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The White Mountain Polarimeter: A telescope to measure polarization of the cosmic microwave background

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UNIVERSITY of CALIFORNIA
Santa Barbara
The White Mountain Polarimeter:
A Telescope to Measure Polarization of
the Cosmic Microwave Background
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Physics
by
Alan Robert Levy
Committee in charge:
Professor Philip Lubin, Chair
Professor Mark Sherwin
Professor Andrew Cleland
March 2006
UMI Number: 3206398
UMI Microform 3206398
Copyright 2006 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, MI 48106-1346
The dissertation of Alan Robert Levy is approved:
Professor Mark Sherwin
Professor Andrew Cleland
Professor Philip Lubin, Chair
January 2006
The White Mountain Polarimeter:
A Telescope to Measure Polarization of
the Cosmic Microwave Background
Copyright 2006
by
Alan Robert Levy
iii
To my wife Lisa,
who has stood by my side “through thick and thin...”
and there has been a lot of “thin.”
iv
Acknowledgements
There are many people without whom this work would not have been possible.
Foremost, I would like to thank Professor Philip Lubin, for the opportunity be a
member of the group and for being my research advisor and Dr. Peter Meinhold
for being a constant, reassuring, and helpful presence in the lab. Everything I
have learned about observational cosmology I owe to Phil and Peter. Larry Wade
has been a great mentor and friend and I thank him for the opportunity to learn
about cryocoolers and cryogenics at JPL.
Many people who have worked in the group, graduate students, undergraduates, and staff, made contributions both large and small towards making the
WMPol instrument a reality and have helped make the lab a fun and interesting place to work. In particular, I would like to acknowledge Markus Ansmann,
Doron Halevi, Josh Marvil, Gerald Miller, Hugh O’Neill, Nate Stebor, Maarten
van der Heide, and Brian Williams for uncounted hours of effort. I could not have
done it without you! I would also like to thank Jeff Childers for many helpful
conversations and contributions over the years as we have gone through graduate
school together. Rodrigo Leonardi, who has done the heavy lifting on the data
analysis, has been a good friend and a real pleasure to work with during the past
two years.
The support of the University of California White Mountain Research Station
was critical to the success of this project and I would like to acknowledge the dedicated WMRS staff. I would also like to thank our collaborators at the University
of Wisconsin, Madison, led by Peter Timbie, collaborators in Italy led by Marco
Bersanelli, and collaborators in Brazil, Thyrso Villela and Alex Wuensche. The
superb UCSB Machine Shop was instrumental in the success of this project.
I thank my family and friends, especially my wife, Lisa, my parents, Merle and
Dennis, my sister Helen and brother-in-law David, Uncle Bob and Aunt Lorraine
plus my parents-in-law, Kate and Bob, and Jacquie, Chris, and R.B. for all the
support I received during this very long process and, particularly, for not asking
too often when I would finally be finished!
Finally, I would like to share my appreciation for Dr. Margaret Ray, Dr. Julie
Taguchi, the doctors, nurses, and staff on 6-central and throughout Santa Barbara
Cottage Hospital, at Sansum Santa Barbara Medical Foundation Clinic, and the
Cancer Center of Santa Barbara without whom I would quite literally not be alive.
v
Curriculum Vitæ
Alan Robert Levy
Education
2006
Doctor of Philosophy, Physics, University of California, Santa
Barbara (expected)
1992
Bachelor of Science, Physics, University of California, Santa
Barbara
Publications
Marvil, J., Ansmann, M., Childers, J., Cole, T., Davis, G. V., Hadjiyska, E.,
Halevi, D., Heimberg, G., Kangas, M., Levy, A., Leonardi, R., Lubin, P., Meinhold, P., O’Neill, H., Parendo, S., Quetin, E., Stebor, N., Villela, T., Williams, B.,
Wuensche, C. A., and Yamaguchi, K., “An Astronomical Site Survey at the Barcroft Facility of the White Mountain Research Station,” New Astronomy (2006),
11:218-225
Childers, J., Bersanelli, M., Figueiredo, N., Gaier, T. C., Halevi, D., Kangas,
M., Levy, A., Lubin, P. M., Malaspina, M., Mandolesi, N., Marvil, J., Meinhold,
P. R., Mejia, J., Natoli, P., O’Neill, H., Parendo, S., Seiffert, M. D., Stebor, N.
C., Villa, F., Villela, T., Williams, B., and Wuensche, C. A., “The Background
Emission Anisotropy Scanning Telescope (BEAST) Instrument Description and
Performances,” The Astrophysical Journal (2005), 158:124-138
Meinhold, P. R., Bersanelli, Childers, J., M., Figueiredo, N., Gaier, T. C., Halevi,
D., Huey, G. G., Kangas, M., Lawrence, C. R., Levy, A., Lubin, P. M., Malaspina,
M., Mandolesi, N., Marvil, J., Mejia, J., Natoli, P., O’Dwyer, I., O’Neill, H.,
Parendo, S., Pina, A., Seiffert, M. D., Stebor, N. C., Tello, C., Villa, F., Villela,
T., Wade, L. A., Wandelt, B. D., Williams, B., and Wuensche, C. A., “A Map
of the Cosmic Microwave Background from the BEAST Experiment,” The Astrophysical Journal (2005), 158:101-108.
Farese, P. C., Dall’Oglio, G., Gundersen, J. O., Keating, B. G., Klawikowski,
S., Knox, L., Levy, A., Lubin, P. M., O’Dell, C. W., Peel, A., Piccirillo, L.,
Ruhl, J., and Timbie, P., “COMPASS: An Upper Limit on Cosmic Microwave
vi
Background Polarization at an Angular Scale of 200 ,” The Astrophysical Journal
(2004), 610:625-634.
Staren, J., Meinhold, P., Childers, J., Lim, M., Levy, A., Lubin, P., Seiffert, M.,
Gaier, T., Figueiredo, N., Villela, T., Wuensche, C. A., Tegmark, M., and de
Oliveira-Costa, A., “A Spin-Modulated Telescope to Make Two-Dimensional Cosmic Microwave Background Maps,” The Astrophysical Journal (2000), 539:52-56
Levy, A. R. and Wade, L. A., “Characterization of Porous Metal Flow Restrictors
for Use as the J-T Expander in Hydrogen Sorption Cryocoolers,” Cryocoolers 10,
Kluwer Academic/Plenum Publishers, New York (1999), 545-552.
Wade, L. A. and Levy, A. R., “Preliminary Test Results for a 25 K Sorption Cryocooler Designed for the UCSB Long Duration Balloon Cosmic Microwave Background Radiation Experiment,” Cryocoolers 9, Plenum Press, New York (1997),
587-596.
Wade, L. A., Levy, A. R., and Bard, S., “Continuous and Periodic Sorption Cryocoolers for 10 K and Below,” Cryocoolers 9, Plenum Press, New York (1997),
577-586.
Honors and Awards
2005
2002-2004
2001
1992
UCSB University Service Award
White Mountain Research Station Graduate Student Research Fellowship
UCSB California Space Grant Consortium Graduate Research Fellowship
David Saxon Award, Physics Department, University of California, Santa Barbara, California
vii
Abstract
The White Mountain Polarimeter:
A Telescope to Measure Polarization of
the Cosmic Microwave Background
by
Alan Robert Levy
The past two decades have been an exciting time in the field of cosmology and,
in particular, studies of the Cosmic Microwave Background (CMB). One of the
hot topics in cosmology research today is measuring and mapping CMB polarization. The White Mountain Polarimeter (WMPol) is a dedicated, ground-based
microwave telescope and receiver system to measure CMB polarization which was
installed in the Barcroft Observatory of the University of California White Mountain Research Station in September 2003. Presented here is a brief review of our
current understanding of big bang cosmology and a description of the WMPol
instrument, the observing conditions at the 3880-meter altitude Barcroft site, the
data acquired during the 2004 observing campaign, and the data analysis.
viii
Contents
Contents
ix
List of Figures
xi
List of Tables
xiv
1 Introduction
1.1 The Cosmic Microwave Background
1.2 CMB Polarization . . . . . . . . . .
1.3 Foregrounds . . . . . . . . . . . . .
1.4 The White Mountain Polarimeter .
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1
5
11
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2 The WMPol Instrument
2.1 Telescope . . . . . . . . . . . . . . . . . . . .
2.1.1 Optical Design . . . . . . . . . . . . .
2.1.2 Mechanical Design and Motion Control
2.1.3 Measurement of Position . . . . . . . .
2.1.4 Control Code and Housekeeping . . . .
2.1.5 Power and Noise Suppression . . . . .
2.1.6 Performance . . . . . . . . . . . . . . .
2.2 Receiver . . . . . . . . . . . . . . . . . . . . .
2.2.1 Feed Horns . . . . . . . . . . . . . . .
2.2.2 Orthomode Transducers . . . . . . . .
2.2.3 Phase Sensitive Section . . . . . . . . .
2.2.4 Amplifiers . . . . . . . . . . . . . . . .
2.2.5 Filters . . . . . . . . . . . . . . . . . .
2.2.6 Detection and Data Acquisition . . . .
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31
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72
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75
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94
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105
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109
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113
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116
118
120
122
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131
5 Data Analysis
5.1 Data Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Removal of Offsets, Auto-calibration Sequences, and Spikes
5.2.2 Applying the Calibration . . . . . . . . . . . . . . . . . . .
5.2.3 Template Removal . . . . . . . . . . . . . . . . . . . . . .
5.2.4 Pixelization . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Noise Estimation, Map-Making, and Angular Power Spectra . . .
5.3.1 Time-Time Noise Covariance Matrix . . . . . . . . . . . .
5.3.2 Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Angular Power Spectra . . . . . . . . . . . . . . . . . . . .
5.4 Systematic Issues . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Status of the Data Analysis . . . . . . . . . . . . . . . . . . . . .
139
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146
146
150
156
161
163
165
168
176
179
182
6 Conclusion
183
2.3
2.4
3 The
3.1
3.2
3.3
3.4
2.2.7 Electronics . .
2.2.8 Cryogenics . .
2.2.9 Performance .
Beam Model . . . . .
Automatic Calibrator
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Barcroft Observatory
Sky Temperature . . . .
Remote Control System
Communications . . . .
Weather Monitoring . .
4 2004 Observing Campaign
4.1 Weather . . . . . . . . .
4.2 Data Collection . . . . .
4.2.1 Data Format . .
4.2.2 Data Recorded .
4.3 Pointing Reconstruction
4.4 Observing Strategy . . .
4.5 Beam Determination . .
4.6 Calibration . . . . . . .
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List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
Hubble diagram . . . . . . . . . . . . . . . . . . .
Primordial abundances of the light elements . . .
CMB temperature spectrum from COBE FIRAS .
CMB dipole anisotropy from COBE DMR . . . .
CMB temperature anisotropy from WMAP . . . .
Angular power spectra from WMAP . . . . . . .
Geometry of Thomson scattering . . . . . . . . .
Examples of E and B patterns . . . . . . . . . . .
Angular power spectra . . . . . . . . . . . . . . .
Temperature and polarization map from DASI . .
T T angular power spectrum and reionization . . .
EE angular power spectrum and reionization . .
Expected BB angular power spectra . . . . . . .
Foregrounds from WMAP . . . . . . . . . . . . .
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2
4
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28
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
Optical design of WMPol telescope . . . .
Drawing of the WMPol telescope . . . . .
Front view of the WMPol telescope . . . .
Telescope in the Barcroft Observatory . . .
Tilt data from the telescope . . . . . . . .
CCD camera image of Vega . . . . . . . .
CCD camera image of Mars . . . . . . . .
Code to operate the telescope . . . . . . .
The “Blue Box” and the WMPol computer
Telescope schematic . . . . . . . . . . . . .
View inside the dewar . . . . . . . . . . .
Schematic of the WMPol receiver array . .
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2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.30
2.31
2.32
2.33
2.34
2.35
2.36
Modeled return losses . . . . . . . . . . . . . . . . . . . . . . . . .
Measured return losses . . . . . . . . . . . . . . . . . . . . . . . .
Radiation patterns of the Q-band and W-band feed horns . . . . .
Transmission of W-band OMT . . . . . . . . . . . . . . . . . . . .
Reflection of W-band OMT . . . . . . . . . . . . . . . . . . . . .
Cross polarization of W-band OMT . . . . . . . . . . . . . . . . .
Phase sensitive section of radiometers . . . . . . . . . . . . . . . .
Q-band amplifier noise . . . . . . . . . . . . . . . . . . . . . . . .
W-band amplifier noise . . . . . . . . . . . . . . . . . . . . . . . .
Microwave filter masks . . . . . . . . . . . . . . . . . . . . . . . .
Q-band filter band . . . . . . . . . . . . . . . . . . . . . . . . . .
W-band filter band . . . . . . . . . . . . . . . . . . . . . . . . . .
W-band diode response . . . . . . . . . . . . . . . . . . . . . . . .
Schematic of the differential amplifier . . . . . . . . . . . . . . . .
Schematic of the offset circuit . . . . . . . . . . . . . . . . . . . .
Noise comparison of time ordered data . . . . . . . . . . . . . . .
Noise comparison of power spectral densities . . . . . . . . . . . .
Diode protection circuit . . . . . . . . . . . . . . . . . . . . . . .
Example of a Q-band PSD . . . . . . . . . . . . . . . . . . . . . .
Example of a W-band PSD . . . . . . . . . . . . . . . . . . . . .
Geometry of reflectors and focal plane . . . . . . . . . . . . . . .
Contour plots of polarimeter beam models . . . . . . . . . . . . .
Contour plots of temperature anisotropy radiometer beam models
Automatic calibrator . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
Drawing of WMPol in the observatory . . . . . . . . . . . .
Installation of WMPol into the observatory . . . . . . . . . .
Integrated histogram of PWV . . . . . . . . . . . . . . . . .
Model of sky temperature at Barcroft . . . . . . . . . . . . .
Example of sky dip data in Q-band . . . . . . . . . . . . . .
Example of sky dip data in W-band . . . . . . . . . . . . . .
Schematic of Stargate control . . . . . . . . . . . . . . . . .
Example of observatory web camera “Clear” image . . . . .
Example of observatory web camera “Partly Cloudy” image
Example of observatory web camera “Mostly Cloudy” image
Example of observatory web camera “Overcast” image . . .
4.1
4.2
Temperature statistics for the observatory . . . . . . . . . . . . . 114
Integrated histogram of wind speed . . . . . . . . . . . . . . . . . 115
xii
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112
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
CCD camera image of Polaris . . . . . . . . . . . . . . .
Sky coverage of Q-band polarimeter channel . . . . . . .
Sky coverage of W-band polarimeter channel . . . . . . .
Q-band polarimeter observation of Tau A . . . . . . . . .
Determination of Q-band beam size . . . . . . . . . . . .
Q-band observations of the Moon . . . . . . . . . . . . .
W-band observations of the Moon . . . . . . . . . . . . .
Example of an automatic calibration sequence in Q-band
Example of an automatic calibration sequence in W-band
Calibrated signals from automatic calibrations . . . . . .
Ratio of automatic calibration signals . . . . . . . . . . .
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121
123
124
127
128
129
130
134
135
137
138
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.22
5.23
Example of data cut . . . . . . . . . . . .
Example of data cut, offsets removed . . .
Example of good data . . . . . . . . . . .
Example of good data, offsets removed . .
Plot of azimuth scanning . . . . . . . . . .
PSD before and after calibration removal .
PSD before and after offset removal . . . .
Q-band polarimeter calibration constants .
W-band polarimeter calibration constants
Spherical geometry for binning . . . . . . .
Binned data with templates . . . . . . . .
More binned data with templates . . . . .
HEALPix grid technique . . . . . . . . . .
Noise correlation at short time scales . . .
Noise correlation at longer time scales . . .
Histogram of data . . . . . . . . . . . . . .
Preliminary Q-band map . . . . . . . . . .
Error per pixel for Q-band map . . . . . .
Histogram for Q-band map . . . . . . . . .
Histogram for Q-band map, log scale . . .
Example of window function . . . . . . . .
Preliminary transfer function for EE . . .
Scan synchronous signal . . . . . . . . . .
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143
144
147
148
149
151
152
153
154
157
159
160
162
166
167
170
172
173
174
175
177
178
181
xiii
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List of Tables
1.1
Key Cosmological Parameters from WMAP . . . . . . . . . . . .
10
2.1
2.2
2.3
2.4
2.5
2.6
Design Parameters of the WMPol Optics . . . . . . .
Major Elements of the Polarimeters . . . . . . . . . .
Design of the WMPol Corrugated Scalar Feed Horns
Specifications of the Orthomode Transducers . . . . .
Parameters of the Polarimeters . . . . . . . . . . . .
WMPol Beam Model Characteristics . . . . . . . . .
34
51
53
57
83
91
4.1
4.2
Ratings of Daytime Web Camera Images . . . . . . . . . . . . . . 116
Primary Reasons for Not Taking Data . . . . . . . . . . . . . . . 119
5.1
Cuts of Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
xiv
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Chapter 1
Introduction
The big bang theory is the idea that the universe was extremely hot and
dense in the distant, but finite, past and it has since cooled and expanded to its
present temperature and size with the structures that we observe today. The big
bang theory rests on three key pieces of observational evidence: The expansion of
the universe, the primordial abundance of light elements, and the existence and
properties of the Cosmic Microwave Background (CMB) radiation.
That the universe is expanding was first noted by Edwin Hubble [Hubble, 1929]
and the expansion of the universe is today parameterized by the Hubble constant,
H0 , where v = H0 d gives the relationship between the recessional velocity, v, of
a galaxy and its distance, d, from us. H0 has been measured by the “Hubble
Space Telescope Key Project to Measure the Hubble Constant” to have a value
1
Figure 1.1: Example of a Hubble diagram [Freedman et al., 2001]. The slope of
the fit determines the Hubble constant; for this plot the best fit is given by 75 ± 10
km s−1 Mpc−1 which is consistent with the results from other methods used by
the HST Key Project for farther away galaxies.
of 72 ± 8 km s−1 Mpc−1 [Freedman et al., 2001]. Figure 1.1 shows an example of
a Hubble diagram for measurements from galaxies that have measurable Cepheid
variables. During a time when the Hubble constant was not well measured it
became common to parameterize it with h by
H0 = 100 h km s−1 Mpc−1 .
(1.1)
For the HST result, h = 0.72 ± 0.08.
According to the big bang model, when the universe is around one second
old an epoch known as big bang nucleosynthesis (BBN) begins [Kolb and Turner,
1990]. At this time, the temperature of the universe has fallen enough (T . 1
2
MeV) such that the neutrinos decouple from matter and electrons and positrons
annihilate leaving only a small residual plasma of baryons (i.e. protons and neutrons) plus electrons in what is at the time a radiation dominated universe. The
density of baryons in the universe is often given as ΩB where, in general,
ρ
ρc
(1.2)
3H02
' 11.2 h2 nucleons / m3 ,
8πG
(1.3)
Ω=
and
ρc =
with ρ being the density of interest, ρc being the “critical” density or the density required to close the universe (today), and G is the gravitational constant.
Another term of interest is the baryon to photon ratio, η, which is given by
η = 2.74 × 10−8 ΩB h2 .
(1.4)
During what is now commonly called “the first three minutes,” protons and neutrons combine to form deuterium, 3 He, 4 He, and 7 Li in amounts that depend on
ΩB h2 or η. As there are no stable atomic nuclei with 5 or 8 nucleons, there is a
significant barrier to building heavier nuclei during BBN and very few, if any, are
formed. Figure 1.2 shows the current theoretical constraints and the observational
limits on the primordial abundance of light elements.
After the first three minutes, once big bang nucleosynthesis is complete, the
next 300,000 to 400,000 years are relatively uneventful. Eventually, the universe
3
Baryon density Ωb h2
0.005
0.26
0.01
0.02
0.03
4He
0.25
0.24
Yp
D
___ 0.23
H
0.22
10 −3
3He
___
H
CMB
D/H p
10 − 4
3He/H
p
10 − 5
10 − 9
5
7Li/H
p
2
10 − 10
1
2
3
4
5
6
7
8 9 10
Baryon-to-photon ratio η10
Figure 1.2: Primordial abundances of the light elements. This figure, from Eidelman et al. [2004], shows the predicted abundances, with observational limits,
of 4 He, D, 3 He, and 7 Li. Yp is commonly used to denote the 4 He mass fraction
while the number densities as compared to hydrogen are given for the other light
elements. η10 = η × 1010 . The thickness of the line for each element is due to theoretical or experimental 1σ uncertainties in nuclear properties while the smaller
white boxes show 2σ statistical (observational) errors and the yellow boxes show
±2σ statistical and systematic errors added in quadrature. The vertical blue area
represents theoretical limits on abundances from standard big bang nucleosynthesis theory and measured limits from WMAP CMB observations are also included.
