))dω ≡ C +
Z ∞
αA(ω)2
−∞
4
cos(k∆z)dω,
(4.2)
where A(ω) is the amplitude of the field at frequency ω and C is a constant offset. Because A(ω)2
is even, the integral over the cosine can be written in exponential form as
Pav (∆z) −C =
Z ∞
αA(ω)2
4
−∞
86
exp(ik∆z)dω .
(4.3)
The spectrum is then given by the inverse transform
4
A( f ) =
2παc
2
Z ∞
−∞
Pav (∆z) exp(−ik∆z)d∆z −
4C
δ k,
αc
(4.4)
where f = kc/2π is the frequency and the integral is over all possible path length differences ∆z.
The resolution of an FTS in frequency, ∆ f , depends on the maximum difference in path lengths
∆zmax :
∆f =
c
.
2∆zmax
(4.5)
A Martin-Puplett Interferometer (MPI) was used to characterize the ABS detectors. An MPI,
shown in Figure 4.2, employs an angled polarizer as the beam splitter, which is more effective than
other beamsplitters at microwave frequencies. Instead of flat mirrors, an MPI employs rooftop mirrors that are made from two mirrors angled at 90◦ with respect to each other. Wire grid polarizers
reflect light parallel to the wires and transmit light perpendicular to the wires. In the MPI setup,
input and output polarizers are added to the system, and a polarizer tilted at a vertical angle of 45◦
is used as a beamsplitter [104]. The necessary compound angle to get a 50% split on the ABS MPI
is 54.7◦ .
Details on the construction of the ABS MPI can be found in [105]. The source is a ∼1000 K
unpolarized blackbody source, which is expected to have a flat response across the ABS detector
bands and thus allows for the measurement of the ABS bandpasses. The beam of unpolarized light
passes through the input polarizer, which polarizes it perpendicular to the plane of the page and is
then collimated by a parabolic mirror. When the light reaches the angled polarizer, it is split evenly
into two parts. The component of the beam that is parallel to the wires in the polarizer reflects off
the polarizer while the component of the beam that is perpendicular to the wires is transmitted. The
two beams are then reflected back to the polarizer by the rooftop mirrors. The rooftop mirrors flip
the polarization of the beams by 90◦ , which allows the reflected beam to pass through the polarizer
and the transmitted beam to reflect off the polarizer. The beams then recombine, interfere, and pass
though an output polarizer. The output polarizer lets only the vertical component of the beam pass
87
Fixed
Rooftop
Mirror
Adjustable
Rooftop Mirror
Figure 4.2: A Martin-Puplett Interferometer is shown above. Just as in the Michelson Interferometer, the light is split into two paths with different lengths, resulting in interference. At microwave
wavelengths, an angled polarizer is more effective than other beamsplitters.
through so that if the beams are completely in phase, the full signal is transmitted, while no signal
is transmitted if the beams are completely out of phase. Polarimeters that are at ± 45◦ would not
measure an interference pattern without the output polarizer because they are only sensitive to one
of the interferometer arms. The transmitted beam can then be optionally collimated by another
parabolic mirror that focuses the beam to the detectors. The MPI used to make measurements on
the ABS detectors has an adjustable mirror length of 15 cm and is designed to operate from 80 GHz
to 3 THz with a resolution of ∼1 GHz [105].
88
4.2
ABS Bandpass Measurements
An MPI was used to characterize the frequency response of the ABS detectors in situ in January
2013; results from this test were first presented in Simon et al., 2014 [67]. Characterization of the
frequency response of the installed detectors is particularly important for ABS because preliminary
measurements of a few devices from the second half of the array showed a ∼12 GHz shift upward
in their bandpasses due to unexpected changes in the deposition material properties between fabrications. Figure 4.3 shows the full configuration of the MPI used for these measurements. The input
and output polarizers are angled such that they are parallel to the beamsplitter so that the light is
polarized vertically when reflecting off the input polarizer and vertical polarization is transmitted
through the output polarizer. Eccosorb1 is added to the back of the input polarizer so that the light
transmitted through the grid is absorbed. There is no output collimator because it would require
another 90◦ bend in the system, and it is desirable in this instance to have a larger beam so that
more detectors can see the signal since the FTS was not beam-filling during the measurements. The
FTS was mounted to the baffle enclosure with the baffle removed. An angled mirror constructed
out of a 12 inch by 12 inch polished aluminum plate was used to reflect the output signal of the
FTS signal into the cryostat in a similar manner as the time constant measurement setup shown
in Figure 3.6. During each measurement, the HWP was stationary, but the angle of the HWP was
occasionally changed between measurements to change the polarization direction.
Each FTS measurement consists of a forward scan of ∼ 120 mm as the translating mirror moves
away from the beam splitter and a backward scan of the same length as the mirror returns to the
starting point. Scans were performed at 0.13 mm/s, so each full measurement took ∼31 minutes.
A total of seven measurements were taken at various HWP angles and mirror tilts. The resulting
timestreams from the detectors are called interferograms. The white light point of an interferogram
corresponds to the point where the adjustable mirror and static mirror are equidistant from the
beamsplitter and the signal is thus maximized. Because each raw interferogram consists of both
a forward and backward scan, each raw measurement consists of two full interferograms. For
1 Emerson
and Cuming Microwave Products, http://www.eccosorb.com
89
Source
Input Polarizer
Collimating Mirror
Angled Polarizer
Detectors
Output Polarizer
Adjustable Mirror
Fixed Mirror
Figure 4.3: The setup of the FTS used for the ABS measurements is shown above. The input and
output polarizers are no longer perpendicular to the path of the beam but are instead 45◦ to the
beam path. It can be seen that adding an output collimator would require an extra 90◦ bend in the
FTS geometry. Eccosorb is added to the back of the input polarizer to absorb the transmitted signal
and reduce stray light in the system.
each measurement, the two maxima of the raw timestream, or white light points, are determined
and used to split the data into separate interferograms for the forward and backward scans. Each
interferogram is recentered so that it represents the measured power as a function of the mirror
position with the white light point at position zero. Next, a second order polynomial from each
interferogram is fit and removed to account for slowly changing drifts caused by the decrease
in intensity from diverging rays as the translating mirror moves farther from the beam splitter,
detector gain drifts, changes in atmospheric loading, and possible moisture buildup in the cryostat
window. The forward and backward interferograms are then binned and averaged together. The
90
average interferogram is apodized with a Welch window2 to bring the interferogram smoothly to
zero and a fast Fourier transform (FFT) is taken to find the detector spectrum or bandpass function
(bandpass). The constant offset in the response is removed by subtracting the average of a flat
section of the spectrum between 500 GHz and 800 GHz, and the bandpass is normalized by setting
the maximum value equal to one [67].
Because the ABS detectors are single-moded and the source is a blackbody with a temperature
of ∼1000 K, the expected response within the ABS detector band is roughly a constant power
per unit frequency. The statistics of the detectors measured are shown in Table 4.1 [67]. For
detectors with multiple measurements, the bandpasses are averaged and the resulting spectrum is
renormalized.
Table 4.1: ABS FTS Measurement Statistics
Wafer Measured
Total
Percent Out of
Live
Percent Out of
Number Detectors Detectors Total Detectors Detectors Live Detectors
1-4
9
100
9.0%
77
12%
1-11
53
140
38%
130
41%
1-14
16
156
10%
104
15%
1-15
11
84
13%
81
14%
Total
89
480
19%
392
23%
A summary of the FTS measurements. A live detector is defined as any detector with a
responsivity greater than zero at the time of the measurement. Also note that 44 of the 89
measured detectors have more than one measurement. Table from [67].
In the same manner, the average bandpass for each wafer is determined (Figure 4.4). It is
important to group each fabrication wafer separately, as changes in fabrication can impact detector
properties. For example, the bandpasses of detectors in wafers 1-14 and 1-15 are shifted upward
in frequency by ∼ 12 GHz compared to detectors in wafers 1-4 and 1-11, which is attributed to
unexpected changes in the properties of the deposition materials between fabrications. Figure 4.5
shows the average bandpass for each wafer separately with its 95% confidence limits, which are
determined by bootstrapping. Wafers 1-4 and 1-11 have sharp band edges, while wafers 1-14 and
2 The
Welch window used for this analysis is defined as w(n) ≡ 1 −
samples and 0 ≤ n ≤ N − 1 is the sample number.
91
n
(N−1)
2
, where N is the total number of
1-15 have less well-defined band edges, especially at higher frequencies. Several detectors from
wafer 1-15 have narrow bandwidths (∼ 145 GHz − 190 GHz) and thus increase the uncertainty of
the high frequency edge of the average band. The least transmissive component of the ABS filters
at frequencies above 160 GHz is a nylon filter at 4 K. However, independent FTS measurements of
the nylon filter show that it only causes a ∼ 2% drop in transmission from 160 GHz to 180 GHz,
indicating that the ABS filters are not the cause of the large decrease in power across the band
exhibited in wafers 1-14 and 1-15. The Dicke bandwidth is defined as
R
( f (ν) dν)2
Bandwidth = R
,
f (ν)2 dν
(4.6)
where ν is the frequency and f (ν) is the spectrum [106]. To avoid noise from low signal regions,
we limit the integration from 120 GHz to 175 GHz for wafers 1-4 and 1-11, 130 GHz to 185 GHz
for wafer 1-14, and 130 GHz to 195 GHz for wafer 1-15. The resulting bandwidths are shown
for each wafer in Figure 4.6. The measured bandpasses can also be used to determine the center
frequency of each detector while observing different astronomical sources. The center frequencies
are then found by
R
ν f (ν)σ (ν) dν
,
Center Frequency = R
f (ν)σ (ν) dν
(4.7)
where the integration is carried out over the same intervals that were used for determining the
bandwidths [107]. Here σ (ν) is the frequency dependence of the source, which is ∝ ν −0.7 for synchrotron emission, ∝ ν 3.6 for dust emission, and a Planck blackbody at 2.725 K for the CMB [36,
37]. The CMB center frequency is plotted as a function of array position in Figure 4.7. The bandwidths and center frequencies of the average bandpasses for each wafer are shown in Table 4.2.
The ± values on the wafer average statistics in Table 4.2 are not the errors but are the statistical standard deviations of the detector distributions for each wafer. The systematic error on the
average bandwidths is
+2.0
−2.5
+1.5
−2.5
GHz, and the systematic error on the average center frequencies is
GHz [67].
92
Average Wafer Bandpasses
Wafer 1-4
Wafer 1-11
Wafer 1-14
Wafer 1-15
Amplitude (a.u.)
1.0
0.8
0.6
0.4
0.2
0.0
80
100
120
140
160
180
Frequency (GHz)
200
220
Figure 4.4: The average bandpass of each wafer is shown above. The amplitudes of the spectra
are in arbitrary units normalized to one. Note that several detectors from wafer 1-15 have narrow
bandwidths (∼145 GHz - 190 GHz) and thus increase the uncertainty of the high frequency edge
of the average band (see Figure 4.5). Image from [67].
Table 4.2: ABS Bandwidth and Center Frequencies
Wafer Bandwidth Synchrotron Center
Dust Center
CMB Center
Number
(GHz)
Frequency (GHz) Frequency (GHz) Frequency (GHz)
1-4
34.6 ± 1.5
143.5 ± 0.7
146.1 ± 0.8
144.0 ± 0.8
1-11
36.1 ± 2.1
145.2 ± 1.2
148.0 ± 1.3
145.8 ± 1.2
1-14
34.9 ± 4.1
153.6 ± 3.4
156.3 ± 3.6
154.1 ± 3.4
1-15
38.4 ± 3.7
156.8 ± 5.5
160.3 ± 6.1
157.4 ± 5.6
The average bandwidths and center frequencies are shown above. The bandwidth of the average
bandpass can be wider than individual bands, especially when there are several populations of
bandpasses as in wafer 1-15. This can be seen by comparing these values with those in Figure 4.6.
Note that the ± values are the statistical standard deviations of the detector distributions. Table
from [67].
93
1.2
Average Bandpass Wafer 1-4
1.2
1.0
Amplitude (a.u.)
Amplitude (a.u.)
1.0
0.8
0.6
0.4
0.2
0.0
80
1.2
100
120
140
160
180
Frequency (GHz)
200
220
Average Bandpass Wafer 1-14
0.6
0.4
0.2
1.2
100
120
140
160
180
Frequency (GHz)
200
220
Average Bandpass Wafer 1-15
1.0
Amplitude (a.u.)
Amplitude (a.u.)
0.8
0.0
80
1.0
0.8
0.6
0.4
0.2
0.0
80
Average Bandpass Wafer 1-11
100
120
140
160
180
Frequency (GHz)
200
0.8
0.6
0.4
0.2
0.0
80
220
100
120
140
160
180
Frequency (GHz)
200
220
Figure 4.5: The average bandpass of each wafer is plotted above with its 95% confidence limits
shown as a band around the average line. Wafers 1-4 and 1-11 have uniform band edges, while
wafers 1-14 and 1-15 have less well-defined band edges, especially at higher frequencies. As
Table 4.1 shows, wafer 1-11 includes data for 4-5 times more detectors than the other wafers.
Image from [67].
94
Wafer 1-11
35.0 GHz
Detectors
Wafer 1-4
14
12 33.7 GHz
10
8
6
4
2
0
Wafer 1-14
6
5 31.6 GHz
4
3
2
1
020
25
30
35
Wafer 1-15
Detectors
31.5 GHz
Bandwidth (GHz)
40
20
25
30
35
Bandwidth (GHz)
40
Figure 4.6: Histograms of the bandwidths for each wafer are shown above. The black text and
vertical lines show the median value of the measured bandwidths for each wafer.
95
15 CMB Blackbody Center Frequency
5
0
5
10
1515
165
162
159
156
153
150
147
144
Freqeuncy (GHz)
10
10
5
5
0
10
15
Figure 4.7: The CMB center frequency of the ABS detectors measured in situ are plotted across
the array above. Each cross represents the two detectors sensitive to orthogonal polarizations
on each pixel, and the two axes are the locations of the pixels in degrees across the array when
the telescope is pointing at the north horizon. Detectors that are white were not measured. The
synchrotron and dust emission center frequencies follow the same pattern across the array as the
CMB center frequencies. Image from [67].
96
4.3
Preliminary ABS Bandpass Measurements Prior to Deployment
FTS measurements were also performed in the high bay at Princeton prior to deployment. When
the FTS measurements were made, only half of the focal plane (wafers 1-4 and 1-11) was in
place, and the HWP was not in place. Additionally, a high-pass thick grill filter with a low cut
off of ∼125 GHz was positioned at 300 K to eliminate the large radio frequency pickup from the
noisy high bay environment. Additionally, there were metal mesh filters and a neutral density
filter (NDF) in front of the cryogenic telescope at ∼4 K [56], which were removed shortly after
deployment and replaced with Polytetrafluoroethylene (PTFE) and nylon filters [57]. Using the
same MPI as that used in the field, three scans were performed by positioning the adjustable mirror
at its minimal distance then moving it at a constant velocity of 0.5 mm/s outward to its maximal
distance.
The bandpasses of these measurements were originally calculated and presented in [73], but
a more detailed analysis of these measurements will be discussed in this section. In the original
analysis of these data, a fourth order polynomial was fit and subtracted from the data to eliminate
long timescale drifts before the white light point was determined. Using the same method described
in Section 4.2, the interferogram was apodized with a Welch window, Fourier transformed to get
the spectrum, and normalized so that the maximum value of the bandpass was one. The Dicke
bandwidths and the center frequencies were calculated using the points where the bandpass first
reaches zero on either side of the spectrum as the integration limits for each measurement. The
center frequency and bandwidths of the detectors are dependent on the integration limits. By
changing the limits of integration in several different ways, the uncertainty in the bandwidth and
center frequencies was determined to be ∼ ±10 GHz. The Dicke bandwidth and center frequencies
with no spectral dependencies (σ (ν) = 1) of the detectors that pass a signal to noise threshold
discussed in Section 4.3.2 are given in Figures 4.8 and 4.9 respectively.
97
Bandwidth
15
Freqeuncy (GHz)
10
5
0
5
10
1515
36.0
34.5
33.0
31.5
30.0
28.5
27.0
25.5
10
5
5
0
10
15
Figure 4.8: The bandwidths of the detectors measured in the lab prior to deployment that pass the
threshold test are shown above with the same convention as Figure 4.7. Note that only half of the
array was installed and that only pixels near the center of the array are illuminated because the FTS
was not beam filling.
4.3.1
Positional Dependence
It is noted in [73] that the individual detector measurements have many dips in their spectra, but
the edges of the bandpasses are similar amongst detectors and the average of all the bandpasses
that pass a signal to noise threshold yield a spectrum that looks similar to the expected bandpass
of the detectors, as shown in Figure 4.10. This effect is attributed to non-uniform illumination of
the feedhorns by the FTS, which could have positional dependence.
Assuming that the beam was symmetric about the center of the array, a subset of detectors that
passed the threshold cuts from the right and left sides of array were grouped together for wafers
1-4 and 1-11. The average bandpasses of these subsets show a qualitative trend, which is shown in
Figure 4.11. Higher on the focal plane (wafer 1-4), the detectors on the left side of the focal plane
have the maximum of their spectra shifted to lower frequencies in the band, while the detectors
98
Center Frequency
15
Freqeuncy (GHz)
10
5
0
5
10
1515
150.4
149.6
148.8
148.0
147.2
146.4
145.6
144.8
144.0
10
5
5
0
10
15
Figure 4.9: The center frequency of the detectors with no spectral dependence that pass the threshold test are shown above with the same convention as Figure 4.7. Detectors on wafer 1-4 are in the
first row of pods, while those for wafer 1-11 are in the second row.
on the right side of wafer 1-4 have the maximum of their spectra shifted to higher frequencies.
