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QUaD: A millimeter-wave polarimeter for observation of the cosmic microwave background radiation

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QUAD: A MILLIMETER-WAVE POLARIMETER
FOR OBSERVATION OF THE
COSMIC MICROWAVE BACKGROUND RADIATION
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF PHYSICS
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
James R. Hinderks
August 2005
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UMI Number: 3186353
Copyright 2005 by
Hinderks, James R.
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I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
Prof. Sarah E. Church
Principal Adviser
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
Prof. Giorgio Gratta
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
rof. Steven Kahn
Approved for the University Committee on Graduate Studies.
iii
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Abstract
This thesis describes the design and performance of the QUaD experiment and
presents some of its earliest results. QUaD is a millimeter-wavelength polarimeter designed for observing the Cosmic Microwave Background (CMB). QUaD was
commissioned at the MAPO observatory at the Amundsen-Scott South Pole Station
in the Austral Summer of 2004/2005, achieved first light in Feb 2005, and began
science observation in May.
QUaD observes the CMB with an array of 31 polarization-sensitive Neutron
Transmutation Doped (NTD) germanium bolometers split between two frequency
bands centered at 100 and 150 GHz. The telescope is a 2.6 m on-axis Cassegrain
design with beam sizes of 6.3' and 4.2' at the two respective observing frequencies.
The resolution and scan strategy are optimized to probe the CMB El-mode power
spectrum over a multipole range of 100 to 2500. The performance of the system has
been characterized with commissioning observations and a high signal-to-noise map
of the CMB temperature anisotropy has been made over a ~ 50 square degree area.
CMB polarization anisotropies, only recently detected, promise a wealth of new
cosmological information. Their observation complements the many successful tem­
perature anisotropy measurements already performed, confirming our basic under­
standing of the early universe and leading to tighter constraints on cosmological
parameters. Furthermore, polarization observations provide a probe of structure
since the last scattering surface and promise unique constraints on inflation through
the imprint of relict gravitational radiation.
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Acknowledgements
QUaD has been a collaborative effort since the beginning and I feel privileged to
have spent the past six years working with the talented group of scientists listed in
Table 1 .3 -1 have learned a great deal from each one of you. This holds especially
true for the Stanford QUaD team with whom I’ve spent innumerable hours in “the
lab.” And of course, building a telescope isn’t much good if nobody puts it to use
and keeps it in shape. So two gold stars to Robert “Do the Dew” Schwartz and Alan
“No Worries” Day for being the best winter-over crew imaginable.
Grad school has certainly been a long process. Throughout, Sarah has been a
terrific advisor and mentor, and has made so many opportunities available to me.
Thanks to the postdocs I worked with in my first two years at Stanford - Brian and
Byron - for teaching me so much about doing physics. Thanks to Keith for teaching
me a great deal about electronics, careful experimental technique, and about knowing
when to just kludge something together. Thanks to Mel for all the great discussions
on cosmology. Thanks to Brad, who was my fellow Church lab grad student for
many years. Working with you was always fun - whether we were in the lab or on
the summit of Mauna Kea. I’ll never forget learning how to install snow chains at
14,000’ or the night we nearly starved to death at South Point. And thanks to Ben
- who has been my partner in crime working on QUaD for the past four years - for
doing so much to make QUaD a success, and for being a great officemate and friend.
Over the years, our lab has been fortunate enough to have a steady supply of
top-quality undergraduates. Seebany, Judy, Marteen, Evan, Kapil, Elizabeth, Ali,
and Tess: thanks for all your hard work and for making lab so much fun. Particular
thanks go to Kapil for his invaluable CAD work on the focal plane and to Evan
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for his excellent senior thesis work on QUaD optical testing (and for his equally
excellent shirts). Also QUaD never would have made it to the Pole on time without
all the packing and shipping help from Tess, in the form of carpentry, manual labor,
chocolate chip cookies, and of course exploding foam.
Acknowledgement is also due to the great people of the Stanford Physics De­
partment who helped make QUaD a success. Thanks to Dana for her indispensable
organizational and administrative help. The extremely talented group of machinists
who actually built much of the QUaD receiver - John, Mehmet, Matt, and Karl­
heinz - deserve special recognition. And finally, thanks to Stewart, Joel, and Khoi
for keeping the Varian building running smoothly, dealing with our endless stream
of deliveries, and keeping the stock room filled with the assorted cable ties, resistors,
and other random bits that saved the day on many occasions.
A few more random words before wrapping this up. To Mike Z, thanks for the
inspirational music and all the cowbell - it was hot. To Angiola, thanks for letting
me try “one more test,” and for not leaving me on the floor by the water fountain. I
wish you hadn’t stolen that towel though. To Ben, thanks for your awesome Dremel
skills. To Cara, thanks for the jokes, the laughter, the offbeat news, and the stories
about Speedy. Thanks to Dave and Becky for introducing me to the Earthquakes, to
Hilton for always knowing where the free food was and to Phil for sending presents
to cheer us up at the South Pole. Special thanks to Sarah, Mel, and Ben for all your
helpful comments on this document. Best of luck to everyone continuing to work on
QUaD, especially Ed, the team’s newest member.
Finally, I arrive at the most important people - my family. Mom and Dad, thanks
for instilling in me a love of science and of learning. I owe everything to the two of
you. To my four amazing grandparents, thanks for all your love over the years. To
the Suns, thank you for welcoming me into your wonderful family, and in particular
thanks to Christina for providing me with a place to live over the last half year while
I wrote this dissertation. And finally to Stephanie: it must be true love when you’re
willing to spend weekend afternoons in the machine shop wearing safety goggles or
in the lab inhaling solder fumes just to be with your husband. Thanks for being the
best thing in my life.
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Contents
Acknowledgements
vii
1 Introduction
1
1.1 Cosmology and the Cosmic Microwave B ackground............................
2
1.1.1
Origin and History of the C M B .................................................
2
1.1.2
The Modern Cosmological P icture..............................................
3
1.1.3
CMB Temperature Anisotropies.................................................
7
1.2 The Polarization of the CMB ................................................................
12
1.2.1
Stokes Parameters
......................................................................
12
1.2.2
Origins and Characterization of CMB Polarization..................
14
1.2.3
Existing Measurements................................................................
22
1.3 The QUaD Experim ent............................................................................
24
1.3.1
Overview
.....................................................................................
24
1.3.2
Science G o a ls ...............................................................................
26
1.4 Thesis O utline............................................................................................
28
2 Experiment Description
2.1 The South Pole Observing Site
31
.............................................................
31
2.2 The DASI M o u n t......................................................................................
32
2.3 O p tic s ........................................................................................................
33
2.3.1
Overview
.....................................................................................
33
2.3.2
Lenses and Cold S to p ...................................................................
34
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2.4
2.3.3
F ilterin g .......................................................................................
36
2.3.4
Corrugated F e e d s........................................................................
39
2.3.5
Polarization SensitiveB olom eters..............................................
40
2.3.6
The Focal P lane...........................................................................
42
Cryogenics................................................................................................
46
2.4.1
C ry o sta t.......................................................................................
46
2.4.2
Sub-Kelvin R efrig e rato r............................................................
48
2.4.3
The Science C o r e ........................................................................
52
2.4.4
T herm om etry..............................................................................
54
3 Readout Electronics
3.1
3.2
57
Description .............................................................................................
57
3.1.1
Bias G e n e ra to r...........................................................................
59
3.1.2
Load Resistor B o x e s ..................................................................
61
3.1.3
Focal Plane W irin g .....................................................................
63
3.1.4
JFET B oxes..................................................................................
65
3.1.5
Lockin Amplifiers.........................................................................
67
3.1.6
The Data AcquisitionS y s te m .....................................................
70
Performance.............................................................................................
71
3.2.1
Functionality T e s ts ......................................................................
71
3.2.2
Noise P erform ance......................................................................
77
3.2.3
Channel C apacitance...................................................................
85
3.2.4
M icrophonics...............................................................................
89
3.2.5
Radio Frequency In terferen ce...................................................
91
4 Receiver Characterization
4.1
4.2
93
Bolometer C haracterization ..................................................................
93
4.1.1
Bolometer M o d e l.........................................................................
93
4.1.2
Load Curves..................................................................................
95
Optical C haracterization........................................................................... 100
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4.2.1 Optical T estbed................................................................................100
4.2.2 Spectral B a n d s ................................................................................102
4.2.3 Optical Efficiency.............................................................................106
4.2.4 Responsivity and Time C onstants................................................. 110
4.2.5 Cosmic Rays and Impulse Response.............................................. 113
4.3 Polarization P ro p erties.............................................................................. 116
4.3.1 Form alism .........................................................................................117
4.3.2 Derivation of the Expected S ignal................................................. 120
4.3.3 The Measurement S e t u p ................................................................ 123
4.3.4 Results and Discussion................................................................... 124
5
Instrument Performance
5.1
131
Optical P erform ance..................................................................................131
5.1.1 Raster M aps......................................................................................131
5.1.2 Feed O ffsets......................................................................................137
5.1.3 B e a m s............................................................................................... 139
5.1.4 Time C onstants................................................................................142
5.2 Calibration
.................................................................................................144
5.2.1 Atmospheric Transm ission..............................................................144
5.2.2 Routine Gain Calibration
..............................................................149
5.2.3 Absolute C alib ratio n.......................................................................155
5.3
Sensitivity and N o ise ..................................................................................159
5.3.1 Optical Loading................................................................................ 159
5.3.2 Noise Equivalent Power....................................................................163
5.3.3 NET and N E Q ................................................................................ 174
6
First Observations
6.1
177
Survey D escription.....................................................................................177
6.1.1 Field Selection
................................................................................ 177
6.1.2 Observing S tra te g y .......................................................................... 179
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6.2
First M aps...................................................................................................182
6.2.1 Temperature M a p s ......................................................................... 182
6.2.2 Polarization M aps............................................................................ 190
6.2.3 Discussion.........................................................................................193
A Focal Plane Temperature Control
197
B Commissioning QUaD
201
B.l
Receiver Testing..........................................................................................202
B.2 Foam Cone Installation..............................................................................202
B.3 Secondary Installation and Alignment..................................................... 204
B.4 Ground Shield Extension...........................................................................205
B.5 Receiver In sta lla tio n .................................................................................206
C Calibration Source Hardware
209
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List of Tables
1.1
QUaD key numbers...................................................................................
26
1.2
QUaD tim e lin e ........................................................................................
27
1.3
The QUaD collaboration........................................................................
30
3.1
QUaD channel t a b l e ..............................................................................
58
3.2
Warm electronics testing noise budget...................................................
82
3.3
Electronics noise b u d g e t ........................................................................
85
4.1
Bolometer parameters
4.2
Average spectral band properties............................................................... 104
4.3
Average optical efficiencies........................................................................ 108
5.1
Measured beam parameters
5.2
Estimated QUaD optical loading
6.1
Temperature map noise.............................................................................. 187
6.2
Single-feed polarization map n o ise............................................................ 190
6.3
Polarization map n o is e .............................................................................. 192
.............................................................................. 101
..................................................................... 140
............................................................ 160
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List of Figures
1.1 WMAP CMB temperature m a p .............................................................
4
1.2 Annotated CMB temperature power sp e ctru m .....................................
8
1.3 WMAP CMB temperature power spectrum ...........................................
9
1.4 Detector orientations for measuring Q and U ........................................
12
1.5 CMB polarization originates from anisotropic Thompson scattering .
14
1.6 Local quadrupole p a tte r n s ......................................................................
15
1.7 E and B Fourier m odes............................................................................
17
..................................................................................
18
1.9 Random E and B p a tte rn s ......................................................................
19
1.10 Predicted CMB power s p e c tra ................................................................
20
1.11 WMAP TE correlation............................................................................
22
1.12 Existing El-mode polarization m easurem ents........................................
23
1.13 Panoramic view of the QUaD telescope.................................................
25
1.14 QUaD predicted El-mode s p e c tr u m .......................................................
28
1.15 QUaD predicted temperature sp ectru m .................................................
29
2.1
QUaD general assembly
.........................................................................
32
2.2
QUaD optical p a t h ..................................................................................
34
2.3 QUaD pixel sc h e m a tic ............................................................................
35
2.4 Cold optics schematic...............................................................................
36
2.5 Average spectral b a n d s ............................................................................
37
2.6 Feed h o rn s.................................................................................................
38
1.8 E and B hot spots
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2.7 Feed horn beam p a t t e r n .........................................................................
39
2.8
PSB module and a b so rb e r......................................................................
41
2.9 Pixel position and o rien tatio n ................................................................
43
2.10 Horn and PSB m ounting.........................................................................
44
2.11 The receiver c o r e .....................................................................................
45
2.12 The QUaD cryostat..................................................................................
46
2.13 Three-stage fridge.....................................................................................
48
2.14 Example fridge operation.........................................................................
49
2.15 A fridge c y c le ...........................................................................................
51
2.16 Focal plane CAD rendering
...................................................................
52
2.17 Focal plane te m p e ra tu re .........................................................................
55
2.18 Installing the focal plane in the receiver.................................................
56
3.1
Electronics overview schematic................................................................
57
3.2
Bias generator schem atic.........................................................................
59
3.3
Cold electronics overview.........................................................................
61
3.4 Load resistor b o a rd ..................................................................................
62
3.5
The focal plane b o w l...............................................................................
64
3.6 JFET m e m b ra n e .....................................................................................
65
3.7 JFET box CAD m o d e l............................................................................
66
3.8
Lockin card sc h e m a tic ............................................................................
67
3.9
Lockin amplifier box p h o to ......................................................................
68
3.10 Measured spectrum of bias g e n e ra to r....................................................
71
3.11 Lockin card filtering d e ta il......................................................................
72
3.12 Lockin 475 Hz LP filter measured response..........................................
73
3.13 Lockin 20 Hz LP filter measured response
..........................................
74
3.14 Lockin 20 Hz LP filter measured response (impulse m e th o d ) ............
75
3.15 Electronics noise testing s e tu p ................................................................
77
3.16 Lockin box noise s p e c tra .........................................................................
78
3.17 Amplifier noise vs. source resistance.......................................................
80
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3.18 Bias n o i s e .................................................................................................
82
3.19 Electronics stability..................................................................................
83
3.20 Bolometer readout including stray capacitance.....................................
86
3.21 Measured QUaD channel capacitance....................................................
87
3.22 Attenuation resulting from stray capacitance........................................
88
3.23 Microphonic response...............................................................................
89
3.24 Microphonic response...............................................................................
90
3.25 Warm RF filtering
..................................................................................
91
Bolometer thermal and electrical m o d e ls ..............................................
94
4.2 Load curves e x am p le ...............................................................................
96
4.3 Bolometer resistance vs. tem p eratu re....................................................
97
4.4 Measuring Q from load c u rv e s................................................................
98
4.1
4.5 The QUaD optical te s tb e d ........................................................................ 102
4.6 Laboratory optical testing with Q U a D ................................................... 103
4.7
QUaD spectral b a n d s..................................................................................105
4.8
Optical efficiency with loadcurves............................................................ 106
4.9
Optical efficiency histogram s..................................................................... 109
4.10 Responsivity c u r v e .....................................................................................110
4.11 Lab time constant measurements ............................................................ 112
4.12 Cosmic ray impulse response..................................................................... 114
4.13 Model QUaD impulse response
............................................................... 115
4.14 Aligning the polarizing grid for t e s t i n g ................................................... 116
4.15 Polarizing grid mounted on receiver w in d o w .......................................... 117
4.16 Polarization response from two h o r n s ...................................................... 118
4.17 Measured PSB orientations........................................................................ 119
4.18 Measured PSB angle and orthogonality................................................... 120
4.19 Measured cross-polar leakage..................................................................... 121
4.20 Cross-polar leakage in QUaD vs. the te s tb e d .......................................... 126
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5.1
Azimuth encoder while m apping............................................................... 132
5.2 Telescope RA/DEC while raster m apping................................................ 133
5.3
Elevation j i t t e r ...........................................................................................134
5.4
RCW38 m a p s ..............................................................................................135
5.5
Measured feed positions ........................................................................... 137
5.6 RCW38 from every f e e d ............................................................................138
5.7 Predicted beam pattern
............................................................................139
5.8 Time c o n s ta n ts ...........................................................................................143
5.9
Skydip d a t a .................................................................................................144
5.10 QUaD tau vs. 350 micron tipper
............................................................ 145
5.11 Tau vs. tim e .................................................................................................146
5.12 Calibration source........................................................................................150
5.13 Calibration source d a ta ...............................................................................151
5.14 Elevation nod e x am p le ...............................................................................153
5.15 A/B ratios from three calibration techniques..........................................154
5.16 d B /d T evaluated for QUaD bands............................................................ 155
5.17 Receiver loading vs. tim e ........................................................................... 161
5.18 Receiver loading...........................................................................................162
5.19 NEP breakdown...........................................................................................163
5.20 Total NEP versus b i a s .............................................................................. 167
5.21 Responsivity curves.....................................................................................169
5.22 Average responsivity................................................................................. 169
5.23 Atmospheric noise time-ordered d a t a ...................................................... 170
5.24 Power spectrum of QUaD noise in NEP units
....................................... 172
5.25 NEP d istrib u tio n ........................................................................................173
5.26 NET d istrib u tio n ........................................................................................174
6.1
QUaD 2005 field ........................................................................................178
6.2
Hit m ap s.......................................................................................................181
6.3
Map filtering
..............................................................................................183
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6.4
QUaD CMB temperature m a p s ...............................................................184
6.5
QUaD temperature maps compared withB2K and W M A P ...................185
6.6
Deck rotation jackknives........................................................................... 189
6.7
Single-feed polarization maps
6.8
Stokes Q maps .......................................................................................... 194
6.9
Simulated Stokes Q maps
..................................................................191
........................................................................ 195
A.l Focal plane temperature control schem atic.............................................198
A. 2 The effect of focal plane temperature co n tro l..........................................199
B.l
Installing the foam c o n e ........................................................................... 203
B.2 Installing the receiver................................................................................. 205
B.3 The receiver room ....................................................................................... 207
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XX
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Chapter 1
Introduction
The Big Bang theory is the cornerstone of modern cosmology. It holds that the
universe began in an extremely hot, dense, and homogeneous state, and that it has
expanded into the cool, clumpy universe we observe today. An abundance of obser­
vations support this model. The first piece of evidence is Hubble’s 1929 discovery
that all galaxies appear to be receding from us with a recession velocity proportional
to distance. The next major piece of evidence came in the late 1940s when Gamow
showed that a hot Big Bang could explain the observed abundances of light elements
in the Universe. The strongest piece of evidence in support of the Big Bang, was
the 1965 discovery of a nearly uniform background glow of thermal radiation, now
known as the Cosmic Microwave Background (CMB).
Today, observations of the CMB are still providing some of the most fruitful data
in the field of observational cosmology. This introduction gives an overview of the
CMB, briefly describing its physical origin and observable properties. The chapter
concludes with a summary of QUaD, a recently fielded experiment that will advance
the state of the art in CMB observations. A detailed description of the design and
characterization of the QUaD experiment forms the bulk of this thesis.
1
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2
CHAPTER 1. INTRODUCTION
1.1
C osm ology and th e C osm ic M icrow ave B ack­
ground
1.1.1
Origin and H istory o f th e CM B
Penzias and Wilson discovered the CMB while trying to determine the origin of an
unknown source of “noise” in a microwave radiometer at Bell Telephone Laborato­
ries in Holmdel, New Jersey [Penzias and Wilson, 1965]. They found what appeared
to be an isotropic background consistent with a thermal source at approximately
3 K. Systematic investigation ruled out a terrestrial source for this signal. Discus­
sion with other researchers - notably Dicke, Peebles, and Wilkinson at Princeton led to the realization that this was likely the CMB [Peebles, 1993]. Their pioneer­
ing observations led to Penzias and Wilson being awarded the 1978 Nobel Prize in
Physics.
The existence of a thermal background radiation at a few Kelvin as a consequence
of the Big Bang had been predicted as early as 1948 by Gamow. The reasoning is as
follows: several seconds after the Big Bang, the universe was composed of a dense
plasma of electrons, protons, and photons. Thompson scattering tightly coupled the
photons with the matter, maintaining thermal equilibrium as the universe expanded
and cooled. However, when the Universe was approximately 400,000 years old, it had
cooled sufficiently that the electrons and protons combined to form hydrogen atoms,
and Thompson scattering no longer coupled the photons to the matter. After this
event, known as recombination or decoupling, the photons free streamed, growing in
wavelength with the expanding Universe.
The CMB photons that we observe today have been travelling for approximately
14 billion years. During this journey, their wavelength has expanded by a factor
of one thousand leaving them in the microwave regime. Throughout the expansion,
they have maintained a thermal energy distribution with the temperature decreasing
as one over the expansion factor. Experiments during the late 1960s confirmed the
spectral shape and measured a temperature of a few Kelvin. The definitive spectral
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1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND
3
measurement came from the FIRAS (Far Infrared Absolute Spectrophotometer) in­
strument onboard the COBE (Cosmic Background Explorer) satellite [Mather et al.,
1994]. The data give a superb fit to a blackbody spectrum with a temperature of
T0 = 2.726K. These CMB observations confirmed the basic picture of the the early
universe as a hot, dense plasma, providing tremendous support for the Big Bang
model.
The early universe was remarkably uniform, as evidenced by the isotropy of the
CMB. However, the structure that we see today in the form of clusters of galaxies
suggests that minute inhomogeneities must have existed even at the earliest times.
Measuring these tiny fluctuations was a great experimental challenge. In 1992, more
than 25 years after the first CMB observations, the DMR (Differential Microwave
Radiometers) instrument on the COBE satellite finally found anisotropies in the
CMB temperature at the low level of one part in 105 [Smoot et al., 1992]. A flurry
of experiments followed, measuring the anisotropies with higher angular resolution
and better sensitivity (although only over small regions of sky). The first-year data
release of the Wilkinson Microwave Anisotropy Probe (WMAP) satellite in 2003
marked another experimental milestone. The satellite produced all-sky maps at five
frequencies with sub-degree angular resolution. Figure 1.1 shows a map from one of
the frequency bands.
1.1.2
T he M odern Cosm ological Picture
Overview
Observations of the CMB, combined with evidence from other types of cosmological
observations, have led to a consistent description of the universe. The following list
summarizes the key tenets of the emerging cosmological picture:
S patial F latness The universe is “flat” which means that Euclidean geometry ap­
plies even on cosmological scales. This is in contrast to the “open” universe
models that were favored even a decade ago in which initially parallel beams of
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CHAPTER 1. INTRODUCTION
4
-200
T (>1K)
+200
Figure 1.1: CMB temperature anisotropies. This is the W band (94 GHz) all-sky
map from the WMAP satellite [Bennett et al., 2003]. The red swath across the
middle is foreground emission from our Milky Way galaxy. Away from the Galactic
plane, the structure is caused by anisotropies in the CMB. The characteristic sizes
of the hot and cold spots leads to constraints on cosmological parameters.
light would eventually diverge. The strongest evidence for a flat universe comes
directly from measurements of the CMB temperature anisotropies [Spergel
et al., 2003].
D ark M a tte r Only a small fraction (~ 10%) of the matter in the universe is nor­
mal, or baryonic. This means that the bulk is in an unknown form, termed
dark matter. The best constraints on the total matter content come from ob­
servations of large scale structure in the universe [Percival et al., 2002]. The
limit on the baryon fraction comes from microwave background observations
[Spergel et al., 2003].
D ark E nergy The bulk (~ 75%) of the energy density of the universe resides in
a completely unknown form termed dark energy. The dark energy appears to
be in the form of an energy field with negative pressure. If the pressure is less
than the negative of one third of the total energy density, then the theory of
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1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND
5
general relativity predicts that the expansion of the universe should accelerate
with time, rather than decelerate. The most direct evidence for dark energy
comes from observations of high-redshift supernovae [Perlmutter et al., 1999,
Riess et al., 2001, Knop et al., 2003].
Inflation The theory of Inflation posits that the universe expanded by a factor of
~ 1050 in the first ~ 10-35 seconds after the Big Bang [Guth, 1981]. This rapid
initial expansion naturally resolves the following weaknesses with the standard
Big Bang model.
• The Flatness Problem - The Big Bang model offers no explanation as to
why the universe would have precisely the critical energy density required
for spatial flatness. In the inflationary model, the present-day horizon
only subtends a tiny fraction of the total universe. Over this limited
scale, the universe appears flat irrespective of curvature that may have
been present in the initial, pre-inflationary universe.
• The Horizon Problem - The isotropy of the CMB temperature on the
largest angular scales presents a problem for the standard Big Bang model.
These regions would not have been in causal contact prior to decoupling
and consequently would not have thermalized. In the inflationary sce­
nario, all these regions were in causal contact before the exponential ex­
pansion, explaining the uniform temperature we see today.
• The Monopole Problem - Particle physics predicts the existence of exotic
particles such as magnetic monopoles that are not observed today. The
rapid expansion of inflation allows these particles to have existed in the
pre-inflationary universe while explaining their scarcity today.
• The Origins of the Initial Perturbations - The Big Bang model postulates
that the anisotropies in the CMB (and the structure we observe in the
local universe) resulted from initial perturbations of the primordial plasma
on all spatial scales. Inflation naturally explains their origin - even the
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CHAPTER 1. INTRODUCTION
6
largest began as tiny quantum fluctuations in the initial universe and were
stretched to cosmological scales during the period of rapid expansion.
Because of these explanations, inflation is an extremely attractive theory. Cur­
rently, however, very little is known about the nature of the inflaton field that
is believed to have driven such a rapid expansion. Further observations of
the CMB, especially its polarization, offer the best hope for elucidating this
mechanism.
Observable Properties of the CMB
The CMB has three observable properties:
• Frequency Spectrum - As previously discussed, the frequency spectrum of the
CMB has been measured to exquisite precision, and it has been found to be
the most pristine example of purely thermal radiation in the universe.
• Temperature Anisotropy - Since it has a thermal spectrum, the intensity of
the radiation can be characterized as a temperature at each point on the sky.
Analysis of the temperature distribution on the sky has led to tight constraints
on many of the cosmological parameters. More detail on this analysis will be
provided in the next subsection.
• Polarization Anisotropy - Observations have shown the CMB to be partially
polarized (Section 1.2.3). It is hoped that future measurements of the polar­
ization pattern on the sky by experiments such as QUaD will lead to tighter
constraints on the cosmological parameters by breaking degeneracies inherent
in the temperature spectrum alone. However, the ultimate goal of CMB polar­
ization studies is to observe and characterize the unique polarization imprint
predicted to arise from inflation. This signature is extremely faint, lying at
least several orders of magnitude below the already faint CMB temperature
anisotropies; however, the potential scientific reward is great. QUaD will cer­
tainly be only one of many experiments needed to fully realize it.
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1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND
1.1.3
7
CM B Tem perature A nisotropies
Anisotropies
Anisotropies in the CMB begin as density variations in the primordial plasma. Overdense regions tend to collapse under the influence of gravity. However, radiation
pressure from the tightly coupled photons resists the collapse. Competition between
these two forces results in oscillations in the plasma. After the photons decouple
at recombination, the radiation pressure is gone, the acoustic oscillations stop, and
the overdense regions collapse under gravity. The photons free-stream, with hotter
photons emanating from overdense regions and cooler photons from rarified regions.
Figure 1.1 shows an all-sky map of CMB temperature anisotropies from the 2003
data release of the WMAP satellite. This is the best measurement of the CMB
temperature anisotropies currently available. The random pattern confirms that
oscillations were present at all scales in the early universe; however, there is a char­
acteristic size to the hot/cold spots of roughly 1° where the temperature contrast is
greatest. This results from the largest mode that just had time to complete one rar­
efaction/compression cycle before decoupling. Smaller modes oscillate proportionally
faster, so a harmonic series of modes exist, each of which ends at a compression or
rarefaction. These show up on the sky as a series of preferred sizes to the hot/cold
spots.
The Power Spectrum
Structure in CMB maps is more conveniently discussed in terms of the angular power
spectrum. The power spectrum is found by making a spherical harmonic expansion
of the observed spatial temperature distribution as
oo
t
(M ) = E
£
E
£=2 m = —£
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(i.i)
CHAPTER 1. INTRODUCTION
8
photon collapse
acoustic oscillations
X—s
M
*3
1st compression
horizon crossing
1st rarefroction
+
diffusion
100
10
1000
m ultipole, I
Figure 1.2: Example CMB Temperature power spectrum with the key features la­
belled. (Figure courtesy of M. Bowden)
where the £ — 1 dipole term is omitted because the intrinsic CMB dipole is obscured
by the apparent dipole resulting from Earth’s motion with respect to the reference
frame defined by the CMB. For a given scale £, the fluctuations are evenly distributed
among the available orientations m = —£, —£+ 1 ,... ,£ with no preferred direction.
The power at a given £ is then defined as an average over the 2^+ 1 possible values
of m as
c, = ^ - 7
£
1 m = —l
M
2 = ( w 2) •
I1'2)
It is a property of the spherical harmonics that the zeros are spaced at the approxi­
mate interval A6 ph 180°/£ (see eg. Peebles [1980]). This associates an angular scale
with each £ value.
Figure 1.2 shows an example power spectrum with some of the key features
annotated. The most prominent feature is the series of peaks beginning around
£ ~ 200. These arise from the previously discussed modes of oscillation that are
extremal at decoupling. The first peak represents a mode that just had time to
maximally compress before decoupling. Peaks at increasing £ alternately correspond
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1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND
9
Angular Scale
0.5°
6000
TT Cross Power
Spectrum
5000
A - COM All O ata
WMAP
CBI
AGBAR
4000
^
O
+
0 .2°
3000
2000
1000
0
10
40
100
400
200
Multipole m o m en t
800
1400
(I)
Figure 1.3: The status of measurements of the CMB temperature anisotropy power
spectrum. This figure is from Bennett et al. [2003].
to modes that reached maximum rarefaction and compression. Above I ~ 1000, the
power is reduced as the angular scale of the fluctuations approaches the thickness
of the “surface” of last scatter. The region between ~ 10 < I < 200 corresponds
to modes that enter the horizon before decoupling, and begin collapsing but do not
reach maximal compression. Fluctuations on the largest angular scales (I < ~ 10) do
not enter the horizon and do not collapse. However, they still produce temperature
anisotropies' (and thus non-zero power in the power spectrum) through the Sachs
Wolf effect. Here denser regions appear colder because photons that climb out of
their gravitational potential well appear redshifted. This gravitational redshift effect
occurs on all angular scales, reducing the effective temperature of the anisotropies.
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CHAPTER 1. INTRODUCTION
10
Current Measurements
Figure 1.3 shows the current state of the art in CMB temperature measurements.
Below I ~ 800 the highest quality data comes from the first data release of the
WMAP satellite. This is an on-going all-sky survey at five frequency bands from 23
to 94 GHz. Several experiments have measured the high-£ region of the spectrum.