4
cools enough for the electrons to combine with the atomic nuclei to form neutral
matter. Once this happens, the radiation decouples from the baryonic matter
and the photons stream (almost) freely from this “last scattering surface” until
reaching us. This radiation is what is today known as the Cosmic Microwave
Background.
1.1
The Cosmic Microwave Background
The first official detection of the CMB was reported by Penzias and Wilson in
1965. Since the discovery of the CMB 40 years ago, many measurements have been
made to determine its spectrum, spatial temperature anisotropy, and polarization.
The CMB temperature spectrum was measured definitively by COBE FIRAS
(COsmic Background Explorer Far Infrared Absolute Spectrophotometer) to be
consistent with a 2.725 ± 0.002 K blackbody [Mather et al., 1999] as shown in
Figure 1.3.
Soon after the discovery of the Cosmic Microwave Background, the first temperature anisotropy seen was the ≈ 3 mK dipole pattern due to our motion relative
to the CMB (see [Wright, 2003] and references therein regarding the detection and
measurement of the CMB dipole). Figure 1.4 displays the COBE DMR (Differential Microwave Radiometer) measurement of the dipole.
5
Figure 1.3: CMB temperature spectrum from COBE FIRAS. The errors on the
34 data points are smaller than the thickness of the theoretical curve. Source:
lambda.gsfc.nasa.gov.
Figure 1.4: CMB dipole anisotropy from COBE DMR. This map of the 3.353 ±
0.024 mK dipole is from the 53 GHz channel of DMR as reported in Bennett
et al. [1996]. WMAP measured the dipole temperature to be 3.346 ± 0.017 mK
consistent with COBE DMR. Source: lambda.gsfc.nasa.gov.
6
Figure 1.5: CMB temperature anisotropy from WMAP (courtesy of the WMAP
Science Team). This map, from Bennett et al. [2003a], uses a combination of the
maps from the five WMAP frequency bands to remove the dipole and the galaxy.
The galactic poles are at the top and bottom of the map.
Since structures such as galaxies and galaxy clusters exist today, temperature
anisotropy at angular scales smaller then the dipole was expected [Peebles, 1993]
and this anisotropy was first measured by COBE DMR [Smoot et al., 1992]. After
COBE, many ground-based and balloon-born telescopes made measurements of
smaller angular scale CMB temperature anisotropy culminating in another full sky
temperature anisotropy map from the WMAP (Wilkinson Microwave Anisotropy
Probe) space mission. Figure 1.5 shows the temperature anisotropy map from the
first year of WMAP data.
To analyze the information contained in a CMB map it is desirable to expand
7
the temperature anisotropy, ∆T , in terms of the spherical harmonics
X
∆T
(θ, φ) =
alm Ylm (θ, φ).
T
l,m
(1.5)
As long as the fluctuations that generate the anisotropy are described by a gaussian
random process, the angular power spectrum given by
Cl ≡ h|alm |2 i
(1.6)
contains all the information [Bennett et al., 1997, Scott et al., 1995]; the angle
brackets indicate an ensemble average including a sum over m as there is “no
preferred direction in the universe” [Bennett et al., 1997]. It is then customary to
plot
l(l + 1)Cl
=
2π
µ
∆T
(θ)
T
¶2
(1.7)
versus l. Figure 1.6 is a plot of angular power spectra from the first year WMAP
data.
Once an angular power spectrum is calculated, it can be compared to angular
power spectra obtained from theoretical models to determine which cosmological
model is the best fit. The model currently favored by observations, including
WMAP, (see Freedman and Turner [2003] for a review) is one in which there is a
period of inflation [Guth, 1981] in the very early universe, implying a nearly flat
(total density, Ω0 ' 1) geometry with quantum mechanical fluctuations expanded
8
Figure 1.6: Angular power spectra from WMAP (Bennett et al. [2003a], courtesy
of the WMAP Science Team) with data from ACBAR [Kuo et al., 2004] and CBI
[Pearson et al., 2003] included. The T T cross power spectrum is equivalent to
that described by Equation 1.7. The definition of the T E cross power spectrum
is given in Section 1.2.
9
Table 1.1: Key Cosmological Parameters from WMAP
Parameter
Value
Total density, Ω0
Dark energy density, ΩΛ
Matter density, Ωm
Baryon density, ΩB
Hubble constant, h
Age of the universe, t0 (Gyr)
Age at decoupling, tdec (kyr)
1.02 ± 0.02
0.73 ± 0.04
0.27 ± 0.04
0.044 ± 0.04
0.71+0.04
−0.03
13.7 ± 0.2
379+8
−7
by inflation to cosmological size to seed the universe with adiabatic density fluctuations. In this model, the universe is made up of ∼ 2/3 dark energy and ∼ 1/3
cold (i.e. non-relativistic) dark matter, or CDM, with less than 5% of the universe made of baryonic matter. During the time between BBN and last scattering,
baryons fall into inflation induced CDM potential wells with the photons opposing
the motion and setting up acoustic oscillations in the photon-baryon fluid. The
CMB is a snapshot of these acoustic oscillations at time of last scattering and
the position, shape, and relative size of the “peaks and valleys” for l & 100 (as
described in Hu et al. [1997]) constrains parameters of the cosmological model.
Table 1.1 gives a list of parameters from the WMAP best fit model.
10
1.2
CMB Polarization
In addition to the temperature spectrum and anisotropy, the third property of
the CMB that can be measured is polarization. In general, a polarized signal can
be fully characterized by the Stokes parameters. Assuming an electromagnetic
wave of the form
~ = Ex (t) cos(kz − ωt + φx )î + Ey (t) cos(kz − ωt + φy )ĵ
E
(1.8)
the Stokes parameters are given by
I ≡ hEx2 i + hEy2 i
(1.9)
Q ≡ hEx2 i − hEy2 i
(1.10)
U ≡ h2Ex Ey cos(φy − φx )i
(1.11)
V ≡ h2Ex Ey sin(φy − φx )i
(1.12)
where the brackets denote a time average. The Stokes parameter I is the total
intensity of the radiation with I 2 ≥ Q2 + U 2 + V 2 . Q and U describe the linear
polarization of the wave and V quantifies the amount of circular polarization and
these are equal to zero in the absence of polarization. The polarization angle can
be defined by
1
α ≡ tan−1
2
11
µ ¶
U
Q
(1.13)
and the polarization fraction, P , by
p
P ≡
Q2 + U 2 + V 2
.
I
(1.14)
I and V are rotationally invariant but Q and U transform under rotation by
Q0 = Q cos(2ϕ) + U sin(2ϕ)
(1.15)
U 0 = −Q sin(2ϕ) + U cos(2ϕ)
(1.16)
where ϕ is the rotation angle. However, it is clear that the quantity Q2 + U 2 is
rotationally invariant and that
Q0 ± iU 0 = e∓2iϕ (Q ± iU )
(1.17)
showing the spin-2 nature of Q and U .
In 1973, the International Astronomical Union chose a convention for defining
Q and U on the sky [IAU, 1974]. In this convention, the +“x”-axis points towards
North while the +“y”-axis points towards East. In other words, the North-South
direction is defined as +Q and -Q is in the East-West direction. +U is in the
NE-SW direction with -U in the NW-SE direction. The polarization angle is then
measured from North through East.
Polarization of the CMB results from Thomson scattering (non-relativistic,
i.e. hν ¿ mc2 , scattering of photons by free electrons without changing the
12
photon frequency) of CMB photons emanating from local quadrupolar temperature anisotropy on the surface of last scattering. The differential scattering cross
section for Thomson scattering is
dσ
3σT 0 2
=
|²̂ · ²̂| ,
dΩ
8π
(1.18)
where σT , the Thomson scattering cross section, is given by
8π
σT =
3
µ
e2
4πε0 me c2
¶2
= 6.65 × 10−29 m2
(1.19)
and
e2
= 2.8 × 10−15 m
4πε0 me c2
(1.20)
is known as the classical electron radius [Jackson, 1975]. For these equations, ²
and ²0 are the incident and scattered polarization directions respectively, e is the
electron charge, me is the electron mass, ε0 is the permittivity of free space, and c
is the speed of light. Figure 1.7 is a diagram displaying how Thomson scattering
induces polarization. Thomson scattering does not cause circular polarization (i.e.
V = 0) and the CMB is expected to be at most ∼ 10% linearly polarized [Bond
and Efstathiou, 1984, Polnarev, 1985, Hu and White, 1997].
The goal of CMB polarization observations, then, is to make a map of the
sky for all of the Stokes parameters − even though V is expected to equal zero,
measurements could help with the evaluation of systematic effects. As the rotation
13
Quadrupole
Anisotropy
I’x
I’y
I’z
e–
Thomson
Scattering
Iy
I’z
Ix
Linear
Polarization
Figure 1.7:
Geometry of Thomson scattering and generation of polarization (adapted from Hu and White [1997], also see web site at
background.uchicago.edu/∼whu/). For the incoming unpolarized radiation on the
left (thick blue lines), the polarized component Iz0 , pointing towards the viewer,
is scattered by the electron in a direction away from the viewer. The other polarized component, Iy0 , is scattered towards the viewer. Likewise, for the unpolarized
radiation at a different temperature coming from the top of the page (thin red
lines), the polarized component Iz0 is again scattered away from the viewer and the
other component, Ix0 , is scattered towards the viewer. This results in the viewer
seeing linearly polarized radiation.
14
properties of Q and U are somewhat inconvenient to work with, a formalism has
been developed to decompose polarization maps into a “gradient” or “divergence”
part (or “mode”) and a “curl” part [Zaldarriaga and Seljak, 1997, Kamionkowski
et al., 1997] as inspired by the Helmholtz theorem. Kamionkowski et al. [1997]
called these “G” and “C” modes, but it has become common today to call them
“E” and “B” modes analogous to the properties of electric and magnetic fields.
Figure 1.8 shows examples of E and B, including their parity properties, and how
they relate to Q and U .
As is done for temperature anisotropy, the E- and B- modes can be expanded
into spherical harmonics:
E(θ, φ) =
X
aE
lm Ylm (θ, φ)
(1.21)
aB
lm Ylm (θ, φ).
(1.22)
l,m
B(θ, φ) =
X
l,m
With these equations, polarization angular power spectra can be defined by
0
0
X
ClXX ≡ haX∗
lm alm i
(1.23)
where X and X 0 can be T , E, or B resulting in six possible combinations: ClT T ,
ClT E , ClEE , ClBB , ClT B , and ClEB . ClT T is just the temperature anisotropy angular power spectrum, ClT E is the temperature−polarization cross-power spectrum
(see Figure 1.6), and ClEE and ClBB are the E-mode and B-mode angular power
15
Figure 1.8: Examples of E and B patterns (from Zaldarriaga [2004]). Notice that
if either E pattern is reflected through a line going through the center it remains
unchanged while one of the B patterns switches into the other under reflection.
16
spectra. Due to the negative parity property of B-mode polarization, the last two
power spectra should formally equal zero though they may still be worth measuring to look for exotic physics and foreground contamination [de Oliveira-Costa,
2005]. Figure 1.9 displays the T T , T E, and EE angular power spectra from
CMBFAST1 [Seljak and Zaldarriaga, 1996] for a model using the WMAP best fit
parameters.
As E-mode polarization results from the Thomson scattering of temperature
anisotropy on the last scattering surface, and, in addition, is not affected by evolving gravitation potentials between the surface of last scattering and us as is the
case for temperature anisotropy, it is an additional probe to verify our understanding of cosmology. Thus, the recent first detections of CMB polarization by DASI
[Kovac et al., 2002, Leitch et al., 2005], WMAP [Kogut et al., 2003], CBI [Readhead et al., 2004], CAPMAP [Barkats et al., 2005], and BOOMERanG [Montroy
et al., 2005, Piacentini et al., 2005] are an important confirmation of results from
measurements of the temperature anisotropy. Precision measurements of the EE
polarization angular power spectrum (and the T E spectrum) can also help to constrain cosmological parameters and break degeneracies. As shown in Figure 1.9,
the peaks of EE power spectrum should (assuming the currently favored model)
coincide with the troughs of the T T power spectrum. The reason for this is that
1
http://www.cmbfast.org/
17
Figure 1.9: Angular power spectra using WMAP best fit parameters. The T T temperature power spectrum is in black, the T E cross-power spectrum in green, and
the EE polarization power spectrum is in blue (BB assumed equal to zero in this
model). The dashed lines in the cross-power spectrum indicate anti-correlation
and the plot shows the absolute value. For a given l value, the matching angular
◦
size is θ ∼ 180l These angular power spectra were generated using a web-based
CMBFAST interface available at lambda.gsfc.nasa.gov.
18
while the peaks in the T T power spectrum are due to density perturbation extrema (maximum and minimum density structures) and the troughs are due to
the doppler effect (angular scales on which motion of the fluid is maximized), the
E-mode polarization is maximized on scales where the fluid is in motion as this
is the condition for which quadrupolar anisotropy is greatest. Figure 1.10 shows
the temperature and polarization map released by the DASI team.
E-mode polarization can also be used improve our knowledge about the epoch
of reionization. As Gunn and Peterson [1965] first pointed out, even a small
amount of neutral hydrogen between a distant object, such as a quasar, and us
should affect the spectrum we measure. Ultraviolet light from the object redshifted to Lyα in the rest frame of an intervening cloud of neutral hydrogen will
cause a “Gunn-Peterson trough” in the spectrum due to absorption. That the
Gunn-Peterson effect was not observed (until recently, see Becker et al. [2001])
was evidence that the universe became reionized at early times, presumably by
emission from the first stars. Once the universe became reionized, Thomson scattering could again scatter CMB photons. Reionization has the effect of reducing
the overall small angular scale temperature anisotropy signal by a factor of e−τ ,
where τ is the reionization optical depth (0.17 ± 0.04 from WMAP), but slightly
different cosmological parameters could produce the same effect so it is difficult
to constrain reionization with just the T T power spectrum. On the other hand,
19
Figure 1.10: Temperature and polarization map from DASI. The CMB temperature anisotropy is shown with yellow meaning a hot spot and red, a cold spot.
The black lines show the strength and orientation of the polarization. The size
of the white circle in the lower left corner approximates the angular resolution of
the DASI polarization observations. Source: astro.uchicago.edu/dasi/
20
Figure 1.11: T T angular power spectrum with (red) and without (black) reionization.
reionization creates an unmistakable signal in the EE power spectrum at large
angular scales. Figure 1.11 and 1.12 compare T T and EE angular power spectra
for a no reionization case versus reionization as measured by WMAP using the
TE spectrum.
Although B-modes are not induced by the scalar density fluctuations mentioned above, they can be generated by vector and tensor fluctuations. Vector
perturbations are associated with vortical motion (like eddies in a fluid) and are
expected to be damped out by expansion of the universe. However, if the level
of B-modes is large compared to that of E-modes (which may be ruled out by
observations thus far) then it could be an indication of “new” physics such as
21
Figure 1.12: EE angular power spectrum and reionization. The no reionization
case is, again, in black and WMAP reionization (τ = 0.17 ± 0.04) in red.
decaying cosmological defects [Hu and White, 1997]. Tensor fluctuations are due
to gravitational waves (believed to be generated by inflation) which distort space
in a quadrupolar fashion, creating both E- and B-modes. Assuming, no vector
contribution, a detection of B-modes could help determine the energy scale of
inflation [Kosowsky, 1999]. A final major source of possible B-modes is via gravitational lensing which should distort the polarization field and could induce a curl
component. Figure 1.13 compares expected BB angular power spectra, including
lensing, to EE, T E, and T T .
22
Figure 1.13: Expected BB angular power spectra from Kaplan et al. [2003]. The
BB angular power spectrum due to gravitational waves and/or lensing is predicted
to be at least a factor of 10 below the EE spectrum.
23
1.3
Foregrounds
Although they lead to interesting science, reionization and gravitational lensing can be considered extragalactic “foregrounds” as they affect the CMB signal
that comes from the surface of last scattering. There are also galactic foregrounds
that could make it more difficult to measure CMB polarization, namely synchrotron radiation, free-free emission, and dust emission. These foregrounds have
been reasonably well characterized for temperature anisotropy measurements but
it is not well understood how polarized they are. Since the signals from these
foregrounds are expected to all have a frequency dependence different from each
other and from the CMB, the solution is to observe at different frequencies to try
to separate the foreground from the CMB signal.
The frequency, ν, dependence of foregrounds can be described by the flux
density, Sν ∼ ν α , or antenna temperature, TA ∼ ν β , with β = α − 2 [Bennett
et al., 2003a]. In general,
Z Z
Sν =
Bν (θ, φ)dΩ
(1.24)
where Bν is called the brightness or specific intensity and dΩ is the infinitesimal
solid angle sin θdθdφ. The commonly used units of flux are Janskys or Jy with
1 Jy ≡ 10−26 W m−2 Hz−1 . For blackbody radiation, Bν is given by the Planck
24
law,
2hν 3
1
Bν (T ) = 2 hν/kT
c e
−1
(1.25)
where h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant,
and T is the physical temperature of the blackbody. For the radio and microwave
it is often possible to work in the Rayleigh-Jeans limit, hν ¿ kT , and in this
regime ehν/kT − 1 ' 1 +
hν
kT
−1=
hν
,
kT
leaving
BR−J (ν, T ) =
2ν 2
kT.
c2
(1.26)
Brightness temperature, Tb , can then be defined by
Tb =
c2
Bν
2kν 2
(1.27)
which reduces to Tb = T in the Rayleigh-Jeans limit.
While the brightness temperature is the quantity that is usually desired, antenna temperature, “the convolution of the brightness temperature with the beam
pattern of the telescope,” [Rohlfs, 1986] is what is measured. Following Kraus
[1986] and Rohlfs [1986], we can define a normalized antenna power pattern,
Pn (θ, φ) such that
Z Z
ΩA =
Z Z
Pn (θ, φ)dΩ
(1.28)
4π
ΩM =
Pn (θ, φ)dΩ
main lobe
25
(1.29)
where ΩA is the antenna beam area (integrated over the entire sky) and ΩM is
the area of the main lobe, both in steradians. The antenna temperature, TA , is
then given by
1
TA =
ΩA
Z Z
Ts (θ, φ)Pn (θ, φ)dΩ
(1.30)
where Ts (θ, φ) is the source temperature. This simplifies considerably if the source
is very small compared to the main beam so that
TA =
Ωs
Ts ,
ΩA
(1.31)
where Ωs and Ts are the solid angle and average temperature of the source. Similarly, if the source is much bigger than the main beam, but small compared to
the entire sky, then
TA =
Ω0M
Ts ,
ΩA
(1.32)
with
Z Z
Ω0M
=
Pn (θ, φ)dΩ.
(1.33)
source
If the side lobes of the beam are not significant then
Ω0M
ΩA
∼ 1 and TA ' Ts .
Figure 1.14, from Bennett et al. [2003b], is a plot of the major known microwave
foregrounds. Synchrotron radiation, which dominates at low frequency, is due to
the acceleration of relativistic (cosmic-ray) electrons in galactic magnetic fields
with
Tsynch (ν) ∝ ν β
26
(1.34)
and β ≈ 3. Synchrotron radiation could be as much as 75% polarized, however
it is expected that Faraday rotation and non-uniformity of magnetic fields would
reduce the level of polarization to less than 20% [Bennett et al., 2003b, Keating
et al., 1998]. The other foreground at low frequency is free-free or Bremsstrahlung
emission. This is generated in ionized clouds of hydrogen in the galaxy (HII
regions) by free electrons interacting with and being accelerated by protons. The
free-free spectrum is given by
Tf ree−f ree (ν) ∝ ν −2.15
(1.35)
at frequencies greater than 10 GHz [Bennett et al., 2003b]. Free-free emission
should not be polarized [Rybicki and Lightman, 1979] but it can be ∼ 10% polarized by Thomson scattering [Keating et al., 1998].
On the high frequency side, ν ≥ 100 GHz, vibrational thermal dust emission dominates and the expected frequency dependence is 1.5 ≤ βdust ≤ 2. It
is unknown at this time how much this dust emission might be polarized, but it
is expected that the polarization fraction is no more than 10% [Montroy et al.,
2005]. There is also the possibility of rotational dust emission from spinning dust
grains in the range of 10 − 100 GHz [Draine and Lazarian, 1998] but this foreground is not well understood let alone how much it might be polarized. Lazarian
and Finkbeiner [2003] (and references therein) provides a review of the current
27
$QWHQQD7HPSHUDWXUHM.UPV
.
.D
4
9
:
&0% $QLVRWURS\
6\
QF
K
6N\
)U
U
R
HH
.S
6N
IU WUR
\
HH Q
.