Closer to the center of the focal plane (wafer 1-11) this trend reverses such that detectors on the
left have their maximum frequency shifted to the right of the band and vice versa. Thus, when
opposing sides are averaged, the bandpass is much flatter than the individual spectra because the
two competing shifts are averaged over.
The center frequencies of the detectors is a more quantitative measure of this trend. For each
subgroup, the mean center frequency and its standard deviation are calculated for the subgroups
in wafers 1-4 and 1-11 to determine if the spectra exhibit positional dependence. In wafer 1-4,
the left subgroup has a center frequency of 144.5 ± 0.5 GHz, while the right subgroup has a
center frequency of 144.2 ± 0.8 GHz. For wafer 1-11, the center frequency of the right subgroup
is 147.2 ± 0.5 GHz, and the center frequency of left subgroup is 148.1 ± 0.4 GHz. Thus, the
difference in center frequencies for the subsets of detectors are not statistically significant.
99
1.0
0.5
0.8
0.0
0.5
Amplitude (max=1)
Amplitude (a.u)
1.0 Interferogram ABS1-4 detectors
0.6
0.4
0.2
1.00 10 20 30 40 50 60 70 80
Distance (cm)
5
0
5
1.0
1.0
Amplitude (max=1)
Amplitude (a.u)
10 Interferogram ABS1-11 detectors
Spectrum ABS1-4 detectors
1.2
1.4 1.6 1.8 2.0
1e11
Frequency (Hz)
Spectrum ABS1-11 detectors
0.8
0.6
0.4
0.2
100 10 20 30 40 50 60 70 80
Distance (cm)
1.0
1.2
1.4 1.6 1.8 2.0
1e11
Frequency (Hz)
Figure 4.10: The interferograms (left panels) and spectra (right panels) of the ABS 1-4 (top panels)
and ABS 1-11 (bottom panels) detectors. The thick blue line is the average spectra of the plotted
detectors. While individual pixels have independent dips and peaks, the average bandpass is similar
to the expected bandpass. Figure modified from [73].
4.3.2
Spectra Cutting Threshold
The original analysis in [73] only uses detector spectra that pass a signal to noise threshold that
is defined by taking the ratio of an average value of the spectrum in the range of the expected
bandpass to an average value of the spectrum at a range of higher frequencies where the bandpass
is expected to be flat. To check that the results of the threshold cuts made intuitive sense, the
detectors that pass the threshold were determined as a function of their position on the array. The
majority of the detectors that pass the threshold are near the center of the focal plane, which is
where the FTS beam was focused. This is consistent with the FTS beam not illuminating the full
100
Figure 4.11: The left two panels show the FTS spectra of detectors in Column 16, which is high
on the focal plane, while the right two panels show spectra of detectors in Coulmns 1 and 2, which
are near the center of the array. Each group is split into two subgroups across the y-axis of the
focal plane. The right subsets are plotted in the top panels, while the left subsets are plotted in the
lower panels. The bandpasses on opposite sides of the array appear to have different shifts in the
peak power locations, which switches directions between detectors near the top of the focal plane
and center of the focal plane.
focal plane and indicates that the threshold cut is consistent with the expectation that detectors in
the center of the focal plane have higher signal to noise.
To determine if the threshold cut was biasing results, the cases where the threshold was not
met were analyzed. When the threshold cuts are eliminated completely, the bandpass still has a
similar shape with well defined edges but has added noise as shown in Figure 4.12. Thus, there is
no evident bias introduced by using this method of threshold cutting.
101
1.0
0.5
0.8
0.0
0.5
Amplitude (max=1)
Amplitude (a.u)
1.0 Interferogram ABS1-4 detectors
0.6
0.4
0.2
Amplitude (max=1)
Amplitude (a.u)
1.00 10 20 30 40 50 60 70 80
Distance (cm)
20 Interferogram ABS1-11 detectors
15
10
5
0
5
100 10 20 30 40 50 60 70 80
Distance (cm)
Spectrum ABS1-4 detectors
1.0
1.0
1.2
1.4 1.6 1.8 2.0
1e11
Frequency (Hz)
Spectrum ABS1-11 detectors
0.8
0.6
0.4
0.2
1.0
1.2
1.4 1.6 1.8 2.0
1e11
Frequency (Hz)
Figure 4.12: The interferograms and spectra of the eight columns of detectors used in the preliminary analysis. The thick blue line indicates the average spectrum for the detectors. When all of
the detectors from the eight columns are averaged over, there are still well defined edges for the
spectrum and a flatter top to the combined spectrum.
4.4
Optical Measurements of 220/350 GHz Detectors for AdvACT
Two prototype 220/350 GHz3 pixels were fabricated by NIST and optically tested in November
2013. Single prototype pixels were mounted in individual modules with rubber cement and bonded
to shunt chips which contain the rest of the TES circuitry as shown in Figure 4.13. These modules
were then bonded to the multiplexing SQUID readout chips and smooth-walled Al feedhorns were
3 These
prototype pixels are sometimes referred to as 220/270 GHz pixels because the original design of the upper
band featured an upper band centered at 270 GHz. This was changed to 350 GHz before fabrication, but this change
was not reflected in the labels imprinted on the chips during the fabrication process.
102
installed. The full setup can be seen in Figure 4.14. The feedhorns used during this test had a
design error that resulted in the horn throat waveguide diameter being larger than the detector
block waveguide, which resulted in a step in the waveguide and the possibility that the waveguides
were not concentric.
Figure 4.13: A single 220/350 GHz prototype pixel (center) in a module is shown above. It is
bonded to two shunt resistor chips.
4.4.1
Bandpass Measurements
In preparation for FTS measurements, IV curve measurements were made with a 300 K load and
a bath temperature of 110 mK to determine if the detectors could operate with a 300 K load. The
results showed that all but two detectors of the same polarization on the same pixel were saturated.
The IV curve measurements were then repeated with a cold (∼77 K), liquid nitrogen (LN2 ) load.
With a cold load, fewer detectors were saturated, indicating that a cold load should be used for the
FTS measurements.
103
Figure 4.14: The final test configuration for the two 220/350 GHz pixels is shown above. Each
module is ∼1.8 cm across and has a smooth-walled aluminum feedhorn. The shunt chips are wired
to a multiplexing chip for readout.
The FTS at NIST is a commercial polarized FTS manufactured by Blue Sky Spectroscopy.
The NIST test cryostat optics are optimized for measurements at 150 GHz, so the transmission
through the system across the 220 GHz and 350 GHz bands was modeled. All FTS measurements
were taken with a detector bath temperature of 110 mK, and each FTS spectra is found from the
average of four FTS scans and normalized to one. The first round of FTS data were taken with a
blackbody source at 1050◦ C, 500◦ C, and 250◦ C. As expected from the IV curve measurements, a
single 220 GHz detector and a single 350 GHz detector were the only operational detectors with
the blackbody source. Figures 4.15-4.17 show these measurements. The measurements of these
spectra show some out-of-band features. However, the features decrease with decreasing load
temperature, indicating that the features were likely due to the detectors being close to saturation.
Next, FTS data with a lower detector bias and a LN2 cold load were taken. The lower optical
power of the cold load allowed for the measurement of an additional 350 GHz detector sensitive to
orthogonal polarization on the same pixel. Spectra of these measurements are shown in Figure 4.18
plotted alongside their predicted bandpasses. The predicted bandpasses for the 220/350 GHz de104
tectors are determined by taking simulations of the 90/150 GHz passbands, scaling the frequency
axis by a factor of 2.4, and multiplying the result by the modeled transmission. The 220 GHz
band is roughly consistent with the predicted bandpass, but the 350 GHz band is shifted to lower
frequency and is better fit with a frequency scaling factor of ∼2.27. The two 350 GHz detectors
have consistent bandpasses as is shown in Figure 4.19.
Pixel 64-220B 1050 C Blackbody Source
Pixel 64-350B 1050 C Blackbody Source
0.8
0.8
0.6
0.6
Power
1.0
Power
1.0
0.4
0.4
0.2
0.2
0.00
100
200
300
400
Frequency (GHz)
500
0.00
600
100
200
300
400
Frequency (GHz)
500
600
Figure 4.15: Measured FTS spectra for the 220 GHz detector (left) and 350 GHz detector (right)
with a 1050◦ C blackbody source are shown above. Out-of-band features can be seen above the
bandpasses of both detectors. The spike at low frequency is likely a systematic of the system.
Pixel 64-220B 500 C Blackbody Source
Pixel 64-350B 500 C Blackbody Source
0.8
0.8
0.6
0.6
Power
1.0
Power
1.0
0.4
0.4
0.2
0.00
0.2
100
200
300
400
Frequency (GHz)
500
600
0.00
100
200
300
400
Frequency (GHz)
500
600
Figure 4.16: Measured FTS spectra for the 220 GHz detector (left) and 350 GHz detector (right)
with a 500◦ C blackbody source are shown above. The out-of-band features seen in Figure 4.15
have decreased with the decrease in loading, indicating that these features are likely due to the
detectors being near saturation power.
105
Pixel 64-220B 250 C Blackbody Source
Pixel 64-350B 250 C Blackbody Source
0.8
0.8
0.6
0.6
Power
1.0
Power
1.0
0.4
0.4
0.2
0.00
0.2
100
200
300
400
Frequency (GHz)
500
0.00
600
100
200
300
400
Frequency (GHz)
500
600
Figure 4.17: Measured FTS spectra for the 220 GHz detector (left) and 350 GHz detector (right)
with a 250◦ C blackbody source are shown above. At this lower temperature, the out-of-band
features have decreased even further.
Pixel 64-220B LN Source
1.0
Pixel 64-350B LN Source
Measured
Simulated
1.0
0.6
0.6
Power
0.8
Power
0.8
0.4
0.4
0.2
0.0150
0.2
200
250
300
350
Frequency (GHz)
400
Pixel 64-350A LN Source
1.0
Measured
Simulated
0.8
Power
0.6
0.4
0.2
0.0150
Measured
Simulated
200
250
300
350
Frequency (GHz)
400
450
0.0150
200
250
300
350
Frequency (GHz)
400
450
Figure 4.18: Measured FTS spectra of a single multichroic pixel taken with an LN2 load
are shown in blue for the 220 GHz detector
(top left), the 350 GHz detector (top right), and
an additional 350 GHz detector sensitive to orthogonal polarization (bottom). The green lines
show the predicted detector responses which include simulations of the detector design and
the transmission through the test cryostat optics.
The 220 GHz band is roughly as expected, but
both 350 GHz bands are shifted to lower fre450
quency.
106
Pixel 64-350A and 350B LN Source
350A
350B
1.0
0.8
Power
0.6
0.4
0.2
0.00
100
200
300
400
Frequency (GHz)
500
600
Figure 4.19: The two measured spectra from the orthogonal 350 GHz detectors on the same pixel
are plotted together above. Their bandpasses are highly consistent, particularly at the band edges.
4.4.2
Beam Measurements
To characterize the cold beams, 2D step and lock-in beam maps of the 220/350 GHz prototype
detectors were performed at NIST with a 250◦ C blackbody source. The beams were fit to a 2D
Gaussian beam. The results are shown in Figure 4.20. Because the feedhorn throat waveguide diameter was larger than the detector block waveguide, there could have been misalignments between
the feedhorn and the detector that could have impacted the beam measurements. Additionally, the
rough optical efficiencies of the two responsive detectors were measured as 20-30%, which is
lower than expected. An investigation into the low optical efficiency and beam measurements with
a corrected feedhorn design were planned but were not performed because the high band of the
multichroic AdvACT array was changed from 220/350 GHz to 150/230 GHz.
107
Figure 4.20: The beams for the 350 GHz and 220 GHz detectors are shown above with their
Gaussian fits. These beams could be distorted by possible misalignments of the feedhorns.
108
Chapter 5
ABS Data Selection Pipeline and Analysis
The data analysis process has several stages: pre-processing, data selection, map making, and
power spectrum and parameter estimation. During pre-processing, the data are filtered, glitches are
identified and masked, the detector noise is characterized, and the data are calibrated. After preprocessing, the data must pass a series of data selection criteria before map-making, power spectra
calculation, and further analysis can begin. The data selection process is critical for eliminating
data with any defects or where individual detectors are not operating properly. The data selection
criteria must be stringent enough to catch and discard these cases while not eliminating good data.
The data selection process for ABS will be described in Section 5.1.
Once the data have passed the data selection criteria and have been demodulated (Section 3.1),
maps of intensity and polarization can be made. ABS uses a blind analysis to avoid selection
bias, so the data selection, calibration models, and systematic error estimates are finalized by using
a series of null tests. Once the data are unblinded, the power spectra and fits of cosmological
parameters are calculated. Section 5.2 summarizes the data analysis of the first two seasons of
ABS observation.
109
5.1
ABS Data Selection Pipeline
Preliminary data selection criteria for ABS for Season 1.1 (September 13, 2012 to November 20,
2012) were presented in Visnjic, 2013 [57].1 This chapter will discuss the final data selection criteria for Seasons 1 and 2 for the ABS primary field (Field A). Each of the 24 pods that make up
the ABS focal plane array has 22 readout lines, 20 of which are wired to detectors and two2 of
which are dark SQUID lines. The dark SQUID lines and a single detector that has a disconnected
wire have been eliminated from this analysis, leaving a total of 479 detectors. Each approximately hour-long ABS observation is a constant elevation scan (CES). The first step in the data
selection process eliminates entire CESes that are not scanning the primary field properly and is
described in Section 5.1.1. Next, data selection criteria for individual CES TES timestreams are
implemented. These criteria fall into six categories: determining if the detectors are operating
properly (Section 5.1.2), eliminating timestreams with too many glitches (Section 5.1.3), eliminating timestreams with excess scan synchronous signal (Section 5.1.4), ensuring that the timestreams
are stable and roughly Gaussian distributed (Section 5.1.5), determining if the noise properties of
the timestreams are nominal (Section 5.1.6), and eliminating timestreams where the detectors are
under high loading conditions (Section 5.1.7). After the rest of the data selection criteria are complete, only CESes with more than 150 TESes are passed on to the final analysis. The following
describes each data selection criteria that the data must pass before analysis in order of application.
The impact of each cut is discussed in Section 5.1.8 and summarized in Tables 5.1 and 5.2 .
5.1.1
Determining if the Telescope is Operating Nominally
First, CESes where the telescope is not scanning or operating under normal conditions are determined and excluded from further analysis. Properties of the scan and the rotation frequency of
the HWP are used to determine if the telescope is operating under nominal conditions. Figure 5.1
shows the distributions of the scan and HWP rotation properties along with their cutting thresholds
1 Akito
Kusaka further refined the data selection criteria and developed several algorithms to identify glitches in
the timestreams.
110
with no other data selection applied. Two periods with known malfunctions in other telescope
systems are also excluded.
Scan Duration ≥1000 s:
Nominal CESes are typically ∼60-90 minutes, so CESes that are too
short (less than 1000 s) are eliminated from further analysis.
5◦ ≤ Scan Width ≤25◦ : For Seasons 1 and 2 the nominal scan width is ∼7-10◦ , while it is ∼1520◦ for Season 3. CESes with scan widths not between 5◦ and 25◦ are eliminated from further
processing.
Scan Period ≤100 s: The scan period is 1/ fscan , which is usually ∼20 s. However, the scan
period can sometimes be longer due to motor malfunctions. Additionally, some moon scans are
slower and and overlap with the primary field. Scan periods that are too long are thus cut. The
limit of ≤100 s is a loose criteria meant primarily to catch outliers.
HWP Frequency ≥2.5 Hz: The nominal HWP rotation frequency is 2.55 Hz, so CESes where
the HWP rotation frequency is less than 2.5 Hz are cut. Slow HWP rotation frequencies occur
when there are pressure failures in the HWP air bearing system or when the HWP is spinning up
to speed after being shut off.
No GPS Malfunction: Between day numbers 642.83 and 652.44 in Season 2.2 (October 3-14,
2013), the ABS GPS was malfunctioning. This impacted the unix time, resulting in significant
offsets in the telescope pointing. Thus, all CESes in this period have been excluded from further
analysis.
No Focal Plane Regulation Malfunction: Between day numbers 361.1 and 366.5 in Season 1.2,
the heaters that control the focal plate temperature regulation were operating in a bang-bang state
where they were oscillating between 0% and 100% power. In the nominal state, there is only
111
a variation of a few percent about 10% heater power. Thus, all CESes in this period have been
excluded from the analysis.
1000000
Number of Timestreams
Number of Timestreams
500000
400000
300000
200000
100000
600000
400000
200000
00
00 1000 2000 3000 4000 5000 6000 7000
Scan Duration (s)
10
20
30
Scan Width (deg)
40
50
2.5
3.0
Number of Timestreams
700000
600000
Number of Timestreams
900000
800000
700000
600000
500000
400000
300000
200000
100000
00
800000
500000
400000
300000
200000
100000
50 100 150 200 250 300 350 400
Scan Period (s)
0
0.0
0.5
1.0
1.5
2.0
HWP Frequency (Hz)
Figure 5.1: Histograms of the scan duration (top left), scan width (top right), scan period (bottom
left), and HWP rotation frequency (bottom right) are shown above for the full set of CMB data
with no data selection applied. The black lines represent the cutting thresholds used in the ABS
data selection pipeline. For all the histograms in Section 5.1, the vertical axis counts the number
of CES-TES timestreams for 480 TESes, where each CES is 60-90 minutes long.
5.1.2
Determining if the Detectors are Operating Properly
Detectors that are non-responsive or not operating properly must be found and excluded from the
analysis. The responsivity, IV curves, and the signal at the second harmonic of the HWP are all
used as measures of each detector’s operation state.
Non-Zero Responsivity: Individual TESes that consistently have zero (or close to zero) responsivity are cut for all CESes.