The two shown here are from CBI (Cosmic Background Imager), an interferom­
eter operating from Chile, and ACBAR (Arcminute Cosmology Bolometer Array
Receiver), a bolometer-based instrument observing from the South Pole.
Cosmological Parameters
Our knowledge of the Universe on its largest scale is given in terms of a small
number of measurable values known as cosmological parameters. The following lists
those that most influence the shape of the CMB power spectrum; these describe the
density, composition, and expansion rate of the universe.
• Qo - The total energy density of the universe in units of the critical density.
• h - The Hubble constant, in units of 100 km/s/Mpc.
• ^6 - The fractional density of baryonic matter in the universe.
•
- The fractional density of matter (including baryonic and dark).
• Qa - The fractional density of dark energy (note:
+ flm = U0).
The precise shape of the CMB power spectrum, in particular the location and
relative heights of the acoustic peaks, probes these parameters. For example, the
location of the first peak in t space probes the horizon size at decoupling, measuring
the geometry of the universe on the largest possible scale. This directly leads to con­
straints on Qo- As a second example, adding mass in the form of baryons (increasing
flb) allows the plasma to fall deeper into the potential wells before rebounding due
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1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND
11
to photon pressure. This enhances the compressional (odd-numbered) peaks in the
power spectrum relative to the rarefactional (even-numbered) peaks.
Inflationary theories make predictions about the spatial power spectrum of the
primordial potential fluctuations that eventually give rise to the observed CMB
anisotropies. There are three possible types of metric perturbations that each evolve
separately:
Scalar m odes correspond to the fluctuations in the gravitational potential that
give rise to the CMB temperature anisotropy power spectrum.
V ector m odes arise from rotation motions in the plasma. They are not enhanced
by gravitational collapse and so are damped relative to scalar and tensor modes
as the universe expands. They are thus expected not to leave an observable
imprint on the CMB and will not be discussed further.
Tensor m odes distort the metric in an analogous manner to a background of gravi­
tational radiation. These contribute to the CMB temperature and polarization
spectrum; however, their contribution to the temperature spectrum is swamped
by the scalar modes.
The following parameters describe the power spectrum of the initial perturbations:
• A - The amplitude of the scalar perturbations.
• ns - The spectral index of the scalar perturbation spectrum. The currently
favored value of ns = 1 describes a scale-invariant spectrum in which pertur­
bations of all wavelengths have equal power.
• dns/dlnk - This describes a “running” spectral index that varies with scale.
• r - The ratio of the amplitude of the tensor to the scalar perturbation spectrum.
Measuring these parameters constrains theories such as inflation that predict the
initial spectrum of perturbations. In particular, measurement of a non-zero value of
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CHAPTER 1. INTRODUCTION
12
Q Detector
U Detector
x+y
Figure 1.4: The geometry for Q and U detectors described in eqs. 1.7 and 1.8.
r provides a direct test of the inflationary model. Current observations limit r to be
less than 0.71 [Spergel et al., 2003], but no theoretical lower limit exists.
1.2
T h e P olarization o f th e C M B
1.2.1
Stokes Param eters
Incoherent, partially polarized radiation such as the CMB can be described by a set
of intensities known as the Stokes parameters. The total intensity of the radiation
is represented by X, which can be decomposed into unpolarized (/up) and polarized
(Ip) components as
X = / up +
/p .
(1.3)
The degree of polarization, p, is defined as the ratio of the polarized intensity to the
total
P= J-
(1-4)
For linear polarization, as is expected for the CMB, the two intensity quantities Q
and U specify the angle, y, of the electric field of the polarized radiation with respect
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1.2. THE POLARIZATION OF THE CMB
13
to the locally-defined x axis as
Q
=
/ p cos 2x,
(1.5)
U
— i psin2x.
(1.6)
Experimentally, Q can be measured as the difference between the intensities mea­
sured by two orthogonal detectors aligned with the local x and y axes as
Q = (£ ? ) - ( E l ) =
I , -
(1.7)
Similarly, U can be measured by differencing detectors aligned with a set of axes
rotated by 45° (here denoted as the x + y and x — y axes) as
^
—
(El+y) ~ (Ex-y)
=
Ix+y ~ h - y
(1 -8 )
The total intensity, I is given by I = Ix + Iy = Ix+y + Ix- y. Figure 1.4 shows the
experimental setup to clarify the geometry used in eqs. 1.7 and 1.8. From, eqs. 1.5
and 1.6, a measurement of the parameters Q and U gives the polarized intensity and
angle as
ip = Q2 +W2 and
tan2 x =U/Q.
(1.9)
Measurements of the Stokes parameters X, Q, and Ucompletely describe partially
linearly polarized radiation.
Note that this treatment has omitted the effect of
the fourth Stokes parameter V, which quantifies the degree of circular polarization
present. Since this component is expected to be zero for the CMB, a number of
present experiments (including QUaD) are concentrating on measuring only X, Q,
and U.
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14
CHAPTER 1. INTRODUCTION
. ! Incident
V Warm radiation
" T \
Incident
Cool radiation
Partially polarized
\ | scatt
scattered radiation
Figure 1.5: Temperature anisotropies lead to polarization via Thompson scattering.
Warm radiation is incident on a free electron from the top and bottom while colder
radiation comes from the sides. This corresponds to a quadrupole anisotropy in the
local temperature distribution. The electron does not scatter radiation polarized
along the line of sight (i.e., the polarization must be perpendicular to the outgoing
wavevector) leading to a partially polarized outgoing wave.
1.2.2
Origins and Characterization of CM B Polarization
Origins
It was first noted in 1968 that anisotropies in the local temperature distribution as
seen by an electron at the surface of last scattering would lead to a partially polar­
ized CMB [Rees, 1968]. In the primordial plasma, electrons and photons interact
via Thompson scattering, which has a polarization-dependent cross section. The
differential Thompson cross section, dar/dCl, depends on the incident and outgoing
polarization directions (E and E' respectively) as daT/dCl oc \E ■E'\2. In particu­
lar, an electron does not scatter incident radiation polarized along the line of sight.
An isotropic distribution will thus result in an unpolarized scattered wave. How­
ever, a local quadrupole anisotropy, as illustrated in Figure 1.5, results in partial
polarization of the outgoing wave.
Due to the symmetry of the Thompson cross section, only the quadrupole moment
of the local temperature distribution (as seen by a free electron in the primordial
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1.2. THE POLARIZATION OF THE CMB
hot
15
m=0
cold
crest
hot
Scalars
\
(Compression)
Tensors
(Gravity Waves)
Figure 1.6: (left) An m = 0 pattern arises from a scalar perturbation, (right) An
m = 2 pattern arises from a tensor perturbation. See text for more explanation.
Figures from Hu and White [1997].
plasma) leads to a net polarization. In terms of the spherical harmonics y^mi there
are three possible quadrupole patterns corresponding t o m = 0, m = ±1, and
m = ±2. These patterns have physically distinct origins, arising from scalar, vector,
and tensor perturbations respectively [Hu and White, 1997].
Figure 1.6 (left) shows the local quadrupolar pattern resulting from a scalar per­
turbation. Here we consider a single plane wave (Fourier mode) of the gravitational
potential and a free electron in trough (cold region). Due to the Doppler boost
from its velocity, infalling matter from above and below emits warm radiation to­
ward the free electron in the center. The electron “sees” an azimuthally-symmetric
quadrupole in the local temperature distribution oriented parallel to the wave vector
of the Fourier mode. Analogously, an electron located on a crest sees a quadrupole
perpendicular to the wave vector. Figure 1.6 (right) shows the m = 2 pattern result­
ing from a tensor perturbation. An electron on the crest of a passing gravitational
wave sees space stretched in the plane of the perturbation, resulting in a qualitatively
different quadrupole pattern from the scalar case.
Thompson scattering converts these local temperature anisotropies into partially
polarized outgoing waves. In a coordinate system oriented along the wave vector of
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CHAPTER 1. INTRODUCTION
16
the perturbation (up/down in Figure 1.6), the scalar mode results in a pattern that is
purely Stokes Q (since the polarization direction is always parallel or perpendicular
to the wave vector). The tensor mode results in a mixture of Q and U [Hu and
White, 1997].
The observed polarization pattern on the sky results from the superposition of
the signals from many different scalar and tensor modes with randomly oriented
wave vectors. Because of this superposition, the resulting pattern will contain both
Stokes Q and U components (even if only scalar modes were present). Because of
this mixing, a Stokes parameter description of the all-sky CMB polarization pattern
does not allow an easy separation of the contributions from scalar and tensor modes.
The following subsection introduces a mathematical tool, the E-B decomposition,
designed to accomplish just this.
E and B decomposition
Polarization direction is a spin-2 quantity since it is invariant under rotation by
180°. The full CMB polarization pattern on the sky can be expanded in terms of
spin-2 spherical harmonics in an analogous manner as the temperature anisotropies
are expanded in scalar spherical harmonics. Like the scalar spherical harmonics,
the spin-2 harmonics form a complete and orthogonal basis. Linear combinations
of the spin-2 harmonics can be formed that transform as scalars. These are named
“E-modes” after the closely related curl-free pattern of a static electric field. Simi­
larly, linear combinations that transform as pseudo-scalars are named “B-modes” in
analogy with a divergence-free magnetic field. Any full-sky polarization map can be
expanded in terms of these E and B modes. The E/B decomposition was introduced
in Zaldarriaga and Seljak [1997] and Kamionkowski et al. [1997].1 Physically, this
decomposition is useful because scalar perturbations produce only E modes whereas
tensor perturbations produce both E and B modes.
1The latter use the notation of G (grad) and C (curl) modes rather than the now more common
E and B introduced by the former.
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1.2. THE POLARIZATION OF THE CMB
E Pattern
17
B Pattern
Figure 1.7: Example E (left) and B (right) Fourier modes. In both cases, the wave
vector lies along the x axis running horizontally.
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18
CHAPTER 1. INTRODUCTION
E Pattern
B Pattern
> \ ii i i i i
\ \ \m i i i i
Itil//
I I I l l l / / >'
\w w WI' III/////"
■ •' \ \ \ W I I I
• • '\ \ W W \ II
NN\
^w
///////// /
" / / / /
i i i i
>i / / / / 1 ii
\\\w
I\
IIII
■ Iw w w \ •
\ \ \ \ \ \
S V
I III w \ '
I I
IIV I \
•
\
E Pattern
/
/
/
< / / / / / / / /
"lit/I/"
11111111
>
i 11 1111i >
>
M i i n
i i
>
>
i i i i I i 11
i '
II M11 \\ \\ \\ \\ \\ \V'
' \\\\\\\\
\
\ \
\
\
\
N N X
B Pattern
\\
\ \
\ \ \ \\ \ \ V'
\ \ \ \ \\ \ \ \ i
\ \ \ \I I I i i
>>il
i///IIIi >
////////<
i
ii
iiI
I VII
IIII
1111
\\ \\ \\ \\ \11\ I
WWW I
WWW \
\ \\ \
IIIi II I1 w
w
\\w
\v \\ \
Figure 1.8: E and B “hot spots” formed from the superposition of eight (properly
phased) plane waves of the form shown in Figure 1.7 evenly distributed in angle Note
that the E mode patterns are invariant under reflection whereas the B patterns are
not.
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1.2. THE POLARIZATION OF THE CMB
19
E Pattern
; '
- * * /
' / / /
' s / /
/ ✓ / /
T
-
1
V »
•
/
/
/
/
/
/
\
V '
i l l '
.........
......
- '
/
/ / . . N N S \
/
! i \ \ \ \ i
* v \ W
' I /
\ \ \ \ • / /
X X ✓ /
.
B Pattern
1 \
\
-
-
-
'
* /
I
\
\
I I V \
< / x .
/ / I I V■
Ii Ii In V> ---------I I I .
—
—
..
S\
\ \
III
III
Figure 1.9: E and B patterns generated from the superposition of pure Fourier modes
with random amplitude and wave vector.
Over a small region of sky, the flat sky approximation can be used and the spin-2
harmonics reduce to the mathematically simpler Fourier modes [Bunn, 2002]. Figure
1.7 shows representative E and B Fourier modes. For the E modes, the polarization
aligns parallel or perpendicular to the wave vector, like the polarization pattern
resulting from a scalar density perturbation. For B modes, the polarization aligns at
a 45° angle to the wave vector. A superposition of E and B modes is thus necessary
to create the polarization pattern generated by tensor perturbations.
Figure 1.8 shows how the Fourier modes can be superposed to create characteris­
tic E and B mode patterns. Note that like the scalar perturbations from which they
originate, the E patterns lack a handedness. In contrast, the gravitational waves
that create the B modes do have have a defined chirality which is reflected in the
resulting patterns. Figure 1.9 shows E and B patterns resulting from the superposi­
tion of random Fourier modes. Inspection of the two maps reveals the characteristic
“hotspot” patterns shown in Figure 1.8.
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CHAPTER 1. INTRODUCTION
20
density oscillations
reionization
lensing
n
u
(N
gravity waves
+
100
-100
50
200
400
600
800
/ (angular scale)
1000
1200
1400
Figure 1.10: The four CMB power spectra for the standard cosmological model (solid
lines). Annotations indicate physical processes responsible for key features. See text
for explanation. The dashed lines show the gravitational wave (tensor mode) con­
tribution to the E and B spectra (note the roughly equal magnitude of the two)
assuming a value of r = 0.1. The dashed-dotted line shows the gravitational lensing
contribution to the B mode spectrum which dominates at small angular scales. Dot­
ted lines show the expected change in the spectra resulting from reionization (using
the WMAP measured value of r ~ 0.17). Figure from Carlstrom et al. [2003] and
derived using the CMBFAST computer code of Seljak and Zaldarriaga [1996].
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1.2. THE POLARIZATION OF THE CMB
21
The power spectra
The E/B decomposition results in a set of coefficients for the multipole expansion
of the polarization field, E^m and Bem, analogous to the agm of eq. 1.1 for the
temperature field. In analogy with eq. 1.2, six power spectra can be formed: C j T,
C j E, C f E, CBB, C j B, CEB. The last two of these vanish since the B field has opposite
parity to the T and E fields. The remaining four spectra completely describe the
two-point statistics of the CMB. If, as predicted by inflation, the CMB is a Gaussian
random field then these four power spectra encode all the information that can be
obtained from the CMB.
Figure 1.10 shows simulated spectra. The E-mode spectrum is dominated by
contributions from scalar perturbations, but lies more than an order of magnitude
below the temperature spectrum. Acoustic oscillations in the primordial plasma
lead to peaks in the E-mode spectrum as in the temperature spectrum (Section
1.1.3). The two sets of peaks are out of phase because the polarization spectrum
depends on the velocity rather than the density of the plasma at the surface of last
scatter. The correlation expressed by the TE spectrum reinforces the common origin
(but complicated relationship) of the peaks in the T and E spectra. Gravitational
waves (tensor modes) are seen to contribute roughly equally to the E and B spectra,
as described in the previous subsection; however, in the E spectrum, the scalar
contribution dominates. Scalar perturbations do not generate B modes: hence the
emphasis on measuring the B spectrum for probing inflation.
Two sources of secondary anisotropy, reionization and gravitational lensing, effect
the shape of the spectra. Reionization occurred when a fraction of the neutral
hydrogen in the interstellar medium was ionized, likely due to emission from the
first generation of stars. The resulting free electrons lead to polarization via the
same mechanism of anisotropic Thompson scattering responsible for the primary
polarization signal. Reionization leads to power on large angular scales (low I)
corresponding to the larger horizon size at this latter epoch. Gravitational lensing,
resulting from massive objects such as clusters of galaxies between us and the surface
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CHAPTER 1. INTRODUCTION
22
WMAP TE Cross Power Spectrum
3
Reionization
2
1
0
1
0
10
40
100
200
400
800
1400
Multipole moment (I)
Figure 1.11: The WMAP TE correlation. The lowest-^ data point is interpreted to
result from reionization. Figure from Bennett et al. [2003].
of last scattering, mix a small fraction of the polarized power between E and B
modes. This mixing occurs at small angular scales where it dominates the expected
B-mode signal. This sets a limit on the values of the tensor scalar ratio that could
be measured even with a perfect instrument of ~ 10-4 [Knox and Song, 2002]. If the
relict tensor modes lie below this level, they cannot be measured from the CMB.
1.2.3
E xisting M easurem ents
The temperature power spectrum is well-characterized over a broad range of angular
scales as described in Section 1.1.3 and shown in Figure 1.3. Polarization measure­
ments; however, are in their infancy. CMB polarization has been detected by five
experiments (in chronological order): DASI, WMAP, CBI, CAPMAP, and B2K.
The measurements are shown in Figure 1.12. No detection of B modes has yet been
made.
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1.2. THE POLARIZATION OF THE CMB
E -M ode Spectrum
23
-
Current Data
100
CM
*
3
DASI o
CBI a
CAPMAP x
B2K □
50
«■>
o
+
-5 0
-100
500
1000
1500
2000
m ultipole, I
Figure 1.12: Existing E-mode polarization measurements. See text for data refer­
ences. Thanks to M. Bowden for her assistance in preparing this plot.
• D A SI - The Degree Angular Scale Interferometer was a 13-element interfer­
ometer operating in the frequency range of 26-36 GHz. DASI was located at
the South Pole and observed from 1999-2003. The DASI team made the first
detection of CMB polarization and the first measurement of the E-mode power
spectrum in their second season of operation (the first season as a polarimeter)
[Leitch et al., 2002a], [Kovac et al., 2002]. Polarization observation continued
for a total of three seasons resulting in the reduced error bars shown in Figure
1.12 [Leitch et al., 2005]. QUaD is the successor to the DASI experiment. It
is located at the same site and uses the same telescope mount (Section 1.3.1).
• W M A P - The radiometers onboard the WMAP satellite are inherently po­
larization sensitive. Figure 1.11 shows the measured TE correlation resulting
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24
CHAPTER 1. INTRODUCTION
from the first season of observation [Kogut et al., 2003].
• C B I - The Cosmic Background Imager is an interferometer operating at 2636 GHz from the Chajnantor plateau in the Chilean Andes. It has a similar
design to DASI and shares many components, but its larger size allows higher
angular resolution. As with DASI, it initially observed the CMB temperature
and was later modified for polarization measurements. It made observations
with polarization sensitivity from 2002 through 2004 [Readhead et al., 2004].
• C A P M A P - The Cosmic Anisotropy Polarization MAPper is composed of
four 90 GHz correlation polarimeters observing from the Bell Laboratories 7
m telescope at Crawford Hill in Holmdel, NJ [Barkats et al., 2005].
• B 2K - B2K was another flight of the successful BOOMERANG experiment
(Crill [2001], Lange et al. [2001]) upgraded with polarization sensitive bolome­
ters (PSBs) [Jones, 2005]. B2K observed the CMB with four 145 GHz PSBs
from an altitude of ~ 35 km on an 11 day flight over Antarctica. The B2K
measurement of the E-mode spectrum is described in Montroy et al. [2005].
1.3
T h e Q U aD E xp erim en t
1.3.1
Overview
With the exception of CAPMAP, all existing measurements of the E-mode spec­
trum come from temperature experiments that were retrofit for polarization sensi­
tivity. The current data are broadly consistent with the prediction from the standard
cosmological model; however, much greater sensitivity is needed to confirm this in
detail. Further progress requires a new generation of experiments, designed from the
start as polarimeters.
Achieving first light in early 2005, QUaD is the first such experiment to come
online. The name reflects the merger between the DASI team and the former QUEST
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1.3. THE QUAD EXPERIMENT
25
Figure 1.13: The QUaD telescope contained within the much larger ground shield.
The 2005 winter telescope operator ( “winter-over”), Robert Schwartz, sets the scale.
collaboration in 2003. At this time, DASI had recently completed a survey resulting
in the first detection of CMB polarization. The QUEST collaboration was developing
a state-of-the-art millimeter-wave polarimeter and optical system, but had not yet
built a telescope mount. The two groups combined their complementary hardware
by upgrading the DASI mount with the new receiver and chose the name QUaD
(QUEST and DASI) to reflect the merger.
The resulting instrument combines a focal plane array of 31 PSBs with an optical
system that was designed to minimize systematic effects in polarization observations.
QUaD observes in two frequency bands centered near 100 and 150 GHz which align
with windows in the atmospheric transmission function and lie near the minimum
of the expected polarized foreground contamination. The experiment is located at
the Geographic South Pole, the premier site for millimeter-wave observations.
Three tables in this section (1.1, 1.2, and 1.3), summarize the key instrument
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CHAPTER 1. INTRODUCTION
26
Table 1.1: QUaD key numbers.
Primary diameter (mm)
2640
Secondary diameter (mm)
450
Frequencies (GHz)
100 150
Bandwidths (%)
28 27
Nominal beam sizes (arcmin) 4.2 6.3
Pixels
12
19
Available pixels 2005 season1 10 16
Sensitivity2 (fj,K sec1/2)
350 380
1Non-functional pixels will be replaced in the 2005/2006 summer season.
2The numbers quoted here axe the NEQ p e r pixel. Section 5.3 defines NEQ and describes how
these numbers were obtained.
parameters, the time line of the experiment, and the people involved. Figure 1.13
shows an overhead, panoramic photograph of the experiment. The section concludes
with a summary of the science goals that we hope to accomplish during our multi­
year observing campaign.
1.3.2
Science Goals
E E S p ectru m - QUaD will make the first precision measurement of the E-mode
power spectrum (Figure 1.14). Compared with existing measurements (Fig­
ure 1.12), a three-year QUaD observation will extend the /-space coverage
by a factor of two above the recent B2K experiment and reduce the error
bars in this extended frequency range by an order of magnitude relative to
existing measurements from DASI and CBI. Previous measurements have de­
tected polarized power in the CMB at high significance. QUaD will be the
first experiment to convincingly measure the features in the spectrum. The
existence of acoustic peaks in the El-mode spectrum, if detected, will confirm
our understanding of the underlying mechanism generating CMB polarization.
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1.3. THE QUAD EXPERIMENT
27
Measuring these spectral features is the primary QUaD science goal.
B B S p ectru m - QUaD will place new upper limits on the power in B modes over a
large range of angular scales. A detection of B-modes caused by gravitational
lensing of E-modes may be possible.
P a ra m e te r E stim atio n - The E-mode measurement and B-mode limits place tighter
constraints on the values of cosmological parameters, especially the inflationary
parameters r and ns.
T T S p ectru m - QUaD will measure the CMB temperature power spectrum at
high multipoles at two frequencies (Figure 1.15, left). Combining this with
data from ACBAR and CBI may help shed light on the origin of the excess
power seen above I ~ 2000 by CBI [Kuo et al., 2004], [Mason et al., 2003].
Table 1.2: QUaD timeline
1999
Initial concept
2000
Proposal
Initial optical design
2001-2002
Optical design finalized
Primary mirror manufactured
Electronics, focal plane, and cryostat design
2003
Laboratory testing of receiver components
Installation of primary mirror on DASI mount
Mar. 2004
Integration and laboratory testing of receiver
Nov. 2004
Commissioning at the South Pole
Feb. 2005
Engineering observations
May 2005
Science observations begin
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CHAPTER 1. INTRODUCTION
28
50
40
CM
D
t=
30
CN
O 20
+
500
1000
1500
2000
m u lt ip o le , I
Figure 1.14: QUaD predicted first-year EE power spectrum. The red points are from
the first season of observation and the blue points from a three-year survey. Points
without error bars represent upper limits. Figure courtesy M. Bowden.
1.4
T h esis O u tline
This thesis describes the QUaD instrument, with particular emphasis on the design
and characterization of the receiver. The following list summarizes the main topics
covered in each chapter.
C h a p te r 1: Introduction and science background
C h a p te r 2: Instrument description
C h a p te r 3: Readout electronics description and characterization
C h a p te r 4: Receiver characterization focusing on the results of laboratory testing
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1.4. THESIS OUTLINE
29
1000
800
(N
D
t=
600
CN
400
200
1200
1400
1600
1800
2000
2200
m ul ti po le, I
Figure 1.15: Predicted QUaD first-year TT power spectrum (red) and three-year
result (blue). Note that atmospheric 1 / / noise limits temperature observation to
smaller angular scales than for polarization.
C h a p te r 5: Instrument performance based primarily on data from South Pole com­
missioning observations
C h a p te r 6: First-year survey description and preliminary data
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CHAPTER 1. INTRODUCTION
30
Table 1.3: The QUaD collaboration: People, institutions, and the main institutional
responsibilities during the design and commissioning phase. Currently, all institu­
tions are taking part in the data analysis.
T h e Q U aD C ollab oration
C altech / JP L
A. E. Lange, J. J. Bock, J. Kovac
Detectors and JFET Modules
C ardiff U n iversity
W. K. Gear, P. A. R. Ade, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo,
C. Tucker, M. Zemcov
Cryostat design, cryogenics, filters design, optical component design and manufac­
ture
C o llege d e France
K. M. Ganga
Simulations, software, and science support
N a tio n a l U n iv ersity o f Ireland, M a yn ooth
J. A. Murphy, C. O’Sullivan, G. Cahill
Optical design and modelling
S tanford U n iv ersity
S. E. Church, M. Bowden, J. R. Hinderks, E. Kirby, B. A. Rusholme, K. Thompson
Receiver integration and characterization, focal plane design and manufacture, read­
out electronics, optical testing
U n iv ersity o f C hicago
J. E. Carlstrom, C. Pryke, E. M. Leitch
Telescope and mount, data acquisition system, receiver installation, optical align­
ment, and control system software
U n iv ersity o f E dinburgh
A. N. Taylor, M. L. Brown, P. Castro
Software development and science support
T h e S o u th P o le
R. Schwartz, A. Day, C. Hammock
Telescope and receiver operation and maintenance.
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Chapter 2
Experiment Description
This chapter provides a description of the QUaD experiment including the observing
site, the telescope mount, the optics and the cryogenics. Discussion of the readout
electronics (including both the cryogenic and room temperature subsystems) is de­
ferred until Chapter 3.
2.1
T h e S ou th P o le O b servin g S ite
QUaD is located at the Martin A. Pomerantz Observatory (MAPO), approximately
750 meters from the Geographic South Pole. The precise location (obtained from
a GPS receiver) is 45°54T4.8”W, 89°59’36.3”S at an elevation of 2785 m. The
observatory is part of the Amundsen-Scott South Pole Station, which is overseen by
the National Science Foundation’s Office of Polar Programs.
This site is unsurpassed for ground-based, millimeter-wave observations, [Lane,
1998, Lay and Halverson, 2000, Peterson et al., 2003, Bussmann et al., 2005]. The
winter precipitable water vapor averages only 0.26 mm due to the inland location,
the high altitude, and the extreme cold temperatures. The atmospheric conditions
are stable over long periods of time with minimal diurnal variation. The six month
“night” during the winter season allows for virtually uninterrupted observation. The
location near Earth’s axis permits deep integrations on small areas since the entire
31
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CHAPTER 2. EXPERIMENT DESCRIPTION
32
Deck r o t a t i o n a x i s
S eco n d ary mirror
Foam co ne
P r i m a r y g u a r d ring
Receiver
Readout electronics
Elevation bearing
A z im u th a x is
Figure 2.1: The QUaD telescope (the QUEST receiver and the DASI mount),
southern celestial hemisphere is accessible all year.
2.2
T h e D A S I M ount
The DASI mount provided a robust and stable platform for the successful Degree
Angular Scale Interferometer CMB experiment that observed from 1999 through
2003 [Leitch et al., 2002b], An independent tripod structure supports the telescope
mount, isolating it from mechanical activity in the surrounding building. The room
just beneath the mount connects via an extension corridor with the MAPO labora­
tory. The entire area, including the interior of the mount itself (the receiver room),
is heated to provide a nearly room-temperature environment for the telescope and
receiver. This key feature meant that mechanical and electronic components of the
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2.3. OPTICS
33
QUaD receiver did not have to be designed to cope with the extreme temperatures of
the Antarctic winter (average winter temperature ~ —60 °C). Additionally, it allows
nearly all maintenance and troubleshooting of the receiver and drive components,
including the daily cryogen refills, to be performed without donning the “extreme
cold weather gear” needed for outdoor activity.
The mount is an altitude-azimuth design, with absolute pointing and tracking
errors under V RMS. An optical pointing camera combined with a frame grabber
are integrated with the data acquisition system (DAS). Daily observations of bright
stars keep the pointing model up to date. The entire face plate of the mount (which
supports the receiver and telescope optics) can rotate about the optical symmetry
axis. Termed “deck” rotation, this feature is critically necessary as it allows the
feeds to scan across the same patch of sky at different orientation angles. This
would otherwise be impossible at the South Pole site, since there is no natural sky
rotation. Figure 2.1 shows the QUaD receiver installed on the DASI mount.
2.3
O ptics
2.3.1
Overview
The QUaD telescope uses an on-axis Cassegrain design that was partially based
on the COMPASS experiment [Farese et al., 2004, Piccirillo et al., 2002], including
an identically-designed primary mirror.
QUaD also adopted COMPASS’s strat­
egy of supporting the secondary mirror with a transparent foam cone to avoid the
potentially-polarized scattering that would result from metal feed legs.
Figure 2.2 shows the QUaD optical path. The telescope collects incident radiation
and brings it to a focus inside the receiver where a pair of cryogenic reimaging lenses
couples the radiation onto the focal plane array of 31 polarization-sensitive pixels.
Optical elements inside the receiver reject unwanted radiation both spectrally (filters)
and spatially (feed horns and cold stop). Figure 2.4 shows the major optical elements
in the receiver.
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CHAPTER 2. EXPERIMENT DESCRIPTION
34
Focal Plane
W* —-Waveplate
(not present 2005 season)
Figure 2.2: (left) The QUaD optical path, (right) The foam cone encloses the
primary mirror and supports the secondary. The lenses and focal plane are contained
in the cryogenically cooled receiver that mounts below the primary (see Figure 2.1).
Each of the 31 pixels is comprised of optical filters to determine the spectral
bandpass, a corrugated microwave feed horn and a pair of orthogonal polarization
sensitive bolometers (Figure 2.3). The PSBs absorb radiation polarized along their
axis of sensitivity and a thermistor detects the associated minute increase in tem­
perature.
To achieve the sensitivity necessary for detecting the faint CMB signal, the
bolometers must be cooled to sub-Kelvin temperatures. To this end, the QUaD
receiver is housed in a two-stage liquid nitrogen/liquid helium cryostat. Section 2.4
describes the cryogenic design of the receiver including the cryostat and the subKelvin refrigerator used to cool the bolometers to their operating temperature of
~ 250 mK. The following sections detail the cryogenic optical components.
2.3.2
Lenses and Cold Stop
The two re-imaging lenses were made from high density polyethylene (HDPE) on
a CNC lathe in the Stanford Physics Machine shop. A proprietary anti-reflection
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2.3. OPTICS
Incident Radiation
35
LP Filter
Throat
(HP Filter)
PSB Pair
Readout
V ~ Ix - Iy
Figure 2.3: Schematic of a QUaD pixel. A filter determines the high frequency edge
of the spectral bandpass, and the corrugated feed determines the beam pattern. The
narrow waveguide throat section of the feed horn sets the low frequency band edge.