S
VW
'X
)UHTXHQF\*+]
Figure 1.14: Foregrounds from WMAP. This plot, from Bennett et al. [2003b],
shows the modelled, frequency dependent emission levels for three major known
foregrounds: synchrotron, free-free, and dust. Also shown is the CMB anisotropy
as a function of frequency (in red) which is flat at low frequency where the
Rayleigh-Jeans approximation is still valid. The composite galactic emission for
two WMAP (galactic plane) sky cuts, retaining 77% and 85% of the sky respectively, are shown as dashed lines. The five WMAP radiometer bands are indicated
in the background. Source: lambda.gsfc.nasa.gov/product/foreground/.
28
situation for dust emission in the microwave. To summarize, the level of possible
polarized foregrounds is not well understood at this point. However, it is hoped
that CMB polarization measuring telescopes will be able to cover large parts of
the sky at multiple frequency bands to help shed some light on this issue.
1.4
The White Mountain Polarimeter
Even from this brief introduction to the Cosmic Microwave Background, it is
obvious that measurements of CMB polarization will help to increase our understanding of cosmology. Because of this exciting potential to learn more about
our universe, the White Mountain Polarimeter (WMPol), a dedicated instrument
for measuring E-mode polarization at the sub-degree angular scale, was designed,
constructed, and installed at a high altitude observatory to observe the CMB.
The next chapter discusses the WMPol instrument in detail including the telescope and receiver and their performance. Chapter 3 is about the observing site
at the University of California White Mountain Research Station Barcroft Facility
where WMPol was installed and reports the observing properties at the site as
well as the infrastructure set up to support telescope operations. Chapter 4 gives
a summary of the 2004 WMPol observing campaign including information about
the weather, the data collected, our observing strategy, and how pointing recon-
29
struction and measurements of the beam size and calibration were accomplished.
Finally, Chapter 5 is a summary of the data analysis technique and we conclude
with a status report about the data analysis and the WMPol instrument.
30
Chapter 2
The WMPol Instrument
The WMPol telescope and receiver were designed specifically to measure CMB
polarization and take advantage of previous experience in the group in building
microwave telescopes for CMB observations.
2.1
2.1.1
Telescope
Optical Design
The WMPol telescope is an off-axis Gregorian telescope similar to that of
BEAST [Childers et al., 2005, Figueiredo et al., 2005], which is a telescope dedicated to mapping CMB temperature anisotropy, and uses identical aluminum
coated carbon fiber reflectors. Figure 2.1 shows the optical design including the
31
2.2-meter parabolic primary, 0.9-meter ellipsoidal secondary, and the dewar that
houses the receiver.
The telescope design obeys the Dragone-Mizugutch condition [Dragone, 1978,
Mizugutch et al., 1976]. Meeting this condition ensures that the beam remains
symmetric as it passes through the optics and that there is no cross-polarization
component in the far field which is critical for a polarization observation. The
Dragone-Mizugutch condition for an off-axis Gregorian telescope is given by Dragone [1978] as
µ
tan α =
e+1
1−e
¶
tan β,
(2.1)
where 2α is the angle between the axis of the feed and the axis of rotation of
the secondary (major axis), 2β is the angle between the axis of rotation of the
secondary and the axis of rotation of the primary (axis of the parabola), and
e is the eccentricity of the secondary. Table 2.1 (adapted from Childers et al.
[2005] and Figueiredo et al. [2005]) gives the characteristics of the optical design
including the values for 2α, 2β, and e.
2.1.2
Mechanical Design and Motion Control
The WMPol telescope is mounted on top of a table that rotates in azimuth.
The table is attached to a shallow cone that rests on four smaller conical roller
32
3000
Y (mm)
2000
1000
Primary
Reflector
0
Secondary
Reflector
Dewar
-1000
-2000
-1000
0
1000
2000
Z (mm)
Figure 2.1: Optical design of WMPol telescope. The primary reflector (with its
parent parabola), the secondary reflector (with its parent ellipsoid), and the dewar
are shown. Radiation from the sky is focused by the primary at the common focal
point of the primary and secondary (the origin of the plot) and then focused by
the secondary at the phase center of the central horn in the dewar.
33
Table 2.1: Design Parameters of the WMPol Optics
Parameter
Value
Primary focal length (mm)
1250.0
Primary max. physical dimension (mm) 2200.0
Primary min. physical dimension (mm) 1966.1
Secondary
Secondary
Secondary
Secondary
semimajor axis (mm)
semiminor axis (mm)
focal length (mm)
eccentricity, e
Feed angle, 2α (degrees)
Angle between axes, 2β (degrees)
34
886.7
853.4
240.7
0.2714
58.2
35.4
bearings. A motor drives the motion in azimuth by rotating one of the roller
bearings through a harmonic reducing gear.1 This table, as described in Meinhold
et al. [1993], was used previously to observe CMB temperature anisotropy from
the South Pole.
The telescope itself consists of a section that is mounted directly to the table
and another section (held by two bearings) that can move in elevation via a linear
actuator. The motors for the azimuth drive and elevation actuator are controlled
by a dual-axis motion controller2 that uses relative encoders for feedback and linear
servo amplifiers3 to drive the motors. Removable switches that limit the motion in
azimuth to approximately ±5◦ were installed to prevent the possibility of damage
to the telescope during remote operation. Figure 2.2 shows the major elements
of the telescope, Figure 2.3 is a photograph of the telescope at UCSB before
bringing it up to the Barcroft Observatory, and Figure 2.4 shows the telescope in
the observatory. Aluminized mylar covers the telescope on the sides, back, and
underneath to reduce stray light from the observatory reaching the optics.
1
Harmonic Drive Technologies, Nabtesco Inc., Peabody, MA 01960, http://www.harmonicdrive.com
2
Galil Motion Control, Rocklin, California 95765, http://www.galilmc.com/
3
Western Servo Design, Carson City, NV 89706, http://www.wsdi.com/
35
Figure 2.2: Drawing of the WMPol telescope with primary, secondary, dewar, and
frame shown.
2.1.3
Measurement of Position
The position of the telescope in azimuth and elevation is measured by two 16bit absolute encoders4 and tilt is measured by two biaxial clinometers,5 one with
a ±100 range and the other with a ±10◦ range. Figure 2.5 presents the measured
tilt of the telescope as a function of azimuth position.
An optical CCD camera6 is used to help determine pointing by imaging stars
at night. The optical camera is spatially calibrated (conversion from pixels to
4
Gurley Precision Instruments, Troy, New York 12180, http://www.gurley.com/
Applied Geomechanics Inc., Santa Cruz, CA 95062, http://www.geomechanics.com
6
Watec America Corp., Las Vegas, NV 89120
5
36
Figure 2.3: Front view of the WMPol telescope.
37
Figure 2.4: Telescope in the Barcroft Observatory. A USB web camera is housed
in the small rectangular box on the dome (upper right) next to the shutter.
38
Figure 2.5: Tilt data from the telescope using ±100 full scale clinometer. The lower
curve is for tilt perpendicular to the optical axis or East-West when the telescope
is pointing towards the NCP. The upper curve is tilt parallel to the optical axis or
North-South when the telescope points towards the NCP. The spikes in this data
occur when the telescope is stopped during the testing to ensure that no cables
are stressed as the telescope is moved in azimuth.
39
Figure 2.6: CCD camera image when telescope is staring at Vega. The field of
view of the camera is approximately 2.7◦ × 2.0◦ .
angle on the sky) by recording an image of a known field of stars, measuring the
number of pixels between stars, and calculating the angular size of a pixel by
using star charts such as TheSky.7 Figure 2.6 displays one of the fields used for
calculating the calibration and Figure 2.7 is an image of Mars. The measurement
and calculation yields a value of 15 ± 0.3 arcsec/pixel in both the horizontal and
vertical directions. The size of an image is 640 × 480 pixels.
7
Software Bisque, Golden, CO 80401, http://www.bisque.com
40
Figure 2.7: CCD camera image of Mars. In this image the telescope is staring at
Mars.
41
2.1.4
Control Code and Housekeeping
A Windows-based PC operates the telescope using code written by Markus
Ansmann (A UCSB undergraduate student at the time) with the programming
language Delphi.8 This code, using a graphical user interface, controls the telescope motion and reads position and tilt, takes data through a data acquisition
card,9 operates the optical CCD camera, and controls the automatic calibrator as
described in Sections 2.4 and 4.6 below. Figure 2.8 shows the code interface. The
telescope motion can be controlled both manually or by setting up a simple scan
or tracking an object. The calibrator can also be placed in front of the receiver
manually or on a preset schedule.
The “housekeeping” electronics are contained inside an enclosure called the
“Blue Box.” Figure 2.9 is a photograph of this electronics box and the WMPol
computer. The function of the Blue Box is to receive the power from power
supplies and distribute power to the receiver, encoders, and other devices and also
route signals to the data acquisition card. The Blue Box contains the electronics
to measure temperatures on the telescope and measure the power used by the
telescope and receiver. There are also push-button relays (with indicator lights)
that can be used to manually control power to elements of the receiver, switches
8
Borland Software Corporation, Cupertino, CA 95014, http:/www.borland.com
Measurement
Computing
Corporation,
Middleboro,
MA
http://www.measurementcomputing.com/
9
42
02346,
Figure 2.8: Code to operate the telescope. The graphical user interface allows all
aspects of the telescope to be monitored and controlled by clicking buttons and
entering information in text windows.
43
to manually control the reference signal going to the receiver, and LCD panel
meters that can be used to monitor power going to the receiver.
The temperatures are measured using AD59010 ambient temperature sensors.
Temperature sensors are placed at two points on each reflector, one is placed on
the cryocooler compressor, and one is left loose to measure the air temperature.
Voltage and current transducers,11 using the Hall effect, measure the power drawn
from the radiometer power supplies.
2.1.5
Power and Noise Suppression
A great deal of effort went into arranging the power connections to the telescope to suppress noise. Separate isolated linear power supplies12 are used for the
receiver and housekeeping electronics and isolation transformers are used on the
computer and receiver power supplies. All telescope power comes from a dedicated
ferroresonant uninterruptible power supply, or FERRUPS,13 and separate cables
from the FERRUPS bring power to the telescope drive, telescope computer, and
receiver. In addition, the linear servo amplifiers are installed on the azimuth and
elevation drives specifically to reduce noise. Figure 2.10 displays how the various
elements are the telescope are interconnected.
10
Analog Devices Inc., Norwood, MA 02062-9106, http://www.analog.com
LEM U.S.A., Inc., Milwaukee, WI 53218, http://www.lemusa.com
12
Power-One, Camarillo, CA 93012, http://www.power-one.com/
13
Powerware, Eaton Corp., Raleigh, NC 27615, http://www.powerware.com/
11
44
Figure 2.9: The “Blue Box” and the WMPol computer. The Blue Box, computer,
and data acquisition break-out box are held in a frame on the telescope. The
Blue Box is on the bottom, the middle black box is the WMPol computer, and
the aluminum box above the computer contains a break-out board that takes the
signals from the receiver and the Blue Box and sends them to the data acquisition
card in the computer.
45
Figure 2.10: Telescope schematic. The boxes labelled X10 are remote control
modules as described in Section 3.2. For clarity, the elements of the receiver and
cryogenic/vacuum system are not shown.
2.1.6
Performance
The telescope has proved to be quite robust. The only mechanical element of
the telescope that required repair since installation was the coupling between the
azimuth motor and drive which was relatively straightforward and successfully
completed in January 2004.
When the pulse width modulated servo amplifiers used to drive the telescope
in azimuth and elevation were replaced with the linear ones to reduce noise, we
found during testing that the current capability of the linear servo amplifiers was
a little low. The amplifiers are equipped with a safety feature that turns them
46
off if the current limit is exceeded. During normal operation of the telescope, this
limit was rarely reached but there were occasions where the servo amplifiers had
to be reset by power cycling. We also had to reset Galil controller occasionally
but, in general, this was not a significant issue.
The code to run the telescope has worked well, in general. There were, however,
two issues that were discovered early on as the code was used in earnest to collect
data. The first issue was that acquiring both data and camera images caused the
code to eventually crash and the computer to reboot. This problem was mostly
solved by implementing a separate code to record camera images. When observing
objects, rather than the normal scanning about the NCP, it was more convenient
to use the main code to acquire camera images. Although the computer did
sometimes crash during these times, it turned out to be only a slight, though
annoying, inconvenience. The other issue was that the code would often crash
for unexplained reasons after taking about 140,000 samples (∼ 1.5 or 4 hours
depending on whether the data rate was 10 or 25 Hz). A fix was implemented
so that the code could check itself and restart scanning and data acquisition if it
had crashed, which meant that the telescope could collect data for several hours
or overnight without being monitored or losing a lot of data.
47
2.2
Receiver
The microwave receiver system consists of two pseudo-correlation polarimeters,
one in Q-band (38 − 46 GHz) and one in W-band (82 − 98 GHz) plus a W-band
radiometer to measure CMB temperature anisotropy. These frequency bands were
chosen as the combination of signals due to foregrounds (see Figure 1.14) and the
atmosphere (Figure 3.4) are minimized in these bands. The front-ends of the
receivers are contained inside an evacuated vacuum vessel (dewar) and cooled to
below 30 K with a cryogenic refrigerator. Figure 2.11 is a photograph of the
inside of the dewar. The receivers view the optics through a 10.8 cm diameter
50 µm thick mylar vacuum window which was measured to have a radiometric
temperature of 3(±1) K in W-band and 1(±1) in Q-band. A 0.3 cm thick sheet
of microwave transparent extruded polystyrene (“blue foam”) is attached to the
radiation shield inside the dewar between the receivers and the window to block
infrared radiation and thus reduce the heat load on the cold stage.
The receiver topology is similar to the design of the NASA WMAP radiometers
[Jarosik et al., 2003] and the baseline design for the Low Frequency Instrument
(LFI) for ESA-Planck [Seiffert et al., 2002]. As described further below, the purpose of using the pseudo-correlation technique is to remove, as much as possible,
the 1/f noise of the amplifiers and the downstream electronics from the radiome-
48
Figure 2.11: View inside the dewar. The W-band polarimeter horn (top, small
horn) is aligned with the optical axis of the telescope and the two W-band horns
underneath are for the W-band anisotropy radiometer. The Q-band polarimeter
horn is tilted 4◦ towards the W-band polarimeter horn due to the curvature of the
focal plane when off of the optical axis.
49
Figure 2.12: Schematic of the WMPol receiver array. Microwave radiation enters
the radiometer through the vacuum window in the dewar (right) where it is fed
into corrugated scalar feed horns.
ter signal. 1/f noise is parameterized by the “knee” frequency where 1/f noise
component and white noise component are equal and, thus, the total noise at the
knee frequency is equal to
√
2 times the white noise.
The polarimeters are designed to measure the (local - i.e. in telescope reference
2
2
frame) Stokes -Q parameter, or hEhor
i − hEver
i, while the anisotropy measuring
radiometer is designed to measure the temperature difference between two points
on the sky separated by ∼ 1◦ . Figure 2.12 is a schematic of the receiver and
Table 2.2 identifies the sources of various elements of the polarimeters.
50
Table 2.2: Major Elements of the Polarimeters
Device
Corrugated scalar feed horns
Orthomode transducers
180◦ hybrid couplers
Cryogenic amplifiers
Warm amplifiers
Phase switches
Adjustable attenuators
Bandpass filters
Microwave detector diodes
Differential amplifier
Source (Q-band)
Source (W-band)
Univ. of Milan (Italy) INAF-IASF (Italy)
Custom Microwavea
Vertex RSIb
QuinStarc
Millitechd
JPL/UCSB
JPL
Avantek
JPL
e
PMP
PMP
Aerowavef
Aerowave
UCSB
UCSB
PMP
PMP
UCSB
UCSB
a
Custom Microwave, Inc., Longmont, CO 80501, http://www.custommicrowave.com
Vertex RSI,Torrance, California 90505, http://www.tripointglobal.com
c
QuinStar Technology, Inc., Torrance, California 90505, http://www.quinstar.com
d
Millitech, Inc., Northampton, MA 01060, http://www.millitech.com
e
Pacific Millimeter Products, Golden, CO 80401, http://www.pacificmillimeter.com
f
Aerowave, Inc., Medford, MA, 02155
b
51
2.2.1
Feed Horns
As shown in Figure 2.12, conical corrugated scalar feed horns [Villa et al., 1997,
1998] couple the microwave radiation from the telescope to the radiometers. Any
CMB polarization measurement, like WMPol, requires feed horns with a highly
symmetric radiation pattern, extremely low cross-polarization, low loss over a
relatively large bandwidth (∼ 20% for WMPol), and optimal sidelobe rejection.
The optimized electromagnetic design for the W-band feeds requires throat section
grooves ∼ 0.13 mm thick and ∼ 1.5 mm deep. To meet these requirements, the
W-band feeds were manufactured via electroforming and they have a measured
deviation from the theoretical mandrel dimensions of less than 10 microns. The
larger physical size of the Q-band feeds and their corrugations make it possible to
machine the horns from an aluminum cylinder rather than electroforming. Both
the W-band and Q-band feeds were provided by collaborators in Italy. The main
design parameters for the WMPol feeds are reported in Table 2.3. Figure 2.13
shows the modeled return loss of the Q-band and W-band feeds and Figure 2.14
given the measured return losses. Figure 2.15 displays the modeled radiation
patterns of the feeds which were verified by measurements in Italy.
52
Table 2.3: Design of the WMPol Corrugated Scalar Feed Horns
Parameter
Flare angle (degrees)
Aperture diameter (mm)
Aperture corrugation depth (mm)
Aperture corrugation width (mm)
Throat diameter (mm)
Throat corrugation depth (mm)
Throat corrugation width (mm)
Number of corrugations
Corrugation step (mm)
Design return loss (dB)
FWHM (degrees)
Side lobe level (dB)
53
Q-band
W-band
7
27.16
1.9
1.45
9.04
3.55
1.45
34
2.17
< −35
20
< −30
7
12.08
0.88
0.67
2.972
1.51
0.13
37
1.00
< −35
20
< −30
Figure 2.13: Modeled return losses of the Q-band (dashed line) and W-band (solid
line) feed horns as a function of frequency normalized to the center of the nominal
bands. For Q-band (33 − 50 GHz), the center frequency is 41.5 GHz, while for
W-band (75 − 110 GHz) the center frequency is 92.5 GHz.
54
Figure 2.14: Measured return losses of the Q-band (dashed line) and W-band
(solid line) feed horns as a function of frequency normalized to the center of the
nominal bands as in Figure 2.13.
55
Figure 2.15: Modeled radiation patterns of the Q-band and W-band feed horns.
The solid line is the response of the Q-band horn while the dashed line is the
W-band horn response.
56
Table 2.4: Specifications of the Orthomode Transducers
Parameter
Q-band
Passband (GHz)
36.0 − 43.0a
VSWR
1.2 : 1 Max
Insertion loss (dB)
0.1 Max
Cross polarization (dB)
−35
a
W-band
85.0 − 105.0
1.5 : 1 Max
Not specified
−30
the useful band of Q-band OMT was measured to extend to 46 GHz
2.2.2
Orthomode Transducers
For each polarimeter, the radiation from a horn feeds into an orthomode transducer (OMT) through a short section of circular waveguide. The purpose of the
OMT is to separate the two polarizations of the incoming radiation. The OMTs
use an asymmetric configuration meaning that the OMT has a “main” output arm
co-linear with the input and a “side” output arm perpendicular to the input. The
design specifications for the Q-band and W-band OMTs are reported in Table 2.4.
Figures 2.16, 2.17, and 2.18 present, as an example, performance measurements
of the W-band OMT.
2.2.3
Phase Sensitive Section
After the OMT in the polarimeters, the two polarizations are split and go into
the two inputs of a 180◦ hybrid coupler. The two outputs of the hybrid coupler
57
Figure 2.16: Transmission parameters of W-band OMT. The s21 and s12 in the
legend refer to whether the measurement was taken in the forward (from input
port “1” to output port “2”) or reverse direction. The “m” or “s” indicates
whether the main or side output ports are being used where the signal sent into
the OMT is polarized in the same orientation as the port. For OMTs (and many
other passive devices) s21 and s12 should be equivalent.
58
Figure 2.17: Reflection parameters of W-band OMT. The s11 and s22 in the legend
refer to whether the measurement was taken in from input port “1” or output port
“2.” The “m” or “s” indicates whether the main or side output ports are being
used where the signal sent into the OMT is polarized in the same orientation as
the port.
59
Figure 2.18: Measurement of cross polarization of W-band OMT. The measurement indicates how much power (. 0.1%) sent into one of the output ports is
transmitted through the other output port.
60
Figure 2.19: Simplified diagram of phase sensitive section of radiometers.
begin the two legs of the phase sensitive part of the radiometer. Figure 2.19 is a
simplified view of the phase sensitive section of each radiometer. Operationally,
the hybrid coupler (also known as a “magic tee”) takes the two input signals and
splits them evenly among the two outputs. For one of the input signals (entering
the H-plane port), the two split signals remain in phase. For the other input (the
E-plane port), the output signals are 180◦ out of phase.