112
Good Bias Flag:
For each CES, TES timestreams without the “good” bias flag are cut. The good
IV flag is determined based on the slope of the normal branch. If it is in the expected slope range,
the TES is marked as good. If it is not, the TES has other classifications.
Passes 2 fm Data Selection Criteria:
For each CES, TES timestreams that do not pass the 2 fm
data selection criteria described in Section 3.4 are cut. Flag 1 indicates that the detectors are
“type 1” detectors, and flag 0 detectors are nominal. For Season 1, both flag 0 and flag 1 detectors
q
q
2
2
must fulfill 0 < χCES < 6. For flag 0 detectors in Season 2, 0 < χCES
< 6. Season 2 flag 1
q
q
2
2
detectors require a tighter constraint of 0 < χCES
< 4.5. The χCES
distributions are shown in
Figure 3.20.
0.0< 1/ηbin <1.0: For each TES timestream in each CES, the binned value of η is calculated
from the IV curve as described in the time constant section (Section 3.2.4). Values of 1/ηbin greater
than or equal to 1.0 represent bad fits of ηbin , and values of 1/ηbin that are less than or equal to
zero are unphysical. Figure 5.2 shows the distribution of 1/ηbin for the full set of CMB data along
with its cuts.
1/ηbin
Figure 5.2: The distribution of 1/ηbin across the first two seasons is shown above with its cutting
thresholds in black. Values less than or equal to zero represent non-physical values, and values
greater than or equal to one represent bad fits.
113
5.1.3
Eliminating Timestreams with Too Many Glitches
Glitches in the timestreams are found and masked during pre-processing [74], but timestreams
with too many glitches are excluded from further analysis. Glitches can be caused by flux jumps in
the readout SQUIDs, readout glitches, cosmic ray hits, and flareups in noise. These data selection
criteria are shown in Figure 5.3.
Number of SQUID Jumps ≤ 2.5: SQUID jumps are discrete large amplitude jumps in the
timestream. Timestreams with jumps greater than 50σ are rejected. Otherwise, each jump is
corrected during pre-processing. If there are more than 2 SQUID jumps2 in a detector timestream
for a given CES, then the TES timestream is cut for that CES. Typically, if there are more than 2
SQUID jumps in a given timestream, there are readout issues.
Number of 2 Sample Glitches ≤ 100: To find two sample glitches, the HWP template (A(χ))
is subtracted and the timestream is broken up into sections that are 0.125 s long to minimize 1/ f
noise. With this division, the primary variation in signal is due to the detector noise. Next, the
data for every two samples are averaged for every adjacent pair. This value is then compared to the
average of all the data in the section. Two sample glitches (which can sometimes ring for up to four
samples) have timescales ∼10 ms, which are unphysically short. Thus, a two sample glitch usually
indicates a readout glitch. These glitches are masked in the timestream during pre-processing. For
each CES, TES timestreams with more than 100 two sample glitches above 10σ are cut.
Number of 10 Sample Glitches ≤ 200: To find ten sample glitches, the HWP template (A(χ))
is subtracted and the timestream is broken up into sections that are 0.25 s long to minimize the 1/ f
noise. Next, the data for every ten samples are averaged and compared to the average of all the
data in the section. Ten sample glitches usually show a sharp increase in signal with a ∼10 sample
decay on the order of the detector time constants. This is the same behavior that would be seen
2 Note that the data selection code uses a limit of > 2.5 SQUID jumps for the cut, but there are only integer numbers
of jumps, so no more than 2 SQUID jumps per timestream are permitted.
114
if a cosmic ray hit the detector, causing a spike in TES power. Once detected, these glitches are
masked in the timestream during pre-processing. For each CES, TES timestreams with more than
200 ten sample glitches above 10σ are cut.
Fraction Masked from Noise Flareup ≤ 25%: Occasionally, there are temporary flare ups in
the 1/ f noise of the demodulated timestream. These regions are masked during pre-processing
by Fourier transforming the timestream and masking that region. However, for each CES TES
timestream, if the masked fraction of the timestream is greater than 25%, then that timestream is
cut.
800000
700000
600000
500000
400000
300000
200000
100000
00
Number of Timestreams
800000
600000
400000
200000
00
4
6
8
10
Number of Timestreams
900000
800000
700000
600000
500000
400000
300000
200000
100000
00
2
Number of SQUID Jumps
20 40 60 80 100 120 140 160
Number of 2 Sample Glitches
900000
800000
700000
600000
500000
400000
300000
200000
100000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
Number of Timestreams
Number of Timestreams
1000000
50
100
150
200
Number of 10 Sample Glitches
250
Fraction of Masked Noise Flareup
Figure 5.3: Histograms of the number of SQUID jumps (top left), number of 2 sample glitches
(top right), number of 10 sample glitches (bottom left), and fraction of masked 1/ f noise flareup
(bottom right) are shown above for the full set of CMB data with no data selection applied. The
black lines represent the cutting thresholds used in the ABS data selection pipeline. Glitches
are masked and corrected in pre-processing, but CES TES timestreams with many glitches are
eliminated from further analysis.
115
5.1.4
Eliminating Timestreams with Excess Scan Synchronous Signal
One source of telescope systematic error is signals dependent on the azimuthal angle of the telescope from ground structure. If this so-called scan synchronous signal (SSS) is too large in a given
TES timestream, then that TES timestream must be cut. Figure 5.4 shows the distributions of SSS
statistics across the full dataset for the first two seasons.
2 ≤ 50: For each CES and each TES timestream, the azimuth is binned in 20
Sum of the χSSS
bins to look for scan synchronus structure. The ABS SSS is modeled by a 20th order Legendre
polynomial [74], which is removed from the demodulated and binned timestreams to eliminate the
2
2
SSS.3 After the removal, the reduced χReal,SSS
and χImaginary,SSS
are calculated for the model of
2
2
zero signal, and timestreams with χReal,SSS
+ χImaginary,SSS
>50 are cut.
2 Over Good TESes ≤ 5:
Median χSSS
There is a subset of “good” detectors from batch A whose
CES TES timestreams pass the data selection for a reference period in Season 1 at a high rate. For
2
2
each CES, the median value of χReal,SSS
+ χImaginary,SSS
of these good detectors is determined, and
the CES is cut if it is greater than five.
Broad Bump Static SSS Filter ≤0.6: For each CES, TES timestreams with a large amount of
slowly varying scan synchronous signal are cut. A log-normal Gaussian G( f ) that is a function
of frequency f with a width of 0.05 (corresponding to a width of ∼ ±12% in frequency) and a
standard deviation σ is fit around the scan frequency of ∼37.5 mHz. The broad bump static SSS
filter value is then given by
R 3σ
−3σ
G( f )(Pdata ( f ) − Pf it ( f ))
R 3σ
−3σ G( f )Pf it ( f )
,
where Pdata ( f ) and Pf it ( f ) are the power spectra of the data and fit, respectively.
3 Akito
Kusaka and Kevin Crowley developed the model for the SSS.
116
(5.1)
Median χ2SSS of Good Detectors
Number of Timestreams
400000
350000
300000
250000
200000
150000
100000
50000
01
χ2SSS
5.1.5
Figure 5.4: If there is excess scan synchronous
signal in a given CES TES timestream, then
that timestream must be cut. Histograms of
2
2
χSSS
(top left), the median χSSS
over a subset
of good TESes (top right), and the broad bump
static SSS filter (bottom) for Seasons 1 and 2 are
shown with their cuts in black.
0
1
2
3
4
5
Broad Bump Static SSS Filter
6
Determining if the Timestream is Stable and Gaussian Distributed
The statistical properties of each CES TES timestream are calculated and used to determine if the
timestream is stable and roughly Gaussian distributed over the course of each measurement. These
data selection criteria are shown in Figure 5.5.
Raw and Demod Stationarity ≤ 0.2: To find the stationarity for each TES timestream for each
CES, the glitch masks are applied and A(χ) is removed from the timestream. The timestream is
then broken up into 0.25 s intervals to minimize the 1/ f noise. The DC offset is then subtracted
from each interval. Next, the root mean square (RMS) of the data for each 50 s interval is calculated
and compared to the average over all 50 s intervals. If the variation in the noise level of the TES
timestream is larger than 20%, then the TES timestream is cut. This process is completed for both
the raw and demodulated timestreams.
117
Raw Skewness ≤ 0.3: For a given CES, if the absolute value of the skewness of a raw TES
timestream is greater than 0.3, then the TES timestream is cut.
Raw Kurtosis ≤ 5: For a given CES, if the kurtosis of a raw TES timestream is greater than 5,
then the TES timestream is cut.
Number of Timestreams
300000
Number of Timestreams
450000
400000
350000
300000
250000
200000
150000
100000
50000
0
0.0
250000
200000
150000
100000
0.5
1.5
1.0
Demod Stationarity
2.0
0
0.0
2.0
450000
400000
350000
300000
250000
200000
150000
100000
50000
02
Number of Timestreams
600000
500000
400000
300000
200000
100000
01.0
0.2
0.4
0.6
Raw Stationarity
0.8
1.0
8
10
Number of Timestreams
700000
50000
0.5
0.0
0.5
1.0
Raw Skewness
1.5
0
2
4
6
Raw Kurtosis
Figure 5.5: Histograms of the demodulated stationarity (top left), raw stationarity (top right), raw
skewness (bottom left), and raw kurtosis (bottom right) are shown above for the full set of CMB
data with no data selection applied. The black lines represent the cutting limits. These data selection criteria are slightly more aggressive than the scanning, glitch, and SSS criteria.
118
5.1.6
Determining the Noise Properties of the Timestream
The noise power Pn as a function of frequency f can be modeled as a combination of white noise
and “1/ f ” noise and is given by
Pn ( f ) = A2 (1 + ( f / fknee )k ),
(5.2)
where A is the amplitude of the noise, k is an exponent that is fit from the noise spectrum, and fknee
is the knee of the 1/ f k noise. The distributions of the noise properties are shown in Figure 5.6.
Demod χP2n above 0.5 Hz ≤ 4:
For each CES, each demodulated TES timestream is fit to
2
the white noise plus 1/ f noise model in Equation 5.2 above 0.5 Hz. The reduced χReal,P
and
n
2
χImaginary,P
of the fit are calculated, and TES timestreams with χP2n >4 are cut.
n
Demod χP2n below 0.5 Hz ≤ 3:
For each CES, each demodulated TES timestream is fit to Equa-
2
tion 5.2 below 0.5 Hz with the scanning frequency and its harmonics removed. The reduced χReal,P
n
2
and χImaginary,P
of the fit are calculated, and TES timestreams with χP2n >3 are cut.
n
√
√
20 aW s ≤ Demod White Noise Amplitude ≤150 aW s: The amplitude of the demodulated white noise is determined for each TES timestream in a given CES. In the analysis, the
√
timestreams are weighted by their white noise. If the noise is high (above 150 aW s), then the
CES TES timestream has little weight and is cut. Timestreams with unrealistically low white noise
√
(below 20 aW s) are also cut. When the noise is this low, there has usually been a calibration
error. Timestreams with low noise are heavily weighted, so the lower noise limit must be more
conservative than the upper limit.
Demod Knee Frequency ≤ 50 mHz: For each CES, the knee frequency of each TES
timestream’s noise is determined using Equation 5.2 and the TES timestream is cut if the
noise is greater than 50 mHz. The median knee frequency of the detectors is 2.0 mHz [95], so this
119
cut catches extreme outliers.
Demod χ2Pn Above 0.5 Hz
Demod χ2Pn Below 0.5 Hz
√
Demod White Noise (aW s)
Demod Knee Frequency (Hz)
Figure 5.6: CES TES timestreams with too much noise (or falsely low noise) must be eliminated
from further analysis. The final maps are noise weighted, so timestreams with falsely low noise
are detrimental to the analysis. Histograms of the demodulated χP2n above 0.5 Hz (top left), demodulated χP2n below 0.5 Hz (top right), demodulated white noise amplitude (bottom left), and
demodulated 1/ f k knee (bottom right) are shown above for the full set of CMB data with no data
selection applied. The black lines represent the cutting thresholds used in the ABS data selection
process.
5.1.7
Eliminating Detectors Under High Loading Conditions
Under high loading, detectors can begin to exhibit non-linear behavior as they become saturated.
High loading can result from both atmospheric loading and missing the bias target for a given
detector.
120
0 mm<PWV<3 mm:
For each CES, if the PWV>3 mm, then the CES is cut. A PWV of
3 mm represents relatively high loading, and many detectors begin to exhibit non-linear behavior.
Negative PWV values are unphysical, but can result when the PWV is recovered using the 2 fm
signal as described in Section 3.4.3 and indicate that the detectors are not operating properly.
f3dB ≥ 30.0 Hz: As the detector loading increases, the 3dB frequency of the detector decreases.
For each TES in each CES, if the 3dB frequency is less than 30 Hz, the timestream is cut. A
3dB frequency of 30 Hz represents a relatively slow time constant, which likely indicates that the
detector is under high loading. Additionally, at low 3dB frequencies, the systematic polarization
angle shift from the time constants described in Section 3.2.5 is larger.
140000
Number of Timestreams
Number of Timestreams
300000
120000
250000
100000
200000
150000
100000
50000
06
4
2
0
2
PWV (mm)
4
6
8
80000
60000
40000
20000
00
100
200
300
400
3dB Frequency (Hz)
500
Figure 5.7: Detectors under high loading can begin to exhibit non-linear behavior or become saturated. A low 3dB frequency often indicates that the detector is under high loading or not operating
properly. Histograms of the PWV (left) and 3dB frequency (right) are shown above for the full set
of CMB data with no data selection applied with their cuts in black.
121
5.1.8
Impact of the Data Selection Criteria
Table 5.1 shows each cut applied individually to the full set of data from Seasons 1 and 2. The
number of CES TES timestreams and TES hours of data are determined after each cut is applied,
and the percentage is the percent of total CMB observation hours cut. The most significant cuts
are on the stationarity of the timestreams and the 2 fm cuts. However, many of these cuts have
significant overlap with the zero responsivity cut. Thus, Table 5.2 shows each cut applied successively to the full set of Season 1 and 2 CMB observation data. The number of timestreams and
TES hours after each cut are shown along with the percentage of CMB observation hours cut from
the remaining number of hours after the previous cut. Expressed this way, the detectors with zero
responsivity are the largest cut fraction of data. After the cuts, the median number of TESes that
remain per CES is 241. Overall, the total CMB observation time of the primary field used for data
analysis is 461237.74 TES hours, which is cut from a total of 1148462.64 TES hours. Thus, 59.8%
of the original observation time is ruled out by the data selection criteria.
122
Table 5.1: Data Selection Criteria Applied Individually
Cut Name
Timestreams TES Hours % Cut
Total Number
1024102
1148462.64
0%
Scan Duration ≥ 1000 s
982429
1144161.62 0.37%
5◦ ≤ Scan Width ≤25◦
1014043
1146971.35 0.13%
Scan Period ≤ 100 s
1021707
1147701.16 0.07%
HWP Frequency ≥ 2.5 Hz
1009253
1135360.79 1.14%
No GPS Malfunction
977639
1092973.42 4.83%
No Focal Plane Regulation Malfunction
1008295
1133087.67 1.34%
Non-Zero Responsivity
751412
842704.94 26.62%
Good Bias Flag
845478
947501.07 17.50%
Passes 2 fm Data Selection Criteria
704482
794092.10 30.86%
0.0< 1/ηbin <1.0
826533
926330.06 19.34%
Number of SQUID Jumps ≤ 2.5
1018647
1142178.84 0.55%
Number of 2 Sample Glitches ≤ 100
936207
1045408.56 8.97%
Number of 10 Sample Glitches ≤ 200
974196
1089401.29 5.14%
Fraction Masked from Noise Flareup ≤ 25%
958853
1072542.67 6.61%
2 ≤ 50
Sum of the χSSS
790335
887465.22 22.73%
2
Median χSSS Over Good TESes ≤ 5
914890
1029568.19 10.35%
Broad Bump Static SSS Filter ≤0.6
778129
876479.18 23.68%
Demod Stationarity ≤ 0.2
702068
788927.51 31.31%
Raw Stationarity ≤ 0.2
761996
852923.41 25.73%
|Raw Skewness| ≤ 0.3
968373
1085036.64 5.52%
Raw Kurtosis ≤ 5
987783
1107184.90 3.59%
Demod χP2n above 0.5 Hz ≤ 4
772866
864924.17 24.69%
2
Demod χPn below 0.5 Hz ≤ 3
779729
872865.81 24.00%
√
Demod White Noise 20-150 aW s
773593
868360.71 24.39%
Demod Knee Frequency ≤ 50 mHz
949421
1071625.68 6.69%
0 mm<PWV<3 mm
936924
1057128.25 7.95%
f3dB ≥ 30.0 Hz
814932
913436.44 20.46%
The impact of each data selection technique applied individually to the full data set is shown above.
While many of the cuts exceed 20%, they have significant overlap with the zero responsivity cut,
which cuts ∼27% of the data.