The two orthogonal bolometers in the PSB pair each measure the intensity of the
incident radiation along their axes of sensitivity (x and y). The readout differences
the intensities, resulting in a signal proportional to the Stokes parameter Q = Ix —Iy.
Note: the intensity signal from each detector is actually read out and stored. The
differencing happens in software during analysis.
coating was applied to both surfaces of the lenses by collaborators at the Univer­
sity of Cardiff. Both lenses are cooled with liquid helium to reduce their thermal
emission. Radiative loading combined with the long thermal path separating them
from the helium can results in an operating temperature of ~ 10 K (thermodynamic
temperature).
The lenses serve two purposes. First, they decrease the F-number of the slow
beam off the secondary mirror. This reduces the physical size of the focal plane and
feed horns. Additionally, they form an image of the primary mirror between the
second lens and the focal plane, at the location labelled “4 K cold stop” in Figure
2.4.1 Two lenses were necessary to achieve a good focus at both the focal plane and
the cold stop.
A knife-edged aluminum aperture surrounds the image of the primary at the cold
stop. The underside of the knife-edge is blackened with carbon-loaded Sty cast so as
to be absorbing [Bock, 1994]. To understand the operation of the cold stop, it is
lrThe original design also called for a rotating, cryogenic, half waveplate at the location of
the cold stop to modulate the polarization signal at the detectors. Due to difficulties with the
manufacture of the waveplate, it will not be used during the 2005 observing season.
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CHAPTER 2. EXPERIMENT DESCRIPTION
36
300K
rtc
Window (AR-coated UHMW PE)
IR blocker
77K
IR blocker
12 cm edge
IR blocker
4K
9 cm edge
8 cm edge
Camera lens (AR-coated HDPE)
Field lens (AR-coated HDPE)
4K cold stop
500mK
7 cm edge
Band defining filters (see text)
250mK
Feed
PSB module
Figure 2.4: The optical components in the receiver. The black lines to the left
illustrate the nested structure of thermal shielding.
useful to think of the system in reverse with the feed horns transmitting radiation.
The system is designed so that the main beam (down to -20 dB) of the feed horns
passes through the stop aperture while the sidelobes are absorbed by the blackened
knife edge. This results in a well-defined beam on the primary and prevents the pos­
sibly large and time-varying signal that could result if the sidelobes passed through
the rest of the optics and landed on a warm object such as the ground or the moon.
2.3.3
Filtering
Bolometers are inherently sensitive to a broad range of frequencies, so filtering is
needed to limit the response to the desired band. Figure 2.4 shows the filter chain
required to provide an accurate bandpass with very low out-of-band leaks. Filtering
is also required to reduce the radiation loading on the various cold stages.
The spectral bandpass for each feed is set using two different techniques. The
low frequency edge of the band is set by the waveguide throat section of the feedhorn
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2.3. OPTICS
37
QUAD A verage Band
0.6
W
c
o
h-
0.4
0.2
0.0
0
100
200
300
Freq (GHz)
Figure 2.5: QUaD average spectral bands (red, blue), the South Pole atmospheric
transmission (solid black), and the CMB spectrum (dashed black). The QUaD bands
are normalized in terms of absolute transmission per polarization; however, they have
been scaled upwards by a factor of two for clarity on this plot.
(Section 2.3.4). The high-frequency band edge is set via low-pass filters mounted on
the front of each feed.
The two frequency bands were chosen to correspond with windows in the atmo­
spheric transmission function (see Figure 2.5). The upper edge of the 100 GHz band
is set around 110 GHz to avoid the 119 GHz Oxygen line. The 150 GHz band begins
above this line and cuts off around 170 GHz to avoid the 183 GHz water line. Table
4.2 lists the average band center frequency and bandwidth.
The low-pass filters are made from multiple layers of copper mesh sandwiched
between dielectric [Lee et al., 1996, Ade et al., 2002]. These resonant, metal mesh
filters leak power at the harmonics of their cutoff frequency; consequently, a stack
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CHAPTER 2. EXPERIMENT DESCRIPTION
38
150 GHz
5.7cn-l
3.75cn-l
3.65cm-l
100 GHz
Figure 2.6: QUaD corrugated feeds, band-defining filters, and filter caps. The length
of the 100 GHz (150 GHz) feed is 100 mm (102 mm), not including the filters and
filter cap.
of several filters with staggered cutoff frequencies is needed to completely block outof-band radiation. In QUaD, this is accomplished with three filters at 100 GHz
and with two at 150 GHz. The optimal filter stack for each frequency band was
determined through testing many different combinations (Section 4.2.1 and Kirby
[2004]).
Figure 2.6 shows the filters mounted in front of the feed horns. They are retained
by a thin-walled brass cap that slips over the feed and is held in place with aluminum
tape. A thin ring of indium is used to make a light seal between the filter cap and
the first filter. A beryllium-copper wavy washer provides thermal contact between
the filter stack and the feed horn, and compensates for any differential contraction
during cool down. The filters are symmetric and so are expected to have very low
cross-polar leakage (Section 4.3).2
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2.3. OPTICS
39
E-plane
theoretical
• measured
03
3,
2«c
£c
40-1
-JO
-25
-20
-15
-10
-5
0
5
10
15
20
30
off-axis angle (deg)
Figure 2.7: QUaD 100 GHz feed horn beam pattern, predicted and measured. The
beam measurement was made at NUI Maynooth and published in Cahill et al. [2004].
2.3.4
Corrugated Feeds
Feed horns are needed to efficiently couple radiation onto the bolometers. The beam
pattern of the feed determines the illumination pattern on the cold stop (and thus
primary mirror). Figure 2.7 shows the modelled and measured beam pattern of a
100 GHz feed. The beam width is chosen to give a -20dB edge taper roughly 12.5°
from the beam center, corresponding to the edge of the cold stop and the primary
mirror. Since the far-held beam pattern is given by the Fourier transform of the
primary illumination, the edge taper is necessary to reduce the sidelobes of the
telescope beam on the sky.
QUaD uses corrugated feeds which are substantially more expensive than smoothed
walled feeds, but offer a number of advantages that outweigh their greater cost. The
A/4 depth corrugations in the interior of the feeds change the boundary condition to
E — 0 along the walls (instead of the usual E\\ = 0). This produces an aperture held
2The effect of the filters on cross-polar leakage was roughly characterized during laboratory
optical testing - no measurable change in cross-polar leakage was seen when filters were added or
removed from the chain.
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CHAPTER 2. EXPERIMENT DESCRIPTION
40
distribution that closely approximates a Gaussian which results in low side lobes,
and a symmetric beam that preserves linear polarization through the feed structure.
The profiled shape of the feed allows for reduced physical length compared with a
conical feed with the same sidelobe levels.
The internal diameter of the feed reaches a minimum in a section known as
the throat. This forms a waveguide that acts as a high-pass filter allowing only
wavelengths below cutoff to propagate. The metal-mesh low-pass filters before the
feed ensure that only a single waveguide mode is transmitted. Higher-order modes
do not preserve linear polarization and are thus undesirable. The final section of the
horn flares out again to couple the radiation with the bolometer module.
The front end of the feeds was designed by collaborators at NUI Maynooth and
the back end, by collaborators at Caltech. Thomas Keating Ltd3 manufactured the
horns by electroforming copper onto aluminum mandrels that are later dissolved.
The horns are then gold-plated to prevent oxidation. The design and performance
of the QUaD feeds is described in Cahill et al. [2004].
2.3.5
Polarization Sensitive Bolom eters
A polarization sensitive bolometer (PSB) is a specialized form of bolometric detector
that is only sensitive to radiation of a given linear polarization. This subsection
briefly describes the operation of a standard bolometer. Then, the specialized design
of the QUaD PSB is discussed.
The basic operation of a bolometric detector is extremely simple. Incident radi­
ation warms an absorber that is connected by a weak thermal link to a bath of fixed
temperature. A thermistor on the absorber changes electrical resistance in response
to the /iK-level temperature fluctuations caused by varying incident optical power.
This operation is described quantitatively in Section 4.1.1.
A traditional bolometer has a solid absorber. Recent CMB temperature experi­
ments have employed “spider web” bolometers wherein most of the absorber is etched
3Station Mills, Billingshurst, West Sussex, RH14 9SH UK
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2.3. OPTICS
41
Figure 2.8: (a) A QUaD PSB module contains two PSBs in a protective housing, (b)
Schematic representation of a single PSB absorber. The thermistor chip is shown
red. A conducting ring surrounds the absorber (shown green) to provide better
thermal contact with the thermistor.
away leaving only a fine mesh [Bock et al., 1995, Mauskopf et al., 1997]. As long as
the spacing of the mesh is much less than a wavelength, absorption is unhindered.
The advantages of the mesh design are a reduced cross-section to cosmic rays and a
lower heat capacity which results in faster response times.
The polarization sensitive bolometer (PSB) takes this concept even further. In­
stead of a spider-web design, the absorber is a series of parallel wires. The resulting
structure absorbs radiation polarized along the grid axis while transmitting the or­
thogonal polarization. Figure 2.8 shows a schematic representation of a QUaD PSB.
The devices are fabricated from silicon-nitride (Si3N4) at the JPL Micro Devices
Laboratory using photolithography. The absorber is metalized by depositing a layer
of gold (~ 120
A)
over a thin layer of titanium (~ 20
A).
The thickness of the
metalization layer, the width of the conductors, and their spacing was optimized
for maximum coupling using numerical simulation and experimentation with trial
devices (at Caltech/JPL). Non-metalized legs run perpendicular to the conductors
for mechanical support. Tests with trial devices show that they have negligible
impact on the optical properties. [Jones et al., 2003]
A neutron transmutation doped (NTD) germanium thermistor, located on one
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CHAPTER 2. EXPERIMENT DESCRIPTION
42
side of the absorber, measures temperature changes.4 A thermally conducting ring
surrounding the absorber helps couple the thermistor to the entire absorber area.
The absorber and thermistor are thermally isolated from the bath temperature with
the dominant conducting path being through three leads near the thermistor (shown
in green in Figure 2.8). The central lead also carries the electrical signal from the
thermistor. The two additional leads were designed to be laser ablated if decreased
thermal conductivity was desired. For QUaD, this operation was not performed.
For safe handling and mounting, the delicate PSBs are housed in brass modules.
In order to measure both linear polarizations, two PSBs in orthogonal orientations
are mounted in each module. They are spaced 60 /xm apart to ensure that they sam­
ple the same electric field. The interior of the module forms a cylindrical integrating
cavity with the detectors located A/4 from the back wall. The module design is
optimized to maximize absorption of incident radiation. Details of the absorber and
cavity design for the very similar PSBs used on the BOOMERANG 2K experiment
can be found in Jones et al. [2003].
2.3.6
T he Focal Plane
The focal plane holds the feed horns and PSBs at the correct position inside the
cryostat and also thermally connects them to the sub-Kelvin refrigerator. The optical
design required that the feed horns lie on a curved surface in order to maintain a
sharp focus over the entire 1.5° field of view. The focal “plane” thus had to be a
curved surface which presented a substantial design and manufacturing challenge.
The entire assembly was modelled using the IDEAS CAD package and machined on
a 3-axis CNC mill in the Stanford Physics Department machine shop out of a solid
block of 6061 aluminum.5 The focal surface is a section of a sphere with radius of
4J. Beeman, www.haller-beeman.com
5We chose to make the focal plane from aluminum rather than copper for several reasons. First,
aluminum is much less expensive, both for the raw material and machining costs. Since it required
more than a full-week of machine time, this was not a small matter. Secondly, aluminum resulted in
a substantial savings in weight which is important both for mechanical and thermal considerations.
We felt that these reasons outweighed the increased thermal conductivity of copper.
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2.3. OPTICS
43
Figure 2.9: The position and orientation of the 31 pixels on the focal plane. The
layout is composed of three regions: a central grouping of seven 150 GHz pixels
(red), a middle ring of twelve 100 GHz pixels (blue), and an outer ring of twelve 150
GHz pixels (red). Each feed is oriented along one of two possible angles (differing
by 45°) corresponding to Stokes Q and U. Although not shown in this figure, the
feeds for the two frequencies differ in diameter (Figure 2.6). Figure courtesy of B.
Rusholme.
curvature 175 mm.6 The diameter (as would be measured with a ruler across the
top of the “bowl”) is 305 mm.
The PSBs reference and heatsink to the mounting flange on the rear of the
feedhorns but are attached to the focal plane bowl for mechanical stability. An
alignment pin sets their angular position. Mounting holes were drilled to allow
two different angular positions for each PSB, differing by 45° (allowing each pixel
to be changed between Stokes Q or U). Figure 2.9 shows the final positions and
orientations of the PSBs for the 2005 season.
6For ease of manufacture, the “bowl” is not a smooth surface, but rather is a staircase approx­
imation made from a series of discrete steps. After the shape was roughed out, flats and mounting
holes for the feed horns and PSBs were added. This machining was done on the same CNC machine,
but this time the bowl was mounted on a rotary table which in turn was mounted on a sine table.
For each feed position, the rotary table and sine table were set to the correct angles by hand.
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CHAPTER 2. EXPERIMENT DESCRIPTION
44
Figure 2.10: The mounting arrangement for QUaD horns and PSB modules. The
protruding bracket below the PSBs is to support the readout wiring.
The focal plane bowl provides the top surface of a cylindrical enclosure that
houses the PSB modules and the load resistor boards. This enclosure is necessary
to block stray infrared radiation from the PSB modules which are themselves not
light-tight. The load resistor boards (Section 3.1.2) mount vertically inside the
enclosure as shown in Figure 2.16. The inner surface of the enclosure, not including
the underside of the bowl, is blackened with carbon-loaded Stycast to reduce stray
light.
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2.3. OPTICS
45
Figure 2.11: QUaD receiver core including the focal plane, JFET boxes, hexapod,
and cold wiring. The feed horns and cylindrical light-tight bolometer enclosure
axe at 250 mK. Vespel legs stand this off from the intermediate temperature (~
400 mK) stage below. A Vespel hexapod isolates the intermediate stage from the
4 K baseplate. Low thermal conductivity ribbon cable, wrapped around the Vespel
legs, connects the focal plane to the JFET boxes on the bottom right and reads out
thermometers located on both temperature stages. The cutout in the 4 K baseplate
is for access to attach the focal plane to the fridge during installation (see Section
2.4.3).
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CHAPTER 2. EXPERIMENT DESCRIPTION
46
2.4
C ryogenics
The cryogenic systems, including the cryostat and the refrigerator, cool the focal
plane for optimum bolometer performance. The cryostat is designed so that the key
receiver components - the focal plane array and associated electronics - live in an
easily removable inner section known as the “science core” (Figure 2.11). A twotiered structure made from thin-walled Vespel tubing supports the roughly 10 kg
focal plane assembly and thermally isolates it from the 4 K baseplate. A compact
helium adsorption refrigerator, also attached to the baseplate, further cools the focal
plane to the operating temperature of ~ 250 mK.
2.4.1
Cryostat
Window
Cold stop
LN2 tank
LHe tank
Focal plane
ridge
Hexapod
4 K baseplate
Figure 2.12: The QUaD cryostat. The liquid nitrogen tank and thermal shield is
shown in blue. The liquid helium tank and shield is shown in red. The intermediate
temperature stage (orange) and thermal shield surround the focal plane. The two
purple rectangles underneath the focal plane are the JFET boxes.
The QUaD cyrostat was designed by collaborators at the University of Cardiff
and manufactured by AS Scientific.7 Figure 2.12 shows an exterior photograph of
7www.asscientific.co.uk
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.4. CRYOGENICS
47
the cryostat along with an annotated schematic highlighting the key components.
The upwards-looking cryostat attaches to the faceplate of the DASI mount. When
installed, the main body lies below the primary mirror in a small enclosure known as
the receiver room. A narrow snout, containing the two reimaging lenses protrudes
through the primary hole into the volume enclosed by the foam cone. Both of these
spaces are heated to nearly room temperature throughout the season meaning that
the cryostat did not have to be specially designed to deal with the extreme cold
of the South Pole winter. Figure B.3 shows the cryostat and associated readout
electronics mounted in the receiver room.
Within the cryostat, thin-walled aluminum shields surround each thermal stage.
For added insulation, each shield is wrapped with multi-layer super insulation (MLSI).
The focal plane itself is surrounded by a similar shield that is tied to the interme­
diate head of the sub-kelvin refrigerator, maintaining a temperature near 400 mK.
Filtered apertures on the top of each shield allow the optical signal to reach the focal
plane, while blocking out-of-band IR radiation.
The liquid cryogens are contained in concentric, toroidal tanks that surround
the science core. A G-10 truss structure supports the tanks, providing rigidity with
minimal thermal conductivity. Sections of thin-walled stainless steel bellows limit
the conductivity through the refill tubes. The volume of the two tanks is 35 L and
21 L for nitrogen and helium respectively. This results in maximum hold times of
roughly 2.5 and 1.5 days for the two stages. In practice, both tanks are refilled once
per day.
The refill tubes on the cryostat are inaccessible when it is installed in the DASI
mount. Fills are thus performed via two short extensions of flexible transfer line
that are attached to one of the fill tubes on each tank. These extension sections are
installed before mounting the cryostat. The additional fill tube in each tank serves
as a vent and also contains an electronic level gauge that monitors the cryogen
consumption.
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CHAPTER 2. EXPERIMENT DESCRIPTION
48
2.4.2
Sub-K elvin Refrigerator
Figure 2.13: The QUaD 3-stage fridge, mounted in the cryostat.
QUaD uses a three-stage adsorption refrigerator to cool the focal plane.8 Com­
pared with other sub-Kelvin coolers, adsorption refrigerators offer high cooling power
and simplicity of operation. The QUaD fridge provides two cold heads at different
temperatures. The first, known as the ultra cold head, provides the coldest tem­
perature in the system (approximately 250 mK). This cools the focal plane, feed
horns, load resistors and bolometers. The second fridge cold head, known as the in­
termediate head, operates at approximately 400 mK. Sinking all of the sub-K wiring
and the focal plane radiation shield to this stage reduces the thermal loading on the
ultra-cold stage, allowing colder temperatures to be reached.
8Chase Research Cryogenics, 35 Wostenholm Road, Sheffield S7 1LB, United Kingdom
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.4. CRYOGENICS
49
/ / /
/ / / ,
/ / /
/ / / /
/
\
pump
condensation point
still
Cold Head
Figure 2.14: A single-stage helium adsorption fridge. The upper chamber, known as
the pump, contains charcoal that adsorbs helium gas, lowering the vapor pressure
above the liquid helium contained in the still below. The two chambers operate
at different temperatures and axe only joined by a delicate section of thin-walled
stainless steel tubing. When all of the liquid in the still has been adsorbed, the
fridge needs to be cycled in order to continue cooling. The charcoal is warmed using
the embedded heater resistor, driving off the adsorbed gas which liquifies at the
condensation point and collects in the still. The entire system is sealed and has no
moving parts.
Figure 2.14 illustrates the concept of operation for a simpler, single-stage fridge.
The basic physical principal is that the boiling point of a liquid can be reduced by
lowering the pressure of the vapor above it.9 Fridges of this design use charcoal to
pump a helium bath located in the still. When the liquid is entirely boiled away, the
fridge can no longer cool and it needs to be cycled. This is accomplished by passing
an electric current through heater resistors embedded in the charcoal. The charcoal
is warmed to approximately 50 K, driving off the helium vapor which liquifies and
collects in the still below.
A three-stage fridge, as is used in QUaD, combines one helium-4 stage with two
helium-3 stages. The helium-4 stage operates off of a 4 K baseplate and provides
the colder temperature necessary to condense helium-3 in the other two stages. The
two helium-3 stages provide the intermediate and ultra-cold temperatures used to
cool the focal plane to the sub-Kelvin temperature necessary for optimum bolometer
9This principle is familiar to anyone who has boiled water at a high altitude.
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CHAPTER 2. EXPERIMENT DESCRIPTION
50
sensitivity. The intermediate stage is used to buffer the ultra-cold stage, reducing the
thermal loading on the latter. Bhatia et al. [2000] details the design and operation
of this type of fridge.
For minimum thermal resistance, the fridge is mounted directly on the underside
of the LHe tank. This allows for greater condensation efficiency during cycling and
a lower final temperature. The fridge is located on the opposite side of the cryostat
from the refilling tubes. The fill tubes must remain near the top of the cryostat
when the telescope is tipped down in elevation. Placing the fridge on the opposite
side ensures that the fridge base remains in contact with the liquid at all elevations.
The three stages combined with the large mass of the focal plane complicate the
fridge cycle. Optimizing the QUaD cycle for maximum hold time with minimum
cycle time required a considerable effort. The procedure that was developed allows
the QUaD fridge to be cycled in approximately four hours and results in hold times
for the ultra-cold and intermediate stages of 30 and 24 hours respectively. Figure
2.15 shows an example fridge cycle. The fridge cycling procedure is implemented
by a special-purpose computer that communicates with the main control system via
ethernet.10
10The fridge control system was designed by collaborators at the University of Cardiff.
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2.4. CRYOGENICS
51
Pump Temperatures
60
H e-4 pump
Inter pump
Ultra pump
Q.
0
1
2
3
4
5
3
4
5
hours
Cold Heads
10
Intermediate head
Ultracold head
8
6
4
2
0
0
1
2
hours
Figure 2.15: Fridge component temperatures during a typical cycle. The start time
of this graph is 30 MAY 2005 12:00 UTC.
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CHAPTER 2. EXPERIMENT DESCRIPTION
52
Feed horns
Focal plane
Load resistors
400 mK Ring
Vespel hexapod
JFET boxes
4K baseplate
Figure 2.16: Model of the focal plane and supporting structure. The 250 mK light
shield beneath the focal plane is not shown, allowing the load resistor boards to be
seen. The support legs connecting the intermediate stage (400 mK ring) to the focal
plane are also not shown in this rendering. Compare this model with the completed
assembly in Figure 2.11.
2.4.3
T he Science Core
The receiver “science core” is comprised of the focal plane and associated mechanical
and electrical support hardware. The entire structure is mounted to a removable
baseplate for easy installation into the cryostat. A two-tiered structure made from
thin-walled Vespel tubing (0.031” wall thickness) supports the 250 mK focal plane
and thermally isolates it from the 4 K baseplate. Cryogenic JFET amplifiers are
mounted to the baseplate beneath the focal plane. Figure 2.16 shows the main
components and Figure 2.11 shows the completed assembly.
The two-tiered focal plane support structure was designed for maximum rigidity
with minimal thermal conductivity. The supports in the first tier are arranged into
a hexapod structure that provides exceptional rigidity with a minimum of material.
The legs are 6” long and are made from type SP-1 Vespel. The second tier legs
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2. 4. CRYOGENICS
53
are shorter (1.75”) so that a simple vertical “table leg” arrangement of supports
provides adequate rigidity. The shorter legs are made from graphite-loaded Vespel
(SP-22) which provides a factor of two lower thermal conductivity than SP-1 over
the 400 mK to 250 mK temperature range. An aluminum ring, heat sunk to the
intermediate fridge temperature (~ 400 mK), joins the two tiers. This two-tiered
design is necessary to reduce the thermal load on the fridge ultra-cold stage.
Both stages are attached to their respective cold heads on the fridge via flexible,
copper heat straps. The straps are made from braided OFHC shielding found in
high-quality speaker cable. Up to nine pieces of this braid are twisted together to
obtain a substantial cross sectional area (of order 1 cm2). For improved conductivity,
the straps were annealed prior to installation. Good coupling between the stages and
the cold heads improves the efficiency of the fridge cycle and decreases the operating
temperature of the focal plane.
The Vespel legs that support the focal plane provide natural attachment points
for the signal wiring that runs between the stages (Figure 2.11).
All the non-
isothermal wiring in the cryostat is 44 SWG manganin (0.0032”) for low thermal
conductivity. These thin manganin wires are woven into a robust ribbon cable along
with nylon thread for strain relief.11 These cables are then routed along the Vespel
legs, wrapping them in a helical pattern to lengthen the thermal path.
Two additional Vespel legs were added running between the 400 mK ring and
the JFET modules in order to simplify the wiring along this critical signal path.
Rigidly fixing down these wires is extremely important for reducing susceptibility
to microphonic pickup. High-impedance bolometers are particularly vulnerable to
this form of pickup wherein mechanical vibration generates an electrical signal by
modulating the capacitance between the wiring and ground. In addition to being
tightly wrapped around the Vespel supports, the QUaD wiring was fixed down at
regular intervals using a combination of teflon tape and waxed lacing tape.
The structure was designed so that the predicted contributions to the fridge heat
n www.tekdata.co.uk
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CHAPTER 2. EXPERIMENT DESCRIPTION
54
load were nearly equally divided between the Vespel mechanical supports and the
manganin signal wiring. The estimated load from these two sources is 50 /iW and
0.4 n W on the fridge intermediate and ultra cold heads respectively. The total
loading on the two fridge stages is estimated from fridge load curves as roughly
400 /j,W and 3 fiW.
The large focal plane mass (~ 10 kg) combined with the thermally isolating
support structure results in a very long cool down period. Starting at room temper­
ature, both tanks are initially filled with liquid nitrogen. Approximately seven days
later, the focal plane reaches 100 K at which point the inner tank is filled with liquid
helium. Two more days of cooling are then required before the fridge can be cycled.
Actively-heated gas-gap heat switches speed up the cool down. These switches are
turned off once the focal plane temperature approaches 4 K.
2.4.4
Therm om etry
Temperature sensors monitor all the major cryogenic components including the focal
plane, the fridge (pumps and cold heads), the baseplate, the snout (which holds the
two lenses), and the liquid nitrogen can. Silicon diode sensors (Lake Shore DT-470
series) are used for components that operate at or above liquid helium tempera­
tures.12 Germanium resistance temperature sensors, known as GRTs, monitor the
sub-Kelvin components (Lake Shore GR-200 series). Diodes mounted on the focal
plane are used to monitor the cool down from room temperature; however, their
large power dissipation (~ 15 fiW) necessitates that they be switched off during
sub-Kelvin operation. Both types of sensors are read out by the same custom hard­
ware that interfaces with the fridge. A separate system consisting of an AC-biased
thermistor, a heater resistor, and commercial controller maintains the focal plane
at a constant temperature during operation (Appendix A). Figure 2.17 shows the
temperature readout from the focal plane and intermediate stage GRT sensors over
the course of a routine CMB observation.
12Lake Shore Cryotronics, Inc. www.lakeshore.com
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2.4. CRYOGENICS
55
Focal Plane
0.257
0.256
g 0.255
Q.
E
® 0.254
0.253
0.252
I
10
15
hours
Intermediate Stage
0.435
^ 0.430
*
CL
E
<D
l“ 0.425
0.420
0
5
10
15
20
hours
Figure 2.17: Focal plane (top) and intermediate stage (bottom ) temperature as
measured by their respective GRT sensors during CMB observation on May 31,
2005. The temperature control system maintains the focal plane at an extremely
stable temperature. The four small positive spikes seen on the focal plane temper­
ature occur during load curves (Sections 4.1 and 6.1.2) - at maximum bias, power
dissipation in the load resistors is sufficient to warm the focal plane above the set
point. The intermediate stage temperature is not controlled. The two large step
changes in temperature correspond to changes in the “deck” rotation angle wherein
the cryostat is rotated 60° about the optical axis (Section 6.1.2). The telescope was
at an elevation angle of roughly 45° while this data was taken.
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CHAPTER 2. EXPERIMENT DESCRIPTION
Figure 2.18: (top) Inserting the science core into the cryostat. The cryostat is in­
verted so that it is looking downwards. The entire 4 K baseplate plus focal plane
assembly is lowered in. Extreme care is necessary during this operation to avoid
disturbing the fridge, (bottom ) Once the 4 K baseplate is bolted in place, braided
OFHC copper heat straps are used to attach the ultra and intermediate fridge heads
to the two thermal stages of the hexapod. Access is through a cutout in the 4 K
baseplate which is then sealed with a thin aluminium plate. Kapton-coated rib­
bon cables (shown unplugged here) connect the 55-pin hermetic connectors on the
cryostat bottom (covered with red caps) to the JFET boxes.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 3
Readout Electronics
3.1
D escrip tio n
V+
Cold Electronics
Amplification /
Demodulation
(gain = 100,000)
AC
Bias
Gen.
to ADC
JFET
Buffers
Reference ffeq.
Figure 3.1: QUaD readout electronics overview. The variable resistor symbol denotes
the thermistor on the bolometer’s absorber.
The thermistor chip on each PSB registers the temperature change of the ab­
sorber arising from fluctuations in the incident optical power. The readout elec­
tronics measure the thermistor resistances while contributing minimal noise in the
frequency range of interest. The block diagram in Figure 3.1 overviews the compo­
nents involved.
The QUaD readout chain begins with the bias generator. This circuit makes two
57
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CHAPTER 3. READOUT ELECTRONICS
58
Table 3.1: Breakdown, by function, of the 96 channels of readout.
62
8
4
8
3
11
Light detectors1
Dark detectors2
Resistors3
Shorts4
Thermistors5
Unused
1These channels readout the 31 PSB modules attached to feed horns. This is the science
data.
2These readout the four “dark” PSB modules. Rather than being attached to horns,
these modules are blanked off. They serve as monitors of the focal plane temperature.
3These channels are attached to 10 Mfl metal film resistors mounted on the focal plane.
They were intended as monitors of the electronics noise; however, failure to adequately
restrain their wiring has resulted in excess microphonic noise in these channels making
estimation of the electronics noise difficult.
4These channels are attached to low-impedance shorts. They serve as monitors of the
JFET and warm amplifier noise (but not any noise from the bias). See Section 3.2.2.
5The thermistors are used to monitor the focal plane temperature (Appendix A).
sine waves, 180 degrees out of phase that are used to bias the bolometers. Each
bolometer is wired in series with two cold load resistors, forming a balanced bridge
circuit. The bridge is followed by two stages of amplification. First, cold JFET
followers located just below the focal plane buffer the high-impedance bolometer
signals, reducing their susceptibility to pickup and interference. The buffered signals
then exit the cryostat where they axe further amplified and demodulated by warm
lockin amplifiers. In the final step of the chain, the data acquisition system digitizes
and stores the amplified and filtered signals. The following subsections describe the
detailed operation of each module.
The QUaD electronics, including the load resistors, JFETs, and warm lockin
amplifiers, provides 96 channels of readout. Most (62) of these are used for reading
out our science data from the 31 PSB modules attached to feed horns. An addi­
tional eight channels readout four “dark” PSB modules which are blanked off rather
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3.1. DESCRIPTION
59
than being attached to feed horns. These serve as sensitive monitors of the focal
plane temperature. The remaining channels are divided between housekeeping and
monitoring tasks and spares. Table 3.1 lists the channel-by-channel breakdown and
Figure 3.3 outlines how the 96 channels are divided between the four load resistor
boards and two JFET boxes.