Following the derivations in Seiffert et al. [2002] and Jarosik et al. [2003], if
the signals into the first hybrid, in voltage units, are A and B then the signals
that leave the first hybrid are
A+B
A−B
√
and √ ,
2
2
61
(2.2)
where the plus or minus sign signifies the phase of the B signal. Then, after
HEMT amplification, the signals s1 and s2 are
µ
¶
A+B
√
s1 =
+ N1 G1 (t)
2
µ
¶
A−B
√
s2 =
+ N2 G2 (t),
2
(2.3)
(2.4)
where G1 (t) and G2 (t) are the time dependent amplifier gains (the total gain in
each leg, taking into account lossy elements) and N1 and N2 are the noise voltages
added to the signal by the HEMTs in each leg.
A 180◦ phase switch is installed in each leg to facilitate changing one of the
path lengths by λ/2, thereby changing the sign on one of the signals: s1 or s2 .
Only one of the phase switches is actively used (i.e. modulated) and the second
switch, which balances the phase and gain effects of the first switch, remains in
a fixed phase state. Equation 2.2 is used again to find the two signals out of the
second hybrid except A and B are replaced with s1 and s2 with the result
1
R= √
2
µ
¶
µ
¶
A+B
A−B
1
√
√
+ N1 G1 (t) ± √
+ N2 G2 (t),
2
2
2
(2.5)
where R is as labeled in Figure 2.19 and the “±” indicates that the result depends
on the phase state of the active phase switch. The result for L is the same except
that the “±” is replaced with a “∓.”
The outputs of the second hybrid go to microwave detector diodes, which are
also known as square-law detectors, as the output voltage is proportional to the
62
input microwave power (voltage squared). Thus, the output of a detector diode is
VR
¶
µ 2
¶
A2 + B 2
A + B2
2
2
2
+ N1 G1 (t) +
+ N2 G22 (t)
2
2
¾
±(A2 − B 2 )G21 (t)G22 (t)
g
=
2
½µ
(2.6)
where VR is the voltage from the diode detector on the “R” leg and g is the gain
of the diode. This equation is relatively uncomplicated as the A, B, N1 , and
N2 voltage signals are all uncorrelated with respect to each other meaning that
their time averages are zero and, except for A2 , B 2 , N12 , and N22 , time averages
of their products are also equal to zero so all the cross terms from squaring R
cancel out. VL , again, has the same form except that the “±” is replaced with
“∓” and it is assumed that the diode gain is the same for both diodes. As can be
seen in Equation 2.6, taking the difference VR − VL will result in a signal that is
proportional to A2 − B 2 as desired.
Switching the phase switch and using a lock-in amplifier to take the difference
VR+ − VR− where the subscripts “+” and “-” denote the phase switch state would
also give the same result as VR − VL . However, in order to avoid adding in extra
noise due to the 1/f noise of the amplifiers, a switch rate higher than the 1/f knee
frequency of the amplifiers (& 2 kHz for W-band) is required for VR+ − VR− as the
gain, G1 (t) and G2 (t), can change significantly on longer time scales. On the other
hand, a more modest switch rate ∼ 100 Hz should be sufficient for VR − VL to
63
remove downstream (post-detector diode) 1/f as subtracting the diodes removes
1/f at the (∼ MHz) bandwidth of the diodes.
The above derivation assumes that the components behave ideally and taking
into account non-ideal behavior can become very complicated, especially as the
HEMT amplifiers and other components can have phase variations as a function
of frequency. In general, though, phase mismatching causes some mixing between
the A and B on the output signals thus lowering the signal to noise ratio. To
minimize the effects of mismatching, adjustable attenuators are installed in the
phase-sensitive paths to match the gain of the two paths and thin brass shims
(approximately λ/40 or 0.23 mm for Q-band and 0.10 mm for W-band) are used
to match the phase lengths of the two paths.
The W-band CMB temperature anisotropy radiometer is similar to the polarimeters except that two horns feed into the first hybrid coupler and the outputs of the second hybrid coupler feed into a single pole double throw PIN switch
modulated at 5 kHz which then feeds a square-law detector diode. Phase sensitive
detection at this modulation frequency provides a signal that is proportional to
the temperature difference between the two points on the sky that the horns view.
Due to space limitations and other considerations, adjustable attenuators are not
used in the phase sensitive paths; instead, the gains are matched through small
changes in the bias voltages. In addition, phase switches are not used but the 5
64
kHz switch frequency is high enough to overcome 1/f gain fluctuations.
2.2.4
Amplifiers
The microwave amplifiers used to increase the incoming microwave radiation
power by a factor of approximately 106 before being detected are the core of the
WMPol receiver. Low-noise High Electron Mobility Transistor (HEMT) monolithic microwave integrated circuit (MMIC) amplifiers are used in the cryogenic
front-ends as well as in the back-ends of the W-band radiometers. These amplifiers are made up of multiple stages of field effect transistors that are cascaded to
achieve the desired gain. The input microwave signal AC couples to an antenna
attached to the gate which has the effect of modulating the current between drain
and source and providing about 6 dB of gain per transistor. For the W-band amplifiers, the MMIC devices were manufactured by TRW14 using designs by Sandy
Weinreb at JPL15 and the amplifiers were assembled into gold-plated brass “bodies” and tested at JPL. The Q-band devices (manufactured by HRL16 ) were also
designed and provided by Sandy Weinreb and the amplifiers were assembled at
UCSB. Figures 2.20 and 2.21 display the measurements of amplifier noise as a
function of frequency for a Q-band and a W-band amplifier while refrigerated to
14
TRW Space and Electronics Group, Redondo Beach, CA 90278
Jet Propulsion Laboratory, Pasadena, CA 91109, http://www.jpl.nasa.gov
16
HRL Laboratories, LLC, Malibu, CA 90265-4797, http://www.hrl.com
15
65
Figure 2.20: Q-band amplifier noise. The mean noise temperature for the 38 to
46 GHz band is 68 ± 2.4 K. The gain of the amplifier is approximately 20 dB and
the 1/f knee frequency is 50 − 60 Hz.
less than 20 K in a test dewar. Noise of the microwave amplifiers is quantified by
P = kT β,
(2.7)
where k is Boltzmann’s constant and the noise temperature, T , is the temperature
of a blackbody that would emit the same amount of power, P , within bandwidth,
β, in the Rayleigh-Jeans (hν ¿ kT ) limit.
66
Figure 2.21: W-band amplifier noise. The mean noise temperature for the 82
to 98 GHz band is 50 ± 0.74 K. The gain is approximately 25 dB and the knee
frequency is typically 1 − 2 kHz.
67
2.2.5
Filters
Since using the full bandwidth of the amplifiers is not advisable - there may be
frequencies where the gain is low, noise temperature is high, or the amplifiers are
otherwise not well behaved - microwave filters are used to define the bandpass of
the radiometers. The Q-band filters are on microstrip in a body that uses coaxial
connectors while the W-band filters are a suspended substrate design housed in a
body that uses waveguide. Both filters are made from copper on teflon (CuFlon17 ).
Figure 2.22 shows the structures used for the Q-band and W-band filters and
Figures 2.23 and 2.24 present the measured Q-band and W-band filter bands.
For W-band, the filters were placed between the cryogenic amplifier stages
and the back-end amplification. It was advantageous to place the filters in that
position as the small amount of loss plus the reduction in power going to the
warm amplifiers helped prevent the third amplifier in each chain from receiving
too much input power and becoming compressed, meaning that the amplifier gain
is no longer constant with input power. As the losses and phase changes as a
function of frequency for the W-band filters were small and well matched, having
the filters in the phase sensitive paths did not pose a problem. For Q-band, the
coaxial connectors required that the filters be placed between the second hybrid
and the detector diodes but, in fact, this was desirable as it was important for
17
Polyflon Company, Norwalk, CT 06851, http://www.polyflon.com
68
Figure 2.22: Microwave filter masks. The Q-band filter mask is above (green) and
the W-band filter mask is below (blue). Masks with these patterns are used in
a multi-step etching process which leaves the same pattern in copper on teflon.
These filter structures are approximately 0.5 inch (1.27 cm) long and 0.050 inch
(0.127 cm) wide. The 0.032 inch (0.0813 cm) structures that extend out at the
ends of the W-band filter extend into waveguide while for Q-band, pins that couple
to coax are attached at the ends of the filter element with conducting epoxy.
69
Figure 2.23: Q-band filter band. The different lines denote each of the filters used
in the Q-band polarimeter.
70
Figure 2.24: W-band filter band. The different lines denote each of the filters used
in the W-band radiometers.
71
the Q-band polarimeter that there be as little attenuation as possible between the
cryogenic and warm amplifier. The reason for this is that the cryogenic Q-band
amplifiers only had ∼ 20 dB gain, so any extra attenuation would significantly
increase the total polarimeter noise due to an increased noise contribution by the
back-end amplifier.
2.2.6
Detection and Data Acquisition
The outputs of the radiometers go to square-law detector diodes. Figure 2.25
shows examples of diode response as a function of frequency. The diode outputs
are fed into a ×100 gain differential amplifier before going to a lock-in amplifier
referenced to the phase modulation frequency. Figure 2.26 displays the schematic
of the differential amplifier circuit. The lock-in was originally designed at UCSB
to function at a modulation frequency of 10 or 100 Hz though frequencies up to
1 kHz were found to be acceptable. Finally, the output of the lock-in goes to
an ideal integrator and the data acquisition card in the telescope computer. The
individual diode signal levels after ×100 gain are also recorded. These DC levels,
as mentioned previously, do not benefit from the 1/f removal that differencing the
diodes provides and do not go to a lock-in amplifier. However, these measurements
were found to be very helpful for calibration (see Section 4.6) and measuring sky
temperature (Section 3.1).
72
Figure 2.25: W-band diode response. The different lines show the response of
the two detector diodes used in the W-band polarimeter to an input signal of -30
dBm or 1 µW. The manufacturer specifies a minimum sensitivity of 0.25 mV/µW
under similar test conditions.
73
Figure 2.26: Schematic of the differential amplifier circuit. The input signals are
first measured by low voltage noise OP27 amplifiers before going to the AMP02
instrumentation amplifier. The gain on each OP27 is manually adjustable with a
trimming potentiometer to adjust for differences in diode response.
74
During the commissioning of the instrument, it was found that the polarized
offsets were rather high (∼ 10%) which limited the amount of gain that the polarimeter output could be multiplied by before going to a data acquisition channel.
The offset was due to a, as yet unexplained, change in DC signal out of the diodes
when the phase switches were in different states. Figure 2.27 shows the schematic
of a circuit designed to remove this offset and allow for the overall gain on the
polarimeters to be increased such that the polarimeter noise would exceed the
data acquisition noise. Figures 2.28 and 2.29 compare time ordered data (offsets
removed) and power spectral densities of radiometer data and data from a “blank”
channel to show that radiometer noise dominates.
2.2.7
Electronics
The Q-band cryogenic MMIC-based amplifiers use biasing circuitry that was
originally designed for the BEAST back-ends as described in Childers et al. [2005].
The commercial warm Q-band amplifiers require only a +12 VDC bias. The biasing of the W-band HEMT amplifiers, cryogenic and non-cryogenic, is accomplished
with electronics that provide constant voltage to the gate and drain of each transistor with the source connected to a common ground. For each W-band amplifier,
the drains of all four transistors are tied together and the four gates are divided
into two pairs that each share a bias voltage.
75
Figure 2.27: Schematic of the offset circuit. A manually adjustable voltage between -10 and +10 VDC is sent into one input of the AMP02 to remove the offset
from the polarimeter signal. The four resistors allow for gains between ×1 and
×100.
76
Figure 2.28: Noise comparison of time ordered data. The Q-band polarimeter
data, with offsets removed, (black) is overlayed by a blank channel (white). The
standard deviation of the Q-band data is 27 mV and it is 0.92 mV for the data
from the blank channel.
77
Figure 2.29: Noise comparison of power spectral densities. Shown are Q-band
polarimeter data (solid) and a blank channel (dots). The voltage noise at 12.5 Hz
is 6.8 mV/Hz1/2 for the Q-band data and 0.25 mV/Hz1/2 for the blank channel.
These data were collected at a 25 Hz sample rate.
78
In addition to the bias electronics, other functions of the radiometer electronics include biasing of the phase switches, temperature control of the microwave
components outside the dewar, and cryogenic temperature sensing. The phase
switch bias electronics send a manually adjustable constant current between 10
and 20 mA to each phase switch. Switching is enabled by sending a TTL signal to
the electronics, which causes the current to be either positive or negative thereby
activating one of the two diodes paths in the switch. Temperature regulation of
the warm microwave devices at approximately 305 K is accomplished by power
resistors supplied by an isolated power supply and controlled by a servo circuit
with the output of AD590 temperature sensors providing feedback. The cryogenic
sensor electronics bias silicon diode temperature sensors18 with 10 µA and return
the temperature-dependent voltage across the diode.
All the radiometer electronics and the microwave components outside of the
dewar are contained in a contiguous aluminum shield. To reduce noise, the dewar
is electrically isolated from the telescope frame except for two ground connections.
One ground connection goes from the dewar to the cryogenic refrigerator cold head
and the helium compressor through the compressed gas lines and electrical cable
that connect the cold head to the compressor. Another ground connection from the
dewar to the radiometer power supply ground ensures that the dewar ground con18
Lake Shore Cryotronics, Inc., Westerville, OH 43082, http://www.lakeshore.com
79
Figure 2.30: Diode protection circuit. The 1N4148 diodes ensure that potentially
damaging voltage spikes are shunted to ground rather than transmitted to the
amplifiers. The diodes also prevent the biases from exceeding the “safe” levels of
±0.5 VDC for the gates and +1.4 VDC for the drain as referenced to the common
ground.
nection is not severed if the cryocooler power cable is disconnected from the wall.
Diodes on the bias wires to protect the amplifiers from electrostatic discharge,
similar to circuits already on the bias cards, were installed inside the dewar and
on the W-band back-end amplifiers. This circuit is shown in Figure 2.30.
2.2.8
Cryogenics
To cool the cryogenic elements of the receiver, a two-stage Gifford-McMahon
cycle cryogenic refrigerator19 is used with helium as the refrigerant. The first stage
19
Leybold Vacuum Products Inc., Export PA 15632, http://www.leybold.com/
80
of the refrigerator cools a radiation shield to approximately 70 K to reduce the
thermal load on the second stage, which cools the receiver.
An oil-free vacuum pump20 was originally used to evacuate the dewar. This
unit is old and eventually had an electronics failure and was replaced with a
two-stage mechanical rotary vane pump. A 0.01 to 100 millitorr Pirani vacuum
gauge21 is used to monitor pressure inside the dewar.
To facilitate remote operation, protect the dewar from contamination, and
reduce load on the vacuum pump, a normally-closed pneumatic vacuum valve
is placed between the dewar and vacuum pump. A maintenance-free oil-less air
compressor22 is used to provide air at a pressure around 80 psi to actuate the
valve. This air compressor is located on the ground floor of the observatory and
a long hose feeds air to the telescope using quick disconnect fittings. A solenoid
valve controls whether pressurized air reaches the pneumatic valve to open it and
in-series pressure switches measure the pressure on both sides of the pneumatic
valve and prevent the valve from opening, by stopping air flow, if the pressure
on either side of the pneumatic valve is near atmospheric pressure indicating that
either the vacuum pump is malfunctioning or the dewar has developed a vacuum
leak.
20
DanVac, Aurora, IL 60506, http://www.danvac.com
Vacuum Research Limited, Pittsburgh, PA 15222, http://www.vacuumresearch.com
22
Campbell-Hausfeld, Harrison OH 45030, http://www.chpower.com
21
81
2.2.9
Performance
The system noise temperatures of the Q-band and W-band polarimeters are
measured using manual calibrations of the non-differenced DC channels as described in detail in Section 4.6. The resulting Q-band noise temperature is 128
(±0.61) K and the W-band noise temperature is 120 (±2.9) K. The high noise
temperature, especially for the Q-band system, is mostly due to the quality of amplifiers that were available to us at the time the receivers were assembled, tested,
and deployed. Although better amplifiers are now available, they have not yet
been installed into the WMPol receiver. The measured room temperature losses
due to the OMT and hybrid coupler before the cryogenic amplifiers are less than
0.5 dB for Q-band and 1.5 dB for W-band. This means that the maximum contribution to the polarimeter noise temperature due to front end losses, assuming the
polarimeters are at a physical temperature of 30 K, is 4 K for Q-band and 12 K for
W-band. Table 2.5 is a list of receiver noise temperatures, effective bandwidths,
and sensitivities for the Q and W polarimeters.
The radiometer equation, as given by Kraus [1986], is
s
∆T = KTsys
1
+
∆νef f τ
µ
∆G
G
¶2
,
(2.8)
where ∆T is the sensitivity, or minimum detectable signal, K is a constant that
√
depends on the type of radiometer ( 2 for a correlation system due to the the dif-
82
Table 2.5: Parameters of the Polarimeters
Channel
Tsys
(K)
∆νef f
(GHz)
Q-band (38-46 GHz)
W-band (82-98 GHz)
128
120
8.0
12.6
Sensitivity
(mK·s1/2 )
3.4
3.0
ferencing), Tsys is the system noise temperature, ∆νef f is the effective bandwidth
of the radiometer, τ is the integration time (nominally one second), and
∆G
G
is a
measure of gain fluctuations leading to additional 1/f noise power. Ideally, the
correlation radiometer, would negate the gain fluctuation leaving
∆T =
√
Tsys
.
∆νef f τ
2p
(2.9)
Given the measured results for Tsys and ∆νef f , the expected sensitivity for the
polarimeters are 2.0 mK·s1/2 and 1.4 mK·s1/2 and there is a factor of 1.8 to 2.1
between the expected and measured sensitivity. The error on the mean measured
sensitivity is ±0.01 mK·s1/2 for Q-band and ±0.03 mK·s1/2 for Q-band.
Effective bandwidth, as defined by Kraus [1986] as
∆νef f
R
[ G(ν)dν]2
,
=R
|G(ν)|2 dν
(2.10)
where G(ν) is the frequency dependent gain, is measured by taking data on a
83
spectrum analyzer at 20 kHz and measuring
∆V
∆T
1
=
=p
,
V
T
∆νef f τ
(2.11)
√
where ∆V is the white noise level of the data, in Volts/ Hz, and V is the DC
diode signal. ∆νef f is calculated after dividing
∆V
V
by
√
√
2 to convert to Volts· s.
The estimated error on measurements of the effective bandwidth are ±10%.
Figures 2.31 and 2.32 shows examples of power spectral densities for 80 minutes
of data obtained at a 25 Hz data rate while looking at a stable sky. As can be
seen in the plots, the 1/f knee for the Q-band data is less than 0.1 Hz while for
W-band the 1/f knee is approximately 4 Hz. The knee frequency for the W-band
system was much better when tested at UCSB (< 1 Hz) but efforts to diagnose the
cause of the higher 1/f in the field have also not been successful. When initially
setting up the receiver, a switch rate of 100 Hz was used, with a data rate of 10
Hz (integration of 10 cycles for each data point), but the modulation frequency
was changed early in the observing campaign to 250 Hz, 25 Hz data rate, which
did result in some improvement of the polarimeter noise.
The W-band anisotropy measuring radiometer failed soon after the telescope
was installed in the Barcroft Observatory and repeated attempts to discover the
problem have not been successful.
The cryogenic refrigerator used to cool the front ends of the radiometers has
84
Figure 2.31: Example of a Q-band PSD of data collected while observing the
sky from the Barcroft Observatory. The calibrated noise level at 12.5 Hz is 3.5
mK·s1/2 .
85
Figure 2.32: Example of a W-band PSD of data collected while observing the
sky from the Barcroft Observatory. The calibrated noise level at 12.5 Hz is 3.0
mK·s1/2 .
86
two known issues. First, the cold end of the refrigerator is known to have a
mechanical problem that slightly reduces performance and seems to cause the
cooler and dewar to warm up after about fourteen days of continuous operation.
In order to recycle the system, the inside dewar temperature has to be brought
up all the way to ambient temperature (& 280 K) before cooling down again;
this process requires approximately 24 hours. The other issue is overheating of
the refrigerator’s helium compressor during the middle of the day during summer.
The compressor is liquid-cooled, with a fan plus radiator to draw heat away from
the compressor motor. There is a thermal cutout that prevents damage due to
overheating. During winter, a 50 − 50 water-antifreeze (ethylene glycol) mix is
used to prevent the coolant from freezing during times when the compressor is
shut down. This mix has reduced thermal properties as compared to pure water
and is not sufficient to transfer heat during midday from the compressor motor
in the increased summer temperature conditions. Once this issue was discovered,
replacing the anti-freeze mix with distilled water solved the problem. Other than
these two issues (and having to replace the vacuum pump), the cryocooler/vacuum
system worked well during the campaign.