123
Table 5.2: Data Selection Criteria Applied Successively
Cut Name
Timestreams TES Hours % Cut
Total Number
1024102
1148462.64
0%
Scan Duration ≥ 1000 s
982429
1144161.62 0.37%
◦
◦
5 ≤ Scan Width ≤25
981471
1143407.99 0.07%
Scan Period ≤ 100 s
980992
1142847.30 0.05%
HWP Frequency ≥ 2.5 Hz
968538
1130055.07 1.12%
No GPS Malfunction
922075
1074565.85 4.91%
No Focal Plane Regulation Malfunction
908184
1059268.98 1.42%
Non-Zero Responsivity
666348
777208.41 26.63%
Good Bias Flag
659109
768811.74
1.08%
Passes 2 fm Data Selection Criteria
606848
708955.98
7.79%
0.0< 1/ηbin <1.0
606650
708725.16
0.03%
Number of SQUID Jumps ≤ 2.5
604984
706786.13
0.27%
Number of 2 Sample Glitches ≤ 100
545472
635801.12 10.04%
Number of 10 Sample Glitches ≤ 200
543504
633463.48
0.37%
Fraction Masked from Noise Flareup ≤ 25%
520711
606916.37
4.19%
2
Sum of the χSSS ≤ 50
513641
598501.16
1.39%
2
Median χSSS Over Good TESes ≤ 5
497528
579731.39
3.14%
Broad Bump Static SSS Filter ≤0.6
483748
564098.89
2.70%
Demod Stationarity ≤ 0.2
463663
540048.92
4.26%
Raw Stationarity ≤ 0.2
456409
531572.96
1.57%
|Raw Skewness| ≤ 0.3
446747
520252.24
2.13%
Raw Kurtosis ≤ 5
446676
520169.63
0.02%
2
Demod χPn above 0.5 Hz ≤ 4
429030
499189.19
4.03%
2
Demod χPn below 0.5 Hz ≤ 3
424610
493938.83
1.05%
√
Demod White Noise 20-150 aW s
424512
493823.17
0.02%
Demod Knee Frequency ≤ 50 mHz
418763
487277.76
1.33%
0 mm<PWV<3 mm
408384
475641.63
2.39%
f3dB ≥ 30.0 Hz
407912
475094.60
0.12%
Cut CES if < 150 Timestreams
396047
461237.74
2.92%
The impact of each data selection technique applied successively to the data is shown above. In
this scheme, the largest data selection criteria is the cut on detectors with zero responsivity.
124
5.2
ABS Analysis Summary
Maps of the Stokes I, Q, and U parameters are constructed using the first two seasons of ABS
primary field observations. These maps are then used to calculate the power spectra and fit cosmological parameters. To estimate the power spectra, ABS uses a Pseudo-C` estimator [108] first
developed by Kendrick Smith for the QUIET experiment [109, 110], which is a modified version
of the Monte Carlo Apodized Spherical Transform EstimatoR (MASTER) [111, 112].4 Using this
method, both the auto-correlation spectra (C`EE and C`BB ) and the cross-correlation temperature to
E-mode (TE) C`T E spectra are calculated.
Measuring the C` spectra defined in Equation 1.26 requires uniform observations of the full sky.
In practice, ground-based telescopes cannot observe the full sky and observations target smaller
patches of the sky to gain the sensitivity necessary for measuring the faint polarization signals
in the CMB. Additionally, perfectly uniform coverage is difficult to achieve due to scan patterns
and gaps in observations when the instrument is unable to observe due to inclement weather or
mechanical malfunctions. To estimate the C` spectra from these observations, the Pseudo-C` technique requires a mode-mode coupling kernel that can be calculated from pixel weights, the beam
window function, and the transfer function, which is a result of the data processing and filtering. The beam window function for ABS is determined from observations of Jupiter [63]. To
estimate the effects of the data processing and filtering on the transfer function, MASTER uses
Monte Carlo (MC) simulations, which is more computationally efficient than using a maximum
likelihood framework to analytically compute the transfer function. Figure 5.8 shows an estimate
of the E-mode spectrum that ABS would measure based on these MC simulations. The increased
efficiency of MASTER allows the ABS analysis to perform more checks for signal contamination
and calibration errors (null tests) and evaluate systematic errors [50].
ABS employs a blind analysis to avoid selection bias. This means that the data selection,
calibration, and an evaluation of systematic effects are finalized prior to looking at the measured
4 Akito
Kusaka and Srinivasan Raghunathan developed the null tests and masks for the ABS analysis, Steve Choi
worked on the TE spectrum and source masks, and Glen Nixon developed a model of the beam.
125
`(` + 1)C`/2π(µK 2)
102
Simulated E-mode Spectrum for ABS
101
100
10−1
10−2
10−30
100
200
300
Multipole (`)
400
500
Figure 5.8: The estimated measured E-mode spectrum for ABS is shown above in blue with a
simulated E-mode signal in black. The simulated E-mode signal is passed through the MC simulations that model the effects of the ABS data processing and filtering, which gives the estimated
measured E-mode spectrum for ABS.
CMB power spectra. Instead, to catch possible systematic effects that have not been accounted for
or were introduced during processing, ABS uses a suite of 21 null tests. For each null test, the data
are split into two subsets. Each split is designed to catch a certain systematic effect that would
contribute differently to each subset. For example, the data are split between detectors from batch
A and batch B to test for any possible systematic effects due to detector performance. The maps
from each subset are differenced and the spectrum of the difference map is calculated. If there are
no systematic effects, the spectrum of the difference map should be consistent with a white noise
spectrum.
Each time the data selection criteria or the instrumental models are adjusted, the null tests can
be re-calculated. The null tests are thus a powerful tool for constraining and eliminating systematic
effects. For example, on ABS, the fit of the white noise spectrum was adjusted from a fit above and
below 1 Hz to a fit above and below 0.5 Hz with a tightened χP2n constraint below 0.5 Hz based on
126
the null tests. Additionally, null tests showed that the broad bump static SSS filter criteria could be
relaxed, allowing for more data to be used in the analysis. The null tests for ABS were also used
to define the cleanest ` range for analysis.
A χ 2 fit of each null spectrum is determined, and MC simulations are used to compare the
computed χ 2 value to the distribution of expected χ 2 values. The probability to exceed (PTE) of
each null test is then calculated as the percent of χ 2 values from the MC simulations that exceed the
calculated χ 2 value. Each null test passes if 0.025 <PTE< 0.975 [74]. A low PTE indicates that
the spectrum was not null, while a high PTE indicates that the errors were likely poorly estimated.
The PTE thus determines if the χ 2 values of the null tests are consistent with statistical fluctuations.
While the null tests constrain the systematic uncertainty, the systematic errors on ABS are
quantified by running the full MASTER analysis pipeline with different models of instrumental
characterization, including the pointing, beam window function, SSS, responsivities, time constants, and detector polarization angles.
Only once the data selection and calibration models are finalized and the systematic error evaluation is complete are the resulting power spectra examined. However, for CMB observations, null
tests do not represent a perfect measure of the quality of the data since there are some systematic effects that the null tests cannot detect like an error in the responsivity calibration (see Section 3.3.1).
Thus, some further calibration checks and changes to the data selection are necessary after the data
have been unblinded.
ABS was a pathfinder experiment that fielded new detector technologies and a continuouslyrotating HWP while taking sensitive measurements of CMB polarization. One of the main contributions by ABS was demonstrating the effectiveness of a continuously-rotating HWP and developing an analysis framework for demodulation. The ABS experiment is one of the first CMB
experiments, along with MAXIPOL and EBEX, to use the A(χ) function defined in Equation 3.3
in the analysis [95, 96, 113], which will be of great use to CMB experiments that are now planning
to employ HWPs like AdvACT [114], POLARBEAR-2 [115], and the LiteBIRD satellite [116].
127
Chapter 6
Wideband Spline-Profiled Feedhorns for
AdvACT
AdvACT will use the available focal plane area on ACT more efficiently both through using multichroic pixels (effectively doubling the number of detectors) and by using a single 150 mm wafer
of detectors for each array instead of six 76 mm wafers as in ACTPol. The use of 150 mm wafers
enables a higher detector packing density and thus a higher sensitivity, which is only achievable
through the development of feedhorns that have a small aperture while maintaining beam coupling
efficiency. Additionally, any asymmetry between the E-plane and H-plane beams can lead to temperature to polarization leakage and E-mode to B-mode leakage. Thus, an ideal horn for AdvACT
would have high beam coupling efficiency and maximal symmetry between the E-plane and Hplane beams across the multichroic frequency bands. These features are more easily achieved with
larger apertures, so a compromise is required.
Corrugated feedhorns can approach near ideal beam symmetry and are currently used by ACTPol for both of the 150 GHz arrays and the 90/150 GHz array [117, 77]. However, for the small
aperture sizes desired for AdvACT, the corrugations used in the ACTPol feedhorns represent a
non-negligible fraction of the area required by each feed, which decreases the achievable coupling efficiency as defined below in Equation 6.2. The ring-loaded corrugated horns of ACTPol’s
128
90/150 GHz array (Figure 6.1) are 7 mm in diameter, but the target aperture size for the AdvACT
90/150 GHz array is 5.2 mm. Unlike corrugated feedhorns, small aperture conical feedhorns (Figure 6.2) have near maximal beam coupling efficiency but poor beam symmetry. Spline-profiled
feedhorns (Figure 6.2) can be designed to interpolate between these cases and optimize a combination of beam symmetry and beam coupling efficiency [118]. Section 6.1 will discuss the AdvACT
spline-profiled feedhorn design process, Section 6.2 will discuss the electromagnetic modeling of
the AdvACT feedhorns, and Section 6.3 will discuss measurements of the first fabricated AdvACT
feedhorn array. Some of the work in this chapter was first presented in Simon et al., 2016 [91].
7 mm
Figure 6.1: A cross section of the 90/150 GHz ACTPol feedhorn design is shown above. The first
five corrugations on the left are ring-loaded. The dark spots in the bottom ring-loaded features are
air bubbles in the wax filling the feedhorn, not defects. The pixel-to-pixel spacing on the AdvACT
90/150 GHz arrays is too small to allow for the corrugated feedhorn design.
Figure 6.2: The final optimized 90/150 GHz spline-profiled feedhorn design is shown above in
blue with its full waveguide section. The 90/150 GHz conical feedhorn design that was used as
a comparison to the spline-profiled horn is shown in red. The conical design is the same length
as the spline-profiled feedhorn without its waveguide section and has the same input and output
aperture sizes.
129
6.1
Feedhorn Development
The wideband spline-profiled feedhorns for AdvACT are designed by numerical optimization.
Markov chain Monte Carlo (MCMC) optimization is used to determine a feedhorn profile that
minimizes a penalty function, which is the difference between the calculated E-plane and H-plane
beams across a given range of frequencies [119], while estimating the beam coupling efficiency.
The penalty function p is defined as
θ =θstop
p≡
∑
∑
Frequency θ =0
(E 2 − H 2 )2 ,
(6.1)
where E and H are the amplitudes of the E-plane and H-plane beams (respectively), θ is the radial
coordinate of the beam in degrees, and θstop = 20.4◦ is defined by the 1 K Lyot stop of the AdvACT
optics. The frequencies that the penalty function is summed over are linearly spaced frequencies
within the desired observation band of the detector that are chosen for optimization. Table 6.1
shows the frequencies used for the optimizations of each feedhorn design. In general, the beams of
the feedhorns at low frequencies within the band are less symmetric than those at higher frequency.
To weight the symmetry of the lower band more in an attempt to get more even beam symmetry
across the bands, a logarithmic frequency spacing was implemented. However, it yielded similar
results to the linearly spaced frequencies, so the final design was performed with linear spacing.
The beam coupling efficiency is defined as
R θstop 1 2
(E + H 2 ) sin θ dθ
Beam Coupling Efficiency = R0180◦ 12
.
0
2
2
2 (E + H ) sin θ dθ
(6.2)
The beam coupling efficiency is not optimized on, but it is used as a selection criterion for each
feedhorn candidate after the MCMC optimization is complete.
The MCMC optimization first inputs a given feedhorn profile into an electromagnetic simulator
to determine the E-plane and H-plane beams and calculates the penalty function p. Next the optimization produces a new feedhorn profile by randomly varying the basis parameters of the previous
130
Table 6.1: Feedhorn Optimization Frequencies
Feedhorn
28/41 GHz
Number of Frequencies Frequencies (GHz)
25
24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
48
90/150 GHz 19
75, 80, 85, 90, 95, 100, 105, 110, 115, 120,
125, 130, 135, 140, 145, 150, 155, 160, 165
150/230 GHz 16
125, 135, 145, 155, 165, 175, 195, 205, 215,
225, 235, 245, 255, 265, 275, 285
The optimization frequencies for each feedhorn design are shown above. The optimization
frequencies are linearly spaced and have 16-25 values for each horn.
feedhorn profile and determines if the profile meets a set of criteria, which are designed to prevent
crashes and extreme solutions. If the criteria are failed, the simulation produces another random
feedhorn profile. If the criteria are passed, the feedhorn profile is input into the electromagnetic
simulator, the profile’s penalty function and whether it is lower than that of the previous profiles
is determined, and the optimization process is repeated for a pre-determined number of iterations.
Another method of optimization, Powell’s method, which minimizes a function of several variables
by changing one variable at a time was also tested [120], but this method was less efficient than
the MCMC optimization. Further details of the MCMC optimization are described below.
6.1.1
Electromagnetic Simulation Software
The electromagnetic mode-matching routine, ccorhrn,1 is used to calculate the radiation pattern
for the feedhorn. The program calculates the radiation pattern of a feedhorn made up of a series of
azimuthally symmetric circular waveguide sections. The software inputs are a frequency to solve at
and a radial profile of the feedhorn with the width and radius of each circular waveguide section. It
outputs the E-plane and H-plane beams, which can then be used to determine the penalty function.
1 YRS
Associates, YRS Rahmat-Samii et al. (1995)
131
6.1.2
Random Profile Determination
The monolithic 90/150 GHz and 150/230 GHz AdvACT feedhorn arrays are fabricated at
NIST [121]. Each array consists of stacked Si wafers that are each etched, coated with a seed
layer of 200 nm Ti and 1 µm of Cu, aligned, glued on the edges with Stycast 2850 FT epoxy,2 and
electroplated with 3 µm of Cu followed by 3 µm Au. Using photolithography and deep reactive
ion etching (DRIE), each Si wafer has one or two layers of the feedhorn profile etched into it.
Figure 6.3 shows a single layer of the 150/230 GHz feedhorn array, and Figure 6.4 shows the fully
assembled 150/230 GHz feedhorn array.
Figure 6.3: The top wafer of the 150/230 GHz feedhorn stack is shown above after it was coated
with a seed layer of 200 nm Ti and 1 µm of Cu. The thin Si separating the feedhorns is only
100 µm on this wafer.
The thickness of each layer of the feedhorn profile input into the electromagnetic simulation
software is determined by fabrication requirements on the thickness of the Si layers. The thinnest
150 mm wafer that NIST can accommodate in the feedhorn production is 250 µm thick, but NIST
can also triple etch a 500 µm um wafer to get a 167 µm thickness. However, triple etching is
more difficult and time consuming than etching all the way through a wafer, so the largest step
size that still yields a high-performing feedhorn is used, which is determined by running several
simulations with different step sizes. It was determined that for the 150/230 GHz array, a step size
2 Emerson
and Cuming. Billerica, MA 01821.
132
Figure 6.4: The fully assembled and Au coated 150/230 GHz feedhorn array is shown above. To
assemble the array, individual wafers are stacked up, aligned with dowel pins, and glued together.
of 167 µm was needed. Because double etching a wafer takes less time and is significantly easier
than triple etching a wafer, custom 333 µm wafers were used for sections of the feedhorn that
needed 167 µm resolution. The 90/150 GHz array can have a step size of 250 µm and can thus be
fabricated with single etched 250 µm and 500 µm wafers. The 28/41 GHz feedhorn is designed
with 500 µm sections and may be direct machined into Al or fabricated out of stacked laser-cut
500 µm Si wafers. Thus, the thickness of each layer in the electromagnetic simulations τ is the
thickness of each Si etch. However, ccorhrn models each input section separately, so by combining
sections that have the same radius, the beam computation speed can be more than doubled in most
cases.
133
The feedhorn profiles have a monotonically increasing basis to allow for the possibility of direct
machining feedhorns into Al substrates and prevent corrugated solutions. The basis is defined as
20
2π
w = ∑ Ds j sin jz
L
j=0
d=
v=
Z cumulative
Z cumulative
2π
+ Dc j cos jz
L
w dz
(6.3)
ed dz
f = c1 + c2 v,
where L is the maximum allowed length of the feedhorn and z is an array from zero to L with a step
size given by τ. Both the 90/150 GHz and 150/230 GHz simulations allow for a total horn length
of L = 3 cm, and the 28/41 GHz horn allows for a total length of 7 cm. This length is an upper limit
on the allowed length of the feedhorn. The feedhorn profiles with the best performance do not use
the full length L, indicating that they are not constrained by it. The index j is allowed to range from
zero to an upper limit of 20. The amplitudes Ds j , Dc j , c1 , and c2 are all free parameters and define
the feedhorn profile. The initial D and c parameters that are input into the MCMC optimization
will hereafter be referred to as the seed. To get the final radii array of the profile r, the function f
is normalized to one and scaled by the radii of input and output apertures, rin and rout respectively,
r=
f
(rout − rin ) + rin .
max( f )
(6.4)
The input aperture radius is determined by the desired cutoff frequency of the waveguide section of
the horn. In the close-packed regime of AdvACT, the radius of the output aperture is constrained
by the pixel-to-pixel spacing r pixel on the array. The minimum distance that NIST can fabricate
between feedhorn walls is 100 µm, so the radius of the output aperture is thus rout = r pixel − 50 µm.
The MCMC optimization begins with an input seed (D0 , c0 ), and the penalty function p0 is
determined. Random numbers (that can be both positive and negative) are added to each parameter
to make a new profile (Dnew , cnew ), and the penalty function pnew is recalculated. The MCMC
134
simulation then decides whether to take a step by (1) determining if pnew < p0 or (2) by chance if
a random number between 0 and 1 is less than e(p0 −pnew )/0.01 , which allows the simulation to avoid
getting caught in local minima. If the MCMC simulation does not take a step, D0 and c0 remain the
same. If it does, D0 = Dnew and c0 = cnew . This process is repeated for a set number of iterations
until the simulation is complete.