The basic AC bias readout scheme employed in QUaD has a long heritage
of successful use in CMB experiments including SuZIE [Holzapfel et al., 1997],
BOOMERANG [Crill et al., 2003], and BOLOCAM [Glenn et al., 1998]. The QUaD
design is based on these predecessors with improvements such as DC offset removal
and per-channel phase optimization that will be described in the following sections.
3.1.1
Bias Generator
Voltage
Ref.
Switch
Balance
output
Tunable
BP Filter
Multiplying
to 100 GHz bolos
V+
4 MHz
Divide
Multiplying
DAC
to 150 GHz bolos
Digital amplitude control
Figure 3.2: QUaD bias generator.
This circuit generates two sine waves V+(t) = VQsin(w0t) and V-(t) = —V0 sin(oj0t).
Both the amplitude, V0, and the frequency,
ujq are
adjustable under computer con­
trol. The sine wave output must be exceedingly stable in amplitude1 and reasonably
stable in frequency.2 A variety of different sine-wave generation circuits were tried
1Bias amplitude variations look like optical signals in the data and thus must be kept to an
absolute minimum.
2A standard 50 PPM / °C quarts clock oscillator provides adequate stability.
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60
CHAPTER 3. READOUT ELECTRONICS
and the architecture in Figure 3.2 was found to give the best results.
The frequency reference for this circuit is derived from a 4.0 MHz crystal os­
cillator. A programmable divide-by-N circuit slows the clock down to the desired
frequency range of approximately 40 - 250 Hz. The exact value of N is computer
controllable and the output frequency has a resolution of better than 0.1 Hz. This
digital square wave drives an analog switch that selects between two amplifiers of
precise gain equal to plus and minus one. A low-noise 10 V reference (AD587) pro­
vides the input to the switches. The switches and amplifiers are contained in an
AD630 modulator / demodulator chip.
The resulting 20 V peak-to-peak square wave is filtered by a second-order, statevariable bandpass filter. The center frequency is adjustable under computer control
(12-bit resolution) and the quality factor is fixed at ten. During operation, the square
wave generator is set to the desired frequency and the bandpass filter center frequency
is tuned to maximize the output amplitude. The tuning procedure is controlled by
an on-board microcontroller and is fully autonomous. Tuning ensures that the peak
of the bandpass filter is aligned with the fundamental frequency of the square wave
minimizing sensitivity to any component drifts. By three times the fundamental
frequency, the response of the bandpass filter has fallen to approximately 0.0375
relative to the peak making the third harmonic power in the output sine wave at
nearly -40 dB (see Figure 3.10). This level of spectral purity is more than sufficient.
Finally, the sine wave is scaled by multiplying DACs to provide two outputs that
lie in the range 0 -1.5 V and are adjustable with 12-bit resolution. After scaling, lownoise buffers generate balanced outputs for driving the bolometer bridge circuit. One
output drives the 100 GHz bolometers and the other drives the 150 GHz channels.
The bias board provides several features not shown in Figure 3.2.
• A DC bias output mode is available. DC bias is essential for testing (especially
load-curves). Since the bias is at 0 Hz, there is no reduction in bias current
or phase shift (Section 3.2.3). Switching between the AC and DC modes is
performed via the control system.
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3.1. DESCRIPTION
61
F o c a l P la n e
(3 0 0 mK)
—VvW—
FP1
.0
FP2
LRB
ff
FETS 150---- 1
FETS 100
LRB
JF E T box
(4K)
\ (
)\
\r
)K
(77K )
□
□
(3 0 0 K)
150 GHz
signals
V ss
S+
s-
V-
FP4
G L JO,
If
Vdd
v+
FP3
O
LRB
\i \t
)\ )I
□
□
Bias/
pwr
4K
-)(□
250mK
LRB
□
300K
100 GHz
signals
Figure 3.3: (left) A single channel from the QUaD bolometer readout chain. The
thermistor (on the bolometer) is shown as the variable resistor in the top center,
(right) The subsystems in the cold readout chain. Each load resistor box handles
24 channels of readout and each JFET box, 48.
• Bias amplitude monitors are provided for both channels. These consist of
lockin amplifiers on the board that demodulate the scaled AC bias signal. The
resulting DC signals (proportional to the bias amplitudes) are archived with
the rest of the bolometer data.
• Additional circuitry on the bias board provides the power supply voltages for
the JFET amplifiers.
3.1.2
Load Resistor Boxes
Figures 3.1 and 3.3 show the bridge circuit used for biasing the bolometers. For
maximum stability and rejection of electrical interference, the circuit is balanced
and fully differential. All the cold wiring is formed in twisted pairs. Due to thermal
considerations, no shielding is present.
The load resistors, labelled R l in the figures, have a value of 20 MD. They are
substantially larger than the nominal 5-10 MQ bolometers and thus convert the con­
stant voltage bias into a quasi-constant current. Physically, they are on four circuit
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CHAPTER 3. READOUT ELECTRONICS
62
Figure 3.4: QUaD load resistor board inside a protective box. Due to space con­
straints, the boxes were not used in the final design.
boards mounted beneath the focal plane inside the light-tight box. To reduce John­
son noise, they are cooled to the same sub-Kelvin temperature as the bolometers.
The resistor dies are nichrome metal film on a silicon substrate manufactured by
Mini Systems, Inc.3 The dies were housed in surface mount packages by the Sun­
belt Microelectronics Division of Mini Systems. Each package contains 14 dies, 12
of which are used. Jumpers are provided so that the two spare dies can be easily
swapped in to replace defective dies. This, however, has not proved to be necessary.
Each load resistor board handles 24 readout channels. The boards themselves are
standard FR-4 and were manufactured by a local company, Sierra Proto Express.4
Despite the presence of fine traces (8 mil) and small vias (12 mil drill diameter) we
did not experience a single failure even after months of sub-Kelvin operation and
numerous thermal cycles.
Input and output from the board is via surface mount 51-way micro D connectors
manufactured by Cristek Interconnects Inc.5 Christek custom designed this connec­
tor for NASA JPL, and with the proper authorization allowed QUaD to use it. The
3www.mini-systems.biz
4www.sierraprotoexpr ess.com
5www .cristek.com
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3.1. DESCRIPTION
63
long surface mount leads provide some springiness that takes up the differential con­
traction between the fiberglass board and its aluminum mounting structure. Due
to the three rows of fine-pitch leads, soldering these connectors with a conventional
iron is difficult if not impossible. We attached them using solder paste applied with
a custom made stencil from PCBexpress.6 The connectors and board were mounted
in a specially made jig while the solder paste was reflowed in an oven. This method
produced excellent results - after attaching over one dozen connectors there was not
a single faulty joint.
3.1.3
Focal Plane W iring
Wiring within the focal plane assembly connects the load resistor boards to the
individual PSB modules. This high-impedance section of wiring is particularly vul­
nerable to microphonic pickup. To reduce the susceptibility to this pickup, relatively
stiff, large diameter wire was chosen for the focal plane.7 Furthermore, the wiring is
rigidly mounted to the backside of the focal plane using a combination of aluminum
tape and copper mesh. The mesh is screwed to the focal plane, clamping the wires
beneath. It is used in areas where the wiring is too bulky to be effectively fixed with
tape (see Figure 3.5). For neatness, and to reduce susceptibility to magnetic pickup,
the wiring is grouped into twisted quad bundles (one quad per PSB module).
6http://www.pcbexpress.com/essentials/index.php
7Belden 28 AWG stranded copper with PTFE insulation
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64
CHAPTER 3. READOUT ELECTRONICS
Figure 3.5: Two views of the focal plane bowl, (top) Top view showing the curved
bowl, feeds, and filters, (bottom ) Bottom view showing the PSB modules and
wiring.
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3.1. DESCRIPTION
3.1.4
65
JFE T Boxes
1.8 um silicon nitride membrane
Input/output wirebond pads
Figure 3.6: QUaD JFET box membrane (photo courtesy James Bock, JPL)
The high-impedence bolometer signals are carried from the focal plane to the
cold JFET amplifiers located on the 4 K baseplate beneath. This short section of
low thermal conductivity manganin wiring is routed along the Vespel support legs
of the science core (Section 2.4.3). The JFETs buffer these signals, lowering their
impedance which makes them far less susceptible to interference. The roughly 2 m
of low-impedance wiring downstream of the JFETS (leading to the warm lockin
amplifiers) does not need to be routed or tied down as carefully.
In order to keep the JFETs as physically close as possible to the detectors, they
are mounted to the 4 K plate just below the focal plane. The transistors themselves,
however, cannot operate below about 50 K and have a minimum of noise around
120 K. This disparity in temperature between the mounting plate and the desired
operating temperature presents a design challenge.
The JFET boxes used in QUaD (designed and manufactured at NASA JPL)
elegantly solve this problem.8 Bare JFET dies9 are mounted on a silicon nitride
8These boxes were designed at NASA JPL for the Spire satellite mission.
9Siliconix U401
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66
CHAPTER 3. READOUT ELECTRONICS
RF filtered output
48 channel module
RF filtered power
Figure 3.7: QUaD JFET box CAD model (image courtesy James Bock, JPL).From
front to back, the box is roughly 10 cm long.
membrane that is supported by the wires carrying the input and output signals
(Figure 3.6). These wires are formed by lithography and have low thermal conduc­
tivity (~ 0.5 fxW/K) due to their small cross section. The power dissipation in the
transistors themselves is sufficient to warm the membrane to the desired temper­
ature. Each membrane contains 24 dual-matched JFET pairs (48 transistors) and
dissipates approximately 6.5 mW of power. Heater resistors are provided to warm
the membrane at startup, but are not used during normal operation. In addition to
being thermally efficient, this design results in JFET boxes that are very compact
(see the model in Figure 3.7).
Internally, the JFETS are wired as source followers as shown in Figure 3.1 with
a gain of around 0.99. Each bolometer is buffered by a matched transistor pair
contained on the same die. Any drifts in source voltage due to changes in baseplate
temperature result in a common-mode change in the output signal that is rejected
by the downstream electronics.10
10This is extremely important for DC-biased testing with QUaD. In the AC-biased mode, slow
drifts are always rejected by the demodulation process. However, the balanced bridge design with
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3.1. DESCRIPTION
3.1.5
67
Lockin Amplifiers
‘Preamp” out
OUT+
‘Low-gain” out
Switch
Switch
‘High-gain” out
Square
Wave
Demod.
Preamp
xlOO
Reference ffeq. in
BP Filter
Phase
Delay
LP Filter
Offset
removal
xlOO
LP Filter
DAC
Figure 3.8: QUaD lockin card schematic.
After the JFETs, the signals exit the cryostat through hermetic connectors on the
base. Warm lockin amplifier boxes attached beneath the cryostat perform further
amplification and filtering. Each lockin box contains 12 cards each of which processes
the signal from the pair of detectors in a PSB module.
Figure 3.8 is a block diagram of the lockin cards. Each differential signal pair
(from a single detector) first enters a low-noise instrumentation amplifier with a gain
of 100 (AD624). The signals then go through a wide bandpass filter to suppress noise
far from the bias frequency. This bandpass filter is composed of a 4-pole butterworth
low-pass filter with a cutoff of 475 HZ followed by a 2-pole butterworth high-pass
filter with 2.8 Hz cutoff. The filter is designed to have a broad region of flat response
over the possible bias frequency range of 40 - 250 Hz.
The square-wave demodulator (AD630) multiplies the signal by +1 when the
reference signal is positive and -1 when it is negative. This results in a near DC signal
for inputs near the reference frequency. Additionally, there is the usual component at
dual JFETs per channel is still very desirable because it helps ensure that all pickup (regardless of
frequency) is common mode.
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CHAPTER 3. READOUT ELECTRONICS
68
Figure 3.9: A QUaD amplifier box containing ten out of twelve possible lockin cards.
twice the reference frequency familiar from sine-wave lockin amplification as well as
higher order harmonics associated with the square wave reference. The butterworth
low-pass filter (6-pole, / 3jb = 20 Hz) following the demodulator suppresses the highfrequency terms, leaving only the desired low-frequency components.
The demodulator reference signal comes from the bias board and is the same
frequency and phase as the bias itself (but of constant amplitude). A phase delay
on the lockin cards is computer controllable and compensates each channel for the
phase delay caused by stray capacitance inside the cryostat (Section 3.2.3). The
output signal from the 20 Hz low-pass filter is proportional to cos(4>) where (j>is the
phase difference between the input signal and the reference frequency from the bias
board. An automatic, computer-controlled tuning procedure sets the phase delay to
maximize the output signal.
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3.1. DESCRIPTION
69
After amplification, demodulation and low-pass filtering the bolometer signals
are in theory ready to be digitized. In practice, however, this proved not to be
feasible. The signals are typically around 3 Volts with an RMS noise of 0.1 microvolt.
Direct digitization at this point would require an ADC card with greater resolution
than standard 16-bit cards provide. Adequate resolution ADC chips do exist, but
commercial systems using these chips were limited and expensive. A custom solution
with eight channels was successfully designed, but scaling up to the required 96
channels proved difficult.
Instead, we chose a simpler route: DC offset removal. This is possible because
the signals from the sky are a small (10 mV) modulation on top of a large (3 V) DC
voltage from the rectified bias. An instrumentation amplifier driven by a stable DAC
is used to remove the large DC offset and provide further gain of 100 to the signals.
This additional gain of 100 is equivalent to increasing the effective number of bits
of the ADC by 6.6 which makes a 16-bit card more than adequate. An automatic,
computer-controlled procedure performs the tedious task of setting the correct offset
voltage for each channel. This is done as often as necessary to keep the signals from
drifting off scale due to changes in the atmospheric conditions. A final low-pass filter
(30 Hz 2-pole butterworth) further suppresses any high-frequency noise. The DC
offset level (DAC value) is archived allowing the full DC-coupled bolometer voltage
to be reconstructed.
Finally, analog switches on the card determine which of three possible outputs
is routed to the ADC card. The first possibility is the signal after the preamplifier
with gain equal to 100 (referred to as preamp). This output is used for DC-biased
load curves as well as other testing. The second option is the post-demodulation
output with a gain of 500 (referred to as low-gain). The control system uses this
output to determine the required setting for the DC offset removal. It is also useful
for general testing and debugging. The final output option (referred to as highgain) is after the DC offset removal and final amplification. It has a gain of 50,000.
This is the standard output for observation. Whichever output is chosen, buffers
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CHAPTER 3. READOUT ELECTRONICS
70
create a balanced differential output for driving the cable to the ADC, resulting in
an additional factor of two gain.
Each lockin card contains two complete amplifiers, providing the readout for a
PSB pair. Twelve cards are located in each of the four lockin boxes that mount
on the bottom of the cryostat (see Figure 3.9). In addition to the twelve lockin
cards, each box contains a motherboard and an interface card. The interface card
contains voltage regulators that provide ±15 V and +5 V to all the cards, the voltage
reference for the DC offset removal DACS, and isolators for all the digital control
lines. The motherboard contains only connectors and bypass capacitors. All active
components are on cards for easy replacement.
3.1.6
T he D ata A cquisition System
The data acquisition system (DAS) is based on the DASI system with substantial
updates for QUaD. All realtime operations including telescope control and digitiza­
tion of the bolometer data is handled by a VME controller in a crate mounted next
to the cryostat. The controller runs the VXWorks realtime operating system. Two
64-channel, 16-bit ADC cards in the crate digitize the bolometer data (VMIVME3122 from VMIC). A Linux-based PC system provides the user interface and data
archiving for the realtime controller.
Software commands are provided for adjusting nearly all aspects of the readout
electronics including the bias amplitudes and frequency, the lockin phases, dc offsets
and the output mode. Additionally, higher-level commands for automatically setting
the optimum offsets and phases are also implemented. These commands can be
placed in files along with telescope control commands to form complete observing
scripts. A client program allows users anywhere in the world to connect with the
control computer, run scripts, and monitor the signal voltages in realtime.11
11This is limited to the roughly twelve hours per day during which the South Pole has internet
access.
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3.2. PERFORMANCE
71
Measured Bias Spectrum, f0 = 100 Hz
o
1------ |------ 1------ 1------ 1------ 1------ 1------ 1------ 1------ 1------ 1------ p
Measured spectrum
■
<f„/f)xBP
\\
\
-20
g -40
-60
-80
0
500
1000
1500
Hz
Figure 3.10: The bias spectrum.
3.2
3.2.1
P erform ance
Functionality Tests
Bias Generator
The design for the QUaD bias generator evolved from several prototypes that were
used in various bolometer test beds. The final board was populated in stages, testing
each subsystem before stuffing the next. The performance and reliability of the board
was verified with extensive laboratory tests, both by itself and integrated with the
full electronics chain including the cryostat, JFETs, and detectors.
As described in Section 3.1.1, the primary goal of the bias generator is stability
not spectral purity. Nevertheless, a measurement of the spectrum confirms that the
operation is as expected. The circuit creates an approximation to a sine wave by
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CHAPTER 3. READOUT ELECTRONICS
72
Preamp output
lockin
output
Square
Wave
Demod.
Preamp
LP Filter
475 Hz
HP Filter
2.1Hz
LP Filter
20 Hz
Reference Freq.
Figure 3.11: Filtering on the amplifier cards. This shows the location and nominal
cutoff frequencies of the filters that are measured in this section. See Figure 3.8 for
a more complete block diagram.
filtering a square wave with a bandpass filter centered on the fundamental frequency.
We thus expect the spectrum of the output waveform to contain prominent lines
at the odd harmonics. The amplitude of the peaks is determined by the intrinsic
spectrum of a square wave multiplied by the response of the bandpass filter. The
amplitude of the Fourier components of a square wave fall off as f o / f where f 0 is
the fundamental frequency (i.e. the third harmonic is a factor of three down in
amplitude).
The filter in the bias generator is a second order, Q — 10 bandpass filter. The
response of such a filter is given by
BP{u, Q) =
,
y/Q2(uJo - W2)2 + (uqU))2
(3.1)
which has been normalized so that f ( u o) = 1. The measured spectrum, seen in
Figure 3.10, shows the expected pattern of peaks. The function (fo/f ) x B P ( f ) fits
the peak amplitudes, indicating that the circuit is working as expected.
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3.2. PERFORMANCE
|
73
0.8
o
Q.
W
£
0.6
S 04
CO
0.2
0.0
0
200
400
600
800
1000
Hz
Figure 3.12: Measured response of the 475 Hz low-pass portion of the bandpass filter.
The filter is a 4-pole Butterworth. The solid, black line shows the nominal response.
Device-to-device variation is small near the bolometer bias frequency of 110 Hz.
Amplifier Cards
The QUaD amplifier card was developed in parallel with the bias generator, during
which time extensive testing was performed on prototype and intermediate versions.
Once the final design was reached, a contract manufacturer assembled the full com­
plement of approximately 50 cards in several runs. Each card has a large number
of components (approximately 170 passives and 20 integrated circuits) and eight
jumpers allow different modes of operation to be selected. Given all these possibili­
ties for errors, it seemed sensible to test every card for basic functionality. The large
number of cards made individual testing impractical, so different automated testing
procedures were developed. The reader is referred to Figure 3.8 for a block diagram
of the lockin card. Figure 3.11 gives a simplified view concentrating on the main
filters.
The first setup used an SRS 340 synthesized function generator to create test
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CHAPTER 3. READOUT ELECTRONICS
74
1.2
1.0
0.8
Cl
0.6
0.4
0.2
0.0
0
10
20
30
40
Hz
Figure 3.13: Measured response of the 20 Hz low-pass, post-demodulator filter. The
filter is a 6-pole Butterworth. The solid black line shows the nominal response.
signals and a Keithely 2700 benchtop DVM to measure the response. Both instru­
ments were controlled via serial ports on a PC running a custom testing program.
A multiplexer on the DVM allowed up to ten cards to be sequentially tested with
no human intervention. This setup allowed an extremely thorough diagnostic to be
performed.
• Bandpass filter - The low-pass portion of the bandpass filter (/3dB = 475 Hz)
was mapped out by measuring the “preamp” output using the AC voltage
setting on the DVM with different frequency input sine waves. The results are
shown in Figure 3.12.
• Low pass filter - The 20 Hz low-pass filter following the demodulator defines
the system bandwidth. It is the most complicated part of the card in terms
of number of components. To measure its response, the arbitrary waveform
capability of the SRS was used to generate an amplitude modulated signal
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3.2. PERFORMANCE
75
1.2
1.0
0.8
CL
0.6
0.4
0.2
0.0
0
10
30
20
40
50
Hz
Figure 3.14: Filter bands as measured by impulse response testing (see text for
details). This measures the product of the bandpass filter and the 20 Hz lowpass
filter response. Only the 2.1 Hz high-pass edge of the bandpass filter is visible since
the post-demodulator filter cuts off long before the 475 Hz high-pass edge. The solid,
black line shows the nominal response.
consisting of a carrier with a sinusoidal envelope at one tenth the frequency.
After demodulation, an oscillation at the envelope frequency remains. This
signal was played at various frequencies and the output recorded with the AC
voltage setting of the DVM.12 The results are shown in Figure 3.13.
• Phase adjustment - The reference phase adjustment circuit adds a delay to the
demodulator reference to compensate for phase shifts on the signal lines inside
the cryostat. In order to test its operation, a fixed sine wave was applied to
the input and the DC level at the “low-gain” output was recorded for various
phase delays.
12Because the carrier also changed frequencies, the measured response of the 475 Hz low-pass
filter should also be taken into account. For envelope frequencies below 20 Hz (carrier frequencies
below 200 Hz), the correction would be negligible. For higher frequencies, it would be at most 5%.
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76
CHAPTER 3. READOUT ELECTRONICS
• DC offset removal - The DC removal circuit was tested by applying a fixed
sine wave input and monitoring the DC level on the “high-gain” output (see
Figure 3.8) while adjusting the DAC voltage. This confirmed operation of the
DAC and measured the gain of the final amplifier (nominally 100).
Approximately 30 cards were tested using this procedure and several problems
were discovered and repaired. Unfortunately, we did not receive the last batch of
cards until after the bulk of the experiment had shipped to the Pole. Some of the
test equipment had to remain at Stanford, so a new procedure was developed for
testing at the Pole.
The second setup used the bias generator to create test signals and the DAS to
record the response. This setup was able to test a complete box (12 cards) at a time,
but the options were more limited.
• Gain - DC and sine wave inputs were used to measure the DC and AC gains
of the card at the “preamp” and “low-gain” outputs respectively.
• Filters - The 20 Hz post-demodulator filter response was measured in a com­
pletely different way. First, the reference input to the demodulator was set
at a positive voltage. This disables the demodulator, setting it to a constant
gain of one. Next, the bias board was programmed to generate impulse func­
tions one millisecond wide spaced a few seconds apart. The data was recorded
and Fourier transformed in software to give the filter responses seen in Figure
3.14. This also measures the response of the 2.1 Hz high-pass filter which was
not measured in the other setup. However, no information is obtained on the
475 Hz low-pass filter.13
• Phase adjustment - The same procedure as for the previous setup was used.
• DC offset removal - No specific tests were performed; however, basic function­
ality was verified in the course of noise testing (Section 3.2.2).
13The low sampling frequency of the ADC (100 Hz) prevented the impulse method from being
used. The limited frequency range of the bias board (40-250 Hz) prevented direct measurement).
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3.2. PERFORMANCE
77
v+
2K:
AC
Bias
Gen.
Amplifier Card
IK:
2K:
Reference freq.
Figure 3.15: The setup for electronics noise testing.
This procedure found problems in several cards. A final round of testing was
performed once all the cards were installed. This gave us confidence that all the
cards were stuffed correctly and allowed us to confidently interpret the results of the
noise tests described in the next section.
3.2.2
N oise Perform ance
Warm Electronics —Amplifiers and Bias Generator
The noise performance of the QUaD warm readout electronics was extensively tested
using the setup shown in Figure 3.15. The bias generator drives a “fake” bolometer
/ load resistor stack composed of precision metal film resistors.14 The value of 1 k
for the resistors used in place of the bolometers was chosen to contribute m in im al
Johnson noise while at the same time having similar output impedance to the JFETs
that would be driving the amplifier cards in the complete system. The 2 x 2 k load
resistors give a similar division factor as the real bolometer / load resistor stack.
Figure 3.16 shows the results of testing Lockin Box 1 with its final contingent
of 12 amplifier cards. The bias frequency was set to 90 Hz and the amplitude to
7.5 mV RMS across the 1 k resistor which is roughly the same as that used with the
real bolometers. The DAS was used to collect time-ordered data that was Fourier
14Vishay-Dale PTF-56 series with 10 ppm / °C temperature coefficient of resistance, distributed
by Newark Electronics.
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78
CHAPTER 3. READOUT ELECTRONICS
Card 54
Card 2
10
Card 24
10
x5
c
5C
1
0.01
1l .....■
-- l - l . . .
0.10
1.00
10.00 100.00
0.01
0.10
1.00
10.00 100.00
0.01
Hz
Card 4
0.10
Card 5
10
.1..
1.00
10.00 100.00
Card 6
e
N
Ic
11
0.01
0.10
1.00
10.00 100.00
0.01
Hz
- .....0.10
1.00
-
-L. I
10.00 100.00
0.01
Hz
Card 7
0.10
10.00 100.00
Hz
Card 8
10
1.00
Card 9
e
§c
1 1
0.01
0.10
1.00
10.00 100.00
0.01
■
0.10
Hz
1.00
a. 1
....................................
10.00 100.00
Card 10
Card 11
10
1.00
Hz
10.00 100.00
ts
I
ic
0.01
0.10
1.00
Hz
1.00
10.00 100.00
Card 12
10
0
ll ............
0.10
0.10
Hz
c
0.01
0.01
Hz
■
-I..
10.00 100.00
1l .......
0.01
0.10
-I
1.00
Hz
10.00 100.00
Figure 3.16: Noise spectra for the 12 amplifier cards in QUaD lockin box 1 for the
test setup seen in Figure 3.15. These spectra include contributions from the bias
and 1 k fake bolometer. Each card has two independent amplifiers which are shown
in black and red. The large spike at 30 Hz results from beating of the AC bias
frequency (90 Hz for this data set) with the power line mains frequency of 60 Hz.
The spikes at 10 Hz visible in some channels result from beating with the ADC
sampling frequency of 100 Hz.
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3.2. PERFORMANCE
79
transformed in software to produce the spectra seen in Figure 3.16.
The PSDs show a broad flat region at low frequencies and a sharp cutoff corre­
sponding to the 20 Hz bandwidth-defining low pass filter. The white noise level is
computed for each channel as the median of the PSD between frequencies of 1 Hz
and 10 Hz. The average white noise for the 24 channels of box 1 for this setup is
found to be 6.8 nV Hz-1/2. This includes contributions from the amplifier, the bias,
and the test setup itself.
In order to break down the various contributions into a noise budget, each of
these sources is considered in turn:
Test setup: The expected noise from the test setup itself can be calculated as
the quadrature sum of the Johnson noise from the fake bolometer and load
resistors:
esetup = [ej( lk || 4k)j2 = 3.6nV Hz-1/2
where ej — yjAksTR is the Johnson noise of a resistor, R. Since the test setup
operates at room temperature, T ~ 295 K. The value l k || 4 k = 0.8 k is the
effective resistance of the fake bolometer in parallel with the load resistors.
Am plifier: In order to quantify the amplifier noise contribution, noise measure­
ments were made for a variety of source impedances. Different valued resistors
were connected in turn to the inputs of the amplifier (with the minus input also
connected to ground) and power spectra were measured. Figure 3.17) shows
the results for a dozen different resistances between 0 and 20 k.
A simple model including only amplifier noise and Johnson noise of the source
(blue line) does not fit the data. Inclusion of an amplifier current noise term
(green line) results in a much better fit:
e2 = eL P + [eJ (#)]2 + [*n#]2
(3.2)
where in, the current noise density of the input amplifier, is found to be ~
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80
CHAPTER 3. READOUT ELECTRONICS
Amplifier Noise Test Setup
AC
Bias
Gen.
Amplifier
Card
Reference freq.
Amplifier Noise Spectra
100.0
10.0
'n
x
>c
1.0
Gnd
3.9k
20k
0.1
1
100
10
Freq (Hz)
Amplifier N oise vs. Source R esistance
+
Measured
Amp + Johnson
Amp + Johnson + current
20
xN
£
10
10
15
20
25
Res (K)
Figure 3.17: Amplifier noise as a function of source resistance, (top) The testing
setup. Although the bias voltage itself is not used for this test, the bias board still
provides the reference frequency for the lockin amplifier, (middle) Noise spectra
for several of the tested source resistances, (bottom ) The data are well fit by the
quadrature sum of a constant amplifier voltage noise term, an amplifier current noise
term, and the Johnson noise term from the source resistance (eq. 3.2).
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3.2. PERFORMANCE
81
800 fA Hz-1/2. The voltage noise of the amplifier is measured to be eamp =
5.0 nV Hz-1/2 and current noise is seen to be negligible for source impedances
below a few kfl
Bias: Tests were performed to determine the noise contribution of the bias gener­
ator. Spectra were taken with the warm testing setup of Figure 3.15 with the
bias again set at ~ 7.5 mV RMS. Other spectra were taken with a similar setup
except the 2 k load resistors were grounded instead of being connected to the
bias board. Figure 3.18 shows the results. Subtracting the white noise levels
measured with these two different setups gives a value for the bias generator
ebias = 2.8 nV Hz"1^ .
Combining these results yields the noise budget shown in Table 3.2. The warm
readout noise is dominated by the amplifier cards. The next subsection examines
the total electronics noise, including the contribution from the JFETs.
In addition to a low white noise level, the readout electronics are required to
have good low-frequency stability. To allow scans of approximately a minute, it was
desired that the 1 / f knee from the electronics be of order 10 mHz. Figure 3.19 shows
the average power spectrum from Lockin Box 1, computed by averaging the PSDs
from all 24 amplifiers. A fit to a 1 / / noise model results in a knee frequency which
satisfies the design requirement. It should be emphasized that these results represent
the stability of the entire warm electronics chain. The fake “bolometer” was biased
at approximately the same level that would be used with a real bolometer and the
DC offset removal was similarly set to a reasonable value.
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82
CHAPTER 3. READOUT ELECTRONICS
Table 3.2: Noise budget for the results of warm noise testing shown in Figure 3.16.
The first line refers to the contribution from the bias generator. The second line
refers to the noise from 1 k || 4 k warm fake bolometer testing setup. The third line
refers to the noise from the amplifier card (dominated by the voltage noise of the
preamplifier chip).
Source
Bias
Setup
Amplifier
Total
nV Hz”1/2 Percent contribution
2.8
3.6
5.0
6.8
17%
28%
55%
100%
N o ise Spectra with / without Bias
10.0
CN
x
>c
1.0
Card grounded
Fake bolometer grounded
Fake bolometer biased
0.1
1
10
100
Freq (Hz)
Figure 3.18: Spectra used to determine the noise contribution from the bias gener­
ator. The black trace shows the grounded amplifier input noise for reference. The
green trace shows the result for the test setup of Figure 3.15 with the fake bolometer
biased at 7.5 mVRMS- The blue trace results from grounding the load resistors rather
than connecting them to the bias board.