87
2.3
Beam Model
The beam sizes of the radiometers on the sky after passing through the optics
were modeled using GRASP823 by collaborators at INAF-IASF in Italy. Geometrical optics with geometrical theory of diffraction was used for the secondary
reflector, while for the primary reflector physical optics was applied. The geometry, which was analyzed in transmitting mode (i.e. from feed to sky), is shown in
Figure 2.33. In the calculations, far field effects were neglected at the feed level as
the feed aperture is only about 4.5λ and the secondary reflector is at the far field
of the feeds. Gaussian beam models of the feeds for both Q-band and W-band
were used with modeled FWHM beam sizes of 19.4 degrees at 41.5 GHz and 19.3
degrees at 92.5 GHz (see Figure 2.15). Each beam was calculated using a regular
(u,v) grid centered on each beam peak in the range (-0.02, 0.02) at 41.5 GHz
and (-0.01, 0.01) at 92.5 GHz, for both u and v, corresponding to 1.15◦ × 1.15◦
and 0.575◦ × 0.575◦ on the sky. Figures 2.34 and 2.35 show contour plots of the
beam models for the polarimeters and W-band temperature anisotropy measuring
channel. To characterize each beam, an elliptical Gaussian fit of the beam in the
whole angular region of calculation was obtained. The modeled characteristics
are reported in Table 2.6 with expected beam sizes (average FWHM) of the Qband and W-band polarimeters of 18.80 and 8.50 respectively. Measurements of
23
TICRA, Copenhagan, Denmark, http://www.ticra.com
88
Figure 2.33: Geometry of both reflectors (left) and of the focal plane (right) as
inserted into the GRASP8 electromagnetic model. The orientation of the focal
plane coordinate system (Xf ,Yf ) used in the right panel is shown in the left panel.
the beam sizes are discussion in Section 4.5.
2.4
Automatic Calibrator
Since no radiometer is perfectly stable over time, it is useful and typical to have
a device to frequently calibrate the receiver. This allows gain fluctuations in the
instrument to be measured and accounted for when analyzing the data. In the case
of WMPol, a thin dielectric (polypropylene) sheet was mounted to a motorized
frame such that it could be placed in front of the receiver either manually or on
a set schedule to create a small, repeatable, polarized signal. This technique is
similar to that described in detail in O’Dell et al. [2002]. Figure 2.36 shows the
89
Figure 2.34: Contour plots of beam models for the Q-band (left) and W-band
(right) polarimeters. The horizonal axis corresponds with elevation and the vertical axis with azimuth. The first three contours correspond to -3,-6, and -10 dB
below the peak.
Figure 2.35: Contour plots of beam models of the WMPol temperature anisotropy
measuring radiometer. On the left is the model for the WT1 channel and on the
right is the model for the WT2 channel. The horizonal axis corresponds with
elevation and the vertical axis with azimuth. The first three contours correspond
to -3,-6, and -10 dB below the peak.
90
Table 2.6: WMPol Beam Model Characteristics
Parametera
QP
WP
WT1
WT2
Xf (mm)
Yf (mm)
Zf (mm)
α (degrees)
β (degrees)
0.0
-28.6
0.97
0.0
4.0
0.0
0.0
0.0
0.0
0.0
-27.0
17.5
0.56
0.0
0.0
-25.4
-20.6
0.56
0.0
0.0
DIR (dBi)
55.65
62.62
XPD (dB)
39.81
67.01
% DEPOL
0.03 5.6E-05
FWHM X (arcmin)
19.08
8.45
FWHM Y (arcmin)
18.61
8.45
FWHM AVE (arcmin) 18.845
8.45
ELL
1.03
1.0
62.53 62.51
43.52 43.34
0.01 0.01
8.37 8.38
8.63 8.65
8.50 8.52
1.03 1.03
a
QP, WP, WT1, and WT2 are the receiver feeds as defined in Figure 2.33. Xf Yf Zf is
the position of the feed horn phase center in the coordinate system that defines the WMPol
focal plane where Xf Zf is the symmetry plane of the telescope and +Zf points from the
focal plane to the secondary reflector. α is the first rotation about the Yf axis and β is
the second rotation about the new X axis. DIR is the maximum directivity of the co-polar
component. XPD is the cross polar discrimination defined as the ratio between the copolar
maximum and the
√ cross polar maximum. % DEPOL is the integrated depolarization factor
Q2 +U 2 +V 2
defined as (1 −
) × 100 where Q, U, V, and I are the Stokes parameters (see
I
Section 1.2). FWHM X and FWHM Y are the angular resolutions along the major and
minor axis of the elliptical fit, ELL is the ellipticity of the -3 dB contour level
91
orientation of the automatic calibrator with respect to the dewar. The calibration
procedure of the WMPol receiver, including how the automatic calibrator data is
used, is described in Section 4.6.
The automatic calibrator was first installed on the dewar at the end of April
2004. Unfortunately, the frame that held the film was not attached well to the
rod that the motor used to rotate the calibrator into position and frame fell off,
probably due to wind, shortly thereafter. Since the limit switches that control
the motor motion rely on the frame being in place, the calibrator motor burned
out, presumably after running for an extended period of time. The calibrator was
retrieved and brought back to UCSB at the end of May 2004 for repair. After
replacing the calibrator motor, the frame was reattached to the rod with screws
and the calibrator was reinstalled in early July 2004. The calibrator functioned
very well after that but the film was replaced in early September 2004 as it had
become dusty.
92
Figure 2.36: Automatic calibrator. The dielectric sheet is supported by a frame
constructed of fiberglass tubing. During a calibration sequence, the dielectric
sheet is moved in front of the dewar window as shown and unpolarized radiation
from the ambient temperature load and the sky (through the optics) is slightly
polarized after reflecting off of or passing through the sheet to the polarimeters.
This small polarization signal is due to the difference in the reflection coefficients
of the sheet for radiation polarized either parallel or perpendicular to the plane
of incidence. After calibration, the frame is rotated away from the polarimeters
about the pivot point until it rests on top of the dewar. Limit switches are used
to properly position the frame and a digital flag is recorded in the data to identify
when calibration sequences occur.
93
Chapter 3
The Barcroft Observatory
The WMPol instrument is located at an altitude of 3880 meters in the White
Mountains east of Bishop, California at longitude 118◦ 140 1900 W and latitude
37◦ 350 2100 N. The University of California White Mountain Research Station1
(WMRS) operates the Barcroft Facility, which includes the Barcroft Observatory
where the telescope is located. The central building at Barcroft is the Nello Pace
Laboratory.
The Barcroft Facility is accessible during the summer and early fall by a partially unpaved road. During the rest of the year (approximately November through
June), snow conditions require that a Sno-Cat2 be used to travel from the snow
level to the Barcroft Facility. The trip from the Owens Valley Lab (OVL) in
1
2
http://www.wmrs.edu
Tucker Sno-Cat Corp., Medford, OR 97501, http://www.sno-cat.com/
94
Bishop, where WMRS is headquartered, is approximately two hours by car during the summer or four hours by car and Sno-Cat otherwise.
The Barcroft Observatory is located about 70 meters above the main part of
the Barcroft Facility on a plateau that has a clear view of White Mountain peak
(longitude 118◦ 150 1700 W, latitude 37◦ 380 0400 N, altitude 4342 meters). The
observatory is a 18.5 foot (5.6 meter) diameter Ash-Dome3 observatory dome. The
entrance at ground level opens into a work and support space with a stairway that
goes up to a second level where the telescope is situated. Figure 3.1 shows a cutaway drawing of the dome, revealing the position of the telescope, and Figure 3.2
shows the telescope being installed into the dome which required maneuvering it
through the shutter.
The dome rests on a track and is motorized so that it can be rotated in azimuth.
In addition, a motor is used to operate the shutter. In the original design, the
dome rotation and shutter control were actuated by manual jog switches. To
facilitate remote operation, a motion control system almost identical to that of
the WMPol telescope was implemented to rotate the dome. A different system, a
bank of relays, is used for the shutter control. These relays allow the shutter to
be opened or closed manually or by remote control and, for safety, two relays are
required to be actuated to open or close the shutter. One relay is for enabling or
3
Ash Manufacturing Company, Plainfield, Illinois 60544, http://www.ashdome.com/
95
Figure 3.1: Rendered view of the WMPol telescope in the Barcroft Observatory.
96
Figure 3.2: Installation of WMPol into the Barcroft Observatory. The parabolic
primary mirror is protected by foam and elliptical secondary mirror was mounted
to the blue plate after installation.
97
disabling control and the other relay determines whether the shutter is open or
closed.
The longitude, latitude, and altitude of the observatory were measured with
a Global Positioning System (GPS) system4 that was installed in the observatory
during the observing campaign. The GPS unit in the observatory also provides
accurate time in case there is a loss of internet connectivity. The Atomic Clock5
software is used to connect to available time servers (such as at NIST) to synchronize the computers at the observatory with “official U.S. time.”
As the conditions at Barcroft are often cold and dry, small electric oil-filled
radiator heaters are used to keep the temperature comfortable in the observatory, particularly in the ground level work space. A humidifier and an oxygen
concentrator6 are also in the observatory to use as needed. An antistatic blower7
was found to greatly reduce electrostatic discharge which not only makes it more
pleasant to work but also helps protect sensitive equipment from possible damage.
4
Trimble Navigation Limited, Sunnyvale, CA 94085, http://www.trimble.com/index.html
Parsons Technology, Mattel Inc., El Segundo, CA 90245, http://www.mattel.com
6
AirSep Corp., Buffalo, NY 14228, http://www.airsep.com/index.html
7
SIMCO, Hatfield, PA 19440, http://www.simcoion.biz/data/index.shtml
5
98
3.1
Sky Temperature
Although microwave atmospheric emission is known to be highly unpolarized,
the choice of a suitable observing site is mandatory to optimize the data taking
efficiency, reduce systematic effects, and avoid large baseline drifts. The Barcroft
Facility provides an excellent site for CMB observations. Marvil et al. [2006] and
a previous study of atmospheric emission at Barcroft [Bersanelli et al., 1995] show
low water vapor content, with observed precipitable water vapor (PWV) limits as
low as ∼ 0.2 mm. Figure 3.3 shows an integrated histogram of PWV derived from
dewpoint data taken at the observatory from September 2003 through November
2004.
Using an atmospheric modeling code developed at UCSB (hereafter called
ATMOS) the expected zenith sky temperature of the atmosphere as a function
of frequency can be estimated. As reported in Marvil et al. [2006], ATMOS uses
a standard U.S. atmosphere temperature-pressure profile and pressure-broadened
emission by H2 O, O2 , and O3 as referenced from a Jet Propulsion Laboratory line
catalog. Figure 3.4 shows that results of an ATMOS simulation for a sea-level
water vapor density of 10 g/m3 (corresponding to a dew point ∼ 11◦ C) agree well
with measurements of the sky temperature as discussed below.
Alternately, assuming precipitable water vapor content in the range 0.2−6 mm
99
Figure 3.3: Integrated histogram of PWV at the observatory. The PWV values are
derived from dew point measurements taken at the observatory from September
2003 through November 2004 [Marvil et al., 2006].
100
Figure 3.4: Model of the zenith atmospheric sky temperature at the Barcroft
Observatory. Shown in the plot are contributions from H2 O (dashed), O2 (dotted),
and O3 (solid, lower right of plot) for a sea-level water vapor density of 10 g/m3 .
Also shown is the sum of the contributions (solid). The two horizontal lines are
drawn between the 3 dB points of the WMPol Q-band and W-band band passes
at a level corresponding to the zenith sky temperatures measured by WMPol.
101
and calibrating the atmospheric emission model of Danese and Partridge [1989]
with more recent data, zenith atmospheric sky temperatures at the centers of the
WMPol bands in the ranges of 9 − 12 K at 43 GHz and 7 − 16 K at 90 GHz can be
expected [Bersanelli, 2005]. As can be seen in Figure 3.4 the atmospheric emission
spectrum in the 40 − 45 GHz range, dominated by O2 broadened line complex,
is extremely steep so that the tail of the band can contribute significantly to the
zenith sky temperature (see Figure 2.23 for the WMPol Q-band filter band).
The sky temperature is measured with sky dips. For WMPol, the sky dips
are scans in elevation from 32◦ to 48◦ at azimuth 0◦ , which give the zenith sky
temperature after fitting to the model
Tantenna = Tsystem +
Tzenith
,
sin(θ)
(3.1)
where θ is the elevation angle. Examples of sky dip data are shown in Figures 3.5 and 3.6. During the observing campaign, the measured mean zenith sky
temperature was 9 ± 0.2 K and 10 ± 0.6 K for Q-band and W-band respectively
with measurements ranging from 8 − 11 K for Q-band and 9 − 15 K for W-band.
These values agree well with the predicted values and measurements from Marvil
et al. [2006], Childers et al. [2005], and Bersanelli et al. [1995].
102
Figure 3.5: Example of sky dip data in Q-band. The zenith sky temperature is
estimated by fitting the data to Tantenna = Tsystem +Tzenith / sin(θ) where θ is elevation angle. The mean zenith sky temperature during the observing campaign was
measured to be 9.0 ± 0.2 K in Q-band in good agreement with model predictions
and previous measurements.
103
Figure 3.6: Example of sky dip data in W-band. The zenith sky temperature is
estimated by fitting the data to Tantenna = Tsystem +Tzenith / sin(θ) where θ is elevation angle. The mean zenith sky temperature during the observing campaign was
measured to be 10 ± 0.6 K in W-band in good agreement with model predictions
and previous measurements.
104
3.2
Remote Control System
We considered it quite advantageous to be able to operate the telescope remotely. In order to facilitate remote operation and data collection a number of
elements were installed in the observatory to enable monitoring and control of the
telescope.
The core of the remote control system is a Stargate automation system.8 The
Stargate has the capability to control X10 (i.e. on/off signals sent over power
lines) devices and on-board mechanical relays as well as read digital and analog
inputs. The Stargate can accept commands by phone line, internet, or computer
via a serial port. The X10 and mechanical relays are used to turn on and off (or
power-cycle to reset, as needed) the computers and other elements of the telescope.
Figure 3.7 is a diagram of the remote control system set up.
As shown, in Figure 3.7 there are two sets of devices connected to X10 modules. On the left are devices associated with the telescope while on the right are
computers and other hardware that are part of the observatory infrastructure. As
the telescope power comes from a separate UPS than the observatory computer
power, and since the X10 signals cannot travel through a UPS, two communication modules are required, one for each UPS, to send X10 signals to the devices.
In addition, two X10 control wires are sent through mechanical relays in the Star8
JDS Technologies, Poway, CA 92064-6876, http://www.jdstechnologies.com
105
Figure 3.7: Schematic of Stargate control of telescope and observatory. The Stargate automation system, with commands entered either via phone or a web based
interface, uses external X10 or internal relays to control power to the telescope,
computers, and other hardware in the Barcroft Observatory.
106
gate which determine which set of devices (telescope vs. observatory) commands
are sent to.
For some of the items that need to be controlled, X10 is not practical. As
mentioned previously, the shutter control requires a number of relays to open and
close the shutter and two of the mechanical relays in the Stargate unit are utilized
for remote operation. In addition, the compressor for the cryocooler cannot be
run on a UPS due to the large inductive load (plus it runs on 208 VAC single
phase) so it turns out to be much more straightforward to use a mechanical relay
to send power to a solid state relay which is in series with the power wires that
go from the wall to the cryocooler.
When the oil-free vacuum pump was used to evacuate the dewar, it was powered on and off with an X10 relay on the telescope and digital inputs were used to
monitor the pump status. After switching to the mechanical pump, a relay system like that for the cryocooler could have been implemented. Instead, we decided
initially to run the pump continuously which is a perfectly acceptable option for
a mechanical pump and avoids the possibility (when the pump is turned off) of
the pump oil getting too cold and viscous for the pump to operate. Air pressure
to a pneumatic vacuum valve is controlled by a solenoid valve which is actuated
using a Stargate relay. The pressure inside the dewar is monitored by sending an
analog signal from the vacuum pressure gauge to an analog input on the Stargate.
107
In practice, the remote control system was used most often to open and close
the shutter and this was, of course, the most critical feature as far as preventing
potential damage to the telescope. The cryocooler and vacuum system control
were also used several times and occasionally computers and other devices had to
be reset by power-cycling.
3.3
Communications
While it is critical for remote operations to maintain communication with the
observatory, the location of the Barcroft Facility and potential for rough weather
makes communication a challenge. WMRS has installed two systems to connect
to the internet, a satellite connection9 with a dish at the Pace Lab and a wireless
T1 connection through radios10 at the observatory, White Mountain peak, and
OVL. Both internet services connect to a dual ISP “Twin WAN” router11 located
in the observatory which distributes internet traffic to and from the computers in
the observatory and at the main Barcroft facility and balances the load depending
on connection availability and bandwidth. A cellular phone base station was also
installed in the Pace Lab to provide phone service to the observatory and the
two buildings that were used for BEAST. Since there are no electrical power
9
StarBand Communications Inc., McLean, VA 22102, http://www.starband.com/
Wi-LAN Inc., Calgary, AB Canada T1Y 7K7, http://www.wi-lan.com/
11
XiNCOM, WINS International LLC, Hubbard, OR 97032, http://www.xincom.com/
10
108
wires going to White Mountain peak, a system of solar cells and batteries was
implemented to provide power to the radio at the summit while being able to
withstand the harsh conditions there.
Direct communication with the computers at the observatory is achieved by
using the Remote Administrator (Radmin) software.12 Radmin allows for control
of the computers at the observatory from the main Barcroft station and also
from Santa Barbara and potentially anywhere with an internet connection. It is
also possible to transfer files via Radmin which can be very convenient. One of
the computers in the observatory is set up as an FTP server and is the primary
computer used to transfer data from the telescope to UCSB.
3.4
Weather Monitoring
It is important to be able to monitor the weather so that the telescope may be
protected by closing the observatory shutter in case of high winds or precipitation.
To help protect the WMPol telescope from inclement weather and in order to aid
data selection, a commercially available weather station13 and USB web camera14
were installed at the Barcroft Observatory. The weather station has the ability
to measure temperature, relative humidity, barometric pressure, wind speed and
12
Famatech, http://www.radmin.com/
Davis Instruments Corp., Hayward, CA 94545, http://www.davisnet.com/
14
Creative Labs Inc., Milpitas, CA 95035, http://us.creative.com/
13
109
direction, and solar irradiance. The weather station data and camera images are
archived every ten minutes and downloaded to a web site15 at least every half
hour for easy monitoring. The web site also provides the ability to view the web
camera live.
Relative humidity in conjunction with the web camera during the day and the
CCD camera used for imaging of stars during the night are used to determine the
onset of bad weather. To avoid damage to the telescope, the shutter is closed and
data taking suspended if inclement weather is imminent or if the average wind
speed exceeds 20 mph (8.9 m/s) and/or wind gusts exceed 30 mph (13 m/s).
The web camera images are obtained every 10 minutes and daytime images are
rated by eye as “Clear,” corresponding with a cloudless period, “Partly Cloudy”
indicating some scattered clouds, “Mostly Cloudy,” or “Overcast.” Figures 3.8,
3.9, 3.10, and 3.11 show four images with the different daytime ratings. During
nighttime, the optical CCD camera installed on the telescope to assist with pointing reconstruction can be used to monitor cloud conditions by checking whether
or not Polaris is visible. The CCD camera is also sensitive to clouds during the
day.
15
http://moseisley.deepspace.ucsb.edu
110
Figure 3.8: Example of observatory web camera image during a “Clear” ten minute
time period. When the telescope is pointed towards the NCP the camera overlooks
White Mountain peak.
Figure 3.9: Example of observatory web camera image during a “Partly Cloudy”
ten minute time period
111
Figure 3.10: Example of observatory web camera image during a “Mostly Cloudy”
ten minute time period
Figure 3.11: Example of observatory web camera image during a “Overcast” ten
minute time period. The small dark spots are precipitation − hail or snow.
112
Chapter 4
2004 Observing Campaign
After installing the telescope in the Barcroft Observatory at the end of September 2003, a number of months during the middle of winter were spent commissioning and testing the telescope. The observing campaign began on April 23,
2004 and ended on October 17, 2004 with the first winter storm of the season and
the scheduled closure of the Barcroft Facility for winter.
4.1
Weather
During the April through October 2004 observing campaign, the mean temperature was 3.3◦ C with an average daily temperature swing of approximately
8◦ C. Figure 4.1 shows the temperature statistics by month from September 2003
113
Figure 4.1: Temperature statistics for the observatory by month from September
2003 through November 2004. Shown are the monthly high, low, mean, and
standard deviation. From Marvil et al. [2006].
through November 2004. In the integrated histogram shown in Figure 4.2, the
wind speed was lower than our damage-avoidance threshold 93 percent of the
time.