6.1.3
Profile Criteria
Before being input into ccorhrn, each profile must pass a set of criteria to prevent crashing the simulation and prevent extreme solutions. Occasionally, the horn profile calculation from the random
D and c parameters fails (resulting in a blank file), makes only one long waveguide section, or
contains NaN (not a number) values, which all crash the electromagnetic simulations. To prevent
these crashes, the input profile file to ccorhrn is required to have more than one section and no
NaNs. The numerical calculation of the horn profile can also sometimes result in the input and
output aperture radii not matching their defined values rin and rout , so profiles with any sections
less than rin , any sections greater than rout , or where the first radial section is greater than rin are
rejected.
Additionally, there is a class of feedhorns that consist of an almost constant waveguide section
with a radius of approximately rin and a sharp flare at the end of the horn. These profiles are highly
symmetric, but they do not use the full aperture of the horn and thus have extremely poor beam
coupling efficiency. Because of their extreme symmetry, the MCMC simulations will converge to
these solutions, so they must be eliminated. To catch and remove these flared profiles, each profile
must pass several criteria:
(1) The last two sections of the profile near the output aperture must have a small gradient.
(2) The last third of the total horn length must be greater than a certain radius rtest to ensure that
the profile is fully using the aperture.
(3) The gradient near the output aperture must not be too large.
These criteria use the loosest values possible to remove flared profiles while still allowing for a
135
wide range of possible profile solutions and were determined experimentally. For profiles with
wafer thicknesses of 167 µm, 250 µm, and 500 µm, the ideal condition for (1) is that the last two
radii vary by no more than 0.01 cm. For criteria (2), rtest = rout − 0.0543(rout − rin ). To implement
(3), the difference in radii between each section ∆r is determined and multiplied by the length
coordinate z to weight the gradient by length. The criteria for a large gradient at the end of the
horn is then defined as
L
∆r z > ∆rmax ,
2
(6.5)
where ∆rmax is the maximum jump allowed between each section. The ∆rmax varies with step size:
∆rmax,167µm = 0.0204 cm, ∆rmax,250µm = 0.049 cm, and ∆rmax,500µm = 0.06 cm.
6.1.4
Method 1: Iteratively Adding Frequencies
Two methods of feedhorn optimization with the MCMC code were implemented. The first method
starts with a single seed and optimizes it for 100,000 iterations at three frequencies within observation bands. After this optimization is complete, the frequencies that have the lowest and highest
penalty function are determined from a predetermined list of frequencies across the observation
bands and either the most symmetric or the least symmetric frequency is added to the list of optimization frequencies. For each list of four frequencies, two MCMC optimizations with 100,000
iterations are launched using the best fit profile from the previous MCMC optimization. This process is then repeated iteratively until there are seven optimization frequencies. The most symmetric
profile with high beam coupling efficiency is then selected from the results of the 32 final MCMC
optimizations. This process originally took months, but it was fully automated, reducing the run
time to a few weeks. Further, it was empirically determined that only 10,000 iterations were necessary to determine a profile for each MCMC optimization, which would have further reduced the
run time. However, it was determined that this method was highly dependent on the initial seed
and thus did not explore the full range of possible horn profiles.
136
6.1.5
Method 2: Parallel Optimization
To explore the full range of profiles, the final feedhorn design code creates a large number of random profiles and uses them to seed parallel MCMC optimizations. Each MCMC optimization runs
for 10,000 iterations and optimizes on the same ∼ 20 frequencies across the detector observation
bands. The code is run on a 40 core computer at the University of Michigan, which allows for 30
parallel optimizations to run at once. Additional computational power would enable more parallel
runs. By using parallel MCMC optimizations, the run time of the feedhorn optimization has been
reduced to less than two days.
Several runs of parallel MCMC optimizations are completed for each feedhorn design. The
profiles that seed individual MCMC runs can be predefined or are otherwise random profiles.
Thus, promising profiles from previous runs can be further optimized by subsequent runs. A
typical parallel MCMC optimization consists of 4-6 seeds from previous runs, 4-6 linear seeds,
and 18-22 random seeds. This distribution allows for the exploration of new profiles while refining
prospective solutions.
After the horn design is finalized, a length of waveguide section is added to the detector side of
the feedhorn to define the cutoff frequency. The waveguide is typically the same radius as the
OMT, which is equal to rin . However for the 150/230 GHz and 90/150 GHz feedhorns, higher
waveguide cutoff frequencies were desired than the final minimum feedhorn radii provided, so
there are small steps in radius to the waveguide sections. The length and ideal diameter of the
waveguide section is determined by High Frequency Structure Simulator3 (HFSS) simulations
with the full design including the feedhorn and OMT. The waveguide interface plate (WIP)
couples the feedhorn stack to the OMT on the detector wafer. The detector wafer has an
additional 475 µm backside hole behind the OMT with the same radius as the OMT. The WIP has
a thickness of 500 µm and a radius equal to that of the OMT. Thus, the WIP and detector wafer
add an additional 975 µm of waveguide. Additionally, a photonic choke with a waveguide section
3 ANSYS,
Inc. Canonsburg, PA 15317
137
equal to that of the feedhorn is added to the detector side of the feedhorn stack to prevent leakage
between the feedhorns and the WIP. The photonic choke consists of 415 µm wide square pillars
with a spacing of 705 µm for the 150/230 GHz feedhorn and 668 µm wide pillars with a
1135 µm pitch for the 90/150 GHz feedhorn [122]. The 150/230 GHz photonic choke wafer has a
400 µm thick flat section on the feedhorn side of the choke and a section with 200 µm tall pillars
on the WIP side. For the 90/150 GHz horns, the photonic choke is on a 600 µm base wafer, and
the pillar height is 100 µm. Figure 6.5 shows the photonic choke on the fully assembled
150/230 GHz feedhorn array. The 150/230 GHz and 90/150 GHz feedhorn designs have been
finalized. The 28/41 GHz feedhorn is still under development. Table 6.2 summarizes the
properties of each finalized feedhorn design, and Figures 6.2 and 6.6 show the finalized feedhorn
designs for the mid and high frequency arrays, respectively.
Figure 6.5: A photograph of the detector side of the AdvACT 150/230 GHz feedhorn array is
shown above. The photonic choke prevents leakage between the interface of the feedhorn stack
and the WIP and is the last layer of the feedhorn stack before the WIP.
6.2
Feedhorn Modeling
Before fabrication, the feedhorn designs are validated by simulating the beams using both ccorhrn
and an electromagnetic finite element method solver called High Frequency Structure Simulator
(HFSS) to simulate their properties and response to fabrication tolerances. Using the HFSS beams,
138
Table 6.2: Feedhorn Design Parameters
Array
rin
rout
Horn Waveguide Waveguide Photonic
(mm) (mm) Length Radius
Length
Choke
(mm) (mm)
(mm)
Thickness
(µm)
90/150 GHz 1.14 2.6
16.5
1.14
3.0
700
150/230 GHz 0.745 2.325 14.494 0.709
2.5
600
The properties of each feedhorn stack.
Total
Length
(mm)
20.200
17.594
Figure 6.6: The final 150/230 GHz feedhorn design is shown above, including its waveguide section. The cutoff frequency of the feedhorn defines the low edge of the 150 GHz bandpass. The
waveguide section thus serves as a high-pass filter that was designed after the rest of the feedhorn
design was optimized. The final feedhorn includes a step down in radius between the feedhorn and
waveguide sections to provide a higher cutoff frequency.
the beam coupling efficiency, cross-polarization, return loss, far field beams including the instrument Lyot stop, and the polarization leakages in the power spectra assuming a pair-differenced
detector pair (an extreme case for AdvACT, which plans to use continuously-rotating HWPs)
are then calculated. The 150/230 GHz feedhorn design is compared to a conical feedhorn with
the same length and aperture sizes as the spline-profiled feedhorn and the 90/150 GHz corrugated feedhorn from ACTPol scaled to high frequency with a footprint of radius 2.317 mm. The
90/150 GHz feedhorn is only compared to a conical horn of the same length and apertures since the
90/150 GHz corrugated horn from ACTPol is too large to fit with the desired pixel-to-pixel spacing
for AdvACT. The 150/230 GHz and 90/150 GHz wideband spline-profiled feedhorns developed
for AdvACT have good beam symmetry while retaining a high beam coupling efficiency. Based
on this evaluation, the 90/150 GHz spline-profiled feedhorn improves the mapping speed of the
array by a factor of ∼1.8 over the original ACTPol corrugated design.
139
6.2.1
Modeling Fabrication Tolerances
The radial uncertainty achievable by NIST in the etches for each Si wafer in the feedhorn array
is ±1-2 µm. Before modeling the feedhorns, sections with radii within 1-2 µm are combined to
decrease fabrication time by reducing the number of masks for photolithography necessary to fabricate the feedhorn array and reducing the number of wafers by using 500 µm wafers. The efficiency
and beam symmetry of the feedhorn during these combinations are monitored by calculating the
average beam coupling efficiency and average difference between the E-plane and H-plane half
angles within each observation band.
The 150/230 GHz feedhorn is the most sensitive to changes in beam symmetry and beam
coupling efficiency with variation in fabrication, so its integrated half angle difference and beam
coupling efficiency were calculated as the profile was changed in accordance with the manufacturing tolerances from NIST. To test the radial uncertainty, the radii of each section were all scaled
up and down by 2 µm and then all individually varied by a random amount from -2 µm to 2 µm.
Similarly, the wafer thickness tolerance is ±10 µm, so all the wafer thicknesses were scaled up
and down by 10 µm and then randomly varied to test this tolerance. Additionally, there can be
misalignments as the wafers are stacked to make the feedhorn array due to the tolerances of the
alignment pin holes. The maximum misalignment between wafers is 5 µm with a maximum total
misalignment of 10 µm across the entire feedhorn array. To model this misalignment, the maximum displacement was added in random directions in HFSS for the full length of the feedhorn
while ensuring that the total misalignment did not exceed 10 µm. All of these tests had a negligible
impact on the feedhorn’s properties described in the following sections.
Additionally, the DRIE can add a taper as large as 2◦ to the sidewall of each vertical etch. This
effect is typically more pronounced at the edges of the wafer. In through etches, a thin ring can
be etched away to release the Si inside the feedhorn radius, but for wafers with multiple etches,
the entirety of the material in each radius must be etched away. Thus, the taper is less pronounced
in wafers that are through etched versus double or triple etched wafers. The larger radius of each
section from the taper is on the side of the wafer that was etched. For single etched wafers, the
140
larger radius is stacked toward the output aperture. On double etched wafers, the larger radii are
on the surfaces of the wafer, so the taper is in opposite directions for the two sections. The DRIE
taper minimally decreases the beam symmetry and has a negligible effect at the sub-percent level
on the beam coupling efficiency. However, the feedhorns are modeled both with and without the
taper, and, to be conservative in calculating the leakage, the maximal taper of 2◦ is used in the
calculation of all the quantities described in this section.
6.2.2
Reflection
The reflection is modeled in HFSS with the DRIE taper with 1 GHz resolution. Figures 6.7 and
6.8 show the reflection of each of the feedhorn candidates for the 90/150 GHz and 150/230 GHz
feedhorn designs, respectively. On average, the conical feedhorns have the lowest reflection, but
the spline-profiled horns’ reflections are better than -20 dB for & 90% of their bands.
0
Conical Horn
Spline-Profiled Horn
Reflection (dB)
10
20
30
40
50
6080
100
120
140
Frequency (GHz)
160
180
Figure 6.7: The simulated reflections of each of the conical and spline-profiled feedhorn candidates
for the 90/150 GHz feedhorn are shown above. The cutoff frequency of the spline-profiled horn is
∼78 GHz. Simulations were performed with HFSS.
141
Reflection (dB)
0
Corrugated Horn
Conical Horn
Spline-Profiled Horn
10
20
30
40
50
60
70 140 160 180 200 220 240 260 280
Frequency (GHz)
Figure 6.8: The simulated reflections from HFSS of each of the three 150/230 GHz feedhorn
candidates are shown above. The starting frequency of the plot, 125 GHz, is set by the cutoff
frequency of the spline-profiled horn, which is ∼124 GHz. The excess reflection at high frequency
of the spline-profiled horn is a result of changing the waveguide section of the horn after its full
design as can be seen in Figure 6.9.
Waveguide Cutoffs
The 150/230 GHz feedhorn array moved into production before the waveguide section was finalized. Since the the alignment dowel pin holes had already been incorporated into the masks, the
depth of the pins into the feedhorn stack had already been determined and the length of waveguide
was thus limited to 0.25 cm. Additionally, a higher cutoff frequency was desired, so the waveguide
section was decreased in size. Several candidates for the cutoff were considered including all five
sections having a radius of 0.745 mm (mod 1), all five sections having a radius of 0.720 mm (mod
2), having one section on each side of the five sections with radius 0.733 mm to transition to three
sections of radius 0.720 mm (mod 3), and all five sections having a radius of 0.709 mm (mod 4).
The reflection (Figure 6.9) for each of these modifications was calculated to assess the sharpness
of the cutoff, and the polarization leakage and beam coupling efficiency were also calculated. After considering these quantities along with the detector bandpass cutoff and the atmospheric water
vapor absorption lines, mod 4 was selected as the final 150/230 GHz feedhorn design.
142
A higher waveguide cutoff frequency was also desired for the 90/150 GHz feedhorn. Unlike the
150/230 GHz feedhorn, the mid-frequency feedhorn design had not yet moved into production, so
there were no length requirements. The original mid-frequency feedhorn design had a waveguide
section that matched the diameter of the 2.4 mm OMT, but the waveguide section necessary for
the higher cutoff frequency is 5% smaller with a diameter of 2.28 mm. It was determined that
the coupling to the OMT was improved by not transitioning the smaller waveguide diameter back
up to the diameter of the OMT. However, the transition from the smaller waveguide diameter to
the larger horn diameter must be as slowly varying as possible to retain the beam symmetry. It
was determined that three transition sections with diameters increasing by 15 µm were necessary
to minimize the leakage in the power spectra due to the beam asymmetries caused by the abrupt
transition. In both the 150/230 GHz and 90/150 GHz cases, this complication could be avoided if
the waveguide section diameter was determined before designing the feedhorn.
0
Horn Only
Horn Mod 2
Horn Mod 3
Horn Mod 4
Reflection (dB)
10
20
30
40
50
60120
140
160
180
200
220
Frequency (GHz)
240
260
280
Figure 6.9: The simulated reflections as a function of frequency of the three options for reducing
the diameter of the waveguide section for the 150/230 GHz horn are shown above compared to the
horn with no waveguide sections. The spike in the modified versions around 250 GHz is due to an
extra mode kicking in. This effect has a narrow bandwidth, so the integrated reflection remains low
and its effect on the average beam in the 230 GHz band is negligibly small. For this simulation,
the WIP and cavity behind the OMT were included for an extra length of 975 µm at the detector
side of the horns with 0.745 mm radius.
143
6.2.3
Cross Polarization
The cross polarization is determined from the polarized (rEL3X and rEL3Y ) beam parameters in
dB from HFSS. For these simulations, the radial coordinate of the beam θ ranges from 0◦ -180◦
with 1◦ resolution. The E-plane beam is then given by rEL3X at φ = 0◦ , where φ is the angular
coordinate of the beam, and the H-plane beam is given by rEL3X at φ = 90◦ . The cross polarization beam is given by rEL3Y at φ = 45◦ . All beams are normalized by the maximum value of the
E-plane beam, such that the maximum value of the E-plane beam is equal to one. The cross polarization is then the maximum value of the cross polarization beam. The cross polarization is plotted
for the 90/150 GHz mid-frequency finalized horn design and a conical horn in Figure 6.10 and for
the finalized 150/230 GHz high-frequency horn design, a conical horn, and the scaled corrugated
horn in Figure 6.11. The average cross polarization in each band for these feedhorn designs is
summarized in Table 6.3. The 90/150 GHz spline-profiled horn has more cross polarization in the
low band than the conical horn and less in the high band. For the 150/230 GHz horns, the cross polarization of the spline-profiled horns is less than that of the conical horns, and the spline-profiled
horn also has less cross polarization in the 150 GHz band than the corrugated horn but slightly
more cross polarization in the 230 GHz band.
144
Cross Polarization (Percent)
3.5
Conical Horn
Spline-Profiled Horn
3.0
2.5
2.0
1.5
1.0
0.5
0.080
100
120
140
Frequency (GHz)
160
180
Figure 6.10: The simulated cross polarizations of a conical and spline-profiled feedhorn for
90/150 GHz are shown above. The spline-profiled horn has lower cross polarization in the upper band and higher cross polarization in the lower band.
Cross Polarization (Percent)
14
Corrugated Horn
Conical Horn
Spline-Profiled Horn
12
10
8
6
4
2
0 140 160 180 200 220 240 260 280
Frequency (GHz)
Figure 6.11: The simulated cross polarizations of each of the three 150/230 GHz feedhorn candidates are shown above. The spline-profiled horn has lower cross polarization than the conical horn.
The spline-profiled horn has less cross polarization than the corrugated horn in the 150 GHz band
but has slightly higher cross polarization in the 230 GHz band.
145
6.2.4
Beam Coupling Efficiency
The beam coupling efficiency is determined for each horn profile using the magnitude of E-plane
and H-plane beams from HFSS and Equation 6.2. As with the cross polarization, the radial coordinate of the beam θ ranges from 0◦ -180◦ with 1◦ resolution. Figures 6.12 and 6.13 show the
beam coupling efficiency as a function of frequency for the MF and HF spline-profiled feedhorns
respectively. For comparison, the MF and HF conical horns are plotted in Figures 6.14 and 6.15,
respectively, and the HF corrugated horn is plotted in Figure 6.16. The conical feedhorns have the
least beam symmetry, and thus, as expected, their beam coupling efficiency is maximized. For the
HF horns, the spline-profiled horn has higher beam coupling efficiency in the 150 GHz band than
the corrugated horn but lower beam coupling efficiency in the 230 GHz band. Table 6.3 summarizes the average beam coupling efficiency in each band for both the MF and HF horn candidates.