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3.2. PERFORMANCE
83
Warm Electronics Stability
100
2 0 0 4 1 2 1 2_noise_box1 - A verage PSD of all chan n els
0.001
0.01
1
0.10
10
100
Hz
Figure 3.19: Average noise spectrum for all 24 amplifiers in Lockin Box 1. The
dashed blue lines show the white noise level and a fit to a 1 / / noise model. The
1/ / knee frequency is 7.5 mHz, satisfying the stability requirement. Since the fake
“bolometer” was biased during testing, these results represent the stability of the
entire warm electronics chain including the bias generator and the DC offset removal
circuit.
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84
CHAPTER 3. READOUT ELECTRONICS
Readout Chain
The previous subsection measured the noise from the warm readout electonics. This
subsection describes similar measurements for the entire readout chain, including
the cold JFET buffers. This noise level is extremely important for quantifying the
performance of the receiver. Three different methods were used estimate the end to
end electronics noise over a frequency range of 1 - 10 Hz:
1. In the previous sub-section, the amplifier cards were measured to contribute 5.0
nV Hz-1/2 and the bias to contribute 2.8 nV Hz-1/2. Tests with a prototype
JFETs box at NASA JPL under similar operating conditions as in QUaD
resulted in a median noise of 7.6 nV Hz-1/2. Combining these in quadrature
yields ~ 9.5 nV Hz-1/2.
2. A preliminary run was made with the QUaD receiver where the bolometers
were replaced with 10 Mfl fixed resistors. At the operating temperature of
265 mK, the Johnson noise of the resistor and load resistor network is 11.9 nV
Hz-1/2. The median white noise from 24 channels was 14.5 nV Hz-1/2. The
resistors were biased so that noise contribution from the bias board factors in
at approximately the right level. Subtracting the average measured noise level
from the calculated Johnson noise of the 10 MD fixed resistor results in a total
electronics noise level of 8.3 nV Hz-1/2.
3. In the final receiver configuration, eight of the 96 total channels are configured
as shorts wherein the inputs to the JFET buffers are short circuited together.
These are designed to be used as in situ monitors of the readout noise. Mea­
surements of these eight channels showed a mean noise of ~ 8.25 nV Hz-1/2.
Adding in the expected noise from the bias generator, the total noise is ~ 8.75
nV Hz-1/2.
The second two tests indicate that the electronics have slightly lower noise than
expected. This is likely due to the actual JFETs performing better than the tests
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3.2. PERFORMANCE
85
Table 3.3: QUaD readout electronics noise budget. Note this breakdown is approx­
imate with uncertainty and channel-to-channel variations at the 10% level.
Source
Bias
JFETs
Amplifiers
Total
nV Hz”1/2 Percent contribution
3
7
5
9
10%
60%
30%
100%
on the prototype box indicated. For estimates of the electronics contribution to the
total system noise, a conservative average value of Vn ~ 9 nV Hz-1/2 will be used.
This satisfies the original design requirement that the electronics noise be at or below
10 nV Hz_1//2. A rough breakdown of the various contributions to the electronics
noise are given by the noise budget in Table 3.3. Section 5.3 places the electronics
noise in context by comparing it with other sources of noise in the system (i.e. see
Figure 5.19).
3.2.3
Channel Capacitance
As described in 3.1.4, stray capacitance on the high-impedance signal lines between
the bolometers and the JFET buffers leads to several problems. In order to under­
stand their severity, the capacitance for each channel needs to be measured. This
section describes such a measurement for QUaD.
Measurement Setup
We measured the capacitance, by replacing the bolometers with fixed metal-film
resistors. The “fake bolometer” resistors are the same composition, and are from
the same vendor, as the load resistors. Figure 3.20 shows the bolometer readout
circuit including the stray capacitance on the line between the bolometer and the
JFETs. In this setup, R = 10 Mfl and as usual, the load resistance, R l , is 20
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CHAPTER 3. READOUT ELECTRONICS
86
bias
bob
bias
Figure 3.20: Bolometer readout bridge, including stray capacitance.
Mil. The capacitance is really distributed along the signal cable, but for purposes
of analysis, it is shown here as a lumped element. The main effect is to shunt some
of the (AC) bias current through the capacitor instead of the bolometer.
Basic circuit analysis applied to Figure 3.20 yields the following set of equations:
Fbias = 2/ b i a s " b IboloR
Fgig
/bias
IboloR — Ic
— /bolo T
1
■
iuiC
Ic
that can be solved for the output signal voltage as
R
Fsig = R + 2R l + 2RRLituCVbi3S'
^
A little algebra puts this in a more suggestive form
= R + 2RL ( 1 + iu)ReffC) VyAaa
where R^s=2R l R /(2R l + R) is the effective resistance
The output voltage
^
ofthe bridgenetwork.
(Kig) and the bolometer bias current(/bolo) areexactly what
would result if there were no capacitance times a single pole filter response with
time constant Tc — ReffC.
The single-pole filter response results in a bias current attenuation factor and
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3.2. PERFORMANCE
87
output signal phase delay that is given by:
y/l +oj2t I
4>c = tan -1 u j t c The next subsection applies these equations to measured QUaD data to determine
the channel capacitance.
Q U aD P a ram e te rs
Single Channel Fit
I.UU
QUaD Channel Capacitance
iu u
0.95
u.
<30
<0 -
|
0.85
O O
0.80
0.75
0
50
100
B ias freq (Hz)
150
200
0
20
40
60
80
C h an n el
Figure 3.21: Measured QUaD capacitance, (left) A fit to data for a single channel,
(right) The measured capacitance for all available channels.
Figure 3.21 (left) shows the result for a typical QUaD channel. The data was
taken using the standard readout electronics and data acquisition system. Data
points were taken with the bias generator set to 12 different frequencies between 40
and 150 Hz and the lockin amplifier cards set in “low-gain” mode. After changing
frequency, the phase delay for each lockin channel was set to maximize the signal
and the value of the lockin output voltage was recorded. At each frequency, the
bias monitor (a lockin channel on the bias board) recorded the amplitude of the bias
voltage. This was used to scale the results in order to take account of the small
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CHAPTER 3. READOUT ELECTRONICS
88
Attenuation and P h ase for Typical QUaD Parameters
1.00
Attenuation —
Phase - -
0.98
0.96
.§ 0.94
ra
=>
5
0.92
-20
0.90
0.88
-25
C = 100 pF
R = 5M£1
0.86
0
50
100
150
200
Bias freq (Hz)
Figure 3.22: The reduction in bias current (attenuation) and phase delay versus bias
frequency for typical QUaD channel parameters. The 2005 bias frequency of 110 Hz
is indicated by the vertical line.
frequency dependence (~ 1%) of the bias generators output sine wave amplitude. A
measurement at DC was used to establish the DC gain of the readout electronics. A
one-parameter fit was then applied to the data to find the capacitance.
Figure 3.21 (right) shows the results for each channel. The values range from
approximately 75 - 95 pF with a mean of 85 pF and a standard deviation of 4 pF.
Note that these measurements do not include the focal plane wiring, but do include
the correct number of connectors (since the fake bolometer boards have the same
connectors as the focal plane). A measurement of a sample of the focal plane wiring
(using a capacitance meter) yielded approximately 10 pF. So a conservative estimate
of the total channel capacitance for QUaD is ~ 100 pF. Figure 3.22 shows the bias
current attenuation and signal phase shift that would result for this capacitance
assuming a typical bolometer resistance. At the 110 Hz bias frequency, the average
channel sees a roughly ~ 4% attenuation in bias current and a ~ 20° phase shift.
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3.2. PERFORMANCE
89
Microphonic Noise Spectrum
1000
b a se lin e
b anging
100
N
I
>C
0
200
400
600
800
F re q . (Hz)
Figure 3.23: Microphonic response for a single QUaD channel comparing two cases:
“baseline” (receiver undisturbed) and “banging” (receiver tapped lightly with a rub­
ber mallet). The attenuation above 400 Hz is from the electronics bandpass filter
(Figure 3.8).
3.2.4
M icrophonics
The microphonic response of the receiver was measured by tapping the cryostat
lightly with a rubber tipped mallet while recording the bolometer signals with a
spectral analyzer. The bolometers were DC biased and the “preamp” readout mode
of the warm amplifiers was used. This allowed the full bandwidth to be monitored
rather than the narrow, 20 Hz bandwidth available with either of the demodulated
outputs. Figure 3.23 shows the microphonic response for a single channel from 0 Hz
through 800 Hz. Figure 3.24 plots several channels over the more limited range
of possible bias frequencies. Correlation among the channels can be attributed to
vibrations of the entire focal plane structure rather than the individual channel wires.
In particular, the 100 and 150 GHz channels travel through independent cabling and
JFET boxes. Results for the same test with the telescope scanning in azimuth were
indistinguishable from the baseline (stationary) case - a testament to the smooth
operation of the DASI mount.
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90
CHAPTER 3. READOUT ELECTRONICS
B a se lin e
1000
150-44C
100-14C
150-01H
N
I
100
>c
10
100
150
200
250
Freq. (Hz)
1000 F
B anging
1---'---r
'--- 1---'---' 1 '---'---'---'--- 1---'---
150-44C
100-14C
150-01H
0
50
100
150
200
250
Freq. (Hz)
Figure 3.24: Microphonic response for three channels over the possible bias frequency
range.
The cleanest region of the spectrum is around 200 Hz. Indeed bolometer noise
tests with the bias frequency set here showed a complete absence of microphonic
features. It was, however, felt that this frequency range was too high given the
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3.2. PERFORMANCE
91
QUaD
Receiver
■Hermetic connector
nn
RF-tight interface box
■Filtered “D” connector
■Electronics boxes
Cabling to DAS
Figure 3.25: Warm RF filtering. All lines entering or leaving the cryostat pass
through filtered connectors (shaded gray) at the entrance to the RF-tight interface
box. Figures 4.6 and B.3 show photographs of the electronics boxes attached to the
cryostat.
capacitance effects measured in the previous section (Figure 3.22). Instead, a bias
frequency of 110 Hz was chosen. Operating in AC bias mode with this bias frequency,
all channels are free of microphonic resonances over the frequency range of interest
(Figure 5.24).
3.2.5
Radio Frequency Interference
A signal wire connecting the bolometers to the data acquisition can act as antenna,
picking up radio-frequency (RF) power. Some of the RF power dissipates in the
bolometer’s thermistor chip which heats the detector and produces a spurious signal.
Because of the negative temperature coefficient of resistance for NTD germanium
thermistors (eq. 4.7), radio frequency interference (RFI) always results in a negative
voltage signal. Frequencies of order 1 GHz are most problematic since they couple
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CHAPTER 3. READOUT ELECTRONICS
92
well to typical wire lengths. Unfortunately, this frequency range is heavily used by
modern wireless communication equipment.
To reduce susceptibility to RFI, QUaD filters all lines entering or leaving the
cryostat using filtered D connectors15 as shown in Figure 3.25. A second stage of
filtering occurs as the signals pass through the 4 K baseplate inside the cryostat
using filtered micro-D connectors.16 Despite this filtering, the short section of wiring
connecting the JFETS to the focal plane is still vulnerable to pickup from RF en­
tering the cryostat through the optical window. In order to minimize capacitance
on this high-impedance wiring, no filtering is provided at the entrance to the focal
plane enclosure (see Section 3.2.3).
With the cryostat window blanked off, testing with an RF sweep generator
showed no response, indicating that the filtering is working. On the contrary, with
the window open considerable interference was seen at frequencies in the range
~ 1 — 10 GHz. In both cases, negligible response was seen to low frequency RF
(~ 10 MHz), presumably due to the attenuation resulting when such long-wavelength
radiation passes through the 6 ” cryostat window combined with its poor coupling to
the short internal wiring.
Fortunately for QUaD, the South Pole in winter provides an extremely clean RF
environment. Due to the sensitive nature of many of the experiments operating at
the site, sources of RFI are strictly monitored. During the winter, the use of wireless
communication devices is prohibited in the area surrounding QUaD (known as the
Dark Sector) except in emergencies. Since installing the receiver in the telescope in
February 2005, no trace of RFI has been detected.
15Spectrum Control Series 700 connectors with pi filters (www.spectrumcontrol.com).
16Cristek Inc., (www.cristek.com).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 4
Receiver Characterization
4.1
B o lo m eter C h aracterization
The QUaD receiver was integrated and characterized at Stanford from April through
October of 2004 prior to shipping it to the South Pole. This chapter presents the
results of that testing.
4.1.1
Bolom eter M odel
A simple model, shown schematically in Figure 4.1, describes the thermal and elec­
trical operation of a bolometer. A model for the thermal operation of a semicon­
ductor bolometer and its noise properties is developed in the pioneering papers by
Mather [Mather, 1982, 1984]. Sudiwala et al. [2002] describes the process by which
model parameters are determined through laboratory measurements on actual de­
vices. Runyan [2002] provides a good review of the subject. The treatment presented
in this section is based on these references.
The model assumes that the absorber, warmed by optical power from incident
radiation and electrical power dissipation in the thermistor operates at a temper­
ature, Tboio, greater than the baseplate temperature, Tbase. The optical power is
typically referred to as Q while the electrical power is called P. Power flows from
93
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CHAPTER 4. RECEIVER CHARACTERIZATION
94
bias
Absorber ( 7 ^ )
Thermistor (R0, A)
bias
bolo
Thermal link (Gfl, p)
Baseplate (Tbase)
Figure 4.1: (left) Bolometer thermal model, (right) Bolometer electrical readout
circuit.
the bolometer to the baseplate through a thermal link with temperature-dependent
conductivity. In thermal equilibrium, the power flowing into the absorber equals
the power leaving. This is expressed quantitatively by the power-balance equation
which is written as follows
P + Q = ( ThoX° G (T )dT
(4.1)
base
where G (T) is called the differential thermal conductivity. For semiconductor bolome­
ters, G(T) can be modelled with a power law:
G(T) = G„ ( P j
(4.2)
where To is an arbitrary reference temperature. For QUaD, typical values are Gq ~
100 pW /K and /3 ~ 1.3 for To = 300 mK. Using this model for G(T), the powerbalance equation becomes
P + Q = T S °°+ l ) { T g £ - T ^ ) .
(4.3)
The electrical power dissipated in the thermistor can be manipulated into three
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4.1. BOLOMETER CHARACTERIZATION
95
standard forms using Ohm’s law:
(4.4)
The voltage across the thermistor, V)0io, can be related to the bias voltage and
current using the schematic of the readout circuit shown in Figure 4.1:
(4.5)
Vrbo'°
R ( T ) + 2 R ,V'"'“‘
(4.6)
The final step is to relate the thermistor resistance to temperature. For NTD Ger­
manium thermistors, a simple functional form gives excellent results:
(4.7)
The parameter R q depends on exact size and shape of the thermistor chip and varies
considerably from device to device. On the other hand, A is a property of the
material and tends to be more stable.
Equations 4.3 through 4.7 determine the incident optical power, Q, given mea­
surements of Vboioi Vbias and Tbase- First, however, the bolometer must be character­
ized by determining the device-dependent parameters Ro, A, G0, and (3. This is the
subject of the next section.
4.1.2
Load Curves
The load curve is the fundamental tool for determining the parameters of a particular
bolometer. The test involves recording the bolometer voltage while ramping the bias
voltage from zero to some maximum value. Using equation 4.5, the results can be
plotted as bolometer voltage versus bias current. Equation 4.6 allows the bolometer
resistance to be determined. Load curves can be taken under a variety of optical
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CHAPTER 4. RECEIVER CHARACTERIZATION
96
L oad C u r ve s : P S B 1 5 0 - 1 2 H
R e s is ta n c e : P S B 1 5 0 -1 2 H
6
10
LHe
LN2
8
4
6
>
E
a
o
.6
4
>
2
LHe
LN2
RT
0
0
5
10
2
15
20
Bios (nA)
0
0
2
4
6
3ias (nA)
8
10
Figure 4.2: Three load curves for a single PSB looking at different temperature loads.
loading conditions (various values of Q).
Figure 4.2 shows sample load curves for the same device looking at three different
temperature blackbody loads - room temperature, liquid nitrogen and liquid helium.
For low bias current values, bolometers behave like ordinary resistors. But increased
bias current results in self-heating which causes a deviation from Ohmic behavior.
For small amounts of optical power and large bias currents the load curves “turn
over” entering a regime where increased bias results in less signal. For heavily loaded
bolometers, it is difficult to apply enough bias current to see this effect.
The load curves shown in Fig 4.2 were taken using three different temperature
blackbody loads. The room-temperature load was a sheet of unpainted Eccosorb
CV-3 (egg-carton shaped absorbing foam) placed over the cryostat window. The
liquid nitrogen load was a styrofoam cooler filled with LN2 with a piece of the same
Eccosorb foam placed inside. Dry styrofoam was found to be extremely transparent
at the frequencies of interest (Transmission > 0.99). A small fan was placed to
blow a steady stream of warm air through the gap between the load and window to
ensure that condensation did not form on the cold load. The liquid helium load was
a similar, but smaller styrofoam box (owing to the greater cost and much smaller
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4.1. BOLOMETER CHARACTERIZATION
97
QUAD 2005 Dark D etectors R(T)
18
150-53C:
150-32H:
150-01C:
1 50-01H:
100-43C:
100-22C:
R,
R,
Rt
R0
R0
R0
81.0, A = 42.5
99.2, A = 45.5
= 156.8, A = 40.3
= 135.6, A = 38.7
= 156.5, A = 37.1
17
or
c
16
15 L
1.60
1.70
1.80
1/SQRT(T)
1.90
2.00
Figure 4.3: Resistance vs. temperature for the six dark detectors in QUaD.
heat capacity of liquid helium). The load was covered with a styrofoam lid with a
small (1 cm) hole used for transferring the helium. The load held liquid for just over
the minute necessary for the load curve.
The standard procedure for determining the parameters R q and A, is with a
series of ‘dark’ (Q = 0 ) load curves at different baseplate temperatures, obtained
by blanking off the bolometer inside the cryostat. The low-bias points of each load
curve are used to determine the bolometer’s resistance. The power-balance equation
(eq. 4.3) shows that with Q = 0and P very small, r boi0 ~ Thase. A sequence of load
curves at differentvaluesof Tbase maps out R(T q0i0) allowing the parameters R q and
A to be determined. A coordinate transformation
x = l/V f
(4.8)
y = Ini?
(4.9)
linearizes eq. 4.7 which is useful for plotting the results as in Fig 4.3. Deviation
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CHAPTER 4. RECEIVER CHARACTERIZATION
98
L oa di ng : P S B 1 5 0 - 1 2 H
801 '
....................................................
60 -
?
3
40 -
a
20
0
-
_,_,—,—, i ,_,_,_, i ,_,_,_,_i_,_
0
5
10
15
20
Bias (nA )
Figure 4.4: The optical loading, Q, for the three load curves in Figure 4.2. For each
load temperature, the power is independent of bias, indicating a successful fit for
Go and (3. As noted in the text, it is difficult to make an absolute measurement
of the loading due to sensitivity to the bolometer parameters and the baseplate
temperature. Also, these results are not corrected for the approximately 2 pW of
loading due to emission from inside the cryostat (Section 5.3.1).
from a straight-line, especially for the coldest points, is common. This indicates
stray power warming the detector, or a temperature offset between the bolometer
and the baseplate thermometer. Reliable measurements of R q and A axe difficult
and require careful experimental technique to ensure that no stray light warms the
detector under test.
With Ro and A known, any load curve can be used to fit for Go and f3. Equation
4.7 is used to convert V^o into Tbolo and eq. 4.4, to find P (the electrical power).
The derivative of the power balance equation gives:
which can be manipulated so that a linear fit gives the two unknown parameters
Go and (3. In practice, the results from the linear fit should be used as the starting
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4.1. BOLOMETER CHARACTERIZATION
99
values for a non-linear fit to the difference equation
(4.11)
where the subscripts 1 and 2 refer to two successive points of the load curve.
With these parameters known, the power-balance equation can be used to solve
for the optical power, Q, at every point of any load curve:
(4.12)
Figure 4.4 shows the results of this procedure for the three load curves presented at
the beginning of this section. As expected, Q is constant for all bias values indicating
a successful fit.
The values of Q obtained in this way can be used to estimate the loading caused
by emission from filters and other optical elements in the system (Section 5.3.1).
They can also be used to estimate the loading from the atmosphere (Section 5.2.1).
However, it should be emphasized that an absolute measurement of the loading at
any given time is extremely difficult because it requires an accurate knowledge of the
bolometer parameters and the baseplate temperature. Aside from the difficulties of
calibrating a sub-Kelvin thermometer, the true baseplate temperature seen by the
bolometer is itself difficult to measure due to the finite conductivity of the focal
plane and Kapitza resistance at interfaces.1
We intended to dark test all of the QUaD detectors in a separate test bed be­
fore installation; however, time constraints made this impossible. Detector failures
prevented many of the devices we did test from being used in the final instrument.
Common PSB failure modes included the following:
• Popcorn noise - Random discrete jumps in the bolometer voltage resulted in an
1Assuming the parameter A is known, a dark load curve can be fit for Rq and a temperature
offset from the assumed baseplate temperature. These are found to be as high as 10 mK for the
dark load curves in Figure 4.3 with substantial device to device variation. Uncertainties in the
baseplate temperature at this level lead to uncertainties in Q of order G S T ~ 1 pW.
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CHAPTER 4. RECEIVER CHARACTERIZATION
100
RMS noise level several orders of magnitude higher than normal. The problem
was eventually traced to a bad batch of NTD thermistors affecting an entire
run of PSBs.
• Open circuit - The electrical connection would open, often during thermal
cycling. This was usually due to a bad wire bond between the connector and
the PSB membrane.
• Electrical short - An electrical connection between the two halves of the PSB
pair. This usually also implied an undesirable thermal short between the de­
vices, resulting in high measured cross polar leakage. This usually resulted
from machining tolerances placing the two membranes too close (nominal sep­
aration ~ 60
In the end, only seven out of the 62 total light detectors have known values of R q
and A. Table 4.1 summarizes the parameters for these devices. The six functioning
dark detectors also listed in the table were characterized in situ (see Figure 4.3).
4.2
O p tical C h aracterization
4.2.1
Optical Testbed
Prior to integration, optical testing was performed on individual pixels using the
optical testbed shown in Figure 4.5. The testbed design and the testing results are
detailed in [Kirby, 2004]. The optical testbed is a simplified version of the QUaD
receiver with minimal fore optics and a single feed. It is based on a downwardlooking LN2 / LHe cryostat and uses a single-stage helium-3 adsorption refrigerator
to achieve bolometer temperatures of order 265 mK. The single-stage fridge requires
a baseplate temperature below ~ 2.5 K in order to condense helium-3, so pumping
on the LHe bath is required. As in QUaD, the focal plane is thermally isolated from
the baseplate via Vespel legs. The electronics are a scaled down version of the full
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4.2. OPTICAL CHARACTERIZATION
101
Table 4.1: The bolometer parameters for the subset of QUaD detectors that have
dark characterization. The top section of the table lists the detectors that are now
open to light. The R q and A parameters for these detectors were determined in
a separate test bed prior to installation in QUaD. The Go and (3 parameter were
fit from a load curve under typical observing conditions. The bottom section lists
detectors that are currently dark. They were characterized in QUaD (R ( T ) data
shown in Figure 4.3).
PSB
Ro
(n)
150-12H 93.4
150-12C 82.6
150-21H 80.5
150-21C 78.9
150-04H 133.5
150-04C 94.3
150-15C 113.8
150-01H 156.8
150-01C 96.0
150-32H 99.2
150-53C 81.0
100-43C 135.6
100 - 22 C 156.5
A
Go
(pW/K)
(K)
41.0
120.7
40.8
152.0
41.2
129.7
41.4
155.9
39.8
159.3
123.4
40.0
39.3
107.0
40.3
117.6
41.2
116.1
45.5
92.3
42.5
98.3
38.7
48.5
51.2
37.1
P
1.47
1.45
1.44
1.46
1.42
1.36
1.35
1.41
1.43
1.82
1.70
1.52
1.55
QUaD readout including a duplicate bias board, single amplifier card, and a custom
two-channel JFET box.
Tests performed with the testbed include:
• Spectroscopy - Various combinations of band-defining filters were tested at 100
and 150 GHz to find a combination that yielded the desired cutoff with no outof-band leaks. Measurements of the final filter stack in QUaD are described in
Section 4.2.2.
• Beam pattern - The FWHM for each frequency feed was measured and found
to agree with the predicted value.
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CHAPTER 4. RECEIVER CHARACTERIZATION
102
HDPE window
Vacuum j a c k e t
77K shield
4K shield
150 GHz f e e d
He3 frid g e
PSB nodule
L ig h t- tig h t
en clo su re
V e sp el le g s
4K b a s e p la t e
Figure 4.5: The QUaD optical testbed, (left) Photo with all thermal shields re­
moved. The JFET box is visible in the foreground and the load resistor box is
located to the left of the feed, (right) Assembly drawing.
• Optical efficiency - The optical efficiency was measured for several devices at
each frequency. These early tests showed the low efficiency of the 100 GHz
channels that is seen in QUaD (Section 4.2.3).
• Cross polar leakage - The cross polar leakage was measured for multiple devices
at both frequencies. Again, these early tests showed the poorer performance
of the 100 GHz channels relative to the 150s. Comparison of the testbed and
QUaD results is presented in Section 4.3.
4.2.2
Spectral Bands
The QUaD spectral bands are fixed at the low-frequency end by the feed horn throat
and on the high end by metal-mesh low-pass filters as described in Section 2.3.3. Dur­
ing development, the filter bands were tested with a Fourier transform spectrometer
(FTS) at Stanford. Once the filter stack was finalized and installed, every pixel was
tested with an FTS at the South Pole.
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4.2. OPTICAL CHARACTERIZATION
103
Figure 4.6: The QUaD receiver setup for laboratory testing with the Stanford FTS.
An FTS is a Michelson interferometer with one fixed and one movable mirror. The
bolometer voltage is recorded as the moving mirror varies the path length resulting
in an interference pattern known as an interferogram. The Fourier transform of
the interferogram gives the transmission function of the pixel being tested. The
transmission function (or spectral response function) is denoted f(v).
Figure 4.7 shows the transmission spectra for all 31 feed horns. For plotting, the
transmission spectra are normalized so that the peak is equal to one. Normalization
is discussed more in the next section. Feeds that will not be used in final CMB
analysis due to problems with one PSB are shown dashed.
The measured bandpass is typically characterized by several parameters including
a center frequency {vq) and a bandwidth (Ai/). These parameters are useful for
estimates and general discussions of the band properties; however, in practice noisy
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104
CHAPTER 4. RECEIVER CHARACTERIZATION
Table 4.2: Average spectral band properties.
Num
~L2
19
vq (GHz)
A u (GHz)
A v (%)
94.5 ± 0.6
149.5 ± 0.6
26.5 ± 2
40.5 ± 2
28
27
data and complicated bandpass shapes make them difficult to quantify. Multiple
definitions are commonly used, and each leads to slightly different values on realworld data.
For QUaD, we defined the band center to be
=
fo° v f { v ) d v
foo Y ,
Jo f {y) dv
4.13
which is a band-weighted average frequency. For the bandwidth, we used the half­
power points of the transmission spectra (FWHM). Table 4.2 gives average values
of these parameters for the spectra in Figure 4.7.
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4.2. OPTICAL CHARACTERIZATION
100
120
140
160
160
200
100
120
140
160
105
100
120
140
160
180
200
100
120
140
160
160
200
1 5 0 -0 6
100
120
140
160
180
200
100
120
140
160
160
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
180
200
100
120
140
160
160
200
100
120
140
160
180
200
100
120
140
160
180
200
1 0 0 -0 5
1 0 0 -0 6
1 0 0 -0 7
1 0 0 -0 8
1 0 0 -1 0
1 0 0 -1 1
1 0 0 -1 2
1 0 0 -0 9
Figure 4.7: The QUaD spectral bands as measured at the South Pole. The bands
shown dashed correspond to feeds with at least one non-functional channel.
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106
CHAPTER 4. RECEIVER CHARACTERIZATION
Power Difference 1 5 0 - 1 2 H
0.5
LN2
RT
0.4
E 0.3
JZ
o
2
0.0
0
20
40
60
80
Electrical Power (pW)
100
Figure 4.8: Power difference computed from the load curves in Figure 4.2.
4.2.3
Optical Efficiency
Definition
The optical efficiency is defined as the fraction of in-band power incident on the
receiver that is actually detected by the bolometer. It is always less than one because
of reflection and absorption losses from each element in the optical chain. Values of
40% are typical of state-of-the-art millimeter-wave receivers.
The optical power (Q) incident on a PSB for observations of a beam-filling,
blackbody source is given by an integral over frequency:
Q = \ J Aflfniv) B (T , v) du
(4.14)
where Afl is the throughput of the optical system and /„ is the normalized spec­
tral response. The factor of 1/2 arises because the PSB detects only one linear
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4.2. OPTICAL CHARACTERIZATION
107
polarization .2 In the Raleigh-Jeans limit, eq. 4.14 can be simplified to
Q = kT
J f n(u) du
(4.15)
where the equality AQ. = A2 (valid for single-moded optical systems such as QUaD)
has been used. The efficiency can then be defined as the band-average of the nor­
malized transmission:
V
=
1 ~
1^2 —
[
Jvi
f n ( v ) d v
(4.16)
If the power contained outside the band interval (^i, vf) is small, we can approximate
eq. 4.15 as Q « kT rj Au which isfrequently used for estimates. Note this defines 77
as the efficiency of the detector to radiation polarized alongits axis of sensitivity.
M easurement with Load Curves
Load curve measurements can be used to normalize the raw spectra as measured
from the FTS (sec 4.2.2). In principal, eq. 4.3 allows rj to be determined for any
characterized bolometer from a single load curve observing a blackbody of known
temperature; however, as noted in Section 4.1, sensitivity to the parameters and
internal emission from the receiver make this difficult. Another method, involving
two load curves, avoids this problem and does not require knowledge of any of the
bolometer parameters.
Two load curves are taken while looking at beam-filling blackbody loads at two
different temperatures, T\ and T2 . The curves are plotted in units of bolometer resis­
tance versus electrical bias power. Figure 4.8 shows the results for a single detector
looking at room temperature and liquid nitrogen loads. Lines of constant resistance
(horizontal) on the plot correspond to lines of constant bolometer temperature (eq.
4.7) and thus constant P + Q (eq. 4.3 assuming constant baseplate temperature);
the curve corresponding to the colder load requires more electrical power to warm
2The factor of 1/2 could be absorbed into / n(y)i however, the definition here makes comparison
of efficiencies with total power experiments simpler.