Table 4.1 lists for each daytime web camera image rating (see Section 3.4
for a description of the rating system) the percentage of daytime images during
the observing campaign that have that rating. Periods that are rated “Mostly
Cloudy” or “Overcast” (24% of the time) are considered to be times when the
114
Figure 4.2: Integrated histogram of wind speed, 23 April 2004 to 17 October 2004.
The upper curve is 10 minute average wind speed and the lower (dashed) curve is
10 minute peak wind speed. The average wind speed was below 20 miles per hour
(8.9 m/s) and the peak wind speed was below 30 miles per hour (13 m/s) 93% of
the time during the observing campaign. The steps in the peak wind speed curve
are an artifact of how the weather station bins data.
115
Table 4.1: Ratings of Daytime Web Camera Images
Rating
Percentage of time
Clear
Partly Cloudy
Mostly Cloudy
Overcast
46%
30%
15%
9%
weather conditions do not result in useful radiometer data. A small fraction of
the time (< 10%) there is no camera image available when data was collected.
Loss of images results from either a loss in communication between UCSB and
the observatory or if the camera “freezes-up” requiring a power-cycle reset.
4.2
4.2.1
Data Collection
Data Format
The data collected by the telescope was stored in Flexible Image Transport
System (FITS) format. We chose FITS format due to the large amount of software available within the astrophysics community for manipulating FITS files. In
general, each file consists of a FITS header and 30,000 samples (or 20 minutes, for
data taken at 25 Hz) for each of the 38 data channels. The FITS header describes
116
when the file was created and which data channel each field in the file is associated
with. The name of each file is the Universal Time (UT) that the file was created,
in the format “hhmmss.fts,” and the telescope clock was always set to UT rather
than local time. All the files from a particular day (0:00 through 23:59 UT) are
stored in a directory named “yyyymmdd” where “yyyy” is 2004 for the observing
campaign. CCD camera images were stored as Joint Photographic Experts Group
(JPEG) files, mostly for convenience, with file names and directory structure like
that of the data files.
During the observing campaign, nine of the 38 data channels were used for
radiometer data and the rest were used for “housekeeping” data. For both polarimeters, the values for the differenced channel and each non-differenced DC
channel (see Section 2.2) were recorded. For the W-band temperature anisotropy
measuring radiometer, the two outputs of the commercial lock-in were recorded as
well as a DC output of the pre-amplifier used before the lock-in. The housekeeping channels included the time each sample was taken (referenced to 0:00 UT),
the position of the telescope in azimuth and elevation as given by the absolute
encoders, the tilt of the telescope as given by the two tilt meters, the (cryogenic)
temperature at four places inside the dewar, the temperature of each radiometer
“back-end” (the temperature controlled section outside the dewar), the temperature at six places on the telescope (including two temperature sensors on each
117
reflector), and the status of the automatic calibrator position. The feature to measure telescope and receiver power usage did not seem to work well and was not
used. We reserved one data acquisition channel as a “blank” channel, a channel
shorted to ground, to be able to check for systematic effects.
4.2.2
Data Recorded
During the campaign, data were recorded during just over half of the available time. Table 4.2 describes the various reasons for not observing. Inclement
weather, including precipitation and high wind speed, was a major factor and
the Stargate automation system was damaged on multiple occasions, we believe
due to lightning, causing a great deal of down time. Additional levels of surge
protection were added to the Stargate communication lines during the observing
campaign but the seasonal lightning storms ended before it could be determined
whether this solved the problem. Lightning and other extreme weather conditions
also caused some communications outages but, fortunately, no damage to the telescope was suffered during these incidents. As more experience is gained with the
communications infrastructure, it is expected to be more reliable. The cryocooler
also halted data collection for two reasons as described in detail in Section 2.2.9.
Once the separate code to record CCD camera images was implemented (20 May
2004), CCD camera images were recorded whenever data was collected.
118
Table 4.2: Primary Reasons for Not Taking Data
Issue
Hours
Total possible observing time (4/23/04 to 10/17/04)
Weathera (snow, hail, rain, high wind)
Problems with remote control system (often caused by lightning)
Scheduled power outages
Recycle cryocooler
Various glitches (computer/code crashes, cryocooler overheating, etc.)
Telescope maintenance and manual calibrations
Acquired data
4272
615
955
71
147
121
194
2169
a
Only includes hours where weather was the primary cause of not taking data. There
were ∼ 1300 hours total during the observing campaign when the dome shutter was
required to be closed due to bad weather.
119
4.3
Pointing Reconstruction
Given measurements of azimuth, elevation, longitude, latitude, altitude, time,
and tilt of the telescope, the goal of pointing reconstruction is to determine what
part of the sky the telescope is observing at all times. The usual ways of defining
position on the sky are in either equatorial coordinates, right ascension (RA) and
declination (δ), or galactic longitude (l) and latitude (b).
In order to help determine the WMPol pointing, the Moon and stars were used
to align the optical CCD camera with the radiometric channels. Observations of
the Moon were used to find the central pixel positions of the radiometers in the
CCD camera. Comparing the pixel position of the center of the Moon for Q-band
and W-band channels yielded a 54 ± 1 arcminute angular separation on the sky
between the two polarimeters. Subsequent observations of the pixel position of
Polaris in the CCD camera allowed calculation of any offset between the polarimeters and the position of the telescope as defined by the encoders. Based on these
measurements, the estimated pointing error is ±30 for the Q-band polarimeter
and ±20 for the W-band polarimeter. As can be seen in Section 4.5 below, these
estimated errors are at least a factor of five smaller than the measured beam size.
To verify that there are no changes in the pointing on a day-to-day basis,
the CCD camera took images at all times at a rate around one per minute. In
120
Figure 4.3: CCD camera image of Polaris. In the image, taken while scanning the
telescope, Polaris is the brightest star with SAO 209 close to and to the upper
right of Polaris and λ Ursae Minoris (SAO 3020) is at the far upper left of the
image. The field of view of the camera is approximately 2.7◦ × 2.0◦ .
addition, 1200 seconds each night of observation were spent staring at Polaris and
λ Ursae Minoris at approximately 7:00 UT to build up a data base that revealed
any changes in the pointing of the telescope or CCD camera. Figures 4.3 shows
an example of a CCD camera image of Polaris.
121
4.4
Observing Strategy
The WMPol scan strategy was to maintain the telescope at a constant elevation
of 37.6◦ and scan the sky in azimuth ±450 about the NCP with a period ∼ 10
seconds. This strategy allowed us to observe a small patch of sky over many
months to obtain the desired number of samples per pixel. The useful region of
the sky observed has an area of 5.5 square degrees in the Q-band polarimeter
channel and 1.1 square degrees for the W-band polarimeter channel. The larger
coverage of the Q-band polarimeter is due to the 540 offset of the Q-band beam
from the optical axis. Figures 4.4 and 4.5 show HEALPix (see Section 5.2.4 for a
description of HEALPix) plots of the sky coverage during the observing campaign.
This scan strategy only allowed for the measure of the Q Stokes parameter which
is only half of the linear polarization information; given sufficient observing time,
the U Stokes parameter could also be measured by scanning off of the NCP or by
physically rotating the receiver about the optical axis by 45 degrees and repeating
the observation.
4.5
Beam Determination
Measurements of the beam size were accomplished using the Moon and Tau A.
Due to the telescope design and the way the observatory shutter is constructed,
122
Figure 4.4: Sky coverage of Q-band polarimeter channel. For the best 769 hours
of data, the sky coverage in Q-band is 5.5 square degrees after removing pixels
with a very small number of samples. The scale below the plot shows the number
of samples per pixel with each sample consisting of 0.04 seconds of integrated
data. The plot is centered on the NCP but the coverage is not symmetric due to
gaps in the data from weather and other issues. The grid lines correspond to two
hours in RA and 0.5 degrees in declination. For this HEALPix plot, Nside = 512
meaning that the size of each pixel is approximately 6.870 .
123
Figure 4.5: Sky coverage of W-band polarimeter channel. For the best 769 hours
of data, the sky coverage in W-band is 1.1 square degrees. The plot scale, grid,
and pixelization is identical to that of Figure 4.4
124
the telescope can, in general, observe objects between 33 and 48 degrees elevation.
This usually means that objects are at most available for observation for about
one hour each day when either rising or setting, though at night during summer
objects near the ecliptic may be low enough in elevation to observe for much
of the night. It was found that the best way to observe an object was to set
up a drift scan, scanning back and forth 1 to 3 degrees in azimuth at constant
elevation above (below) the rising (setting) object, and allow the object to pass
through the scan. One complication is that the objects away from the NCP also
move rapidly in azimuth which necessitates adjusting the dome position so that
the object stays near the center of the shutter. During a one hour period it was
typical to be able to complete five to ten drift scans of an object, adjusting the
telescope position and dome azimuth after each scan. Although objects can, in
theory, be observed during the daytime if the pointing model is well understood,
it was found to be challenging enough to do observations at night when the CCD
camera could image objects and help with pointing that no daytime observations
of objects were attempted.
Once scan data is acquired, a RA, δ map is generated as in Figure 4.6, a
Q-band observation of Tau A. A model of the source (Tau A, or the Crab Nebula, has a largest angular dimension ∼ 60 ) is convolved with beam models with
different FWHM beam sizes until a best fit to the data is found. Based on this
125
technique, the measured FWHM beam size of the Q-band polarimeter from Tau
A observations is 240 ± 30 as shown in Figure 4.7. This result is similar to the
220 ± 20 quoted in Childers et al. [2005]. Presumably due to 1/f issues, Tau A has
not yet been detected with the W-band channel but, by using Moon observations,
a FWHM beam size of 120 ± 30 was found. Figures 4.8 and 4.9 show observations
of the Moon with both polarimeters.
It is not clear why the measured beams sizes for both WMPol and BEAST are
different from the model though any misalignment in the optics would result in
a larger beam size. The WMPol receiver was not optimized for planet detection
− a higher switch frequency and higher gain channel (after removing the offset or
AC coupling) so that the DC channels were not data acquisition noise dominated
would have made it easier to detect planets and measure the beam size of the
instrument. Had planets been easier to detect, an iterative effort to measure the
beam size, adjust the optics, and remeasure may have helped achieve a beam size
closer to what was expected.
A larger range of motion of the telescope in elevation could have made it
possible to set up a source to measure the beam size. The condition for far-field
diffraction,
R>
a2
,
λ
(4.1)
where R is the distance from the aperture to the far-field point, a is the size of
126
Figure 4.6: Q-band polarimeter observation of Tau A. The data were obtained by
scanning at constant elevation and allowing Tau A to drift through the scan. This
map is in equatorial coordinates, centered near the position of Tau A, and consists
of data taken during seven constant elevation scans totaling 2472 seconds of data.
The scale below the plot shows the mean signal per pixel. The grid spacing is 150
and the pixel size corresponds to HEALPix Nside = 1024 or the size of each pixel
is approximately 3.440 .
127
Figure 4.7: Determination of Q-band beam size. The minimum reduced χ2 is at
a beam size of 24 arcmin.
128
Figure 4.8: Q-band observations of the Moon using a DC channel. Similar to the
Tau A observations, these data were taken by allowing the Moon to drift through
eight constant elevation scans totaling 2292 seconds of data. The scale below the
plot gives signal level of each pixel as compared to the maximum signal pixel. The
grid spacing is 1◦ and the pixel size corresponds to HEALPix Nside = 1024 (3.440
pixels).
129
Figure 4.9: W-band observations of the Moon using the same technique as for
Q-band (Figure 4.8).
130
the aperture (approximately 2.2 m, the size of the primary reflector), and λ is the
wavelength (0.71 cm for 42 GHz and 0.33 cm for 90 GHz), leads to an approximate
required distance of the source of 680 m for Q-band and 1470 m for W-band. At
20◦ elevation, about the lowest the WMPol telescope could point, a minimum
source height of 230 m at a distance of 640 m for Q-band or 500 m at a distance
of 1380 m for W-band is required, which is not trivial to achieve.
4.6
Calibration
Calibration of the receiver was accomplished with multiple techniques. Manual
calibrations of the non-differenced channels of the polarimeters were performed
by recording the radiometer signals while an ECCOSORB1 ambient temperature
load was placed in front of the radiometers and comparing to the signal levels
when viewing the sky. The noise temperature was then determined using
Tnoise =
Tambient − Y · Tsky
,
Y −1
(4.2)
where Y is the ratio of radiometer signals when looking at the ambient temperature
load versus looking at the sky (Vambient /Vsky ), Tambient is the physical temperature
of the ambient load, and Tsky is the radiometric sky temperature (at the elevation
of the telescope − usually 37.6◦ ) as determined from sky dips.
1
Emerson & Cuming Microwave Products, Randolph, MA 02368, http://www.eccosorb.com
131
To calibrate the polarization channels, a grid of 150 µm diameter copper wires
with a 635 µm spacing between wire centers was used. This grid was held at
an angle of 45 degrees with respect to the dewar window which provided a large
polarized signal due to the difference between the temperature of the sky and
an ECCOSORB ambient temperature load (see Figure 2.36 for the orientation,
where the automatic calibrator is replaced by the copper wire grid for manual
calibration). The power reflection for radiation incident on a wire grid is given by
Larsen [1962] and Lesurf [1990] as
Rk =
1+
[ 2s
λ
1
s 2
ln( πd
)]
(4.3)
2 2
R⊥ =
d 2
( π2λs
)
2 2
d 2
)
1 + ( π2λs
,
(4.4)
where Rk and R⊥ are the power reflection coefficients for radiation polarized parallel and perpendicular to the direction of the wires respectively, s is the spacing
between the centers of the wires, d is the diameter of the wires, and λ is the wavelength of interest − again around 0.71 cm for Q-band and 0.33 cm for W-band.
For both Q-band and W-band, the calculated reflection of the parallel component
is & 99% and the reflection of the perpendicular component is negligible (. 1%).
Hence the incident radiation from the ECCOSORB polarized parallel to the grid
is reflected towards the polarimeters while the radiation polarized perpendicular
to the grid is transmitted through the grid and away from the polarimeters. Simi-
132
larly, the radiation from the sky polarized perpendicular to the grid is transmitted
through to the polarimeters while the radiation polarized parallel to the grid is
reflected away. For the actual calibration, measurements with the grid oriented
in both the horizontal and vertical direction were used to find the calibration
constant with
G=
|Vver | + |Vhor |
,
2(Tambient − Tsky )
(4.5)
where G is the calibration constant, Vver and Vhor are the voltage signal levels
from a polarimeter when the grid is in the vertical or horizontal orientation, and
Tambient and Tsky are as given for Equation 4.2 above.
As this calibration procedure was manual and required changing the lock-in
gain, we also used the automated calibrator described in Section 2.4 to perform
a relative calibration every 10 minutes. For each manual calibration of the polarized channels, a transfer standard was calculated and used to convert from the
automatic calibrator. This transfer standard, α, takes the form
α=
|∆Vf ilm |
,
G|Tambient − Tskymean |
(4.6)
where ∆Vf ilm is the polarimeter signal offset due to placing the film in front of the
dewar, Tskymean is the measured mean radiometric sky temperature at elevation
37.6◦ , and G is the calibration constant (Volts per Kelvin) from a manual grid
calibration. Figures 4.10 and 4.11 show examples of the signal level change in the
133
Figure 4.10: Example of an automatic calibration sequence in Q-band. Placing
the dielectric film at a 45◦ angle in front of the radiometers creates a relatively
small polarization signal that is easily detected.
polarization channels due to the automatic calibration.
As given by O’Dell et al. [2002], the difference in reflection coefficients (with
respect to the plane of incidence) for the film is given by
µ
R⊥ − Rk '
πf d
c
¶2
(n4 − 1)(n2 − 1)(3n2 − 1)
,
2n4
(4.7)
where f is the frequency of incident radiation, d is the thickness of the film, c is the
(vacuum) speed of light, and n is the (real) index of refraction of the polypropylene
film. Assuming a refractive index of 1.5 and a film thickness of 0.002 inches
134
Figure 4.11: Example of an automatic calibration sequence in W-band.
135
(50 µm) and multiplying R⊥ − Rk by a temperature difference, Tambient − Tsky ,
of 260 K, the expected polarized signal due to the film is 0.37 K for Q-band (42
GHz) and 1.7 K for W-band (90 GHz) with a ratio of (90/42)2 or 4.6. Figures 4.12
and 4.13 show, for 500 WMPol data files, the measured calibrated signals when
placing the film in front of the polarimeters and the ratio of those signals. While
the measured signal is less than predicted, the mean ratio of the measured signals
is within 10% of the prediction.
One of the issues resolved at the beginning of the campaign was how often to
calibrate. Manual calibrations were performed whenever possible (i.e. someone
qualified to perform the calibration was at Barcroft) but, in practice, successful
manual calibrations, including sky dips, only occurred about once per month.
However, special care was taken to perform manual calibrations before and after
any changes were made to the instrument that would affect the gain or calibration
of the polarimters such as when the switch rate was changed from 100 Hz to 250
Hz. For the automatic calibrator, different periods between calibration sequences
and durations of sequences were tried with the end result being that automatic
calibrations were set to occur every ten minutes for a duration of 30 seconds. This
guaranteed that there would be at least one full auto calibration for every file,
and that the calibrator would be in place long enough for the calibration signal
to settle without using too much data acquisition time.
136
W-band
Q-band
Figure 4.12: Calibrated signals from 500 automatic calibrations during October
2004. The upper plot (black diamonds) shows W-band calibrations while the lower
plot (blue triangles) shows the Q-band calibrations. The middle plot (red dots)
shows (Tambient − Tskymean )/260. The mean signal is 0.244 (±0.034) K for Q-band
and 1.22 (±0.15) K for W-band. The mean Tambient − Tskymean for this period of
time is 262 K with a standard deviation of 4.9 K.
137
Figure 4.13: Ratio of W-band and Q-band automatic calibration signals from
Figure 4.12. The mean ratio is 5.00±0.04.
138
Chapter 5
Data Analysis
The goal of CMB data analysis is to convert the raw, time ordered, data into
a sky map of the CMB, generate an angular power spectrum, and, if possible,
extract cosmological parameters. The first step in this procedure is to select the
“good” data from the raw data and cut the data that are not useful due to weather
and other issues. Next, the data are reduced such that each sample is associated
with the position on the sky that the telescope was looking at when the sample
was recorded. After that, an estimation of the noise covariance between samples
must be performed before a map is generated. Finally, after the construction
of the CMB map, the angular power spectrum, RMS temperature/polarization
fluctuations versus angular spatial extent on the sky, is calculated and compared
with cosmological models.
139
5.1
Data Selection
To aid the data selection and analysis, a FITS file called the “cube” was created. This file contains a three-dimensional array that stores the mean, standard
deviation, minimum value, and maximum value for each of the 38 data channels
in 7268 data files recorded during the observing campaign. Also stored in the
cube is other useful information such as the date and time of the file, calibration
constants, and ratings for USB camera images taken during the time that a data
file was recorded.
The first part of the data analysis is to determine which of the recorded data
files (raw data) can be used and which should be “cut” due to various issues. Files
that are cut can be flagged in the cube and removed from further consideration.
Table 5.1 gives the number of hours of data that were cut from the raw data
to create the CMB data set. Data files for times when the telescope was not
scanning about the NCP are not included in the CMB data set though data
that were specifically taken for the purposes of pointing reconstruction, beam size
determination, and calibration play a critical a role in the CMB data analysis.
Also, files shorter than 60 seconds are cut as these files are not expected to contain
enough data to be useful. We discovered that during midday in the late spring
and summer the Sun is high enough in the sky to shine directly on the telescope.
140
Table 5.1: Cuts of Raw Data
Issue
Q-band (hours) W-band (hours)
Raw data
2169
2169
Not scanning (testing, calibration, sources)
Short files (less than 60 s)
Saturation (due to Sun)
RMS cut
Cold plate temperature
Weather image
130
<1
188
173
12
92
130
<1
468
295
6
62
Total cut
595
961
1574
1208
Data remaining
This not only causes the secondary reflector to heat up by as much as 20◦ C but
also causes the warm components of the polarimeters to heat up to a temperature
higher than the servo set point. Changes in signal and gain due to this heating
cause the DC signal levels of the polarization channels to exceed the limits of the
data acquisition electronics and we label these data as “saturated.”