Table 6.3: Simulated Feedhorn Performance
Feedhorn
Band
Range
(GHz)
Cross
Polarization
(with
DRIE
taper)
Cross
Polarization
(without
DRIE taper)
Beam
Coupling
Efficiency
(with
DRIE
taper)
46.1%
69.2%
N/A
N/A
65.8%
76.9%
N/A
N/A
N/A
Beam
Coupling
Efficiency
(without
DRIE
taper)
45.9%
68.7%
48.5%
77.4%
65.4%
76.4%
71.9%
90.2%
48.0%
MF Spline
80-110
1.74%
1.74%
MF Spline
125-165 0.32%
0.33%
MF Conical
80-110
N/A
1.14%
MF Conical
125-165 N/A
1.29%
HF Spline
125-175 0.96%
1.02%
HF Spline
195-285 0.39%
0.40%
HF Conical
125-175 N/A
1.32%
HF Conical
195-285 N/A
1.58%
HF
125-175 N/A
1.62%
Corrugated
HF
195-285 N/A
0.30%
N/A
86.6%
Corrugated
The cross polarization and beam coupling efficiency of both bands for perfect realizations of the
finalized spline-profiled designs as well as the other feedhorn candidates are shown above. The
spline-profiled horns show values both with and without the DRIE taper.
146
Beam Coupling Efficiency
1.0
0.8
0.6
0.4
0.2
Average
E-plane
H-plane
0.080
100
120
140
160
Frequency (GHz)
180
Figure 6.12: The simulated beam coupling efficiency of the 90/150 GHz feedhorn is shown above.
The black is the average beam coupling efficiency, and the blue and green are the beam coupling
efficiencies for the E-plane and H-plane, respectively. The beam efficiency of the spline-profiled
feedhorn is less than that of the conical horn.
Beam Coupling Efficiency
1.0
0.8
0.6
0.4
0.2
0.0120
Average
E-plane
H-plane
140
160
180
200
220
Frequency (GHz)
240
260
280
Figure 6.13: The simulated beam coupling efficiency of the 150/230 GHz feedhorn is shown above
with the same convention as Figure 6.12. The beam coupling efficiency is higher than that of the
corrugated horn in the low band and lower than the corrugated horn in the high band.
147
Beam Coupling Efficiency
1.0
0.8
0.6
0.4
0.2
Average
E-plane
H-plane
0.080
100
120
140
160
Frequency (GHz)
180
Figure 6.14: The simulated beam coupling efficiency of a 90/150 GHz frequency conical feedhorn
is shown above with the same convention as Figure 6.12.
Beam Coupling Efficiency
1.0
0.8
0.6
0.4
0.2
0.0120
Average
E-plane
H-plane
140
160
180
200
220
Frequency (GHz)
240
260
280
Figure 6.15: The simulated beam coupling efficiency of a 150/230 GHz conical feedhorn is shown
above. The conical feedhorn represents the nearly optimal case for beam coupling efficiency but
has poor beam symmetry.
148
Beam Coupling Efficiency
1.0
0.8
0.6
0.4
0.2
0.0120
Average
E-plane
H-plane
140
160
180
200
220
Frequency (GHz)
240
260
280
Figure 6.16: The simulated beam coupling efficiency of a high frequency corrugated feedhorn is
shown above. The beam coupling efficiency of the corrugated horn at low frequencies is poor but
the efficiency improves at higher frequencies.
6.2.5
Polarization Leakage
The polarization leakages in the power spectra are estimated using the simulated co- and crosspolar beams from HFSS. The polarization leakages assume a pair differenced detector pair, which
is a strong test of the performance since in AdvACT the half-wave plates will provide significant
mitigation of the systematics and eliminate the need for pair-differencing. The formalism of the
calculation below closely follows a memo from Jeff McMahon.
The electric fields on the sky Ex and Ey are coupled to the electric field in the detectors Ea and
Eb by
  
 
Ea  βax βay  Ex 
 =
  ,
Eb
βbx βby Ey
(6.6)
where a and x as well as b and y are aligned along the boresight. Here βax and βby are the co-polar
beams, and βay and βbx are the cross-polar beams. These quantities are modeled every 10 GHz
within the observation bands of both the MF and HF feedhorns. To model these quantities in
149
HFSS, θ is allowed to range from 0◦ -45◦ with 1◦ resolution, and φ ranges from 0◦ -360◦ with 1◦
resolution. The default setting in HFSS is to source the calculation through the wave port in the x
direction, which gives βax and βay . To model βbx and βby , the source must be changed to the wave
port in the y direction. The complex beams are then given by the sum of their real and imaginary
parts as
βnx = Re(rEL3X) + i Im(rEL3X)
βny = Re(rEL3Y ) + i Im(rEL3Y ) ,
(6.7)
where n is either a or b. The co- and cross-polar beams from HFSS are then masked such that they
go to zero when θ > 20.4◦ to account for the Lyot stop, and a 2D FFT is performed to estimate the
far field beams.
For an ideal bolometer differencing pair at the output of the of the horn, the measured polarized
signal P would be
P = Ea − Eb .
(6.8)
The Stokes parameters using the decreasing phase convention are given by
I = |Ex |2 + |Ey |2
Q = |Ex |2 − |Ey |2
U = 2 Re(Ex Ey∗ )
V = 2 Im(Ex Ey∗ ) .
(6.9)
Here I is the intensity, Q and U describe the linear polarization as defined in Equation 1.22, and
V describes the circular polarization. Substituting Equation 6.6 into Equation 6.8 and using the
definition of the Stokes parameters as in Equation 6.9 gives
P = σ I + δ Q + εU + γV ,
150
(6.10)
where the coefficients are the beam couplings from I, Q, U, and V into P. For an ideal detector,
δ = 1 and σ = ε = γ = 0. The beam couplings are then given by
1 2
2
2
2
σ = (βax
+ βay
− βbx
− βby
)
2
1 2
2
2
2
δ = (βax
− βay
− βbx
+ βby
)
2
(6.11)
(6.12)
∗
∗
ε = Re(βax
βay − βbx βby
)
(6.13)
∗
∗
γ = −Im(βax βay
+ βbx
βby ) .
(6.14)
The beams are then normalized by the maximum of δ and averaged across the low and high bands
of each feedhorn. For the MF array, the lower band is averaged between 80 GHz and 110 GHz and
the high band is averaged from 130 GHz to 160 GHz. For the HF array, the lower band is averaged
between 130 GHz and 170 GHz and the high band is averaged from 190 GHz to 290 GHz. This
calculation is performed for pixels sampled across the full extent of the detector array. As the
distance from the center of the array increases, the ellipticity of the Lyot stop as viewed from the
pixel increases, which results in higher leakage. The central pixel thus gives the lowest temperature
to polarization leakage. While edge pixels exhibit higher leakage, the average leakage beam of
pairs of pixels equidistant from the array center on opposite sides of the array approximates the
behavior of the central pixel. Therefore, the behavior of the central pixel provides an estimate for
the systematics of the array.
To estimate the leakage in the power spectra from beam asymmetries, the window functions [123] of the signal and leakage beams are calculated. For each beam, the magnitude squared
of the FFT of the averaged far field beams is calculated and normalized by the maximum of the
transformed δ beam. Next the 2D functions are binned radially to make a 1D window function.
To account for the rest of the optics, including the 6 m ACT telescope, we normalize the multipole
axis by comparing the δ window function to a window function of a Gaussian beam with full
width at half maximum (FWHM) of 1.3 n arcmin. Here n = 1 for the 150 GHz beams to match
expectations for CODE V modeling of the telescope and camera optics. We scale n by frequency
151
so that n = 150/230 for the 230 GHz beam and n = 145/90 for the 90 GHz beam. The measured
spectra (Figures 6.17 and 6.18) are then determined by multiplying models of the EE and BB
polarization spectra by the δ window function, the temperature to polarization leakage spectrum
(Figures 6.19 and 6.20) is determined by multiplying the modeled TT spectrum by the σ window
function, and the EE to BB leakage (Figures 6.21 and 6.22) is determined by multiplying the
102
102
101
101
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
modeled EE spectrum by the ε window function.
100
10
−1
10−2
10−3
10−4
10
−5
10−6
EE0
10
EE
BB (r=0.01)
BB (r=0)
Spline-Profiled Measured EE
Spline-Profiled Measured BB (r=0.01)
Spline-Profiled Measured BB (r=0)
Conical Measured EE
Conical Measured BB (r=0.01)
Conical Measured BB (r=0)
BB (r=0.01)
−1(r=0)
10BB
Spline-Profiled Measured EE
−2
Measured BB (r=0.01)
10Spline-Profiled
Spline-Profiled Measured BB (r=0)
−3
Measured EE
10Conical
Conical Measured BB (r=0.01)
Conical
Measured BB (r=0)
−4
10
10−5
101
102
Multipole (�)
10−6
103
101
102
Multipole (�)
103
102
102
101
101
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
Figure 6.17: Simulated measurements of the EE and BB polarization spectra of the 90/150 GHz
feedhorn candidates are shown above for the 90 GHz band (left) and the 150 GHz band (right). The
small deviation at small angular scales is due to the size of the beams. The peak in the predicted Bmode spectrum at ` ∼ 1000 comes from gravitational lensing of the dominant E-mode signal [24].
100
10−1
10−2
10−3
10−4
EE
BB (r=0.1)
BB (r=0)
Spline Profiled Measured EE
Spline Profiled Measured BB (r=0.01)
Spline Profiled Measured BB (r=0)
Conical Measured EE
Conical Measured BB (r=0.01)
Conical Measured BB (r=0)
Corrugated Measured EE
Corrugated Measured BB (r=0.01)
Corrugated Measured BB (r=0)
Spline Profiled Measured EE
−1
10Spline
Profiled Measured BB (r=0.01)
Spline Profiled Measured BB (r=0)
−2
10Conical
Measured EE
Conical Measured BB (r=0.01)
−3
10Conical
Measured BB (r=0)
Corrugated Measured EE
−4
10Corrugated
Measured BB (r=0.01)
Corrugated Measured BB (r=0)
10−5
10−6
EE
BB (r=0.1)
0
10
BB (r=0)
10−5
101
102
Multipole (�)
103
10−6
101
102
Multipole (�)
103
Figure 6.18: Simulated measurements of the EE and BB polarization spectra using the
150/230 GHz feedhorn candidates are shown above for the 150 GHz band (left) and the 230 GHz
band (right).
152
100
10−1
10−1
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
100
10−2
10−3
10−4
10−5
10−6
10−2
BB(r=0.01)
BB(r=0.01)
BB(r=0)
Spline-Profiled Temperature Leakage
Conical Temperature Leakage
−3
10BB(r=0)
Spline-Profiled Temperature Leakage
−4
10Conical
Temperature Leakage
10−5
10−6
101
102
Multipole (�)
10−7
103
101
102
Multipole (�)
103
Figure 6.19: The temperature to polarization leakage of the 90/150 GHz spline-profiled (red) and
conical (cyan) feedhorns are plotted with the B-mode signal for r = 0 (green) and r = 0.01 (blue)
for the 90 GHz band (left) and the 150 GHz band (right). The conical feedhorn has slightly more
leakage at 90 GHz and significantly more leakage at 150 GHz compared to the spline-profiled
feedhorn. It is important to note that this is for the extreme case where the detectors are pairdifferenced and no HWP is in use. These leakages can be further mitigated by accounting for
beam asymmetries in analysis and by the use of a HWP as planned.
100
100
10−1
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
10−1
10−2
10
−3
10−4
10−5
10−6
10−2
−3
10BB(r=0.01)
BB(r=0.01)
BB(r=0)
Spline Profiled Temperature Leakage
Conical Temperature Leakage
Corrugated Temperature Leakage
BB(r=0)
−4 Profiled Temperature Leakage
10Spline
Conical Temperature Leakage
−5
Temperature Leakage
10Corrugated
10−6
10−7
101
102
Multipole (�)
103
10−8
101
102
Multipole (�)
103
Figure 6.20: The temperature to polarization leakage of the 150/230 GHz spline-profiled (red),
conical (cyan), and corrugated (magenta) feedhorns are plotted with the B-mode signal for r = 0
(green) and r = 0.01 (blue) for the 150 GHz band (left) and the 230 GHz band (right). On average,
the conical feedhorn has the largest total leakage. The leakage from the corrugated horn is higher
than that from the spline-profiled horn at large scales and smaller at small scales. The transition to
a smaller waveguide section than the horn was optimized for causes a small increase in the leakage
at small angular scales in the high band.
The E-mode to B-mode leakage is several orders of magnitude below the B-mode signal. At
the percent level, the temperature to polarization leakage is not negligibly small, but MCMC simulations of the 150/230 GHz horn design using the estimated far field beam results at 150 GHz
(where the leakage is the worst) determined that the leakage from temperature into the B-modes
153
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
100
10−1
10−2
10−3
10−4
10−5
10−6
10−7
10−8
10−9
10−10
10−11
10−12
10−13
10−14
10−15
101
102
Multipole (�)
103
100
10−1
10−2
10−3
10−4
10−5
−6
BB(r=0.01)
10
−7
BB(r=0)
10
−8
Spline-Profiled
Polarization Leakage
10
Conical
−9 Polarization Leakage
10
10−10
10−11
10−12
10−13
10−14
10−15
101
102
Multipole (�)
BB(r=0.01)
BB(r=0)
Spline-Profiled Polarization Leakage
Conical Polarization Leakage
103
100
10−1
10−2
10−3
10−4
10−5
10−6
10−7
10−8
10−9
10−10
10−11
10−12
10−13
10−14
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
Figure 6.21: The EE to BB leakages of the 90/150 GHz frequency feedhorn candidates are shown
above for the 90 GHz band (left) and the 150 GHz band (right) with the same convention as
Figure 6.19. This leakage is negligibly low.
101
102
Multipole (�)
103
100
10−1
10−2
10−3
10−4
−5
BB(r=0.01)
10
BB(r=0)
−6
10
Spline Profiled Polarization Leakage
−7
10
Conical Polarization Leakage
−8
Corrugated
Polarization Leakage
10
10−9
10−10
10−11
10−12
10−13
101
102
Multipole (�)
BB(r=0.01)
BB(r=0)
Spline Profiled Polarization Leakage
Conical Polarization Leakage
Corrugated Polarization Leakage
103
Figure 6.22: The EE to BB leakages of the 150/230 GHz feedhorn candidates are shown above for
the 150 GHz band (left) and the 230 GHz band (right) with the same convention as Figure 6.19. In
all cases, this leakage is negligibly low.
has a large suppression factor compared to leakage into E-modes (Figures 6.23-6.26). The MCMC
simulations input the far field Q and U beams, which are the far field δ beam and the far field δ
beam rotated by 45◦ (φ45 = φ0 − 45), respectively. The MCMC simulations all use the same CMB
and noise realizations are based on 120 independent 125 square degree patches with 1/3 arcminute
resolution and 0.5 µK-arcminute noise. One 125 square degree patch is simulated and divided by
√
120, which is an underestimate of the sensitivity due to an apodization of the patch with a cosine
√
weighted mask. The 1/ 120 factor is not enough to completely suppress fluctuations in the mean,
so there are ∼ 1σ shifts in some of the points mimicking a real measurement. The green boxes
indicate the measured E-modes, and the cyan boxes indicate the measured B-modes. The B-mode
154
leakage is almost completely from the MCMC realization noise, which indicates that the temperature to polarization leakage from the feedhorn goes almost entirely into E-modes at a negligible
level consistent with the formalism4 presented in Shimon et al., 2008 [124]. Furthermore, accounting for beam asymmetries in analysis could further mitigate the leakage by an order of magnitude
or more, cross-linking in the maps helps identify and quantify this leakage, and the planned HWPs
for AdvACT will significantly mitigate the leakage.
10−1
Temperature to Polarization Leakage
Temperature to Polarization Leakage
10−1
10−2
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
E-mode Signal
10−3
10−4
10−5
10−6
10−2
10−3
BB(r=0.2)
BB(r=0)BB(r=0.2)
BB(r=0) Temperature Lea
Spline Profiled
Spline Profiled Temperatu
B-mode Signal
(r=0.2)
10−4
10−5B-mode Signal (r=0)
10−6
101
102
10 Multipole 10
(�)
1
2
Multipole (�)
103
103
Figure 6.23: Above are simulations of the measured E-mode signal (green boxes) and the measured
B-mode signal (cyan boxes) with the polarization leakage from the feedhorn set to zero. The black
curves are simulated E-mode and B-mode signals for an r = 0.2, while the green and orange lines
represent models where r = 0. Figure courtesy of Jeff McMahon.
4 The
feedhorns presented in this work produce elliptical beams if fed with Ex or Ey polarization. Because the
semi-major axes of these beams are orthogonal, the s2ψ term vanishes and thus the leakage into B-modes vanishes as
shown in Table V of Shimon et al., 2008.
155
Temperature to Polarization Leakage
Temperature to Polarization Leakage
10−1
10−2
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
10−1
10−3
10−4
10−5
10−6
10−2
BB(r=0.2)
BB(r=0)BB(r=0.2)
BB(r=0) Temperature
Spline Profiled
Spline Profiled Tempe
10−3
10−4
10−5
10−6
101
102
2
101 Multipole 10
(�)
Multipole (�)
103
103
Figure 6.24: Using the same convention as Figure 6.23, the B-mode signal has now been set to zero
with the polarization leakage from the feedhorn remaining zero. Here the non-zero cyan boxes
represent the leakage in the B-mode signal from the MCMC realization noise. Figure courtesy of
Jeff McMahon.