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108
CHAPTER 4. RECEIVER CHARACTERIZATION
Table 4.3: Average optical efficiencies. “Inner” refers to the central group of seven
150 GHz pixels and “outer” refers to the outer ring of 12 pixels (Figure 2.9)
100 GHz
150 GHz
150 GHz
150 GHz
all
inner
outer
all
26 ±
35 ±
29 ±
32 ±
6%
5%
5%
6%
the bolometer to the same temperature. So the difference in optical power is equal
to the difference in electrical power:
Q 2 ~ Q i = Pi ~ P2-
(4.17)
This difference should be constant along the load curve and the multiple measure­
ments can be averaged. Equation 4.14 relates the power difference to the load tem­
peratures
A Q2 - A Qx = a J AQ f ( u) [b(T2, v ) - B(TU v)} dv
(4.18)
allowing the normalization constant, a, to be determined. The transmission spec­
trum for this detector can then be normalized as:
fniy) = af{y)
(4.19)
allowing the optical efficiency to be determined via eq. 4.16. It should be noted that
in general ot^rj.
R esults for QUaD
This procedure was applied to QUaD using the spectra described in 4.2.2. The loads
were room temperature and liquid nitrogen Eccosorb as described in Section 4.1.
For the optical efficiency measurements, it is important that the liquid nitrogen load
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4.2. OPTICAL CHARACTERIZATION
1 0 0 GHz
■I
0
10
20
.......
30
40
109
1 5 0 GHz
i'
50
60
E fficie n cy (%)
0
10
20
30
40
50
60
E fficie n cy (%)
Figure 4.9: QUaD optical efficiencies. The shaded region of the 150 GHz histogram
shows the distribution for the central ring of seven feed horns.
is dry, since thermal emission from condensation will make it appear warmer - an
effect that is indistinguishable from reduced optical efficiency. For the same reason,
the cryostat window must be clean and dry.
The results are summarized in Figure 4.9 and Table 4.3. The optical efficiencies
for the central group of seven feed horns are significantly better than the outer
ring of 150 GHz feeds. This is largely attributable to a selection effect; the best
performing detectors from previous runs were grouped in the center because t his
region of the focal plane has the best optical properties. The cause of the generally
poorer performance of the 100 GHz detectors is unknown, but believed to be caused
by the horn bolometer interface (see Section 4.3).
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110
CHAPTER 4. RECEIVER CHARACTERIZATION
Re s p o n s iv i t y : P S B 1 5 0 - 1 2 H
4
LHe
LN2
3
o
>
O
a
if)
o
0
5
10
15
20
Bias (nA)
Figure 4.10: Responsivity of a quad detector.
4.2.4
R esponsivity and Tim e C onstants
D C Responsivity
The DC Responsivity (S dc ) of a bolometer is defined as the change in bolometer
voltage for a small change in incident optical power assuming the bolometer is in
thermal equilibrium during the process:
S dc =
dVboio
dQ
Using the equations in Section 4.1.1 one can derive the following expression
_ RL z - R
DC ~ 2Vmo z + 2R L
(4.20)
where z, the dynamical impedance, given by
dVboio
dibias
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(4.21)
4.2. OPTICAL CHARACTERIZATION
111
is the the slope of the load curve. The responsivity as defined in eq. 4.20 is always
negative for QUaD since our detectors have a negative temperature coefficient of
resistance (eq. 4.7). However, it is common in practice to refer to the absolutevalue
when speaking of responsivity. Figure 4.10 shows responsivity curves corresponding
to the load curves in Fig 4.2. Increased optical loading warms the detector resulting
in decreased responsivity. In practice, bolometers are not biased to be at the peak of
the responsivity curve because here the sensitivity to changes in background loading
is maximized, making the system difficult to calibrate (see Section 5.3.2).
Bolom eter Time Constants
The absorber and thermistor in real bolometers have a finite heat capacity meaning
that it takes some time for them to change temperature. This results in a frequencydependent attenuation to the DC responsivity given in the previous section. This
frequency-dependence must be understood in order to use the bolometer voltages to
accurately reconstruct time-varying signals.
The responsivity can be written as a product of three factors:
ci \
S
H
dVboio dR dT
= ~iRdfdQ-
( 4 ' 2 2 )
The first two factors are frequency independent; however, the last is not. Its fre­
quency dependence can be determined from a simple model. If we apply a small
perturbation AQ{t) = AQe1^1 and assume that the electrical power, P remains
constant, the power-balance equation gives AQ —G A T = C A T where C is the
bolometer’s heat capacity (J/K). Assuming AT = A T(u)eluJt results in
AT
1
-r-pz oc — —
A Q 1 + ILJT
,
4.23
where r = C /G is known as the time-constant of the bolometer. This is the same
form as the response of a single-pole low-pass filter.
The assumption that the electrical power remains constant for changing optical
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112
CHAPTER 4. RECEIVER CHARACTERIZATION
150-13-B
150-14-A
T a u lab: 10.1
T a u lab : 3 2 .7
0.8
0.8
0.6
0.6
0 .4
0 .4
0.2
0.2
0.0
0.0
0
5
10
15
20
F re q (H z)
25
0
30
5
10
15
20
F re q (H z)
25
30
Figure 4.11: Lab time constant measurements for two example detectors Time con­
stants are in ms in the upper right corner of each plot.
loading is incorrect. In fact, the bias current remains (nearly) constant, but in­
creased optical loading results in decreased bolometer resistance and thus decreased
electrical power (P). The decreased P compensates for the increased Q resulting in
the bolometer coming to equilibrium faster than it would have without this electro­
thermal feedback. Including this feedback, the form of eq. 4.23 remains valid with
r replaced by an effective time constant re = C/(G —aP) where a = R~l dR /dT
which is of order —16 K -1 for typical QUaD bolometer parameters. Higher bias
current is seen to result in faster detectors (decreased re). Putting this together, the
frequency-dependent responsivity is given by
S(u) =
S° C .
l+ tU T e
(4.24)
y
’
Laboratory Measurement
The QUaD time constants were measured in the lab with a rotating chopper wheel
mounted between the cryostat window and a liquid nitrogen cold load. The chopper
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4.2. OPTICAL CHARACTERIZATION
113
wheel had alternate transparent and opaque (Eccosorb foam) sections. The resulting
square-wave signal was digitized and demodulated in software. The amplitude was
recorded for a variety of chopper rotation frequencies. The data was taken using the
DC-biased mode of the readout electronics since chopper rotations faster than the
20 Hz cut off frequency were needed. Figure 4.11 shows data and model fits for two
detectors.
Unfortunately, during the test, the bolometer bias current was set a factor of
4.5 higher than the standard observing value (see Section 5.3.2) and the chopped
load presented roughly six times more optical loading than is seen in the field (see
Section 5.3.1). These different operating conditions make the results of these tests
less useful. Section 5.1.4 presents an alternate method of measuring time constants
under typical observing conditions.
4.2.5
Cosmic Rays and Im pulse Response
Being thermal detectors, bolometers respond to many forms of incident energy. The
substantial filtering in the QUaD receiver (see Figure 2.4) prevents out-of-band op­
tical power from reaching the detectors; however, cosmic rays easily penetrate. Even
though PSBs present a substantially reduced cross section relative to a solid ab­
sorber, QUaD still sees a background of cosmic ray events at a rate of ~ 0.5 /
channel / hour.3 Since cosmic ray impacts are essentially instantaneous (relative
to all relevant thermal and electronic time constants), they approximate a delta
function disturbance and thus provide a means of measuring the receiver impulse
response.
Figure 4.12 shows a typical cosmic ray event as well as a best-fit model (blue) of
the receiver impulse response. The model has four free parameters, the bolometer
time constant (r6), the time constant (77 ) of the post-demodulation low pass filter
(/m
b
~ 20 Hz), and an overall scale factor and temporal shift. The filter time
3Note that this rate is low enough that scans containing a cosmic ray impact can simply be
ignored from the main CMB analysis with negligible loss of data.
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CHAPTER 4. RECEIVER CHARACTERIZATION
114
C o sm ic R ay Im pulse R e s p o n s e
2
o
■2
-4
D ata
Spline
Im pulse m odel
■6L
0.0
0.2
0.4
0.6
0.8
1.0
sec
Figure 4.12: A cosmic ray impact shows the receiver’s impulse response.
constant, t/ has been measured for every channel (Figure 3.14), but temperature
variations in the receiver room may slightly change its value which is why it is left as
a free parameter. The good fit of the impulse model to the cosmic ray data indicates
that these four parameters are the most important factors.
The following outlines the derivation of the impulse response model beginning
with the transfer functions for the bolometer and the post-demodulation low-pass
filter. The bolometer transfer function is a simple first-order response:
tfboio(s) = — ~ r
Tb S + 1
(4 .2 5 )
where s= —iu>. The post-demodulation filter is a 6-pole Butterworth with a nominal
3 dB point of20 Hz. The transfer function for a 6-pole filter is
(rjs2 + ArfS + l)(Tjs2 + BrfS + 1)(tj S2 + C tjs + 1)
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(4.26)
4.2. OPTICAL CHARACTERIZATION
115
Impulse Response Model
0.40
0 ms
10 ms
0.30
20 ms
30 ms
0.20
o
>
0.10
0.00
-
0.10
0.00
0.10
0.05
0.15
0.20
0.25
sec
Figure 4.13: Model QUaD impulse response for several different bolometer time
constants.
which is a product of three general, second-order responses. For a Butterworth, the
coefficients are A =
0 .5 1 7 6 3 8 7 ,
B =
\/2 ,
and C =
1 /A
The overall transfer function
is given by the product of these two as
H{s) =
tffilter(s)# b o lo (s)-
(4.2 7 )
The impulse function is determined by inverse Laplace transforming the transfer
function. Since the transfer function is quotient of two polynomials, this can be done
analytically using a partial-fraction decomposition which leads to a series of damped
sine and cosine terms. Figure 4 .1 3 shows plots of simulated impulse responses gener­
ated from this model. The left hand plot shows that for a constant impulse, a longer
bolometer time constant leads to a lower peak voltage and a longer decay; however,
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CHAPTER 4. RECEIVER CHARACTERIZATION
116
Figure 4.14: Aligning the polarizing grid.
the bolometer time constants obtained with this procedure are known to disagree
with those obtained optically [Woodcraft et al., 2003]. For PSBs, the agreement is
worse due to the absorber geometry. Cosmic ray hits thus provide a useful monitor
of the electronics transfer function but not an effective way to measure bolometer
time constants.
4.3
P ola riza tio n P ro p e rties
In order to characterize the polarization performance of the receiver, we measured
the orientation angle of each PSB and its cross-polar leakage. Cross polar leakage
refers to the response of a PSB to linearly polarized radiation oriented orthogonally
to the designed axis of sensitivity. Both of these measurements were performed
with the same setup which involved placing a rotating wire-grid polarizer above the
cryostat window while observing a chopped thermal load read out with a lockin
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4.3. POLARIZATION PROPERTIES
117
Figure 4.15: The polarizing grid mounted on the cryostat.
amplifier synched to a chopper-synchronous reference. In this section, I derive the
expected signal, describe the setup in more detail, present the results, and finally
consider the effects of the measured cross-polar leakage.
4.3.1
Formalism
This section provides a brief introduction to the Jones and Meuller formalisms which
the following sections use to analyze the polarization properties of the receiver. Both
formalisms represent electromagnetic waves of arbitrary polarization as column vec­
tors and optical elements as square matrices. They allow a complicated optical
system, composed of many elements, to be reduced to a single matrix by combining
the matrices corresponding to the individual elements using matrix multiplication.
The Jones formalism represents electromagnetic waves as complex, two-component
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118
CHAPTER 4. RECEIVER CHARACTERIZATION
1 5 0 -1 6 C
150-16H
150 -2 1 C
1 5 0 -2 1 H
g 0.6
in
0.2
0.0
0
100
200
300
400
Grid Angle (deg)
Figure 4.16: Measuring the polarization angles.
column vectors which give the amplitude and phase of the electric field as
E =
E0xei(f,x
\
(4.28)
E oye^
where the E q and 0 are real. An overall time dependence of e™1 is assumed and only
the real part of E has physical significance. The Jones vectors are usually normalized
to unity irradiance so that, for example, a wave linearly polarized at a 45° direction
to the x axis would be represented by the simple expression:
E 45 =
(4.29)
Passing this beam through a horizontally-oriented polarizing grid results in the new
beam, Ef, given by E / = J h E 45. The Jones matrix of a horizontal polarizer, J h, is
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4.3. POLARIZATION PROPERTIES
100 GHz
119
150 GHz
Figure 4.17: Measured PSB orientations.
given by
Jh =
(4.30)
so that Ef = l/\ / 2 (l O) . The output is polarized in the horizontal direction as
expected.
Jones matrices are best-suited to the analysis of completely polarized radiation.
For the case of partial polarization, the Meuller formalism, based on Stokes pa­
rameters, is more appropriate. In this formalism, the radiation is represented by a
real, four-component Stokes vector S = ( l , Q,U, V) • Optical elements acting on
the radiation are represented by 4x4 real matrices. Given a Jones matrix, J, for a
component or system, the corresponding Meuller matrix is given by
Mij = ^ tr
(4.31)
where the a are Pauli matrices [Born and Wolf, 1980].
A more detailed description of these formalisms, including a table of Jones and
Meuller matrices for common elements, can be found in standard optics texts such
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120
CHAPTER 4. RECEIVER CHARACTERIZATION
Polarization Angle
Orthogonality
15
10
5
0
-4
-2
0
2
4
84
86
Error (d eg )
88
90
Error (deg)
92
94
Figure 4.18: Measured PSB orientation angle error and PSB pair orthogonality.
as Hecht [1998]. Examples of the use of Jones matrices to analyze more complex
systems can be found in Lesurf [1990] and O’Dell [2001]. The former analyzes a
polarized Fourier transform spectrometer and the latter, a correlation polarimeter.
Application of this formalism to PSBs is presented in Jones [2005] and reviewed in
the next subsection which applies these methods to the QUaD receiver testing setup.
4.3.2
D erivation of the E xpected Signal
As described earlier, the receiver was tested by rotating a linear polarizing grid
in front of the window while observing a chopped thermal load. From elementary
optics, we expect a sinusoidal response from the PSB as we rotate the polarizing
grid. However, deriving the full result including the effect of cross polar leakage
provides a useful application of the Jones matrix formalism. We imagine orienting
the PSB axis of sensitivity along the x axis and place a linear polarizer oriented at
an angle 0 above it. Written in terms of Jones matrices, the electric field that is
detected by the PSB is given by
E = J p s b J p flE j
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(4.32)
4.3. POLARIZATION PROPERTIES
121
1 0 0 GHz
15 0 GHz
15
10
8
10
6
4
5
2
0
0
0
5
10
Leakage (%)
0
15
5
10
Leakage (%)
15
Figure 4.19: Measured cross-polar leakage.
where J psb and Jp<j are the Jones matrices of the PSB and the polarizing grid
respectively and E* is the unpolarized input radiation.
A PSB acts as an imperfect linear polarizer followed by a total power detector
Jones [2005]. The optical power incident on the PSB will be proportional to the
intensity of E:
Pop, oc ( E 'E ) = ( |r £ |) + ( |£ j |)
(4.33)
where < > denotes time averaging.4
The Jones matrix for the PSB is given by
/
"IpsB —
^
_
(4-34)
where rj ~ 1 and <5 <C 1 parameterize the cross polar leakage [Jones, 2005]. The
4The symbol P opt is used instead of Q to denote the optical power absorbed by a PSB to avoid
confusion with the Stokes parameter Q .
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122
CHAPTER 4. RECEIVER CHARACTERIZATION
Jones matrix for a linear polarizer oriented at an angle, 9, to the x axis is given by
—R
R
0 0
(4.35)
where R is a standard rotation matrix given by
R =
^ cos 9 —sinfl ^
sin 9
cos 9
(4.36)
Simplifying, this gives
1 / 1 + cos 29
sin 29
Jpe — ~
sin 29
1 —cos 29
(4.37)
The initially unpolarized radiation field can be represented with the Jones vector
(4.38)
where 4>(t) is random phase that varies on timescales much faster than the detection
period (~ 10 ms) but much slower than the frequency of oscillation of the electric
field (~ 10 ps) such that (e1(t>^
= 0.
Plugging these expressions into eqs. 4.32 and 4.33 yields Popt(9)- The change
in voltage output of the bolometer is proportional to the change in incident optical
power over a small range: A v oc APopt. Synchronous demodulation of the chopped
source ensures that v — 0 when Popt — 0 which gives the output voltage of the lockin
amplifier as:
v (6) ^ \ (v2 + <52) + ^ (v2 ~ <52) cos 29.
(4.39)
As expected, this is a sinusoid where the period reflects the fact that the polarizing
grid appears identical after a 180° rotation. The maximum value of the sine wave
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4.3. POLARIZATION PROPERTIES
123
is rj2 and the minimum is S2. Cross polar leakage is thus immediately obvious in a
plot of V (9) as an offset between the x axis and the minimum signal.
4.3.3
T he M easurem ent Setup
The polarizing grid is a thin sheet of polypropylene with parallel traces of copper
deposited on one surface with a 10 micron spacing. The grid spacing was verified
using the diffraction pattern created with a standard red laser pointer. The grid was
manufactured by our collaborators in Cardiff using the same lithographic technique
used for filter construction. The polarizing efficiency of the grid (at 150 GHz) is
greater than 99.9%.5
The grid was mounted onto a ball-bearing rotating stage to allow positioning at
any angle. The stage was driven by a high-resolution stepper motor (400 steps per
revolution) through a zero-backlash belt,6 with a gear reduction of 12:1. A micro
switch provided a reference mark once per revolution. The grid was aligned with
respect to the reference mark to better than 0.5° using the diffraction pattern from
a laser pointer (Figure 4.14). Figure 4.15 shows the complete system mounted on
the cryostat window.
During testing, the cryostat observed a chopped 77 K / 300 K load. The chop
frequency was set at ~ 2 Hz. An opto-interrupter provided a chopper-synchronous
reference that was digitized on one of the spare channels of the main data acquisition
system. A software lockin amplifier, synchronized to the digitized reference, was
applied to the signals during the analysis.
Testing was performed with a “step and integrate” sequence whereby the grid
was rotated an amount ~1° then held stationary for several chopper periods. The
DAS recorded data continuously during this process. In order to divide the data into
5The efficiency was determined by measuring the transmission through a stack of two identicallymanufactured grids first with the grids oriented orthogonally and then aligned parallel. The mea­
surement was made with the single-pixel optical testbed (Section 4.2.1) looking through the stacked
grids at a chopped load.
6W.M. Berg, Inc. www.wmberg.com
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CHAPTER 4. RECEIVER CHARACTERIZATION
124
steps, the polarizing grid motor driver set a digital “data good” flag high whenever
the grid wasn’t rotating.
During testing, a stationary Eccosorb mask was placed between the polarizing
grid and the cryostat window. The mask had 0.5” holes drilled through it at the
locations of the beams corresponding to each horn. The 31 beam centers were derived
from the optics model (using Zemax, an optics package) and output to a file. The file
was used to program a CNC mill for precise placement of the holes. The perimeter
of the mask was also machined on the CNC mill to fit snugly in the window holder.
Once the mask was installed, its optimum rotational orientation was determined by
maximizing the signal from the chopped load (before installing the polarizing grid).
In Figure 4.15, the mask is visible through the polarizing grid.
The purpose of the mask is twofold. First, it limits the change in loading on
the detectors during the rotational cycle of the polarizing grid to keep the detector
response linear. As the grid rotates, it alternately appears reflective (minimal load­
ing) or transparent (maximal loading as the detectors see the 300K-77K chopped
signal). Secondly, the reduced aperture limits highly off-axis rays which are known
from optical models to produce higher cross-polar response.
4.3.4
R esults and Discussion
The PSBs in QUaD are nominally oriented at one of four possible angles (0, 45,
90, 135 degrees) as seen in Figure 2.9. The two halves of a PSB pair are always
nominally orthogonal. Figure 4.16 shows test data for two PSB pairs representing
the four different orientations. The signals appear out of phase as expected and
approximately 3% cross polar leakage is seen. Sinusoids are fit to the results for all
the working PSBs and Figures 4.17, 4.18, and 4.19 display the resulting distribution
of orientations and cross polarization.
Most of the PSBs are oriented within ±2° of their nominal position and are
orthogonal to the same tolerance. Several mechanisms contribute to the errors in
PSB orientation including machining tolerances of the focal plane plate and PSB
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4.3. POLARIZATION PROPERTIES
125
modules, transmission through the cryostat optical chain, and placement of the
absorber within the PSB module. In particular the specified tolerance of ±1° on the
absorber position can account for much of the distribution.
The cross polar leakage results are more puzzling. The lower limit of the contri­
bution of the PSBs themselves is believed to be between 2 and 3% based on extensive
numerical modelling and testing of a previous generation of devices [Jones, 2005].
This figure is not in agreement with the QUaD results seen in Figure 4.19 which give
a mean value of 5% at 150 GHz and 8% at 100 GHz. The 150 GHz pixels perform
overwhelmingly better than the 100s and the best approach the 3% specification.
This substantial difference in performance is surprising given that the PSB modules,
feed horns, filtering, and fractional bandwidth in the two cases are extremely similar
and the optical chain is identical.
Prior to integration into QUaD, an optical testbed was used to test individual
pixels with a simplified optical chain that contains no lenses (Section 4.2.1). The
testbed contains a single feed and PSB located on axis. The band-defining and IR
blocking filters are very similar to those used in QUaD.
Testing began with a 150 GHz detector and extremely high levels of cross polar
leakage were measured (~ 10%). Substantial effort was spent trying to determine
the source of the leakage. The interior surface of the cryostat was blackened to pre­
vent stray reflections and great care was taken to ensure that no chopped signal was
leaking around the polarizing grid without passing through it. Tests with different
blocking filters, a narrower bandpass, and a different feed horn showed no improve­
ment. The problem was eventually traced to a thermal connection between the two
orthogonal absorbers in the PSB pair. This particular thermal short was visible at
room temperature as a high-impedance connection between the electrical leads of
the two devices.
Our shipping deadline left us less time for testing the 100 GHz pixels in the
testbed; however, the higher cross polarization result was verified for one pixel. No
definitive explanation was found for the generally poor performance of the 100 GHz
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CHAPTER 4. RECEIVER CHARACTERIZATION
126
PSB15 0 -2 1
oC °-8
CT>
00 0.6
“D
<
t>
N
o 0.4
o
z
0.2
0.0
-200
0
20 0
400
Polarizer Angle (deg)
60 0
PSB100-14
o
C
° -8
1/1 0.6
■o
<D
N
o 0.4
E
o
z
0.2
0.0
-200
0
200
400
Polarizer Angle (deg)
600
Figure 4.20: Comparison of the measured cross polar leakage for the same detectors
in QUaD (solid) and the optical testbed (dashed). The data points from the testbed
are shown as filled circles. Both data sets were taken through a 0.5” Eccosorb
aperture located at the cryostat window. The testbed data points for each detector
are phased to best align with the QUaD data. These are the only PSBs that were
measured in the testbed and installed in the final instrument.
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4.3. POLARIZATION PROPERTIES
127
pixels but the problem likely involves the horn bolometer interface or the horn it­
self since this is the only major difference between the optical chains for the two
frequencies.
This theory is supported by measurements of the horns return loss that were
performed using a vector network analyzer at NASA JPL. Return loss quantifies the
power that is lost to reflection when using the horn to transmit. The horns were
coupled to the analyzer using a modified PSB housing (containing no bolometers).
The return loss for the 100 GHz horns showed a feature around 90 GHz that depended
strongly on the interface between the horn and analyzer. Increased mating force was
able to reduce, but not eliminate this feature. An analogous feature was not seen
for the 150 GHz horns.
There were two PSB pairs that were tested in the testbed and are present in
the final receiver configuration. For both pairs, the results from the testbed were
comparable to, but slightly better than, that achieved in QUaD (see Figure 4.20).
This indicates that the lenses are not a significant source of cross polar leakage. The
large variation seen in Figure 4.19 is attributed to variations in the PSBs, horns,
and their interface.
All PSBs were screened based on warm resistance measurements and close visual
inspection under a microscope. Nevertheless, testing of large numbers of pixels in the
QUaD cryostat revealed PSB modules with intrinsically high cross polarization and
no obvious explanation. Every effort was made to relegate the poorly performing
devices to dark channels or omit them entirely; however, a severe shortage of PSBs
prevented us from being overly discriminating.
Fortunately, the orientation errors and the sources of cross polar leakage are built
into the instrument and are stable with time. They are small enough that they can
be ignored for rough calculations, but they must be included in the final analysis.
The next subsection explores some of the effects of these non-optimalities.
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CHAPTER 4. RECEIVER CHARACTERIZATION
128
R esponse of a PS B to an In p u t of A rb itra ry P olarization
Jones [2005] derives the voltage signal resulting from a PSB in response to input
radiation in an arbitrary polarization state. This subsection outlines that calculation
which results in eq. 4.42.
Since the incident radiation is incoherent and partially polarized, it is more nat­
urally described using Stokes parameters and the Meuller formalism. Recall that
a PSB is equivalent to an imperfect polarizer followed by a total power detector
(Section 4.3.2). The partially polarized incident radiation is represented by a Stokes
vector Si = (X, Q,U, V)r . The PSB first acts as an imperfect polarizer, transforming
the incident Stokes vector,
Si
to
S f
with
S f
= MS'* where M is the Meuller matrix
for the polarizer. The PSB then acts as a total power detector, giving a voltage
response proportional to the X component of S f .
The Meuller matrix for the polarizer, M, can be found from its Jones matrix
using 4.31 with J given by
(4.40)
where R is the rotation matrix defined in eq. 4.36. Since the PSB only detects
the total intensity component (X) of
S f,
we only need to calculate the top row of
S f = MSj to determine the output voltage, v, as
(4.41)
where X/ is the intensity component of S f . Evaluation of the four components of M
listed in eq. 4.41 results in:
v — s (1 + e)X + (1 —e) (Q cos28 + U sin26)
(4.42)
where e = 82/rj2 and 9 is the orientation angle of the PSB and s is a calibration
constant that depends on detector responsivity, optical throughput (Afi), optical
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4.3. POLARIZATION PROPERTIES
129
efficiency, bandwidth, and readout electronics gain. In practice, s is determined
using astronomical calibration (Section 5.2.3).
Implications
From eq. 4.42, the signal from a single PSB at a given angle is a linear combination
of the J , Q, and U components of the incident radiation. The three terms have
different angular dependencies allowing them to be separately determined, from
multiple measurements at different orientations.
The detector cross polar leakage, parameterized by e, results in a loss of sensitivity
to the polarized portion of the radiation, but not in a mixing of T, Q, and U (i.e.
their angular dependence remains unchanged). For a map made with a single PSB,
uncertainty in e translates into uncertainty in the overall calibration of the polarized
map to the total power map but not in a mixing of the individual maps - the
faint polarization signal will not be swamped by leakage from the much brighter
temperature signal.
In principal, a field can be characterized with a single PSB by measuring the
same patch of sky at multiple orientations. However, for a ground-based experiment,
where the large unpolarized atmospheric emission dominates, it is advantageous to
consider the difference signal from the two, nominally orthogonal PSBs in a pair. We
can take into account the small non-orthogonality of the two PSBs by considering
them to be oriented at angles (8,8 + 7t/2 + A) where A < 1 . The difference signal
is given by
va - v b = s(l - e)
^ l / j cos 26 + ( u + y O j sin 28 .
(4.43)
The difference signal is completely insensitive to unpolarized emission. The non­
orthogonality is seen to result in mixing between Q and U\ however, provided A is
known, Q and U can still be uniquely determined with measurements at two angles.
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CHAPTER 4. RECEIVER CHARACTERIZATION
130
In order for the contribution of the unpolarized radiation, I , to cancel upon dif­
ferencing two PSBs, eq. 4.43 assumed that the calibration constant, s, was the same
for the two channels. However, differing detector optical efficiencies, responsivities,
and amplifier gains mean that this will almost never be the case. Since QUaD reads
out both detectors individually, we can correct for this by applying a “software gain”
to the channels during post-processing.
The voltage signal from a QUaD PSB is dominated by unpolarized atmospheric
emission and noise:
vb
- sb1 + nb
where sa and sb reflect differing gains of the two channels and na and nb are uncor­
related random noise (Section 5.3.2).
Consider the difference signal, with a gain correction factor, k, applied to t>6:
va
kvb — (sa
ksb)T -j- na
knb
(4.44)
An obvious method of determining k is to chose the value that minimizes the expec­
tation value of the square of the corrected difference signal for a segment of data:
(4.45)
where () denotes the expectation value.
Equation 4.45 shows that in the limit where the unpolarized signal dominates the
polarized signal and the noise, the correct gain ratio sa/ s b will be obtained. If the
unpolarized signal does not dominate the noise, k will underestimate the true gain
ratio. A technique for generating a large, unpolarized signal using the atmosphere
for the purpose of gain matching is discussed in Section 5.2.2.
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Chapter 5
Instrum ent Performance
QUaD was commissioned at the South Pole during the 2004/2005 summer season
and began CMB observations in May 2005. Appendix B describes the main com­
missioning tasks involved with integrating the receiver and telescope. This chapter
describes tests done to characterize and monitor the performance of the completed
instrument.
5.1
O p tical P erform an ce
The performance of the optical system was verified by observing compact galactic
HII regions, which are the brightest sources visible above the ground shield (0° <
Z A < 55°). Of these, the source known as RCW38 is the brightest.
5.1.1
R aster Maps
Raster maps of RCW38 were among the first observations with QUaD. While track­
ing the source, the telescope was scanned in azimuth as shown in Figure 5.1. The
scans begin with a short period of acceleration, then move at constant velocity, de­
celerate, and finally repeat the motion in reverse to return to the initial position
relative to the source. After a few scans, there is a short pause to change elevation
131
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132
CHAPTER 5. INSTRUMENT PERFORMANCE
-138
oo>
*o
-140
L_
■©o -142
8
uic
£ -144
-146
-148
0
200
400
600
time (sec)
800
1000
Figure 5.1: The azimuth encoder reading while raster mapping RCW38. The overall
negative slope results from tracking the source with sky rotation. The pause after
every fourth constant velocity section (half-scan) allows time for the telescope to
change elevation and the DC offsets to be reset.
by a fraction of a beam width and to reset the DC offsets for the changed air mass.
A simple procedure converts the resulting time-ordered data into a pixelized map:
1. Convert the telescope axis encoder data into a right ascension (RA) and dec­
lination (DEC) value for every data point (sample).
2. Generate an empty, two dimensional array for the map data and a second one
to record the number of hits per pixel.
3. For each ADC data sample, determine which pixel it falls into from the RA
and DEC arrays. Add the data value to the appropriate pixel in the map, and
increment the corresponding entry in the hits per pixel array.
4. Divide the map by the hits array so that each pixel is appropriately weighted.
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5.1. OPTICAL PERFORMANCE
133
T elesco p e Position
-46.0
-46.5
-47.0
oo>
>
O
Ui
Q
S -47.5
-48.0
-48.5
-49.0
134.0
134.5
135.0
135.5
136.0
RA(deg)
Figure 5.2: The telescope RA/DEC position from an early QUaD raster map of
RCW38 shows sections of large elevation jitter. For clarity, only one out of every
four half-scans is plotted and only every fourth elevation step is used. The elevation
jitter problem was resolved shortly after this data was taken (see text).