The Q-band and W-band polarization-sensitive fields of each potential CMB
data file (i.e. scanning about the NCP, not too short, and not saturated) are
141
visually inspected. The time-ordered data before and after removing the DC
offset on these channels for each half scan, one sweep in azimuth from −450 to
+450 or the reverse, are examined along with the power spectral density of both
fields. The RMS of the data after removing the offset is also calculated. Many
files that are found to have a RMS significantly different from the mean have
unusual features in both polarization channels that are presumed to be due to
clouds passing through the beam. These files and others with bad behavior are
removed from the data analysis. Figures 5.1 and 5.2 are plots from a selection of
data, before and after removing the offset, that fail the RMS cut.
After applying the RMS cut, there remained a small number of data files that
survived the cuts but were removed from consideration as either the cold plate
temperature was high, & 35 K, indicating that the dewar was warming up, or the
web camera images taken at the same time as the data were recorded were rated
as either “Mostly Cloudy” or “Overcast” (see Sections 3.4 and 4.1), indicating
that the weather was bad. Different amounts of data were cut for Q-band versus
W-band as the W-band polarimeter is more sensitive to the cold plate temperature
and cloudy conditions and, thus, the additional data cut from Q-band had already
failed the saturation or RMS cut in W-band.
Two additional data selection issues are the automatic calibration and switch
rate. As described in Section 2.4, the automatic calibrator was installed in at the
142
Figure 5.1: Example of data cut. The upper plot (red) is of time ordered data
without the offsets removed of the Q-band polarimeter while the lower plot (black)
is W-band polarimeter data. The spikes that occur at around samples 10,000,
25,000, and 40,000 (25 samples per second) are auto-calibration sequences.
143
Figure 5.2: Example of data cut, offsets removed. The upper plot (red) is of time
ordered data after removing the offsets of the Q-band polarimeter while the lower
plot (black) is W-band polarimeter data. A value of 1 V has been added to the
Q-band data for clarity. Note that the offset removal does not completely remove
the large spikes generated during the auto-calibration sequence as the calibrator
moves in front of or away from the dewar. There is a small section of data between
samples 36,000 and 37,000 that is saturated and the RMS is 0 (also see Figure 5.1).
144
end of April 2004 but broke soon thereafter and was not repaired and reinstalled
until early July 2004. Even without the calibrator, there was no reason to not
collect data but these data are more difficult to use as the only means of calibrating
these data are the manual calibrations that were performed during visits to the
site which occurred over a few days about once per month between April and July.
Also, as mentioned in Section 2.2.9, the switch rate of the receiver was changed to
250 Hz from 100 Hz; this occurred at the end of May 2004. Hence, a significant
fraction of the data (526 hours or ∼ 24% of the total) were recorded at a rate of 10
Hz with the balance recorded at 25 Hz. However, since the automatic calibrator
was not operational for much of this time, these data are not used in the initial
analysis but are also not entirely cut.
Finally, since there were issues during the daytime with the telescope heating
up and the data becoming saturated, especially in W-band, it is obviously of some
concern that there may be problems with daytime data even when the data are not
saturated. Since the time of the data file is recorded in the name of the file, as well
as in the cube, plus the camera image rating is also stored in the cube, including
a “Nighttime” rating for images taken at night, it is relatively straightforward to
analyze daytime and nighttime data separately to see if there are differences and
evaluate whether or not the daytime data, or how much, should be used in the
analysis.
145
5.2
Data Reduction
The next step in the data analysis is data reduction, the goal of which is to
convert the selected time ordered data into data that are organized such that each
sample is calibrated and identified by its position on the sky in RA and δ or other
suitable coordinates. Putting the data into this format allows us to bin the data
and generate a map on the sky. In order to go from time ordered data to reduced
data, the offsets, auto-calibration sequences, and spikes are removed, the data are
calibrated and then binned in azimuth to remove any scan synchronous signal,
and each data point is associated with the position observed on the sky.
5.2.1
Removal of Offsets, Auto-calibration Sequences, and
Spikes
The first procedure of the data reduction, is the removal of the DC offsets,
auto-calibration sequences, and spikes. Figures 5.1 and 5.2 presented the offset
removal technique as a way to identify data to cut, Figures 5.3 and 5.4 show data
before and after removing the offset that survive the cut. As discussed above, the
offset is removed for each half scan in azimuth; Figure 5.5 displays, as an example,
the azimuth as a function of time for a small (80 seconds) selection of the data.
As can be seen in Figures 5.2 and 5.4, the offset removal does not get rid of the
146
Figure 5.3: Example of good data. The upper plot (red) is time ordered data
without the offsets removed of the Q-band polarimeter while the lower plot (black)
is W-band polarimeter data.
147
Figure 5.4: Example of good data, offsets removed. The upper plot (red) is time
ordered data after removing the offsets of the Q-band polarimeter while the lower
plot (black) is W-band polarimeter data. A value of 1 V has been added again to
the Q-band data for clarity.
148
Figure 5.5: Plot of azimuth as function of time during scanning. 80 seconds of
data are shown. The scan period is approximately 240 samples (25 Hz data rate)
or 9.6 seconds and the plot displays 16 half scans, where the mean DC level of the
polarimeter data is removed for each half scan.
149
spikes due to the calibrator and, in any case, it is not desirable to include data
taken during calibration sequences in the CMB data set. The flag recorded in
one of the data channels that reports the calibrator position can be used to very
easily remove all the calibration sequence data from a file as shown, for example,
in Figure 2.28. The positive effect of removing the calibrations is most clear when
examining the power spectral density (PSD) of the data as displayed in Figure 5.6.
If any spikes, i.e. data points that are more than 4σ from the mean, remain after
removing the offset and calibrations, they are also removed as it is expected that
these rare data points may be due to a glitch in the data acquisition.
Removing the offset acts as a high pass filter that removes information at the
half-scan frequency − ∼ 0.2 Hz and below. The loss of this information should
not negatively affect the data analysis as this roll off is around the 1/f knee
frequency of the Q-band polarimeter and much below the W-band knee frequency.
Figure 5.7 compares the PSD of Q-band data (calibrations removed) before and
after removing the offset.
5.2.2
Applying the Calibration
By calibrating the data, each sample is converted from the measured voltage, where the voltage gain will vary over time, into antenna temperature units,
as given by Equation 2.7 as T =
P
,
kβ
which should be independent of voltage
150
Figure 5.6: Power spectral density of Q-band data before and after calibration
removal. The PSD of the data with calibrations (black) have undesirable features
that are removed with the calibrations (red). Notice however, that both plots
have the same behavior as the frequency approaches 12.5 Hz.
151
Figure 5.7: Power spectral density of Q-band data before and after offset removal
(calibrations removed). The PSD of the data with the offset removed (red) rolls
off at low frequencies up to ∼ 0.2 Hz. At higher frequencies, the PSD is identical.
152
Figure 5.8: Q-band polarimeter calibration constants by date of file (July through
October 2004). The calibration constants displayed are for those files that survived
the initial cuts. The red line shows the value of the most recent manual calibration
taken for each file. A calibration constant of “0” indicates that there was no auto
calibration in that file, most likely due to the file being shorter than 10 minutes.
gain fluctuations. The devices and procedures for calibration, as described in
Sections 2.4 and 4.6, lead to a calibration constant in Volts per Kelvin for each
polarimeter signal in every data file. Figures 5.8 and 5.9 present the calibration
constants for Q-band and W-band for each file. Only July through October 2004
are displayed as the auto calibrator was operating consistently only during that
period of time.
153
Figure 5.9: W-band polarimeter calibration constants (similar to Figure 5.8) by
date of file with manual calibration values shown with red line.
154
It is clear that there is some variation in the calibration constants over time
due to changes in ambient temperature, sky temperature, and instrument gain. In
addition, in early September, a few changes were made to the instrument which
affected the gain at a greater level: the malfunctioning W-band anisotropy measuring radiometer was turned off which slightly affected the biases, and thus the
gain, of the W-band polarimeter due to a shared power supply, the calibrator film
was replaced, and a fan was installed to blow air onto the dewar window to prevent
the formation of ice on the window. As can be seen in the figures, these changes
improved the stability of the Q-band calibration and increased the W-band calibration constant slightly. The reason that the manual calibration value from early
September is higher than the auto-calibration values from early September to the
end of the observing campaign is that during the day of that manual calibration,
the weather degraded rapidly and affected the calculation of the transfer standard, α, between the manual calibrations and automatic calibrations. This has
been taken into account in calculating the calibration constants from the auto
calibrations. The odd behavior of the W-band calibration constants at the end
of September is due to W-band polarimeter not working properly during that
time period because of a bad connection between one of the detector diodes and
the differential amplifier and these data are not used further in the CMB data
analysis. The gaps in the calibration data are times that the telescope was not
155
observing as discussed in Section 4.2.2 or due to data that were cut. For the files
that do not have a calibration, a calibration from a nearby file is used, if possible.
5.2.3
Template Removal
It is typical in CMB observations that the telescope is scanned to help reduce
the effects of gain fluctuations in the instrument. However, this scanning usually
causes a scan synchronous signal at some level which must be removed, if possible
and without removing too much CMB signal, to optimize the CMB maps. For
WMPol, this scan synchronous signal is best observed when binning the data in
azimuth-like bins as the observing strategy is to scan in azimuth. In order to
bin properly on the sky, the azimuth must be converted into a projected azimuth
that properly takes into account the elevation of the telescope. Using spherical
trigonometry, the projected azimuth, θAzproj , is given by the law of cosines for a
spherical triangle as
cos(θAzproj ) = sin2 (θel ) + cos2 (θel ) cos(θaz ),
(5.1)
where θel and θaz are the measured elevation and azimuth respectively. Figure 5.10
is a drawing of the spherical geometry. As it is not necessarily straightforward to
predict beforehand the optimal scan synchronous signal removal technique, several
versions are tried to see which one has the best effect on the map and angular
156
Figure 5.10: Spherical geometry for binning. In this geometry, the telescope is
located in the center of the sphere (at the intersection of the two dotted lines)
and the measured change in azimuth angle corresponds to the arc length along the
horizon curve between the two zenith-to-horizon arcs (geodesics). The projected
azimuth is the length of the arc that is above horizon. The telescope elevation is
the angle between the horizon and the projected azimuth arc with the vertex at
center of the sphere.
power spectrum.
The first scan synchronous signal removal technique that was attempted was
to find a template (a value for each bin in azimuth) created by binning many
files of data. This template could then be removed from the binned data for each
file without removing too much information. Options to find such a template
that were tried include binning all the data from the entire observing campaign,
binning by month, and binning by ten day period. Also looked at were splitting
the data into daytime vs. nighttime and binning for the entire campaign, each
157
month, or by ten day period. Additionally, binning the data by hour of the day for
the entire campaign, by month, or by ten day period was explored. In all cases,
it was found that the scan synchronous signal varied too much on a day to day
basis to construct a template that would be valid for reasonable periods of time.
Although the source of our scan synchronous signal and its variability are not well
understood, they are most likely related to sidelobe pickup from the edges of the
dome shutter and the ground which changed temperature significantly from day
to day.
The next option, with Figures 5.11 and 5.12 as examples, is to try a linear
or second (or higher) order fit to the data from each file and remove the fit from
the data. This is a version of the technique used by CAPMAP [Barkats et al.,
2005] among others. As the errors on the mean for the binned data from one
file are relatively large compared to the values of the bins, it is difficult to tell
visually whether removing a linear or second order fit is more appropriate or if
even removing either template is better than no template removal. The effects
of the template removal must be compared when generating maps to determine
which technique gives the best result.
158
Figure 5.11: Binned data with templates. The data from one file is binned in 30
azimuth bins. The mean and standard error for each bin is displayed plus a first
order (blue line) and second order (red parabola) best fit to the binned data are
shown. The reduced χ2 is 0.99 for the linear fit and 0.85 for the parabolic fit so
both are good fits to the data.
159
Figure 5.12: Another example of binned data with templates. These data were
recorded during the daytime when the Sun causes a larger scan synchronous signal.
The reduced χ2 is 12.6 for the linear fit and 4.25 for the parabolic fit indicating
that neither fit is particularly good but that the parabola is a better fit.
160
5.2.4
Pixelization
The final step in the data reduction process is to assign a position on the
sky to each sample as determined from the pointing reconstruction described in
Section 4.3. The Hierarchical Equal Area isoLatitude Pixelization1 , or HEALPix,
package [Górski et al., 2005] was designed specifically for making maps of CMB
data but is useful in any application where optimized pixelized maps on a spherical
geometry are required. HEALPix has been made particularly attractive to the
astrophysics community by incorporating the ability to easily use FITS format
and the Interactive Data Language2 (IDL). The HEALPix technique is to divide
a sphere into equal-area curvilinear quadrilateral pixels. The pixels are distributed
in isolatitude rings between the poles of the sphere with the pixels of each ring
centered at the latitude of the ring. The authors of HEALPix use a base grid of
three rings with four pixels per ring as displayed in Figure 5.13. The number of
2
pixels on the sphere is given by Npix = 12 × Nside
, where Nside is the number of
2
divisions along one side of a base pixel and, thus, Nside
is the number of pixels
each base pixel is divided into. The area of each pixel, in steradians, is then given
by
Ωpix =
1
2
π
.
2
3Nside
http://healpix.jpl.nasa.gov/
Research Systems, Inc., Boulder, CO 80301, http://www.rsinc.com
161
(5.2)
Figure 5.13: HEALPix grid technique. At the upper left is the HEALPix base grid,
Nside = 1, with Nside equal to 2, 4, and 8 for the remaining figures in clockwise
order. A pole of the sphere is located towards the top at the point where three
white pixels meet a light gray one. The black dots define the center of each pixel.
Source: http://healpix.jpl.nasa.gov/healpixBackgroundPurpose.shtml
162
For the WMPol data, each sample is associated with a HEALPix pixel, where
the pixels are labeled by a number from 0 to Npix − 1. HEALPix currently allows
Nside to take values of 2k from 1 to 8192 (20 to 213 ) and a value of Nside is chosen
such that the pixel size is at least a factor of 2 − 3 smaller than the beam size
so the effects of pixelization are less important than the limitations due to the
angular resolution of the instrument. As given in Górski et al. [2005], the angular
resolution of a pixel, θpix (in arcminutes), is defined by
θpix ≡
p
r
Ωpix =
3 36000
.
π Nside
(5.3)
Nside equal to 512 or 1024 corresponds to θpix of 6.87 or 3.44 arcminutes, which are
appropriate choices for the WMPol Q-band and W-band polarimeters respectively.
5.3
Noise Estimation, Map-Making, and Angular Power Spectra
Once the data have been selected and reduced, it is possible to begin making
maps of the data. The publicly available Microwave Anisotropy Dataset Computational Analysis Package3 (MADCAP) is used to perform the noise estimation
and map-making. MADCAP was developed (as part of the COMBAT collabora3
http://crd.lbl.gov/ borrill/cmb/madcap/
163
tion4 ) and is maintained by Julian Borrill, Chris Cantalupo, and Radek Stompor
at the National Energy Research Scientific Computing Center5 (NERSC) of the
Lawrence Berkeley National Laboratory in Berkeley, CA. MADCAP is installed
on the NERSC IBM SP RS/6000 distributed memory computer named “Seaborg”
which has 6080 computing processors divided into 380 nodes.
The map-making algorithm, as given by Borrill [1999], assumes that the time
ordered data, d, have the form
d = As + n,
(5.4)
where A is a t × p matrix that contains the information about the instrument
pointing, s is the pixelized CMB signal (a pixelized map of the CMB), and n is
the time ordered instrument noise. The t index of A indicates the time ordered
sample and the p index represents the (HEALPix, in our case) pixel numbers.
The components Atp are then defined by



 1 if sample RA, δ position ∈ p,
Atp =


 0 otherwise.
(5.5)
With the vector d and matrix A, the maximum likelihood pixelized map estimate, m, is given by [Borrill, 1999]
¡
¢−1 T −1
m = AT N−1
A Ntt0 d,
tt0 A
4
5
http://crd.lbl.gov/%7Eborrill/cmb/combat/
http://www.nersc.gov/
164
(5.6)
where AT denotes the transpose of A and Ntt0 is the time-time noise covariance
matrix given by
Ntt0 ≡ hnnT i.
(5.7)
Hence, the production of a map is reduced to the problem of finding a vector m
that satisfies Equation 5.6.
5.3.1
Time-Time Noise Covariance Matrix
The required output from the noise estimation process is the inverse time-time
noise covariance matrix, or N−1
tt0 in Equation 5.6, which is calculated from the data
in the frequency domain. The first step is to apply a discrete Fourier transform
(in particular, the Fast Fourier Transform or FFT function in IDL) to the data
as given by,
F (u) =
T −1
1X
f (x)e−i2πux/T ,
T x=0
(5.8)
where T is the number of samples. The inverse transform is
f (x) =
T −1
X
F (u)ei2πux/T .
(5.9)
u=0
The power spectral density, P SD, is calculated from
P SD(u) = (Re{F (u)}2 + Im{F (u)}2 )1/2
(5.10)
and the time-time noise covariance matrix is the real part of the inverse Fourier
transform of P SD. As described in Stompor et al. [2002], the inverse time-time
165
Figure 5.14: Noise correlation at short time scales. The correlation coefficients are
given as function of the spacing between samples where one sample equals 1/25
of a second.
noise covariance matrix can be approximated by taking the inverse Fourier transform of P SD−1 and calculated using the MADnes code that is part of the MADCAP package. Figures 5.14 and 5.15 show the calculated time-time noise correlation, which is just the covariance divided by the σ 2 of the data, for a sample of
WMPol data indicating that there is very little correlation in the data, even at
short times scales, and the time-time noise covariance matrix is almost diagonal.
166
Figure 5.15: Noise correlation at longer time scales.
167
5.3.2
Maps
The inputs into the MADCAP map-making procedure (MADmap) are four
vectors that are the length of the number of time ordered data samples. The first
vector contains the value for each time ordered data sample (in either volts or
kelvins) for either the Q-band or W-band polarimeter. The second vector gives
either the calibration constant for each sample to convert from volts to kelvins or
is unused if the data are already calibrated. The third vector supplies the pixel
position for each sample and the fourth vector is the first row of the time-time
noise covariance matrix similar to what is displayed in Figures 5.14 and 5.15. An
iterative process to used to solve for the map.
MADmap, as mentioned earlier, is an implementation of an algorithm (Equation 5.6) to determine the maximum likelihood estimate of the CMB map. Tegmark
[1997] points out that this maximum likelihood algorithm also minimizes the χ2 ,
defined as
χ2 ≡ (d − Am)T N−1
tt0 (d − Am),
(5.11)
for the map (Tegmark [1997] and also see Barlow [1989] for a discussion of χ2
in matrix form). This assumes, however, that the probability distribution for
the noise is Gaussian. Figure 5.16 shows a histogram of the noise from selection
of data; the best fit Gaussian has a reduced χ2 = 1.10 indicating a good fit.
168
MADmap also requires that there are no gaps in the data and that the data are
stationary, meaning that the mean and variance do not change in the data set
and that the covariance is only a function of the spacing between samples. There
are, of course, many gaps in the data due not only to weather and other issues
that caused the data taking to halt but also due to removal of the auto-calibration
sequences. This issue can be addressed by replacing the missing data with fake
data that have the same noise properties as the real data. To prevent the filled-in
data from affecting the result, the fake data are assigned a pixel position that is
otherwise not observed and that pixel can be removed from the final map. As the
offset from the data is removed so that the mean of the data is always close to
0, the main issue for the data being stationary is that the RMS of the data does
change over time due to the sky temperature changing as well as for other reasons.
It is possible, however, to break up the entire data set into smaller chunks that
are stationary, construct sub-maps, and then combine the sub-maps into a final
map.
It is straightforward to construct a naive map without using MADCAP by
averaging the measurements for each pixel but, as Tegmark [1997] shows, constructing a map in this way is sub-optimal and some information about the CMB
in the time ordered data is lost in the naive map. The maximum likelihood
method, however, does not lose any of the CMB information contained in the
169
Figure 5.16: Histogram of a selection of Q-band data with best fit Gaussian. The
offsets, auto-calibrations, and spikes have been removed from the data. The number of samples with a signal level within 0.01
√ V bins are shown by the boxes and
the best fit Gaussian by the line. Standard N 1-σ error bars are approximately
a factor of four smaller than the size of the black boxes. The reduced χ2 of the fit
is 1.10, the mean of the fit is 2.3 mV, and the standard deviation of the fit is 25
mV.
170
data when making maps.
Figures 5.17, 5.18, 5.19, and 5.20 show a preliminary map of the the very
best Q-band data, the associated errors per pixel, and histograms of the number
of samples per pixel. The total amount of Q-band data used for these maps is
30763405 samples, or 342 hours, of only nighttime data from 1216 files. For these
maps Nside = 512 so the pixel size is ∼ 70 . For this map, a second order template
(parabola) was removed from each file by fitting to the binned data though it is
not clear yet that this is the ideal template removal procedure.