156
Temperature to Polarization Leakage
Temperature to Polarization Leakage
10−1
10−2
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
10−1
10−3
10−4
10−5
10−6
10−2
BB(r=0.2)
BB(r=0)BB(r=0.2)
BB(r=0) Temperature
Spline Profiled
Spline Profiled Tempe
10−3
10−4
10−5
10−6
101
102
10 Multipole 10
(�)
1
2
Multipole (�)
103
103
Figure 6.25: Using the same convention as Figure 6.23, the B-mode signal remains set to zero,
but now the polarization leakage from the feedhorn is turned on. The B-mode leakage (cyan) is
the same as in Figure 6.24, indicating that there is no leakage from the feedhorn into B-mode
polarization. Figure courtesy of Jeff McMahon.
157
Temperature to Polarization Leakage
Temperature to Polarization Leakage
10−1
10−2
�(� + 1)C�/2π(µK 2)
�(� + 1)C�/2π(µK 2)
10−1
10−3
10−4
10−5
10−6
10−2
BB(r=0.2)
BB(r=0)BB(r=0.2)
BB(r=0) Temperatur
Spline Profiled
Spline Profiled Tem
10−3
10−4
10−5
10−6
101
102
10 Multipole 10
(�)
1
2
Multipole (�)
103
103
Figure 6.26: Using the same convention as Figure 6.23, the B-mode signal remains set to zero,
the polarization leakage from the feedhorn remains turned on, and the E-mode signal is set to
zero. The green boxes indicate the E-mode leakage from the feedhorn, and the cyan boxes indicate
the B-mode leakage. As before, the B-mode leakage is completely from the MCMC realization
noise. This shows that the temperature to polarization leakage from the feedhorn goes solely into
E-modes, indicating that it is not an issue for B-mode or E-mode detection. Figure courtesy of Jeff
McMahon.
158
6.3
Feedhorn Measurements
Using the ambient-temperature vector network analyzer (VNA) setup at NIST in September 2015,
E-plane, H-plane, and cross-polarization beam measurements of the final 150/230 GHz feedhorn
array were taken with 0.5◦ resolution every 10 GHz across the upper and lower detector bands at
four positions across the array as shown in Figure 6.27. The NIST VNA beam mapper consists of a
transmitter, which sends a signal through the feedhorn being measured and a receiver mounted on
a rotating arm as shown in Figure 6.28. The receiver for the low band (130 GHz-180 GHz) setup
uses a conical feedhorn. The transmitter and receiver used for the low band measurements are
shown in Figure 6.29. Unlike the low band setup, the high band setup (200 GHz-270 GHz) uses a
diagonal feedhorn that has a square aperture that is rotated 45◦ with respect to a square waveguide
section for the receiver. The full high-frequency setup is shown in Figure 6.30. Because the high
frequency band is more sensitive to misalignments and its signal-to-noise is lower than the low
band, further measurements of the high band were taken at a single position (position 7) in January
2016 with the transmitter and receiver moved closer together, 1.6◦ resolution, and AN72 eccosorb
foam around the feedhorn array and the receiver to reduce reflections.
In addition to the full array, a few single pixel test feedhorns without the waveguide sections
were fabricated using the same profile of the 150/230 GHz horn but interpolated to a step size of
250 µm for quick fabrication while the 333 µm wafers used in the final fabrication were ordered.
These interpolated horns were measured both at NIST and the University of Michigan Ann Arbor.
However, only the measurement of the final array will be presented here.
Single pixel test horns for the 90/150 GHz feedhorns are currently being fabricated by NIST.
Unlike the 150/230 GHz test horns, these test horns include the full waveguide section for the
90/150 GHz horn and are fabricated on wafers of the same thickness as the final horns.
159
1
5
2
6
3
7
8
4
Figure 6.27: The positions of the holes in the feedhorn mounting plate (not shown) are mapped
onto the 150/230 GHz feedhorn array. Positions 1, 2, 7, and 8 were measured.
Transmitter
Receiver
Feed Array
Rotating Arm
Figure 6.28: The VNA setup (shown above) consists of a transmitter that sends the signal from the
VNA through the feedhorn array and a receiver on the end of a rotating arm.
160
Transmitter
Receiver
Figure 6.29: The VNA transmitter (top) and receiver (bottom) setups for the low band feedhorn
beam measurements.
Transmitter
Receiver
Figure 6.30: The VNA transmitter (left) and receiver (right) setups for the high band feedhorn
beam measurements. The high band setup uses a diagonal horn for the receiver.
6.3.1
Analysis
To compare the VNA beam measurements to the simulated beams, the beam’s measurements must
be translated in to physical degrees, centered around zero, and normalized. The degrees read out
by the VNA setup are not physical degrees and must be converted. To determine the conversion,
a protractor was used to measure the number of VNA degrees θV NA necessary for the setup to
reach 0◦ , 90◦ , and 180◦ . With this method, it was determined that the angle θ is given by θ =
(180/676)θV NA . The center of the beams is expected to be around θ = 90◦ for the beam before
centering. The center θcenter and peak of the beam are determined by fitting a parabola to the beam
161
between 70◦ and 110◦ and taking its maximum as the peak of the beam and the location of the
maximum as θcenter . This procedure is necessary because there are often dips in the peak of the
beam from reflections in the system when the transmitter and receiver are head on as exemplified
in Figure 6.31. Next, θ is shifted using θcenter so that the beam is centered at θ = 0◦ , and the
beam is normalized by the maximum value of the fit parabola. The cross-polarization beams are
shifted and normalized with the same values as the E-plane beams. In some cases, the shift of
the cross-polarization beam appears shifted with respect to the simulated curve because its offset
is significantly different from the E-plane shift. This is particularly true in cases where the arm
motor is disengaged and the zero has to be reset between the E-plane and cross-polarization beam
measurements.
Figure 6.31: Measurements of the H-plane beams at 200 GHz at each feedhorn position are shown
above truncated at the Lyot stop. The dip in the center of the beam is a result of reflections in the
VNA system when the receiver and transmitter are aligned. Because of this effect, the inner 40◦
around the peak must be fit to a parabola to correctly determine the location and amplitude of the
beam’s location for normalization.
162
Appendix A shows the full set of beam measurements with the simulated beams. The simulated
beams are the smooth curves and have a width determined by the difference between the beam
with and without the DRIE taper. The beams are represented in three ways: (1) E-plane, H-plane,
and cross-polarization beams plotted separately at each frequency for all positions (A.1), (2) Eplane, H-plane, and cross-polarization beams plotted separately at each frequency for all positions
between ±21◦ to represent the beam within the 20.4◦ radius of the Lyot stop (A.2), and (3) Eplane, H-plane, and cross-polarization beams plotted together at each frequency and separately
at each position (A.3). Additionally, measurements of the high frequency band were repeated at a
single position (position 7) with the transmitter and receiver moved closer together, 1.6◦ resolution,
and AN72 eccosorb foam around the feedhorn array and the receiver to reduce reflections. These
measurements are also presented in Appendix A.4 plotted separately for the E-plane, H-plane, and
cross-polarization beams at each frequency for all the measurements at position 7.
The beam measurements are in good agreement with the simulations as shown by Figures 6.32
and 6.33. The measurements are also consistent among positions on the array as shown by Figures 6.34 and 6.35, indicating that the feedhorn array is uniform. The repeated measurements at
position 7 are also consistent with the original measurements. In general, the measured crosspolarization beams do not exhibit the deep null on-axis that is seen in the simulations as a result
of reflections and misalignments in the NIST VNA system. There is a narrow bandwidth feature
in the E-plane at 270 GHz as can be seen in Figure 6.36. This feature appears in all four measured
positions on the array and in all three measurements taken at position 7. However, it is very narrow:
measurements at 269 GHz and 271 GHz do not show the same distortion (Figure 6.37), indicating
that it will only make a small contribution to the average beam.
163
Figure 6.32: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz are shown above for position 1 with their theoretical simulations from HFSS.
The simulations are the smooth curves. The thickness of the theoretical simulations indicates the
difference between simulations with and without a 2◦ DRIE taper. The measurements are in good
agreement with the simulations.
Figure 6.33: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz are shown above for position 7 with their theoretical simulations. Even though
the VNA system is more susceptible to systematic effects at higher frequencies, the measurements
are still in good agreement with the simulations.
164
Figure 6.34: Measurements of H-plane beams at 150 GHz at each of the four feedhorn positions
are shown above. The measurements between horns show that the feedhorns are highly uniform
across the array.
Figure 6.35: Measurements of H-plane beams at 220 GHz at each of the four feedhorn positions
are shown above. The measurements across the array are consistent with each other.
165
Figure 6.36: Left Panel: Measurements of E-plane beams at 270 GHz at each feedhorn position
are shown. The main beam at 270 GHz is distorted at all positions, but this feature has a narrow
bandwidth (see text and Figure 6.37) and thus a small effect on the average beam. The peak in
the cyan curve at ∼ 20◦ is an artifact due to a motor glitch in the rotating arm. Right Panel: The
original measurement of the E-plane beam at position 7 (blue) at 270 GHz is compared with its
simulation (black) and repeated measurements (green and red). The main beam distortion appears
in all the measurements, indicating that this is likely a feature in the response and not a systematic
effect of the measurement.
Figure 6.37: Measurements of the E-plane beams (green) at 269 GHz (left) and 271 GHz (right)
with their simulations (black) are shown. These frequencies do not exhibit the same distortion in
the main lobe as the measurements at 270 GHz, indicating that the feature at 270 GHz has a narrow
bandwidth.
166
6.3.2
Sources of Uncertainty in the Measurements
The VNA setup at NIST has several systematic effects and sources of uncertainty. In general, the
high frequency beams are more sensitive to reflections and misalignments. As mentioned in the
previous section, there is often a dip in the center of the beam because of reflections in the system
when the transmitter and receiver are head on. There are also smooth dips/peaks in some features
of the beam as a result of motor glitches in which the scanning arm motor would swing ∼ −60◦
and then return to the correct position in the middle of a scan. An example of this is shown in the
H-plane scan in Figure 6.38. In the VNA setup, the table with the transmitter and the receiver was
not level, which caused some misalignment. This effect was minimized by leveling the system at
θ = 90◦ by using shims and a level. After the leveling, a coarse alignment was performed by using
a laser coupled to the receiver to align the feedhorn with the receiver. The alignment was refined by
running a few scans and minimizing the variation in the phase in the main beam. A Teflon washer
that sits underneath the arm at the pivot point (Figure 6.39) was worn down on one side more than
the other and caused an uneven tilt in the system, which could be fixed in future measurements by
replacing the washer. Additionally, the scanning arm motor does not have sufficient torque for the
system, so the scanning arm would oscillate about each measurement position instead of coming to
a stop. This oscillation was minimized by turning the motor and reducing its speed, but the effect
could not be fully eliminated. The mounting plate that couples the feedhorn array to the waveguide
in the transmitter was machined, so it has much larger tolerances than the feedhorn array. Any slop
between the feedhorn and the mounting plate would cause additional misalignment in the system
that could be dependent on array position or be systematically the same for all of the feedhorns
measured. Finally, at different positions and when measuring the E-plane, H-plane, and crosspolarization beams, the feedhorn array itself changes position. The feedhorn array is gold-coated
and reflective, so this could cause different reflections between measurements. Measurements at
NIST of the interpolated single pixel horn exhibited less beam asymmetry about zero, which could
be a result of it not having a large reflective surface like the feedhorn array and/or not having a
mounting plate. Thus, reflection off the feedhorn array and/or the mounting plate are likely to be
167
significant effects.
Figure 6.38: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz are shown for Position 8. The smooth dip in the H-plane at ∼-30◦ is an artifact
of a motor glitch.
Teflon Washer
Figure 6.39: The location of the Teflon washer that the VNA beam mapper arm rests on is indicated
in the image above. This washer is unevenly worn, which results in an uneven tilt in the VNA
system.
168
6.3.3
Impact on AdvACT Performance
To compare the measured and simulated beams of the 150/230 GHz array, the full width at half
maximum (FHWM) and beam coupling efficiency as a function of frequency are calculated. First,
the measured beams are averaged about θ = 0◦ . Reflections in the VNA system are maximized
when the receiver and transmitter are head-on, which can result in artifacts in the main lobes of the
beams. To account for this in calculations, the beam within the Lyot stop BLyot (θ ) is modeled by a
Gaussian summed with an exponential:
BLyot (θ ) = Ae
θ2
2c2
+ De| f |θ ,
(6.15)
where A, c, D, and f are all fit parameters. The FWHMs of the E-plane and H-plane beams as a
function of frequency are shown in Figure 6.40. On average, the beam widths of the measurements
are narrower than the simulations in the low band and wider than simulations in the high band.
To calculate the beam coupling efficiency, the measured beams are extrapolated from θ = 80◦ to
θ = 180◦ by fitting an exponential decay to the last 15◦ of the beam measurements. The beam
coupling efficiencies of the E-planes and H-planes as a function of frequency are shown in Figure 6.41. The average measured beam coupling efficiency is in agreement with the simulations
at each frequency as can be seen in Figure 6.42. Small variations as a function of frequency are
ascribed to measurement error. The band-averaged beam coupling efficiency of the low band (130180 GHz) is 68% for the measured beams and 66% for the simulated beams. For the high band
(200-270 GHz), the band-averaged beam coupling efficiency is 75% for both the measured and
simulated beams.
169
FWHM (deg)
Difference (deg)
34
32
30
28
26
24
22
20
18
16
Measured E-plane FWHM
Simulated E-plane FWHM
Measured H-plane FWHM
Simulated H-plane FWHM
8
4
0
4
120 140 160 180 200 220 240 260 280
Frequency (GHz)
Figure 6.40: The FWHM as a function of frequency for the E-plane and H-plane beams is shown
above. The top panel shows the FWHMs of the E-plane (lime) and H-plane (cyan) simulations
plotted with the measured FWHMs of the E-plane (green) and H-plane (blue). A light line is plotted
between the simulations, which were performed every 10 GHz to match the measurements. The
error bars on the simulations represent the variation between models with and without the DRIE
taper. The error bars on the measured FWHMs represent the variance between measurements made
at the four different array positions. The bottom panel shows the difference in FWHM between the
measured and simulated beams for the E-plane (green) and H-plane (blue) beams. On average, the
measured beams are narrower than the simulations in the low band and wider than the simulations
in the high band. Note that the different bands have different VNA setups.
170
Efficiency
Difference
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
Measured E-plane Efficiency
Simulated E-plane Efficiency
Measured H-plane Efficiency
Simulated H-plane Efficiency
0.10
0.05
0.00
0.05
120
140
160
180
200
220
Frequency (GHz)
240
260
280
Figure 6.41: The beam coupling efficiency as a function of frequency for the E-plane and H-plane
beams is shown above. The top panel shows the efficiencies of the E-plane (lime) and H-plane
(cyan) simulations plotted with the measured efficiencies of the E-plane (green) and H-plane (blue).
A light line is plotted between the simulations, which were performed every 10 GHz to match the
measurements. The error bars on the simulations represent the variation between models with and
without the DRIE taper. The error bars on the measured FWHMs represent the variance between
measurements made at the four different array positions. The bottom panel shows the difference in
beam coupling efficiency between the measured and simulated beams for the E-plane (green) and
H-plane (blue) beams. Most of the beam coupling efficiency measurements are within 5% of the
simulations.
171
Beam Coupling Efficiency
0.85
0.80
0.75
0.70
0.65
0.60
0.55
Measured Average Efficiency
Simulated Average Efficiency
0.50120 140 160 180 200 220 240 260 280
Frequency (GHz)
Figure 6.42: The average beam coupling efficiencies of the measured (green) and simulated (black
with grey line) 150/230 GHz feedhorns are shown above as a function of frequency. The simulations and measurements were both performed every 10 GHz. The error bars on the simulations
represent the variation between simulations with and without the DRIE taper, and the error bars
on the measurements only represent the variance amongst the measurements of the feedhorns at
the four positions on the array and do not include systematic contributions. All the efficiencies
are consistent within 3.5% except for the value at 140 GHz where the simulated beam coupling
efficiency is varying rapidly.
172
Chapter 7
Future Work
ABS completed observations in October 2014 and its components were shipped back to Princeton
in January 2016. The responsivity decay observed in half of the array is still under investigation,
and a visual inspection of the pixels is forthcoming. The first two seasons of primary field data
have been analyzed, and the third season of primary field observations is currently being analyzed.
In its third season of observation, ABS upgraded the motor system to enable ∼14◦ -20◦ scans as
opposed to the ∼7◦ scans used in the first two seasons. The third season analysis will use the 2 fm
responsivity model, will correct for the angle shift caused by the time constants, and will use many
of the same data selection criteria as the first two seasons of data, including the 2 fm data selection.
While the ABS instrument is not as sensitive to large-angular scale B-modes as the BICEP2/Keck Array experiments [125], it observes a different patch of the sky, which will be
important for comparisons of foreground modeling. The ABS instrument was an important
pathfinder experiment for fully cryogenic optics, the TRUCE pixels, and continuously-rotating
HWP technologies and analysis techniques. The compact crossed-Dragone design used by ABS
allows for completely cryogenic optics with no need for lenses and a large focal plane area. This
design is now being considered for future CMB polarization experiments such as the proposed
LiteBIRD satellite and the proposed Greenland LEKID Polarimeter (GLP) [116, 126]. Pixels
similar to those used in ABS have also been fielded in SPTpol and ACTPol, and upgraded
173
multichroic pixels building off of the same technologies have been fielded in ACTPol and AdvACT [65, 114]. ABS has demonstrated the advantages of using a continuously-rotating HWP
for ground-based CMB polarization searches. The HWP mitigates 1/ f noise from atmospheric
and instrumental fluctuations, controls systematic effects, and eliminates the need for differencing
orthogonal pairs of detectors to gain polarization sensitivity. In addition to these advantages,
the HWP can also be used in several novel techniques to measure the detector time constants,
the detector responsivity, and for data selection. Ground-based experiments including ACTPol,
AdvACT, the GLP, POLARBEAR-2, and its upgrade the Simons Array as well as the EBEX
balloon and LiteBIRD satellite are now employing or planning to use continuously-rotating
HWPs [114, 126, 115, 113, 116]. The HWP time constant measurements, the angle correction
from the time constant, the 2 fm responsivity, and the 2 fm data selection developed for ABS will
all be employed in the ACTPol and AdvACT data analysis. Additionally, since the detectors no
longer need to be pair-differenced, the HWP has allowed for a slight relaxation of constraints
on beam symmetry, which is consistent with the transition from corrugated to spline-profiled
feedhorns on AdvACT.