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134
CHAPTER 5. INSTRUMENT PERFORMANCE
RCW38 Raw Scan APR 10 HRN150-02
0.1
0.0
-
0.1
-
0.2
Signal (Volts)
1.4 x El (deg)
-0.3
0
10
20
30
40
50
40
50
sec
Elevation Jitter Corrected
0.1
0.0
«
o
>
-
0.2
Signal -1.4 x El
-0.3
0
10
20
30
sec
Figure 5.3: (top) Scan across the source RCW38 showing the effect of elevation
jitter, which was present in early observations with QUaD. The elevation encoder,
overplotted in red, is highly correlated with the bolometer signal, (bottom ) Re­
moving the best-fit scaled encoder signal reduces the effects of elevation jitter except
when scanning across the source. This is purely illustrative as this technique is not
used for any further analysis.
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5.1. OPTICAL PERFORMANCE
135
100 GHz - RCW38 - Row
150 GHz - RCW38 - Row
Polynom ial
Polynom ial
-0 .5
0.0
Feed Difference
-0 .5
Feed D ifference
0.0
Figure 5.4: Maps of the galactic HII region, RCW38 at 100 (left) and 150
(right) GHz. The top two plots are minimally processed - only the mean has been
subtracted from each scan line. The middle plots show the results of subtracting a
fifth-order polynomial from each row. The bottom plots use a neighboring feed to
subtract out the common mode signal. The object faintly visible below and to the
right is a companion source.
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CHAPTER 5. INSTRUMENT PERFORMANCE
136
Because QUaD is very near the Geographic South Pole, the relationship between
AZ/EL and RA/DEC is roughly given by:
RA «
DEC «
AZ + 15 x LST
-E L
where LST is the local sidereal time in hours.
Figure 5.2 shows the telescope
RA/DEC during a raster map of RCW38. The declination axis shows the effects of
“elevation jitter,” a problem that plagued early observations with QUaD. The jitter
introduced an elevation-correlated signal into the time-ordered data that was par­
ticularly noticeable at 150 GHz. Figure 5.3 shows the effect on a single scan across
RCW38.
This problem was determined to result from the change in the telescope balance
point that occurred with the installation of the QUaD receiver. For angles near the
balance point, the servo system tended to oscillate around this unstable equilibrium.
The problem was corrected by shifting the balance point to an elevation below the
ground shield with the addition of several hundred pounds of counter weight.
The raw raster maps can benefit from several simple filters. Removing a bestfit polynomial from every azimuth row acts as a high-pass filter, reducing the slow
drifts that result in the visible “striping” seen in the raw maps. Of course, any
known source must be masked out during the polynomial fit. For observations of
a compact source such as RCW38, feed differencing provides an extremely effective
filter since much of the atmospheric signal is common to all feeds. This technique
also removes astronomical signals on scales larger than the separation between the
two feeds and would therefore not be appropriate for CMB observations. Figure 5.4
shows example maps of RCW38 at both frequencies and the results of these filters.
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5.1. OPTICAL PERFORMANCE
5.1.2
137
Feed Offsets
Accurate knowledge of the feed offsets from the array center is needed in order to
combine maps of the same region made from different feeds in the focal plane. These
offsets can be determined from a large enough raster over a compact source such as
RCW38. If the dimensions of the raster are larger than the telescope field of view,
then each feed independently maps the source. The position of the source in the
map corresponds to the feed offset from the array center. Figure 5.6 shows maps for
all 31 feeds from the April 10th RCW38 raster.
Figure 5.5 compares the measured feed offsets to their nominal positions. The
agreement for the central pixels is good, with some distortion visible in the outer
rings.
QUAD Feed Postions
1 . o i—
i 1—
1------ 1------ 1------ 1------ 1------ 1------ 1------ 1------ 1------ 1------ i------ ]------ 1------ 1------ 1------ r
1------ 11-----—
1—
i—
1—
1—
1—
1—
i—
1—
1—
1—
1—
i—
1—
1—
1—
1—
1—
$
0.5
+xx
-
*-fc
+X
+ x
X
+
I
-b<
-b<
0 .0 -
+x
-0.5-
x*
**
**
+x
+x
+
+xx
*
*
-1.0
i_____ i
i____ ,_I
-0.5
i______ i__i
x+
x-X-
>x-4 . » . x-
**
x+
44
**
-i*
x*-
XX
**
■+*
-1.0 1
Measured +
Nominal x
>t
*4
x+
x+
S
i______ I__,
0.0
i___,
i
I
,_____ ,_____i____ ,____
0.5
1.0
deg
Figure 5.5: QUaD feed positions measured from RCW38.
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138
CHAPTER 5. INSTRUMENT PERFORMANCE
1 5 0 -1 4
1 5 0 -1 5
Figure 5.6: QUaD raster maps of RCW38 from every feed in the focal plane.
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5.1. OPTICAL PERFORMANCE
139
Beam at the Sky
Angle (arcmin)
5
-1 0
-£
<
!
19
-1 0
CO
33
&
15
/f
H v
\j w
/
-30
7/ \ 1(f x\ \\
-40
/
-50
AH k /-V
-60
r
\f\i
lA J \C\
-70
V
V
-80 m
0
92 GHz co-polar
150 GHz co-polar
-2 0
V
-
92 GHz cross-polar
150 Ghfc cross-polar
Figure 5.7: Predicted beam pattern on the sky for the on-axis pixel. Figure courtesy
of the QUaD optics team, NUI Maynooth.
5.1.3
Beam s
Collaborators at NUI Maynooth (see Table 1.3) performed extensive modelling of
the QUaD optical system using Gaussian beam analysis and commercial software
packages (Zemax physical optics module, GLAD, and GRASP8). These calculations
resulted in the predicted beam patterns shown in Figure 5.7. The full width at
half maximum (FWHM) for the two frequencies are expected to be 4.2' at 150 GHz
and 6.3' at 100 GHz. For both frequencies, the peak of the cross-polar response is
below -30 dB relative to the co-polar beam. The modelling process and results are
described in more detail in Cahill et al. [2004] and Cahill [2005].
Measurements of the primary mirror surface indicate an RMS deviation of 0.12 mm
from the ideal parabolic figure. Most of this deviation is due to a “potato-chip” warp
which is well-modelled by a Zernike polynomial fit. This warp results in astigmatism
wherein the mirror has two different focal lengths along orthogonal axes aligned with
the warp. If the system is out of focus, then this effect results in an elliptical beam
pattern. Proper focusing results in circular beams; however, this is found not to
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CHAPTER 5. INSTRUMENT PERFORMANCE
140
Table 5.1: Beam parameters as measured from RCW38 raster maps for the three
groups of detectors: The inner group of 150 GHz pixels, the outer ring of 150 GHz
pixels, and the ring of 100 GHz pixels. The initial focus data is an average of four
data sets taken between April and June 2005. The post refocus data results from
two data sets taken during July 2005. The full width at half maximum (FWHM) is
defined as the average of the FWHMs along the beam’s major and minor axes. The
ellipticity is given by the ratio of the major to minor widths. A/B matching refers
to the RMS deviation of these parameters between the beams of the two orthogonal
detectors in a PSB pair. Coefficients from 2D-Gaussian fits to each channel for each
RCW38 raster run were provided by C. Pryke and were used to generate the average
results in this table.
Beam parameters
Nominal
Initial
focus
July 9
refocus
A/B Matching
Group
FWHM
Ellipticity
FWHM
Ellipticity
150
100
Inner 150
Outer 150
100
Inner 150
Outer 150
100
4.2
6.3
6.2
5.2
6.0
4.7
4.4
5.6
1.0
1.0
1.8
1.5
1.3
1.3
1.1
1.1
0%
0%
1%
1%
1%
1%
2%
2%
0%
0%
2%
3%
2%
2%
2%
3%
be possible over the entire field of view. In particular, the inner and outer rings of
150 GHz detectors cannot be simultaneously focused to be circular. Modelling in­
dicates that this effect does not substantially degrade the polarization performance
of the telescope - even for the most off-axis pixels, the maximal co-polar response is
predicted to remain 25 dB down. The distance between the primary and secondary
was found to be the critical parameter for setting the focus due to the fast ( F /# =
0.5) beam off the primary. The system is much less sensitive to the receiver position
due to the slower beam off the secondary (F /# = 2).
Raster maps of RCW38, like those displayed in Figure 5.4, were used to charac­
terize the QUaD beams. Initial focusing and alignment was performed during the
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5.1. OPTICAL PERFORMANCE
141
summer season (see Appendix B.3). Table 5.1 summarizes the measured beam pa­
rameters. The 150 GHz beams, especially for the inner group, were larger than the
nominal value and showed high ellipticities. The results agreed with the predictions
from the optics modelling and indicated that the secondary was several mm out of
position. Note that despite the defocus, matching of beam parameters between the
two halves of a PSB pair is within a few percent.
The defocus was discovered during initial engineering observations at the start of
the 2005 winter season; however, attempting to refocus at this point was deemed too
risky. The secondary mirror had been designed to have a motorized focusing system
but for several reasons, including mechanical and electrical failures, the system was
not installed. Instead, the secondary mirror is mounted using an improvised system
that was developed on site at the South Pole. Three 1/2” threaded rods hold the
mirror in place on the top cap of the foam cone. Nuts are used to set the secondary
position, which determines the focus. Adjusting these nuts requires reaching in
through the top of the foam cone while standing outside on top of a ladder. The
nuts were custom made from large, rectangular blocks of aluminum which were
designed for gloved hands; nevertheless adjustment is not a simple task.
By early July, QUaD had completed a first pass over the CMB field (Chapter 6).
At this point it was felt that refocusing was necessary to confirm the optics model
in order to aid with planning upgrades for the next observing season. On July 9th,
the winter-over crew adjusted the secondary mirror position with excellent results.
Based on modelling from the optics team, a position was chosen that optimized the
focus for the outer ring of 150 GHz detectors due to the large number of pixels in
this group.
The bottom three rows in Table 5.1 summarizes the results of the refocus. The
beams are smaller and the ellipticity is reduced for all groups of detectors with the
outer group of 150s performing nearly within the initial specification. The 100 GHz
beams are seen to be ~ 10% smaller than the nominal value. Extensive investiga­
tion into this effect has not yet been made, but it likely results from these pixels
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CHAPTER 5. INSTRUMENT PERFORMANCE
142
illuminating the primary more than was expected (edge taper > —20 dB) which will
result in slightly more spillover and higher sidelobes.
Provided the beam shape is known, the ellipticity does not present a problem for
the data analysis. The larger beam size at 150 GHz for the initial focus does degrade
our sensitivity to small angular scales for the first pass over the field, limiting us to
the range I < 2000. The reduced beam sizes after refocusing should enable future
passes over the field to reach our target I of ~ 2500.
Plans are in progress for an improved focusing system that will be installed during
the 2005/2006 summer season. The motorized system will allow the secondary mirror
position to be adjusted under computer control so that more frequent refocusing will
be practical. Commercial ultrasonic measuring systems are being investigated that
will allow real-time monitoring of the critical primary/secondary distance for any
changes that result from the large (50° C) changes in ambient temperature that
occur during the Polar winter.
5.1.4
Tim e Constants
Section 4.2.4 introduced bolometer time constants and described how they were
measured in the laboratory. As noted in that section, the laboratory loading and
bias setting were substantially different than during CMB observations. This section
describes how the time constants were remeasured under more typical observing
conditions.
The method involved scanning the telescope forward and backward (increasing
/ decreasing azimuth) across RCW38 and looking at the delay introduced by the
receiver transfer function (eq. 4.27). Figure 5.8 (top) plots the resulting data against
the azimuth offset, showing the separation in the apparent source azimuth position as
measured from the forward and backward going half-scans. A fit then determines the
value of the bolometer time constant necessary to produce the observed separation.
The bottom plot compares the results with the laboratory measurements.
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5.1. OPTICAL PERFORMANCE
0.3
0.4
143
0.5
0.6
0.7
0.8
az offset (deg)
150
100
w
E
0
10
30
20
40
50
D e tec to r
Figure 5.8: (top) Measuring time constants with RCW38. Forward and backward
scans across the source are plotted versus the azimuth offset. The source appears in a
slightly different position depending on the scan direction due to the delay associated
with the receiver transfer function including the bolometer time constant. Figure
courtesy of C. Pryke. (bottom ) Time constants as measured from scanning across
RCW38 compared with those measured in the lab. The lab values are smaller due
to the higher loading and bias during these measurements (Section 4.2.4). RCW38
time constant values provided by C. Pryke.
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CHAPTER 5. INSTRUMENT PERFORMANCE
144
Sky d ip s d _ 2 0 0 5 0 4 0 4 _ 0 6 1 3 1 2
■ i
i i i i 11
i
i i
i
i i
11
i
11
i
i i
i
i
20
h-5
0
10
20
30
40
50
ZA (c le g )
Figure 5.9: QUaD skydip data from April 4, 2005. The symbols are data points
and the line is a fit to the model described in the text (eq. 5.5). For this data, the
median of the fits to the seven bolometers yields r Tatm = 10.4 ±0.5 K and the tipper
gives Tatm as 222 K making r = 0.047. The different y-intercepts correspond to the
difference in absolute loading reported by the detectors.
5.2
C alib ration
5.2.1
A tm ospheric Transmission
The optical efficiency of the telescope system is reduced by atmospheric absorption.
Similarly, atmospheric emission causes excess loading that warms the bolometers
and leads to excess noise. Both of these affect the instrument sensitivity and thus
must be quantified. For QUaD this is done with a procedure known as a skydip,
wherein the atmospheric emission is measured at multiple zenith angles. Changing
weather conditions, necessitate frequent monitoring.
The quantity of interest is the band-averaged atmospheric transmission as a func­
tion of zenith angle. Using a simple model, we can parameterize the zenith angle
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5.2. CALIBRATION
145
0 .0 8
QUAD05
ACBAR01
0 .0 6
N
I
o
o
in
Q
+ +,
0 .0 4
<
Z>
O
+ +'
0.02
0.00
3
2
4
5
Tqu (3 5 0 Micron Tipper)
Figure 5.10: QUaD skydip data plotted against data from the 350 micron tipper.
The line gives the best-fit linear relation between the two. The red line gives the
relation derived in Runyan [2002] for ACBAR 2001 skydip data with their 150 GHz
band.
dependence as %,tm = e T/ cos6 where r, known as the optical depth, depends on the
frequency band of observation. The atmospheric emissivity, e, is given by
^
1
=
T itm
l - e ~ T/cos6.
(5.1)
As the telescope tips toward the horizon, atmospheric loading increases. Conversely,
loading from the CMB (assumed to be the dominant astrophysical source) decreases
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CHAPTER 5. INSTRUMENT PERFORMANCE
146
0 . 1Q
°
II "
1I '
AS/TRO 3 5 0 Micron Tipper Data
"
I
I r ' ' ■ | " ' ' i T T T T T-rT-rT m
- | - n -n
h -M i- i-T | i i i | i i i | . i i | i i i | i i i | i i ! | i I i | I I , , i i i , i i i , i i , ,
0 .0 4
0 . 0 0
111
■ ■ i ■ i * 1 1 ■ ■ i ■ ■ ■ i ■ ■ ■ 1 1 ■ ■ 1 1 > ■ i ■ ■ * i ■ ■ 1 1 < ■ ■ i ■ < » i ■ ■ ■ i ■ » 1 1 ■ 1 1 1 »■ ■ i ■ ■ » i ■ ■ ■ 1 1 ■ ■ 1 1 1 1 1 1 1 1 1
■ 1 1 1 1 1 1 1
16 21 26 31 0 5 10 15 20 25 3 0 05 10 15 20 25 30 0 4 09 14 19 2 4 29 0 4
_________I_______________ I________________ i_______________ i__
Apr
May
Jun
Jul
Figure 5.11: Atmospheric opacity data from the 350 micron tipper, scaled using the
linear relation in Figure 5.10. QUaD data is overplotted as crosses.
due to the decreased atmospheric transmission. This can be summarized as:
T lo a d ( 0 )
=
^ f ix e d
+e
+ (1 —e)Tcj^B
= r i i x e d + ( l - e - T/<” '’) T “ + e - " “ *',T S B
where
(5.2)
(5.3)
and T^mB are the Raleigh-Jeans temperatures of the atmosphere and the
CMB.1 The constant, Tfixed, includes all sources of loading that do not vary with
1Tatm is a weighted, line-of-sight averaged atmospheric temperature and is not in general the
same as the surface air temperature.
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5.2. CALIBRATION
147
zenith angle such as emission from the filters and the telescope. Simplification yields
2icd(0) = T<tad +
(T Z - TSb) •
(5-4)
The Raleigh-Jeans (RJ) temperature of a black body of thermodynamic temperature
T is defined as
2
J d u f ( u ) 2 ^ k T RJ AO = j dv f(v ) B(v, T) AO
where B (v,T ) is the Planck function and f{v) is the frequency band of the instru­
ment. Simplification yields
rpRj
=
f dv f{ y )B (v ,T )y -2
2k
J d u f(u )
C2
which is dependent on the shape of the receiver’s spectral band but not its overall
normalization. The RJ temperature is always less than the thermodynamic temper­
ature, but the difference becomes insignificant for kT
hu. At the QUaD bands,
the CMB is not in the RJ region. For the QUaD average spectral bands (shown in
Figure 2.5), the RJ temperatures of the CMB are 1.07 K and 0.562 K at 100 and
150 GHz.
Simplifications to eq. 5.4 can be used in practice. First, the atmospheric tem­
perature is sufficiently large (> 200 K) that its physical temperature is the same
as its RJ temperature. Second, the signal from the CMB can be neglected since
it is much smaller than that from the receiver, the telescope, and the atmosphere.
Finally, r / cos 6* -C 1 so eq. 5.1 may be approximated2 as e m t / cos 8. Making these
approximations in eq. 5.2, the loading becomes
T,oad(0) « Tfixed +
(5.5)
CO S0
2A t th e South Pole, T1 5 0 is alw ays less th an ~ 0.1 and Q U aD is restricted to zen ith angles less
th an 45°.
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CHAPTER 5. INSTRUMENT PERFORMANCE
148
Thus with QUaD skydip data alone, it is not possible to separately fit for r and T g . t m Fortunately, we have access to data from the AST/RO 350 micron tipper (located
on an adjacent building) which measures Tatm (and r at 350 microns) several times
per hour.3
During routine observing, QUaD performs one skydip per day. Approximately
30 seconds of integration is performed at each of nine zenith angle steps. For sim­
plicity, the data are taken in DC biased mode. The raw bolometer voltages are
converted to power and then to loading temperature using the procedure outlined
in Section 4.1.2. A load curve, taken immediately following the skydip, is used to fit
for Go and /?. Figure 5.9 shows the results of a typical run for the bolometers with
dark characterization listed in Table 4.1.
The offset present on all the bolometers in Fig 5.9 corresponds to the constant
term in eq. 5.5 and includes contributions from the cryostat internal loading, emis­
sion from the telescope, and the atmospheric loading at zenith. The value is very
sensitive to the focal plane temperature and the parameters Ro and A, resulting in
the large scatter seen in the plot.
In order to have more frequent updates on the atmospheric transmission, without
spending valuable observing time on skydips, a correlation is performed between the
150 GHz r obtained by QUaD and the 350 micron r from the tipper. Figure 5.10
shows the correlation between the two data sets. The best fit line gives the relation
Uso = 0 .0 1 3 4 + 0 .0 1 4 8 r35oMm.
(5-6)
Figure 5.11 shows the tipper data, scaled to 150 GHz using the linear relation, with
the QUaD skydip data overplotted.
3The key to measuring r and Tatm with a skydip is to operate at a shorter wavelength or go to
extremely low elevations such that rT atm/c o s 9 ~ 1 and fitting with eq. 5.4.
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5.2. CALIBRATION
5.2.2
149
R outine Gain Calibration
Bolometric receivers need to be frequently recalibrated since small changes in base­
plate temperature and optical loading (due to changing weather or elevation angle)
cause drifts in the overall gain (via changing bolometer responsivity). The following
describes three methods QUaD uses to monitor the relative system gain.
RCW 38 Row Cals
As discussed in Section 5.1, the Galactic HII region RCW38 is the brightest and
best characterized source available to QUaD. Raster mapping RCW38 with every
feed requires the better part of a day, so frequent recalibration with this technique
would be impractical.
An alternative technique, known as a “row cal” was developed in which each of
the seven rows of the focal plane array are scanned in turn across the source. The
height of the blips from the source provide a gain calibration for each feed. We
currently perform four row cals per day. Each of these is preceded by an observation
known as a “pointing cross” in which the central pixel is scanned in azimuth and in
elevation over the source. This allows any pointing offset between the instrument
and telescope axes to be quantified.
Calibration Source
Design Overview
The QUaD calibration source sits inside the foam cone, just above the secondary
mirror. Figure 5.12 shows a photo of the mechanism and a schematic of its location
and key parts. When the cal source is not in use, the central part of the beam from
each feed passes through the hole in the secondary onto the sky. During a run of the
cal source, a flip mirror behind the secondary hole rotates 45°, directing this part of
the beam through a polarizing grid onto a blackbody source at ambient temperature.
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150
CHAPTER 5. INSTRUMENT PERFORMANCE
source
Rotating grid
>.Flip mirror
Secondary
IRdata
link
Cryostat
snout
(NOT TO SCALE)
f
Figure 5.12: The QUaD calibration source, (top) Photograph showing the major
components, (bottom ) Cartoon placing the calibration source in context. Note, in
order to see the cal source clearly, the primary mirror is shown much smaller and
closer to the secondary than it really is. See Figure 2.1 for an accurate drawing of
the optics.
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5.2. CALIBRATION
151
QUAD Col S o u rc e T est 2 0 0 5 0 3 1 7 c h 3 4 ( c e n tro l pixel)
Mirror u p -
Loading
/
from
mirror
Mirror down
frame
Grid rotating
Mirror frame passing
/th r o u g h beam20
150-16C
Low Gain Mode
1 5 0 -1 6 C
0.5
High Gain Mode
0.0
4.580
4.575
-
0.5
-
1.0
-
1.5
-
2.0
-
2.5
■
4.570
4.585
4.560
4.555
0
200
400
600
s e c x 100
600
1000
0
sec x 100
1000
1500
Figure 5.13: (top left) The reduced cal source flip mirror, (top right) A single run
of the cal source as recorded by the central pixel, (bottom left) Data (black) and
sine wave fit (red) measured in low gain mode, (bottom right) Another run, this time
recorded in high-gain mode.
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CHAPTER 5. INSTRUMENT PERFORMANCE
152
Rotating the polarizing grid produces a modulated signal.4
When the cal source was first operated, the modulated signal was much larger
than expected, and it caused the ADC to saturate when the electronics were operated
in the usual observing mode (the high-gain setting). Additionally, substantial excess
loading resulted when the mirror was flipped down, changing the operating point
of the bolometers and making any calibration results less meaningful. Our solution
was to mill away most of the flip mirror, leaving only a small reflecting disk suspend
in the center with nylon string. Figure 5.13 (top) shows the second version of the
flip mirror and the resulting signal from a cal source run.
The top part of the flip mirror frame still covers the secondary hole resulting in
a small change in the loading level when the mirror is down; however, the problem
is greatly reduced with the new design. At this point, it was felt the amplitude of
the modulated signal could be increased so we doubled the size of the reflecting disk.
Figure 5.13 (bottom) shows the high signal-to-noise data that resulted from the final
configuration.
Origin o f the M odulated Signal
Consideration of how the cal source modulated signal arises reveals a weakness in
the optical design. Minima in the cal signal result when the polarizing grid is anti­
aligned with the PSB axis of sensitivity - the grid appears transparent and the PSB
is loaded by the black body source resulting in a lower voltage. The optical path
here is well-understood and the temperature of the black body source is monitored
with a built in thermometer. Maxima occur when the grid is aligned with the PSB
axis and thus reflective. Here the optical path is not well understood - some of the
reflected power will again pass through the primary hole and fall on the cryostat
window or the primary mirror, the rest will be scattered or absorbed inside the cal
source itself. This is far from ideal.
4The calibration source was designed and manufactured by the QUaD collaborators at the
University of Cardiff. The controlling electronics were rebuilt at the Pole when the original system
was destroyed by static electricity.
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5.2. CALIBRATION
153
El Nod -150-03
A/B Correlation
2.0
150-03A (Volts)
150-03B (Volts)
E levation offset (deg)
0.8
Signal
0.6
S> 0.4
0.5
0.2
G ain A/B = 0 .74
0.0
0
10
20
30
sec
40
50
60
0.0
0.0
0.2
0 .4
0.6
Signal B (Volts)
0.8
1.0
Figure 5.14: (left) The signals from an elevation nod for a single feed, (right) The
signals are highly correlated. The slope of the best-fit line gives the ratio of the gains
from the two detectors.
E levation N ods
We developed a third method of relative calibration known as an elevation (or el)
nod. Here, the telescope performs a miniature sky dip, offsetting in elevation by
1.5° from the initial position. The resulting change in air mass generates a signal of
order a Volt in a typical detector. Figure 5.14 (left) shows the signal from a sample
el nod for the two halves of a PSB pair. The right half of the figure shows a simple,
but very useful, way to analyze the data. The two signals are plotted against each
other and the slope of the best-fit line gives the ratio of the gains. This quantity is
known as the A/B ratio, where A and B refer to the two detectors in the pair. This
method is very reliable since the two detectors are looking through the same feed at
the same column of (unpolarized) atmosphere. El nods can also be used to find the
relative gain from feed to feed, although a correction must be applied to account for
the different air mass seen from different rows.
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CHAPTER 5. INSTRUMENT PERFORMANCE
154
QUAD Relative Calibration
1.6
150-04
150-03
150-02
1.4
row cal
el nod
cal src
1.2
O)
1.0
0.8
0.6
16 MAY 2005 17:45:40
R o w cals:4 El Nods: 132 C alsrcs:1 3 2
0.4
0
5
10
15
20
Hours
Figure 5.15: The A/B gain ratio for three feeds measured using the three different
techniques discussed in this section: RCW38 row calibrations, elevation nods, the
calibration source.
Sum m ary
A comparison and summary of the three calibration methods discussed so far is in
order. Figure 5.15 shows the A/B gain ratio derived from the three methods over
the course of a single observing day.
R C W 38 row cals These provide an absolute calibration for each detector, but the
measurement is slow.
Cal source The cal source gives extremely stable results which provides great reas­
surance in the gain stability of QUaD; however, the relative gain measurements
it gives do not agree with those derived from the other two methods. This is
not surprising given its poorly understood optical path.
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5.2. CALIBRATION
155
dB/dT at T = TCMB
0.8
0.6
0.4
0.2
dB/dT
100 GHz band
150 GHz band
0.0
0
100
200
300
400
Freq (GHz)
Figure 5.16: The factor d B /d T evaluated at T = Tcmb enters into the calibration
via eq. 5.9. It is approximately twice as large for the 150 GHz channels as it
is for the 100 GHz channels. This combined with larger bandwidth and higher
optical efficiency makes the 150 GHz channels more responsive to CMB temperature
fluctuations in terms of V /fjK despite having only ~ 1/2 the throughput.
E levation nods The el nod procedure is simple, quick, and the resulting signals
are well understood. Thus, el nods provide the best method of matching the
gains between detectors on a regular basis.
In summary, the provisional strategy is to use the row cals to normalize the responsivity several times per day and el nods to provide a relative calibration between
detectors on shorter time scales.
5.2.3
A bsolute Calibration
In order to compare our CMB maps with theoretical predictions and results from
other experiments, we need to convert the signals we measure from Volts into a
standard flux unit.
The preferred unit for CMB experiments is
A T c m b in
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/HC
CHAPTER 5. INSTRUMENT PERFORMANCE
156
This gives the temperature fluctuation about T0 = 2.728K necessary to produce the
observed flux. Performing this conversion (from Volts to pK) is called calibration.
The absolute calibration of millimeter-wave experiments is never easy, but the sit­
uation is made more difficult for QUaD. The high ground shield and Polar location
prevent us from observing planets, which are the best-characterized astronomical
calibration sources at these wavelengths. This section presents calibrations obtained
from three different methods. The first estimates the calibration factor from the
laboratory measurements made in Chapter 4. The second method compares QUaD
measurements of RCW38’s flux with published results for this source. Finally, cali­
bration results obtained by comparing preliminary QUaD CMB maps with those of
previous experiments are presented.
Estim ates from Laboratory Characterization
Raw bolometer signals, in units of Voltage as recorded by the ADC, can be converted
into CMB temperature units (Kelvin) as
(5.7)
where the second equality defines the conversion constant, sK/v, from Volts to Kelvin.
The function Pb gives the optical power from a beam-filling astronomical blackbody
source such as the CMB:
(5.8)
where %tm is the atmospheric transmission (Section 5.2.1), rjr is the optical efficiency
of the telescope optics, f n{v) is the absolute spectral bandpass of the receiver defined
in eq. 4.19, A tt — A2 is the throughput, and B(T, v) is the Planck spectrum.
For the QUaD bands, the derivative dP s/dT evaluated at TCMB is given with good
accuracy (a few percent) by evaluating d B /d T at the band center and approximating
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5.2. CALIBRATION
157
the integral as
dPs
dT
1„_
2
.2 .
u
dB
dT
(5.9)
T=TCm b , 1/= vq
where r) is the total optical efficiency of the system given by the product of the
receiver efficiency and the telescope efficiency:
V
= Vr x Vt-
(5.10)
The telescope efficiency is estimated to be ~ 0.82 including loss from the foam cone,
the primary mirror, and most significantly the blockage caused by the secondary
mirror (Table 5.2). This results in an average total efficiency of ~ 0.26 for the
150 GHz detectors, using the average receiver efficiency listed in Table 4.3.
For the QUaD bands, using the average value of the properties at each frequency,
this results in the calibration estimates of
100 GHz: 5.1 - 1 0 ^ x
volt
150 GHz: « ■ U - 4 x
volt
( £ “ ) f 0'82' 026) f ™ ™ ! ) f 3.6 x 10* V/WN
\ % tm )
(m
\
T jrV R
J \
f°-82- ° 32)
VTatmy \
rfrVR
J \
A i/
J \
Nv
J\
S
Dc
f31Xf
)
V/ W) .
S dc
)
Estim ates from RCW 38
The estimates in the previous section rely on using system parameters that are
measured in the laboratory. These parameters are difficult to measure and subject to
error. This section uses the previously measured flux of RCW38 in order to estimate
the calibration factor for QUaD with minimal reliance on laboratory quantities.