The map of Figure 5.17 shows the measurement of the Q Stokes parameter,
2
2
2
hEN
−S i−hEE−W i, where hEN −S i is parallel to the lines of constant RA (the radial
2
lines of the map) and hEE−W
i is then the polarization perpendicular to lines of
constant RA. As can be seen in the map, there is significant scan synchronous
structure in the map close to the NCP (center of the grid) as well as on the outer
edge of the map which will have to be removed before continuing the analysis.
In Figure 5.18 it is clear that the errors per pixel are sufficient to detect the
scan synchronous signal but still approximately an order of magnitude too high
to measure the expected few µK polarization signal. However, once the scan
synchronous signal is removed, we may be able to achieve a statistical detection
of polarization, especially after adding in more of the data.
171
Figure 5.17: Preliminary maximum likelihood Q-band map. 342 hours total of
the best, nighttime, Q-band polarization data are used in this map. The size of
each pixel is approximately 7 arcminutes. The value of each pixel gives the Q
2
2
2
Stokes parameter, or hEN
−S i − hEE−W i where hEN −S i is the polarization parallel
to lines of constant RA (the radial lines in the map). The spacing of the radial
grid lines corresponds to 2 hours in RA and the circular grid lines are separated
by 0.5◦ in declination with the center of the grid on the NCP.
172
Figure 5.18: 1-σ error per pixel for the Q-band map.
173
Figure 5.19: Histogram of samples per pixel for the Q-band map.
174
Figure 5.20: Histogram of samples per pixel for the Q-band map, log scale.
175
5.3.3
Angular Power Spectra
The final piece of the MADCAP package is MADspec, which is used to estimate
any combination of the six possible CMB temperature and polarization angular
power spectra from a map. MADspec is a parallel implementation of the maximum
likelihood algorithm of Bond et al. [1998].
The first function of MADspec is to construct the inverse pixel-pixel noise
covariance matrix, N−1
pp0 , given by
¡ T −1 ¢
N−1
=
A Ntt0 A .
0
pp
(5.12)
Then, using N−1
pp0 , the map (including the RA,δ position of the pixels), and the
window function, MADspec estimates the angular power spectrum with userspecified Cl bins.
The window function is a measure of the sensitivity of a given observation
as a function of l on the angular power spectrum. On the high l (small angular
size) side, sensitivity is limited by beam size and, to a lesser extent, pixel size
assuming that the pixel size used is smaller than the beam size. On the low l
(large angular scale) side, the size and shape of the area on the sky observed is
the limiting factor. Instrument noise, scanning strategy, map making technique,
and any filtering of the data can also play a role. At a minimum, MADspec
requires a window function that takes into account the finite beam and pixel
176
Figure 5.21: Example of window function for a 24 arcminute beam and Nside =
512. This window function is input into MADspec to quantify the effect of the
finite beam size and pixel size.
size; the effect of the size and shape of the map are taken care of by MADspec.
Figure 5.21 displays a window function calculated by HEALpix for a beam size
of 24 arcminutes and Nside = 512 and Figure 5.22 displays a preliminary transfer
function, similar to a window function, generated by simulations that includes the
size and shape of the preliminary maps in Section 5.3.2.
177
Figure 5.22: Preliminary transfer function for EE from simulations. This transfer function takes into account the size and shape of the preliminary maps of
Section 5.3.2 as well as a 24 arcminute beam and Nside = 512. In general, the
transfer function is an estimation of the sensitivity in l-space of an observation
and is the ratio between the “pseudo power spectrum” or the measurement of the
angular power spectrum (e.g. the output of MADspec) and the estimation of the
real angular power spectrum. The behavior of this transfer function at l ≤ 75 is
due to a rapid decline of both the pseudo ClEE ’s and the original simulated power
spectrum and may not be accurate. In other words, the error bars, which have
not yet been calculated for this transfer function, may be large at low l.
178
5.4
Systematic Issues
Part of the data analysis procedure is to try to determine what systematic
issues may affect the result. Systematic errors may develop from either hardware
or in the data analysis software. While some hardware systematic effects can be
modeled and data analysis software can be tested with simulated data to look for
systematics, tests of the data must include a search for possible systematic effects.
One major source of possible systematic error for WMPol which cannot be
tested by the data analysis is in the calibration technique. Although Equations 4.3
and 4.4 predict that the grid reflection is 99% or better, it is not straightforward to
measure this. Tests in the lab have determined that the grids we used are at least
95% efficient. Another possible source of errors is that we did not have a temperature sensor directly on the ambient temperature load but we instead relied on
the average temperature of the reflectors to determine the ambient temperature.
Based on the readings of the temperature sensors on both reflectors, we believe
that the maximum possible error is ±5 K. Since we also used the average sky temperature for our calibrations, the difference from the actual (but unmeasured) sky
temperature for each calibration is also a possible source of error. Combining these
two uncertainties in temperature, the associated calibration error is estimated to
be no more than 2%. It is also not clear what affect “aging” of the film had on the
179
automatic calibrations though we did not see an obvious change when we replaced
the film that could be solely attributed to the new film. Finally, the placement of
the ambient temperature load that was used for the grid and film calibration was
somewhat constrained by the telescope design and it was difficult to determine if
the grid or film completely viewed the ECCOSORB or if they also viewed part
of the dewar. Unfortunately, this issue, which is most likely the largest source
of possible error, has not been well tested at this time. We expect that the net
result of all these effects would be to underestimate the calibration constant in
Volts/Kelvin which would cause us overestimate our noise. One way to check our
calibration is to compare our measurement of Tau A with measurements in the
literature (Johnston and Hobbs [1969], for example) as was done for COMPASS
[Farese et al., 2003, 2004] but this has not yet been completed. Uncertainties in
the model used for COMPASS exceed 10%.
Another source of possible systematic error is scan synchronous signal. Figure 5.23 displays binned Q-band data collected while operating the telescope with
a larger azimuth scan, clearly showing that there is a scan synchronous signal
which we believe is associated with the telescope viewing the edges of the observatory shutter. As mentioned in Section 5.2.3, it is hoped that this effect can be
removed by optimizing the binned data template removal procedure.
180
Figure 5.23: Scan synchronous signal. Two sets of binned Q-band data (black
and red) are displayed from when the WMPol telescope was scanning ±2.00◦ in
azimuth at 45◦ elevation. The mean and standard error for each bin are shown.
181
5.5
Status of the Data Analysis
The analysis of the 2004 data is on-going − the “pipeline” for data selection
and reduction is in place and the first maps in Q-band of the observed region
have been generated. What remains to be completed is to generate angular power
spectra from maps, use them to help iteratively determine the best data to use
and how to best reduce it, and then generate maps and angular power spectra for
that data.
182
Chapter 6
Conclusion
WMPol was designed, built, and tested at University of California, Santa Barbara and installed in the high altitude WMRS Barcroft Observatory to measure
CMB polarization in Q-band and W-band. With this telescope and receiver system over 1200 hours of CMB data were collected in 2004. The WMPol telescope
proved to be very robust during the course of the observing campaign. In addition, a novel remote control system using relatively inexpensive and commerciallyavailable hardware and software was successfully implemented and utilized to operate the telescope over the internet. A “pipeline” to enable data selection and
reduction has been developed and the data is being analyzed with the publicly
available MADCAP software. However, at this time, we do not expect to detect
CMB polarization with the data we currently have.
183
WMPol was shut down in October 2004 for the scheduled winter closure of the
Barcroft Facility. When Barcroft reopened in June 2005, it was discovered that the
transformer that provides power to the Barcroft Observatory was damaged and
that the power required to operate WMPol was not available. This transformer
is in the process of being replaced. However, the scan synchronous signal seen by
WMPol is a significant limitation and we are currently evaluating whether or not
it makes sense to take more data with WMPol or to use a different instrument
in the observatory. In the meantime, another polarization sensitive instrument is
being constructed by the group to measure CMB polarization from the Barcroft
Facility but this telescope will be housed in a different structure.
Lessons learned from WMPol:
1. The modulation rate for the phase switches in the polarimeters was primarily determined by the lock-in amplifier we had on hand. The polarimeter
performance may have improved if we had used a higher switch rate. With a
higher switch rate, we may also have been successful detecting planets with the
DC polarimeter channels which was a major issue for beam determination.
2. Although we should have been able to achieve much better performance
with a Q-band system with available technology, the higher noise temperature
and 1/f knee of a typical W-band HEMT amplifier make it a challenge to get
useful results from a W-band HEMT radiometer. The group does not plan to use
184
W-band HEMT amplifiers for future planned receivers.
3. The pseudo-correlation technique was difficult to implement and it would
be even more complicated to configure a polarimeter to measure both the Q and
U Stokes parameters at the same time. In future telescopes, the group plans to
use an external wire grid modulator that will allow the measurement of both Q
and U with more straightforward total power receivers like used for BEAST.
4. The limited elevation range of the telescope was a considerable drawback
for source detection and beam size determination. Better ability to detect sources
would have helped improve our pointing reconstruction, beam size determination,
and calibration.
5. The small dome shutter size turned out to be more of a problem than we
had hoped. While the protection that a dome offers in the harsh conditions at
the Barcroft Facility is very important, it would have been nice if it was more
retractable. This may have helped with our scan synchronous signal problem.
6. It would have been nice if we had more of our data analysis pipeline in
place while we were taking data. This is probably a common problem...
Worth repeating:
1. The telescope proved to be quite reliable. There were a few annoyances
with our operating code but they were minor. Higher current servo amps. for the
azimuth and elevation motors would have been nice.
185
2. The remote control system was a great idea. We did have some problems
with lightning induced damage and the internet connections were not as reliable as
we would have liked but overall everything worked well and it should be possible
to make these systems more robust now that we have some experience with them.
3. The weather station and web cameras also worked quite well for weather
monitoring.
4. The way we set up the electrical connections in the observatory to suppress
noise was successful. Isolated linear power supplies for different devices and having
all telescope power routed to a single FERRUPS was a good idea. Isolation
transformers on noisy devices, such as computers, seemed to help.
186
Bibliography
D. Barkats et al. First measurements of the polarization of the cosmic microwave
background radiation at small angular scales from CAPMAP. The Astrophysical
Journal, 619:L127 – L130, February 2005.
R. J. Barlow. Statistics: A Guide to the Use of Statistical Methods in the Physical
Sciences. John Wiley and Sons Ltd, Chichester, England, 1989.
R. H. Becker et al. Evidence for reionization at z∼6: Detection of a GunnPeterson trough in a z=6.28 quasar. The Astronomical Journal, 122:2850–2857,
December 2001.
C. L. Bennett, M. S. Turner, and M. White. The cosmic rosetta stone. Physics
Today, pages 32–38, November 1997.
C. L. Bennett et al. First-year Wilkinson Microwave Anisotropy Probe (WMAP)
observations: Preliminary maps and basic results. The Astrophysical Journal
Supplement Series, 148:1–27, September 2003a.
C. L. Bennett et al. First-year Wilkinson Microwave Anisotropy Probe (WMAP)
observations: Foreground emission. The Astrophysical Journal Supplement Series, 148:97–117, September 2003b.
C. L. Bennett et al. Four-year COBE DMR cosmic microwave background observations: Maps and basic results. The Astrophysical Journal, 464:L1+, June
1996.
M. Bersanelli, June 2005. private communication.
M. Bersanelli et al. Effects of atmospheric emission on ground-based microwave
background measurements. The Astrophysical Journal, 448:8–16, July 1995.
187
J. R. Bond and G. Efstathiou. Cosmic background radiation anisotropies in universes dominated by nonbaryonic dark matter. The Astrophysical Journal, 285:
L45–L48, October 1984.
J. R. Bond, A. H. Jaffe, and L. Knox. Estimating the power spectrum of the
cosmic microwave background. 1998.
Julian Borrill. MADCAP – the Microwave Anisotropy Dataset Computational
Analysis Package. November 1999. astro-ph/9911389.
J. Childers et al. The Background Emission Anisotropy Scanning Telescope
(BEAST) instrument description and performances. The Astrophysical Journal
Supplement Series, 158:124 – 138, May 2005.
L. Danese and R. B. Partridge. Atmospheric emission models - confrontation
between observational data and predictions in the 2.5-300 GHz frequency range.
The Astrophysical Journal, 342:604 – 615, July 1989.
A. de Oliveira-Costa. The cosmic microwave background and its polarization.
In Astronomical Polarimetry: Current Status and Future Directions, volume
CS-343. Astronomical Society of the Pacific, 2005.
C. Dragone. Offset multireflector antennas with perfect pattern symmetry and
polarization discrimination. The Bell System Technical Journal, 57(7):2663 –
2684, September 1978.
B. T. Draine and A. Lazarian. Diffuse galactic emission from spinning dust grains.
The Astrophysical Journal, 494:L19+, February 1998.
S. Eidelman et al. Review of particle physics. Physics Letters B, 592:1+, 2004.
URL http://pdg.lbl.gov.
P. C. Farese et al. COMPASS: an instrument for measuring the polarization of the
CMB on intermediate angular scales. New Astronomy Review, 47:1033–1046,
December 2003.
P. C. Farese et al. COMPASS: An upper limit on cosmic microwave background
polarization at an angular scale of 200 . The Astrophysical Journal, 610:625–634,
August 2004.
N. Figueiredo et al. The optical design of the Background Emission Anisotropy
Scanning Telescope (BEAST). The Astrophysical Journal Supplement Series,
158:118 – 123, May 2005.
188
W. L. Freedman and M. S. Turner. Colloquium: Measuring and understanding
the universe. Reviews of Modern Physics, 75:1433–1447, November 2003.
W. L. Freedman et al. Final results from the Hubble Space Telescope key project
to measure the Hubble constant. The Astrophysical Journal, 553:47–72, May
2001.
K. M. Górski et al. HEALPix: a framework for high-resolution discretization and
fast analysis of data distributed on a sphere. The Astrophysical Journal, 622:
759–771, April 2005.
J. E. Gunn and B. A. Peterson. On the density of neutral hydrogen in intergalactic
space. The Astrophysical Journal, 142:1633–1636, November 1965.
A. H. Guth. Inflationary universe: A possible solution to the horizon and flatness
problems. Physical Review D, 23:347–356, January 1981.
W. Hu and M. White. A CMB polarization primer. New Astronomy, 2:323–344,
October 1997.
W. Hu, N. Sugiyama, and J. Silk. The physics of microwave background
anisotropies. Nature, 386:37–43, 1997.
E. Hubble. A relation between distance and radial velocity among extra-galactic
nebulae. Proceedings of the National Academy of Science, 15:168–173, March
1929.
Transactions of the IAU Vol. 15B (1973), 1974. IAU. 166.
J. D. Jackson. Classical Electrodynamics. John Wiley and Sons, New York, NY,
second edition, 1975.
N. Jarosik et al. Design, implementation, and testing of the Microwave Anisotropy
Probe radiometers. The Astrophysical Journal Supplement Series, 145:413 –
436, April 2003.
K. J. Johnston and R. W. Hobbs. Distribution of brightness in polarization of
Taurus A and brightness distribution of NGC 1976 at 9.55-mm wavelength.
The Astrophysical Journal, 158:145–+, October 1969.
M. Kamionkowski, A. Kosowsky, and A. Stebbins. Statistics of cosmic microwave
background polarization. Physical Review D, 55:7368–7388, June 1997.
189
J. Kaplan, J. Delabrouille, P. Fosalba, and C. Rosset. CMB polarization as complementary information to anisotropies. C. R. Physique, 4:917, 2003. astroph/0310650.
B. Keating, P. Timbie, A. Polnarev, and J. Steinberger. Large angular scale
polarization of the cosmic microwave background radiation and the feasibility
of its detection. The Astrophysical Journal, 495:580–+, March 1998.
A. Kogut et al. First-year Wilkinson Microwave Anisotropy Probe (WMAP)
observations: Temperature-polarization correlation. The Astrophysical Journal
Supplement Series, 148:161 – 173, September 2003.
Edward Kolb and Michael Turner. The Early Universe. Perseus Publishing,
Cambridge, MA, 1990.
A. Kosowsky. Introduction to microwave background polarization. New Astronomy Review, 43:157–168, July 1999.
J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and
Holzapfel W. L. Detection of polarization in the cosmic microwave background
using DASI. Nature, 420:772 – 787, December 2002.
John D. Kraus. Radio Astronomy. Cygnus-Quasar Books, Powell, Ohio, second
edition, 1986.
C. L. Kuo et al. High-resolution observations of the cosmic microwave background
power spectrum with ACBAR. The Astrophysical Journal, 600:32–51, January
2004.
Tove Larsen. A survey of the theory of wire grids. IEEE-MTT, 10(3):191 – 201,
May 1962.
A. Lazarian and D. Finkbeiner. Microwave emission from aligned dust. New
Astronomy Review, 47:1107–1116, December 2003. astro-ph/0307012.
E. M. Leitch, J. M. Kovac, N. W. Halverson, J. E. Carlstrom, C. Pryke, and
M. W. E. Smith. Degree Angular Scale Interferometer 3 year cosmic microwave
background polarization results. The Astrophysical Journal, 624:10 – 20, May
2005.
J. C. G. Lesurf. Millimetre-wave Optics, Devices and Systems. IOP Publishing
Ltd, Bristol, England, 1990.
190
J. Marvil et al. An astronomical site survey at the Barcroft Facility of the White
Mountain Research Station. New Astronomy, 11:218 – 225, 2006.
J. C. Mather, D. J. Fixsen, R. A. Shafer, C. Mosier, and D. T. Wilkinson. Calibrator design for the COBE far-infrared absolute spectrophotometer (FIRAS).
The Astrophysical Journal, 512:511–520, February 1999.
P. R. Meinhold et al. The Advanced Cosmic Microwave Explorer - a millimeterwave telescope and stabilized platform. The Astrophysical Journal, 406:12 – 25,
March 1993.
Y. Mizugutch, M. Akagawa, and H. Yokoi. Offset dual reflector antenna. In
Antennas and Propagation Society International Symposium, 1976.
T. E. Montroy et al. A measurement of the CMB < EE > spectrum from the
2003 flight of BOOMERanG. astro-ph/0507514, July 2005.
C. W. O’Dell, D. S. Swetz, and P. T. Timbie. Calibration of millimeter-wave
polarimeters using a thin dielectric sheet. IEEE-MTT, 50(9):2135 – 2141, September 2002.
T. J. Pearson et al. The anisotropy of the microwave background to l = 3500:
Mosaic observations with the Cosmic Background Imager. The Astrophysical
Journal, 591:556–574, July 2003.
P. J. E. Peebles. Principles of Physical Cosmology. Princeton University Press,
Princeton, NJ, 1993.
F. Piacentini et al. A measurement of the polarization-temperature angular cross
power spectrum of the cosmic microwave background from the 2003 flight of
BOOMERanG. astro-ph/0507507, July 2005.
A. G. Polnarev. Polarization and anisotropy induced in the microwave background
by cosmological gravitational waves. Soviet Astronomy, 29:607–+, December
1985.
A. C. S. Readhead et al. Polarization observations with the Cosmic Background
Imager. Science, 306:836 – 844, October 2004.
Kristen Rohlfs. Tools of Radio Astronomy. Springer-Verlag, 1986.
G. B. Rybicki and A. P. Lightman. Radiative Processes in Astrophysics. John
Wiley and Sons, New York, NY, 1979.
191
D. Scott, J. Silk, and M. White. From microwave anisotropies to cosmology.
Science, 268:829–835, May 1995.
M. Seiffert et al. 1/f noise and other systematic effects in the Planck-LFI radiometers. Astronomy and Astrophysics, 391:1185 – 1197, 2002.
U. Seljak and M. Zaldarriaga. A line-of-sight integration approach to cosmic
microwave background anisotropies. The Astrophysical Journal, 469:437–+,
October 1996.
G. F. Smoot et al. Structure in the COBE differential microwave radiometer
first-year maps. The Astrophysical Journal, 396:L1–L5, September 1992.
R. Stompor et al. Making maps of the cosmic microwave background: The MAXIMA example. Physical Review D, 65, 2002. 022003.
Max Tegmark. How to make maps from cosmic microwave background data without losing information. The Astrophysical Journal, 480:L87 – L90, May 1997.
F. Villa, M. Bersanelli, and N. Mandolesi. Design of Ka and Q band corrugated
feed horns for CMB observations. Internal Report 188, ITESRE/CNR, April
1997.
F. Villa, M. Bersanelli, and N. Mandolesi. Design of W band corrugated feed
horns for CMB observations. Internal Report 206, ITESRE/CNR, 1998.
E. L. Wright. CMB observational techniques and recent results. astro-ph/0401001,
December 2003.
M. Zaldarriaga. The polarization of the cosmic microwave background. In Measuring and Modeling the Universe, pages 310–+, 2004.
M. Zaldarriaga and U. Seljak. All-sky analysis of polarization in the microwave
background. Physical Review D, 55:1830–1840, February 1997.
192
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