The spline-profiled feedhorns developed for AdvACT are compact and have been shown to
have good performance in both beam symmetry and efficiency. The 150/230 GHz feedhorn array
has been fabricated, measured, and integrated with the detector array. The 150/230 GHz AdvACT
array was deployed in June 2016. NIST has fabricated single pixel test horns for the 90/150 GHz
feedhorns, and initial measurements of these horns show that they are in good agreement with
the simulations. Fabrication of the full 90/150 GHz feedhorn arrays is currently underway. The
28/41 GHz feedhorn design is still in development at the University of Michigan Ann Arbor, but
several viable candidates have been designed using the methods discussed in Chapter 6. AdvACT
will be one of the most sensitive ground-based CMB polarization experiments, and it will observe
large patches of the sky from its mid-latitude position. The use of a HWP would enable it to
measure or limit primordial B-modes on large angular scales, and its resolution will enable lensing
and galaxy cluster studies that will further our understanding of the fundamental physics of the
174
universe.
175
Appendix A
150/230 GHz Feedhorn Measurements
A.1
Beams at All Positions
Measurements of the E-plane, H-plane, and cross-polarization beams at each frequency are shown
below for feedhorn positions 1, 2, 7, and 8 with their simulations from HFSS in black. The simulations have a width that indicates the difference between simulations with and without a 2◦ DRIE
taper.
176
A.1.1
E-plane Beams
Figure A.1: Measurements of E-plane beams at 130 GHz at each feedhorn position.
Figure A.2: Measurements of E-plane beams at 140 GHz at each feedhorn position.
177
Figure A.3: Measurements of E-plane beams at 150 GHz at each feedhorn position.
Figure A.4: Measurements of E-plane beams at 160 GHz at each feedhorn position.
178
Figure A.5: Measurements of E-plane beams at 170 GHz at each feedhorn position.
Figure A.6: Measurements of E-plane beams at 180 GHz at each feedhorn position.
179
Figure A.7: Measurements of E-plane beams at 200 GHz at each feedhorn position.
Figure A.8: Measurements of E-plane beams at 210 GHz at each feedhorn position.
180
Figure A.9: Measurements of E-plane beams at 220 GHz at each feedhorn position.
Figure A.10: Measurements of E-plane beams at 230 GHz at each feedhorn position.
181
Figure A.11: Measurements of E-plane beams at 240 GHz at each feedhorn position.
Figure A.12: Measurements of E-plane beams at 250 GHz at each feedhorn position.
182
Figure A.13: Measurements of E-plane beams at 260 GHz at each feedhorn position.
Figure A.14: Measurements of E-plane beams at 270 GHz at each feedhorn position.
183
A.1.2
H-plane Beams
Figure A.15: Measurements of H-plane beams at 130 GHz at each feedhorn position are shown.
Figure A.16: Measurements of H-plane beams at 140 GHz at each feedhorn position are shown.
184
Figure A.17: Measurements of H-plane beams at 150 GHz at each feedhorn position are shown.
Figure A.18: Measurements of H-plane beams at 160 GHz at each feedhorn position are shown.
185
Figure A.19: Measurements of H-plane beams at 170 GHz at each feedhorn position.
Figure A.20: Measurements of H-plane beams at 180 GHz at each feedhorn position.
186
Figure A.21: Measurements of H-plane beams at 200 GHz at each feedhorn position.
Figure A.22: Measurements of H-plane beams at 210 GHz at each feedhorn position.
187
Figure A.23: Measurements of H-plane beams at 220 GHz at each feedhorn position.
Figure A.24: Measurements of H-plane beams at 230 GHz at each feedhorn position.
188
Figure A.25: Measurements of H-plane beams at 240 GHz at each feedhorn position.
Figure A.26: Measurements of H-plane beams at 250 GHz at each feedhorn position.
189
Figure A.27: Measurements of H-plane beams at 260 GHz at each feedhorn position.
Figure A.28: Measurements of H-plane beams at 270 GHz at each feedhorn position.
190
A.1.3
Cross-Polarization Beams
Figure A.29: Measurements of cross-polarization beams at 130 GHz at each feedhorn position.
Figure A.30: Measurements of cross-polarization beams at 140 GHz at each feedhorn position.
191
Figure A.31: Measurements of cross-polarization beams at 150 GHz at each feedhorn position.
Figure A.32: Measurements of cross-polarization beams at 160 GHz at each feedhorn position.
192
Figure A.33: Measurements of cross-polarization beams at 170 GHz at each feedhorn position.
Figure A.34: Measurements of cross-polarization beams at 180 GHz at each feedhorn position.
193
Figure A.35: Measurements of cross-polarization beams at 200 GHz at each feedhorn position.
Figure A.36: Measurements of cross-polarization beams at 210 GHz at each feedhorn position.
194
Figure A.37: Measurements of cross-polarization beams at 220 GHz at each feedhorn position.
Figure A.38: Measurements of cross-polarization beams at 230 GHz at each feedhorn position.
195
Figure A.39: Measurements of cross-polarization beams at 240 GHz at each feedhorn position.
Figure A.40: Measurements of cross-polarization beams at 250 GHz at each feedhorn position.
196
Figure A.41: Measurements of cross-polarization beams at 260 GHz at each feedhorn position.
Figure A.42: Measurements of cross-polarization beams at 270 GHz at each feedhorn position.
197
A.2
Beams Truncated at Lyot Stop at All Positions
Measurements of the E-plane, H-plane, and cross-polarization beams at each frequency are shown
below for feedhorn positions 1, 2, 7, and 8 with their simulations in black. The plots are truncates
at ±21◦ to represent the part of the beam within the 20.4◦ Lyot stop. The simulations have a width
that indicates the difference between simulations with and without a 2◦ DRIE taper.
A.2.1
E-plane Beams
Figure A.43: Measurements of E-plane beams at 130 GHz at each feedhorn position truncated at
the Lyot stop.
198
Figure A.44: Measurements of E-plane beams at 140 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.45: Measurements of E-plane beams at 150 GHz at each feedhorn position truncated at
the Lyot stop.
199
Figure A.46: Measurements of E-plane beams at 160 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.47: Measurements of E-plane beams at 170 GHz at each feedhorn position truncated at
the Lyot stop.
200
Figure A.48: Measurements of E-plane beams at 180 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.49: Measurements of E-plane beams at 200 GHz at each feedhorn position truncated at
the Lyot stop.
201
Figure A.50: Measurements of E-plane beams at 210 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.51: Measurements of E-plane beams at 220 GHz at each feedhorn position truncated at
the Lyot stop.
202
Figure A.52: Measurements of E-plane beams at 230 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.53: Measurements of E-plane beams at 240 GHz at each feedhorn position truncated at
the Lyot stop.
203
Figure A.54: Measurements of E-plane beams at 250 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.55: Measurements of E-plane beams at 260 GHz at each feedhorn position truncated at
the Lyot stop.
204
Figure A.56: Measurements of E-plane beams at 270 GHz at each feedhorn position truncated at
the Lyot stop.
205
A.2.2
H-plane Beams
Figure A.57: Measurements of H-plane beams at 130 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.58: Measurements of H-plane beams at 140 GHz at each feedhorn position truncated at
the Lyot stop.
206
Figure A.59: Measurements of H-plane beams at 150 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.60: Measurements of H-plane beams at 160 GHz at each feedhorn position truncated at
the Lyot stop.
207
Figure A.61: Measurements of H-plane beams at 170 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.62: Measurements of H-plane beams at 180 GHz at each feedhorn position truncated at
the Lyot stop.
208
Figure A.63: Measurements of H-plane beams at 200 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.64: Measurements of H-plane beams at 210 GHz at each feedhorn position truncated at
the Lyot stop.
209
Figure A.65: Measurements of H-plane beams at 220 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.66: Measurements of H-plane beams at 230 GHz at each feedhorn position truncated at
the Lyot stop.
210
Figure A.67: Measurements of H-plane beams at 240 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.68: Measurements of H-plane beams at 250 GHz at each feedhorn position truncated at
the Lyot stop.
211
Figure A.69: Measurements of H-plane beams at 260 GHz at each feedhorn position truncated at
the Lyot stop.
Figure A.70: Measurements of H-plane beams at 270 GHz at each feedhorn position truncated at
the Lyot stop.
212
A.2.3
Cross-Polarization Beams
Figure A.71: Measurements of cross-polarization beams at 130 GHz at each feedhorn position
truncated at the Lyot stop.
Figure A.72: Measurements of cross-polarization beams at 140 GHz at each feedhorn position
truncated at the Lyot stop.
213
Figure A.73: Measurements of cross-polarization beams at 150 GHz at each feedhorn position
truncated at the Lyot stop.
Figure A.74: Measurements of cross-polarization beams at 160 GHz at each feedhorn position
truncated at the Lyot stop.
214
Figure A.75: Measurements of cross-polarization beams at 170 GHz at each feedhorn position
truncated at the Lyot stop.
Figure A.76: Measurements of cross-polarization beams at 180 GHz at each feedhorn position
truncated at the Lyot stop.
215
Figure A.77: Measurements of cross-polarization beams at 200 GHz at each feedhorn position
truncated at the Lyot stop.
Figure A.78: Measurements of cross-polarization beams at 210 GHz at each feedhorn position
truncated at the Lyot stop.
216
Figure A.79: Measurements of cross-polarization beams at 220 GHz at each feedhorn position
truncated at the Lyot stop.
Figure A.80: Measurements of cross-polarization beams at 230 GHz at each feedhorn position
truncated at the Lyot stop.
217
Figure A.81: Measurements of cross-polarization beams at 240 GHz at each feedhorn position
truncated at the Lyot stop.
Figure A.82: Measurements of cross-polarization beams at 250 GHz at each feedhorn position
truncated at the Lyot stop.
218
Figure A.83: Measurements of cross-polarization beams at 260 GHz at each feedhorn position
truncated at the Lyot stop.
Figure A.84: Measurements of cross-polarization beams at 270 GHz at each feedhorn position
truncated at the Lyot stop.
219
A.3
Beams Plotted Together at Each Position
Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red) beams at each
frequency are shown below for each position with their simulations in the same colors. The simulations are the smooth curves and have a width that indicates the difference between simulations
with and without a 2◦ DRIE taper.
A.3.1
Position 1
Figure A.85: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 130 GHz for Position 1.
220
Figure A.86: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 140 GHz for Position 1.
Figure A.87: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz for Position 1.
221
Figure A.88: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 160 GHz for Position 1.
Figure A.89: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 170 GHz for Position 1.
222
Figure A.90: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 180 GHz for Position 1.
Figure A.91: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 200 GHz for Position 1.
223
Figure A.92: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 210 GHz for Position 1.
Figure A.93: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz for Position 1.
224
Figure A.94: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz for Position 1.
Figure A.95: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 240 GHz for Position 1.
225
Figure A.96: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 250 GHz for Position 1.
Figure A.97: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 260 GHz for Position 1.
226
Figure A.98: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 270 GHz for Position 1.
227
A.3.2
Position 2
Figure A.99: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 130 GHz for Position 2.
Figure A.100: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 140 GHz for Position 2.
228
Figure A.101: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz for Position 2.
Figure A.102: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 160 GHz for Position 2.
229
Figure A.103: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 170 GHz for Position 2.
Figure A.104: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 180 GHz for Position 2.
230
Figure A.105: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 200 GHz for Position 2.
Figure A.106: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 210 GHz for Position 2.
231
Figure A.107: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz for Position 2. The dip in the E-plane at ∼-20◦ is a motor glitch.
Figure A.108: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz for Position 2.
232
Figure A.109: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 240 GHz for Position 2.
Figure A.110: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 250 GHz for Position 2.
233
Figure A.111: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 260 GHz for Position 2.
Figure A.112: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 270 GHz for Position 2.
234
A.3.3
Position 7
Figure A.113: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 130 GHz for Position 7.
Figure A.114: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 140 GHz for Position 7.
235
Figure A.115: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz for Position 7.
Figure A.116: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 160 GHz for Position 7.
236
Figure A.117: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 170 GHz for Position 7.
Figure A.118: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 180 GHz for Position 7.
237
Figure A.119: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 200 GHz for Position 7.
Figure A.120: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 210 GHz for Position 7.
238
Figure A.121: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz for Position 7.
Figure A.122: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz for Position 7.
239
Figure A.123: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 240 GHz for Position 7.
Figure A.124: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 250 GHz for Position 7.
240
Figure A.125: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 260 GHz for Position 7.
Figure A.126: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 270 GHz for Position 7.
241
A.3.4
Position 8
Figure A.127: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 130 GHz for Position 8.
Figure A.128: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 140 GHz for Position 8.
242
Figure A.129: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 150 GHz for Position 8.
Figure A.130: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 160 GHz for Position 8.
243
Figure A.131: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 170 GHz for Position 8.
Figure A.132: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 180 GHz for Position 8.
244
Figure A.133: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 200 GHz for Position 8.
Figure A.134: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 210 GHz for Position 8.
245
Figure A.135: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 220 GHz for Position 8.
Figure A.136: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 230 GHz are shown for Position 8. The dip in the H-plane at ∼-30◦ is a motor glitch.
246
Figure A.137: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 240 GHz for Position 8.
Figure A.138: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 250 GHz for Position 8.
247
Figure A.139: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 260 GHz for Position 8.
Figure A.140: Measurements of the H-plane (blue), E-plane (green), and cross-polarization (red)
beams at 270 GHz for Position 8. The peak in the E-plane at ∼20◦ is a motor glitch.
248
A.4
Repeated Measurements at Position 7
Measurements of the high frequency band (200-270 GHz) were repeated at a single position (position 7) with the transmitter and receiver moved closer together, 1.6◦ resolution, and AN72 eccosorb
foam around the feedhorn array and the receiver to reduce reflections. These measured E-plane,
H-plane, and cross-polarization beams at each frequency are shown below with their simulations
in black. The simulations have a width that indicates the difference between simulations with and
without a 2◦ DRIE taper. The original measurements are in blue and labeled as s0. Subsequent
scans are labeled from s1-s5.
A.4.1
E-plane Beams
Figure A.141: The original measurement of the E-plane beam at position 7 at 200 GHz is shown
with its simulation and repeated measurement above.
249
Figure A.142: The original measurement of the E-plane beam at position 7 at 210 GHz is shown
with its simulation and repeated measurements above.
Figure A.143: The original measurement of the E-plane beam at position 7 at 220 GHz is shown
with its simulation and repeated measurements above.
250
Figure A.144: The original measurement of the E-plane beam at position 7 at 230 GHz is shown
with its simulation and repeated measurements above.
Figure A.145: The original measurement of the E-plane beam at position 7 at 240 GHz is shown
with its simulation and repeated measurements above.
251
Figure A.146: The original measurement of the E-plane beam at position 7 at 250 GHz is shown
with its simulation and repeated measurements above.
Figure A.147: The original measurement of the E-plane beam at position 7 at 260 GHz is shown
with its simulation and repeated measurements above.
252
Figure A.148: The original measurement of the E-plane beam at position 7 at 270 GHz is shown
with its simulation and repeated measurements above.
253
A.4.2
H-plane Beams
Figure A.149: The original measurement of the H-plane beam at position 7 at 200 GHz is shown
with its simulation and repeated measurement above.
Figure A.150: The original measurement of the H-plane beam at position 7 at 210 GHz is shown
with its simulation and repeated measurement above.
254
Figure A.151: The original measurement of the H-plane beam at position 7 at 220 GHz is shown
with its simulation and repeated measurement above.
Figure A.152: The original measurement of the H-plane beam at position 7 at 230 GHz is shown
with its simulation and repeated measurement above.
255
Figure A.153: The original measurement of the H-plane beam at position 7 at 240 GHz is shown
with its simulation and repeated measurement above.
Figure A.154: The original measurement of the H-plane beam at position 7 at 250 GHz is shown
with its simulation and repeated measurement above.
256
Figure A.155: The original measurement of the H-plane beam at position 7 at 260 GHz is shown
with its simulation and repeated measurement above.
Figure A.156: The original measurement of the H-plane beam at position 7 at 270 GHz is shown
with its simulation and repeated measurement above.
257
A.4.3
Cross-Polarization Beams
Figure A.157: The original measurement of the cross-polarization beam at position 7 at 200 GHz
is shown with its simulation and repeated measurement above.
Figure A.158: The original measurement of the cross-polarization beam at position 7 at 210 GHz
is shown with its simulation and repeated measurement above.
258
Figure A.159: The original measurement of the cross-polarization beam at position 7 at 220 GHz
is shown with its simulation and repeated measurement above.
Figure A.160: The original measurement of the cross-polarization beam at position 7 at 230 GHz
is shown with its simulation and repeated measurement above.
259
Figure A.161: The original measurement of the cross-polarization beam at position 7 at 240 GHz
is shown with its simulation and repeated measurement above.
Figure A.162: The original measurement of the cross-polarization beam at position 7 at 250 GHz
is shown with its simulation and repeated measurement above.
260
Figure A.163: The original measurement of the cross-polarization beam at position 7 at 260 GHz
is shown with its simulation and repeated measurement above.
Figure A.164: The original measurement of the cross-polarization beam at position 7 at 270 GHz
is shown with its simulation and repeated measurement above.
261
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