ACBAR measured the flux density from RCW38 within an 8’ radius with their
150 GHz band [Runyan, 2002]. Averaging their 2000 and 2001 values, Jrcw 38 =
145 Jy with a 10% uncertainty. The uncertainty is dominated by systematics includ­
ing the errors from their planetary calibration, voltage integration, and responsivity
scaling. Coble et al. [2003] found the flux at 90 GHz from RCW38 to be ~ 10%
larger than at 150 GHz, allowing a calibration of the QUaD 100 GHz channels as
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CHAPTER 5. INSTRUMENT PERFORMANCE
158
well.
The integrated flux in an 8’ radius was computed for QUaD raw RCW38 maps
yielding a value in Volts arcmin2 (VRCW38) f°r each channel. This allows a conversion
into units of temperature fluctuations about the mean CMB temperature as:
7
v 1
J RCW 38 x i u
SK/V= I—
V,RCW 38
^ C M B , VQ)
(— ^ - 2 )
Varcmin /
(5.11)
where B (v,T ) is the Planck spectrum and the derivative is evaluated at the measured
band center frequency (Figure 5.16).
In terms of average QUaD values, this yields calibrations of:
TT
100 GHz:
__
uK
( 14.3 Volts arcmin2\ /0.94\
6.0 x 105
x ------V o lt
V
^R C W 38
J VTatm7
150 GHz:
4.6 x 105 ^
x (
volt
V
.
5.12
Volte arcmin^ /094N
^R C W 38
Vratm;
J
Cross Calibration w ith B2K
The final QUaD calibration will come from cross correlating our CMB temperature
measurements with those of B2K for the same region of sky. Chapter 6 discusses
our field selection and overlap with the B2K experiment in more detail, and Figure
6.5 shows our respective maps. A preliminary cross-correlation of the initial maps
yields calibration values that are consistent with the two methods presented above5:
100 GHz:
5.0x 105
150 GHz:
4.3x 105
volt
volt
5Thanks to J. Kovac for providing these calibration results.
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(5.14)
(5.15)
5.3. SEN SITIVITY AND NOISE
159
These values are used to calibrate all of the maps shown in Chapter 6.
5.3
S en sitiv ity and N o ise
5.3.1
Optical Loading
QUaD performs several load curves each day and these can be used to investigate
the total loading as a function of time. From each load curve, eq. 4.12 provides an
estimate of the total optical power falling on the bolometer, just as in the sky dip
analysis. Again, this can only be performed for the seven detectors with known Ro
and A parameters listed in Table 4.1. Figure 5.18 shows the results for load curves
spanning several months.
The dashed blue line in the top plot is the loading predicted by eq. 5.5 based on
atmospheric data from the AST/RO 350 micron tipper and the telescope elevation
angle. The agreement between the black and blue lines over time indicates that the
atmosphere is causing the variations in the loading. This confirms that there is not,
for example, a steady increase of loading that would indicate an accumulation of ice
on the cryostat window or some similar problem.6 Figure 5.17 (bottom, red curve)
shows the nearly-constant difference between total and atmospheric loading.
This analysis can also be used to determine the loading caused by the telescope.
This includes contributions from the foam cone, the primary mirror, and the sec­
ondary mirror. This is possible because in an early test run in December 2004 we
took several load curves and sky dips without the telescope optics. Figure 5.17 shows
the loading from the receiver measured in this configuration (green). This is the total
loading minus the approximately 13.5 K of loading from the atmosphere on that day
at zenith. Comparison with the mean receiver loading from data with the full opti­
cal system (red) indicates approximately 10 K of excess loading from the cone, the
primary, and the secondary. Table 5.2 gives an estimated component-by-component
breakdown accounting for the observed total loading.
6The receiver window cannot be accessed or viewed once the receiver is installed in the telescope.
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CHAPTER 5. INSTRUMENT PERFORMANCE
160
Table 5.2: QUaD estimated loading component by component breakdown. For the
receiver section of the table, the optical component drawing in Figure 2.4 may be
useful.
C o m p o n en t
C om p on en t
Trans.
A tm o sp h ere
T elesco p e
Foam cone
Primary Mirror
Secondary loss
Telescope total
L oading
tem p .
(K )
12.44
In cident
pow er
(pW )
T otal
trans.
0.943
P h ysical
tem p .
(K )
220.00
7.31
0.290
0.975
0.990
0.150
220.00
220.00
32.44
5.50
2.20
4.87
3.23
1.29
2.86
0.297
0.300
0.353
0.96
0.39
1.01
2.36
R eceiv er
Window
Reflection loss
IR filter
0.995
0.010
0.995
220.00
160.00
160.00
1.10
0.08
0.80
0.65
0.05
0.47
0.355
0.359
0.361
0.23
0.02
0.17
IR filter
12 cm edge
IR filter
0.995
0.995
0.995
160.00
160.00
160.00
0.80
0.80
0.80
0.47
0.47
0.47
0.362
0.364
0.366
0.17
0.17
0.17
9cm edge
8cm edge
Lens 1
Reflection loss
Lens 2
Reflection loss
Waveplate
Spillover
0.995
0.995
0.990
0.010
0.990
0.010
1.000
0.030
20.00
20.00
10.00
10.00
10.00
10.00
7.00
7.00
0.10
0.10
0.07
0.07
0.07
0.07
0.00
0.12
0.06
0.06
0.04
0.04
0.04
0.04
0.00
0.07
0.368
0.370
0.377
0.377
0.385
0.385
0.385
0.385
0.02
0.02
0.02
0.02
0.02
0.02
0.00
0.03
7cm edge
Bolo. assembly
Receiver total
0.995
0.387
0.50
0.25
0.00
0.15
0.00
0.09
0.387
1.000
0.00
0.09
1.15
Toted
P ow er at
d ete cto r
(PW )
2.12
5.63
It should again be emphasized that measurements of the absolute loading are
extremely difficult as discussed in Section 4.1.2. All the results in this section may
be in error by a constant loading term of order 0.5 pW reflecting the scatter in the
loading values reported by the seven characterized light detectors. However, loading
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5.3. SEN SITIVITY AND NOISE
161
QUAD Loading Comparison
Total (load curves)
Atmosphere (sky dips)
Other (difference)
Receiver only
o>
17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21
l
Apr
May
Jun
Figure 5.17: Receiver loading (red) determined by subtracting the total loading
(black, measured with QUaD load curves) from the atmospheric loading (blue, mea­
sured by QUaD sky dips). The flatness of the red curve confirms that variable
loading from snow or ice accumulation is not a large factor. The same procedure
was applied to data from Dec 19, 2004, which was taken without the foam cone,
the primary, and the secondary (green line). The measured difference (~ 10 K) is
attributed to loading from the telescope optics.
differences, used to determine atmospheric loading from skydips, are robust to this
offset.
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CHAPTER 5. INSTRUMENT PERFORMANCE
162
QUAD Loading
10
9
8
CD
7
6
5
17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21
5
0.08
c 4
02
1
o 3
in
co
0.07
0 .0 6 °
0.05 .co
2
0.04
1
0.03
17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21
® 60
'•S 40
17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21
Apr
May
Jun
Figure 5.18: (top) The measured loading from approximately 300 load curves, ob­
tained from eq. 4.12 averaged for the seven detectors in Table 4.1. The dashed
blue line shows the loading that would be predicted from the model in eq. 5.5 using
the r and elevation information shown below. The atmospheric temperature data
(not shown) is also from the 350 micron tipper and it varies between approximately
200 and 250 K. (m iddle) Atmospheric opacity data from the AST/RO 350 micron
tipper scaled to 150 GHz using eq. 5.6. (bottom ) The telescope elevation during
the load curve measurements. When CMB observations began in May, we started
taking load curves at the elevation of our observing field rather than returning to
zenith. For the astute observer, the 350 micron tipper was not functioning for a few
days around April 12.
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5.3. SEN SITIVITY AND NOISE
163
NEP PSB 1 5 0 - 1 2 C
100
Total —
Johnson —
Phonon —
Amp —
Photon —
Date: 31 MAY 2 005 2:2 6:60
Elevation:
48.6 deg
Azimuth: -1 5 4 . 1 deg
T fridge:
Loading:
255.0 mK
5.3 pW
I
o
X
I
N
X
CL
L
U
X
0
1
2
3
4
5
Bias (nA)
Figure 5.19: Components of the noise equivalent power (NEP) versus bias current
for a typical QUaD detector.
5.3.2
N oise Equivalent Power
N oise Sources
The sensitivity of bolometric detectors is limited by several different sources of noise.
These include noise from the device itself (Johnson and phonon), from the readout
electronics, and from the quantum nature of the optical signal (photon noise). These
noise sources cause the output voltage of the detector to fluctuate about a mean
value. The fluctuations can be characterized by an RMS value over some bandwidth
or more commonly by the power spectral density given in units of V Hz-1//2.
For millimeter and sub-millimeter detectors this voltage noise is often converted
into a noise equivalent power (NEP) by dividing by the responsivity. Physically,
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CHAPTER 5. INSTRUMENT PERFORMANCE
164
the NEP gives the incident optical power required to generate an output voltage
equal to the RMS noise voltage computed over some bandwidth. Note that a one
second integration is equivalent to 0.5 Hz of bandwidth so that the NEP expressed
in W Hz-1^2 is equal to the optical power that can be measured with a signal to
noise ratio of one in a two second integration.
Figure 5.19 shows the contributions to the NEP for a typical QUaD detector.
Like noise voltages, NEPs from uncorrelated sources add in quadrature resulting in
the total NEP curve shown in black. The various noise sources are reviewed below.
Jo h n so n Noise
The high-impedance thermistor in the bolometer produces John­
son noise just like any resistive device. An approximate form for this term, useful
for estimates, is given by the intuitive expression
NFP2
g2
~ ^ bT R
Johnson ~
where the responsivity is used to convert the voltage noise into an NEP. However,
the non-Ohmic behavior of the thermistor and the presence of the load resistors
complicates the situation. The full expression is given in Mather [1984] as
Johnson
P h o n o n Noise
) ( £ ) ■
Heat flowing out of the absorber through the thermal link is quan­
tized in the form of phonons giving rise to another source of noise. An approximate
form is given by
NEPphonon ~ 4kBT 2G.
Note that division by the responsivity is unnecessary since fluctuations in the power
flowing out of the absorber (~ G At) are equivalent to fluctuations in the incident
optical power (AQ). This simple equation, however, does not take into account the
variation in temperature from Tboio to Tbase along the absorber. The full expression
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5.3. SEN SITIVITY AND NOISE
165
is given as an integral in Mather [1984]
NEPph non = 4fcBG (r )r 2,flWJ tGr(^
J'L. [ G ( W ] it
dt
(5.17)
where T = Tboio- For our power law model, G(T) = G0(T/T0)& with the reference
temperate taken to be the baseplate temperature (T0 = Tbase), the integrals can be
explicitly evaluated as
NEP2
A m plifier Noise
= 4K T*G t f + 1 )f(T / T°)W - l ,
80
(2/3 + 3) [(T/T0)<>+i-l'
(5.18)
The readout electronics contribute to the total NEP as
NEPi P = ^
(5.19)
where Vn is the quadrature sum of the voltage noise arising from the JFETs and
the warm electronics as discussed in Section 3.2.2. The voltage noise, Vn, is approx­
imately white over the frequency range of interest (0.1 - 2.5 Hz) with a value of ~
9 nV Hz-1/2. This mean value of Vn is used for the amplifier noise term in the NEP
curves shown throughout this section.
P h o to n N oise
The incident optical radiation is quantized which leads to two
additional noise terms collectively known as photon noise. The first term is the
standard shot noise due to the random arrival times of the individual photons and
is given by
NEPPoisson = 2Qhu.
The second term, known as the Bose or “bunching” term, arises because photons
are Bosons. Appendix B of Runyan et al. [2003] gives a review of the origin of this
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CHAPTER 5. INSTRUMENT PERFORMANCE
166
term. The NEP associated with the bunching is given by
Ajpp 2 _ Q2
NEPb°“ “ A?
where Au is the optical bandwidth of the receiver. The quadrature sum gives the
total photon noise
NEPp2hoton = N E P|oisson + N E PL .An absolute measurement of the optical loading, Q, is needed to calculate the
photon noise contribution to the NEP which, as discussed in Section 4.1, is difficult.
For a given load curve, the scatter in the values of Q determined from eq. 4.12
(~20%) for the seven optical detectors listed in Table 4.1 differ far more than can
be explained by the scatter in their optical efficiencies (~5%). In order to compare
the detectors more fairly, the loading actually used to compute the photon noise in
the NEP curves in this thesis is the average from the seven estimates. Fortunately,
errors in the assumed loading do not change the shape of the NEP curve since the
photon noise term is independent of bolometer temperature (and thus bias value).
T otal N E P
The total NEP is the quadrature sum of the individual components:
NEPt2otal = NEPj2ohnson + NEPphonon + NEP amp + NEP photon.
(5.20)
The first two terms (Johnson and phonon) are collectively referred to as detector
noise. Advances in detector design and materials has greatly reduced their contri­
bution. Advances in technology can similarly reduce amplifier noise. The photon
noise term can be limited by choosing the best observing site available and reducing
emission from the filters, cryostat, and telescope. Of course, it can never be reduced
below the limit imposed by the photons from the source radiation itself.
The terms that depend on the detector responsivity (Johnson and amplifier)
increase drastically at low bias values as the responsivity drops to zero. For large
biases, the Johnson noise does not increase as fast as the amplifier noise since the
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5.3. SEN SITIVITY AND NOISE
167
QUAD T otal NEP
Date: 31 MAY 200 5 2:26:60
Elevation
Load
15 0 —12H
1 5 0 -1 2 C
1 5 0—21 H
1 50—21C
15 0 - 0 4 H
1 5 0 -0 4 C
1 5 0 -1 5 C
CL
LlJ
z
Bias (nA)
Figure 5.20: Total NEP for a subset of the QUaD detectors.
detector resistance drops. The phonon contribution rises slowly as the absorber
warms with increasing bias.
Figure 5.20 shows the predicted NEP curves for the seven optical detectors listed
in Table 4.1. The curves show the low-frequency limit of the NEP (cu = 0) versus the
applied bias current. The bias level changes the bolometer operating temperature
which effects all the noise sources except the photon term.
Bias Optimization
Determine the best setting of the bolometer bias current for observing provides a
useful application for the NEP curves derived in the previous subsection. For the
detectors in Figure 5.20, the minimum NEP is ~ 6 x 10-17 W Hz-1/2 and it occurs
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168
CHAPTER 5. INSTRUMENT PERFORMANCE
at a bias value of ~ 0.75 nA. In practice, however, a larger bias current is used.
A variety of factors argue in favor of biasing above the NEP minimum. The NEP
rises quickly below the minimum point owing to the rapidly decreasing detector re­
sponsivity. Under biasing any detector, even by a small amount, is thus undesirable.
This is evident in the total NEP curve shown in Figure 5.19.
The minimum point occurs at a different bias for each detector due to variations in
the parameters Ro, A, Go, and (3. However, the internal wiring of QUaD requires all
detectors of a given frequency (100 or 150 GHz) to have the same bias. Additionally,
the minimum point moves for a given detector with variations in loading caused by
changing weather or zenith angle.
Increasing the bias is desirable from the point of view of detector stability. Figure
5.22 (left) shows the average responsivity for all QUaD detectors at three different
elevations (on the same day, April 20, 2005) and thus three different loading levels.
The right plot shows the fractional change in responsivity in going from an elevation
of 55° to 45° which roughly corresponds to the QUaD field. Increasing bias keeps
the bolometer responsivity more stable.
For these reasons, QUaD biases at approximately 1.2 nA. Over-biasing decreases
the detector impedance resulting in additional advantages including reduced sensi­
tivity to microphonic and RF pickup. Increased electrical power also results in faster
detector response due to smaller effective time constants (Section 4.2.4). These ad­
vantages more than outweigh the ~ 5% decrease in raw sensitivity.
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5.3. SEN SITIVITY AND NOISE
169
Load C u r v e -
l c _ 2 0 0 5 0 5 1 8 _ 0 3 1 91 6
Figure 5.21: Responsivity for all channels under typical observing conditions. The
range of bias currents is indicated by the vertical red band (variations in detector
resistance lead to a range of bias currents for a fixed bias voltage).
QUAD Average Responsivity
5x10',8
I I I I r.TTT I ........................
4x 108
_
Responsivity Change
|! .................. I I . . . . . I
8 5 deg
5 5 deg
4 5 deg
3x10',8
£5 3
2 x 1 0 ,8
'
x 10 8
0
0
2
3
Bias (nA)
4
5
0
2
3
Bias (nA)
4
5
Figure 5.22: (left) Average responsivity versus bias at several zenith angles and
thus at different values of loading, (right) The change in responsivity with loading
versus bias current. Higher bias currents lead to responsivities that are more stable
to loading changes.
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CHAPTER 5. INSTRUMENT PERFORMANCE
170
Time Ordered Data (APR 26, HRN 2)
0.10
0.05
cn
=5
0.00
>
- 0 .0 5
-
0.10
0
100
200
300
Time (sec)
Figure 5.23: Typical 150 GHz time-ordered data for two bolometers in a PSB pair
(black and red traces) while observing a source-free region of sky. The green signal
is one half times the difference of the black and red. The individual channels clearly
show the effect of atmospheric noise. The mean has been removed from each signal
before plotting.
N E P from Voltage Noise
This section compares the NEP predicted from the various theoretical noise sources
with an estimate based on the measured voltage noise of the receiver. Figure 5.23
shows a segment of data (four half-scans) from both halves of a PSB pair taken
while scanning the telescope over a source-free region of sky (the CMB field). This
data was taken on a day with good weather conditions (ri50 ~ 0.035); nevertheless,
considerable atmospheric 1 / f noise contaminates the individual channels (red and
black). This noise arises because the atmosphere is not completely homogeneous
- pockets of more and less emissive air drift through the telescope beam causing a
slowly drifting output signal. The effect is worse at 150 GHz because the atmospheric
emission here is dominated by water vapor, which is poorly mixed. Atmospheric
1 / f noise, as opposed to photon noise, is not included in the NEP estimates of
the previous section. The low-frequency noise is highly correlated between the two
channels since atmospheric emission is unpolarized. Differencing, which is required
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5.3. SEN SITIVITY AND NOISE
171
to measure Q or U, results in a much more stable signal (green).
For each detector, division of the raw voltage, V(t), by the product of the elec­
tronics gain (G) and the bolometer responsivity (Sbc) converts to optical power
absorbed by the detector P (t)
p (t) =
(5.21)
Cj OdC
The responsivity of each detector is obtained from a load curve at the same elevation
and weather condition as the time stream data of interest. The DC responsivity is
used because the detectors are fast enough that S(u) is flat over the frequency range
of interest.
Labelling the two halves of a PSB pair as “a” and “b” we can consider the sum
and difference optical power:
Psnm = Pa + Pb
and
Pdiff = Pa - Pb.
(5.22)
The sum signal, Psum, gives the total optical power detected by the feed. This is
the same power that would be measured if a total power bolometer had been used
instead of a PSB pair.
Figure 5.24 shows the resulting power spectral density7 for the sum and difference
signals, labelled
N E P su m
and
N E P d iff.
N E P a2u m
=
In the absence of correlated noise, we expect
N E P d2, „
=
N E P 2 +
N E P d .
( 5 .2 3 )
This is seen in the power spectrum plot as the two curves reach the same noise
level above ~ 5 Hz. The difference signal exhibits a lower 1 / f knee than the sum
signal confirming that
average value of
P S B
N E P d iff
differencing successfully removes atmospheric noise. The
over our frequency range of interest (0.1 - 2.5 Hz) is ~
7The PSDs were computed by averaging the Fourier transforms of the constant velocity section
( ~ 30 seconds) of each of approximately 250 half-scans taken over three hours. Extracting only the
middle portion of each half-scan excludes the turn around period when the telescope is accelerating.
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CHAPTER 5. INSTRUMENT PERFORMANCE
172
NEP PSB 1 5 0 - 1 2
102
103
104
105
100
NEPsum
NEPdiff
EE s p e c t r u m
o
x
<N
IN
X
0.01
0.10
1.00
10.00
100.00
Hz
Figure 5.24: NEP for PSB 150-12 for roughly 3 hours worth of data from May
31, 2005. The telescope was scanning at 0.17 deg/sec on the sky. The (arbitrarily
normalized) E-mode CMB power spectrum is overlaid assuming this scanning speed.
The top x axis is in units of CMB multipole moment (£). The PSB difference power
spectrum is white above £ ~ 100 through the cut off at £ ~ 2500 corresponding
to the 150 GHz beam size of 4’. The spikes seen in the data around 10 Hz are
mostly microphonic resonances. The dashed black line shows the degradation in
NEP that would result from including the reduction in high-frequency gain from the
bolometer’s time constant. This curve assumes a value of 15 ms. Note that NEPsum
and NEPdifr are \/2 greater than the NEP of a single channel.
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5.3. SEN SITIVITY AND NOISE
173
NEP 150 GHz
NEP 100 GHz
4
N E P (10"17 W H z'10)
5
6
N E P (1 0 ‘17 W Hz"1/2)
Figure 5.25: Distribution of NEPs for both frequency bands (solid) and median value
(dashed).
9.2 x 10-17 W Hz-1^2. We interpret this level as the NEP of a feed or PSB pair
including detector noise, amplifier noise, and photon noise, but not atmospheric
1/ f . From eq. 5.23, we divide NEPdiff by \/2 to obtain an estimate of the NEP for
each individual detector in the PSB pair (assuming NEPa ~ NEPb), resulting in
NEPa ~ NEPb
NEP
7=— = 6.4 x 10"17 W Hz”1/2.
V2
(5.24)
Performing this exercise for all detectors results in a median NEP of ~ 4.4 and
5.6 x 10 ~17W Hz-1 / 2 at 100 and 150 GHz respectively. Figure 5.25 shows the distri­
bution of NEPs at the two frequencies. Note that the example detector from eq. 5.24
(plotted in Figure 5.24) happens to lie at the noisy end of the distribution. From the
histogram, the 100 GHz detectors are seen to have a lower average NEP which is due
to the decrease in loading resulting from their lower optical efficiency. This decrease
in loading both lowers the photon noise and increases the average responsivity (3.6
vs. 3.1 x 108 V/W for the 100 and 150 GHz channels).
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CHAPTER 5. INSTRUMENT PERFORMANCE
174
NET 100 GHz
200
400
500
NET 150 GHz
600
(fiK s e c 10)
200
300
400
500
600
N E T ,* ( n K s e c 1'2)
Figure 5.26: Distribution of NETpair for both frequency bands (solid) and average
value (dashed).
5.3.3
N E T and NEQ
The NEP is defined in terms of power absorbed by the detector. For quantifying
overall system performance, it is necessary to put this in terms of the source radia­
tion. CMB observers use the Noise Equivalent Temperature (NET) for sensitivity to
temperature anisotropies and the NEQ for polarization anisotropies, both in units
of fiK sec1/2. These metrics take into account parameters such as throughput, ef­
ficiency, and bandwidth, as well as detector noise level, in order to quantify the
sensitivity of the system to the signal of interest.
The NET can be found directly from the power spectrum of the bolometer voltage
in an analogous manner as the NEP was in the previous section. The detector
voltages are first converted into CMB temperature units (Section 5.2.3) and then
the power spectrum of the signal is found. The NET is usually quoted in units of
/iK sec1/2, not pK Hz-1/2. Conversion to the former requires division by \/2.
The NET of a single PSB gives the size of a CMB temperature fluctuation that
could be measured with a signal-to-noise ratio of one in a one second observation
using only this detector. With a PSB pair, the temperature is estimated by averaging
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5.3. SEN SITIVITY AND NOISE
175
the two detectors8 as Tp = (Ta + T i)/2, which for uncorrelated noise and identical
detectors, leads to
NET
NETk
NETpair = ~ j f =
(5-25)
This states the intuitive fact that a better temperature measurement can be obtained
with two detectors than with one. As an aside, it is worth noting that the NET
obtainable from a total-power bolometer will be lower than NETP since each half
of the PSB pair contributes Johnson and amplifier noise. Thus PSBs are not the
detectors of choice for total power measurements.
Applying this procedure to the working QUaD channels yields a median NETpair
of ~ 380 and 350 /xKsec1/2 at 100 and 150 GHz respectively.The average calibrations
in eqs.
5.14and 5.15 were used with the individualchannelgains
corrected using
elevation nod data. This is the same procedure used to calibrate the maps presented
in the next chapter. Figure 5.26 shows the distribution of NET at the two frequencies.
The 150 GHz pixels are slightly more sensitive (lower NET) than the 100 GHz pixels
due to their higher responsivity in terms of V///K.
The NET can be directly related to the NEP as
NETsingle =
(5.26)
v 2 {dPs/dT) |Tcmb
where the factor of \/2 in the denominator converts from units of Hz-1/2 to sec1/2.
The factor dP s/dT is given by eq. 5.9 and can be obtained from the calibration
factors listed in Section 5.2.3 as dP s/dT =
(sk/v • S
dc)_1-
Assuming identical
detectors, the NET of a pair can be found as
NETpair = —
(5. 27)
These forms are frequently used for estimating the sensitivity of a system during
8The detector signals axe averaged rather than summed because the calibration constants pre­
sented in Section 5.2.3 are normalized to convert the voltage from a s i n g l e PSB into properlycalibrated CMB temperature units. This convention is not universal.
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176
CHAPTER 5. INSTRUMENT PERFORMANCE
a design phase, with the NEP estimated by adding the expected noise sources (eq.
5.20).
The final metric, the NEQ, is applicable only to polarimeters. It gives the sen­
sitivity of a PSB pair to the Stokes parameters Q or U. Since a pair of PSBs is
required to measure Q or U, the NEQ is only defined for a pair of detectors. It
is calculated in the same way as the NETP except the sensitivity is degraded by a
factor of 1/(1 —e) to account for the loss of efficiency caused by cross polar leakage.
Using the values in Figure 4.19, this results in a 5% (8%) degradation relative to the
NET at 150 (100) GHz.
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Chapter 6
First Observations
QUaD began science observations in late May 2005 and completed a first pass over
the CMB field in early July. This chapter describes the observing strategy and
presents a first look at the initial data. The QUaD analysis pipeline is still in its
early stages. Nevertheless, the simple analysis presented in this chapter is sufficient
to confirm that QUaD is meeting its target sensitivity for polarization measurements.
6.1
Survey D escrip tio n
6.1.1
Field Selection
Our field location was constrained by a number of requirements:
• Low foregrounds - The field must be located in a region of low galactic emis­
sion. Emission from dust is predicted to be the dominant foreground at both
observing frequencies [Bowden et al., 2004]. Figure 6.1 shows the dust emission
over the Southern Hemisphere. Away from the Galactic Plane, there are large
regions that are relatively clean.
• Overlap with another experiment - In order to have a cross check on our results
and to help with calibration it is desirable for our field to at least partially over­
lap with a region covered by another CMB experiment. ACBAR, DASI, and
177
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178
CHAPTER 6. FIRST OBSERVATIONS
Figure 6.1: The QUaD fields (white) over a map of galactic dust emission (DIRBE /
IRAS composite infrared map extrapolated to 150 GHz [Schlegel et al., 1997]). The
small and large nested black regions are the B2K deep and wide fields respectively.
Figure courtesy of Ken Ganga.
B2K have all made high sensitivity maps of fields in the Southern Hemisphere,
the later two in both temperature and polarization.
• Point sources - As a check on the pointing and beams, it is desirable to have at
least one bright radio source in the field. WMAP has cataloged the brightest
point sources over the entire sky at our observing frequencies.
The field we chose (white boundary in Figure 6.1) satisfies, these requirements. It
is in an extremely low foreground region, partially overlaps with the B2K deep field,
and contains three bright radio point sources. The field has an area of approximately
50 square degrees which is smaller than optimal size for an E-mode survey [Bowden
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6.1. SURVEY DESCRIPTION
179
et al., 2004]. This reduction in size allows us to cover the field with a higher signal
to noise ratio, a prudent strategy for a new experiment with possibly unknown
systematic effects. The tradeoff, reduced sensitivity to the low I region, is relatively
minor.
6.1.2
Observing Strategy
During commissioning observations, it was noticed that some channels were con­
taminated with a low-level, ground-synchronous signal caused by variations in warm
emission from the ground structure picked up in the instrument sidelobes as the
telescope rotates. The pickup is largest when observing over the MAPO building
(the laboratory space attached to the telescope tower). Similar effects were seen with
DASI leading us to adopt a similar observing strategy. This strategy is designed to
allow redundancy for characterizing and removing this contamination.
The observing region is divided into two adjacent, equal-area patches known as
the lead and trail fields. Each field is 30 minutes wide in RA (7.5° of RA or ~ 5
real degrees on the sky). Observations are synched with the sky rotation so that
successive observations of the two fields occur over the exact same azimuth range.
This ensures that any stable ground contamination will show up equally in the two
fields. Observations are timed to start after the field has rotated passed the MAPO
building.
Because the fields are continuous, maximum flexibility for analysis is retained.
Early indications are that the low-frequency ground pickup can be adequately re­
moved by high-pass filtering the data. In this case, the two fields can be analyzed
as one large area. As a jackknife (consistency check), the difference field (formed
by subtracting the maps of the lead and trail fields) can be analyzed as well. The
downside to this strategy is significant additional complexity - observations must
begin approximately four minutes earlier each successive day. Failure to start at
precisely the appointed time ruins the day’s data.
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CHAPTER 6. FIRST OBSERVATIONS
180
The following list describes the daily observing program in detail. A short sum­
mary of the essential points follows.
• Each day begins with a skydip followed by a full calibration set consisting of a
pointing cross, a row cal, an el nod, a cal source observation, and a load curve.
• Observations begin when the sky has rotated so that the lead field just clears
the MAPO building.
• This field is observed for 30 minutes. After this time, the sky has rotated the
trail field into position and observation switches to this field for another 30
minutes. This process is repeated eight times (for eight hours).
— Each 30 minute field observation consists of 16 azimuth scans divided
among four different elevation steps separated by 0.02° (approximately
1/3 of a beam width at 150 GHz).
— After every elevation step, the DC offsets on the readout electronics are
reset and a partial cal set, consisting of an el nod and a cal source obser­
vation, is obtained.
• Observation is followed by a second full calibration set.
• Next, the telescope is rotated about the optical axis (termed the “deck” axis)
which changes the angles of the PSBs with respect to the sky.
• The entire observing process, including the beginning and ending cal sets, is
repeated at the new deck angle. This completes the day’s observations.
• The approximately six remaining hours are used for cryogen refills, cycling the
fridge, and any small maintenance tasks (for example, removing accumulated
snow from the foam cone and ground shield).
The azimuth scanning speed is 0.2°/sec. Each day covers an elevation range of
0.64°. Successive days work down the field, offsetting in elevation by 0.16°. The
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6.1. SURVEY DESCRIPTION
1 00 GHz - le a d /d k + 5 7
181
150 GHz - le a d /d k + 5 7
Figure 6.2: Hit maps giving integration time in seconds per 1.2 arcmin square pixel.
Maps are shown for the lead field at each frequency and each deck rotation angle.
Note the larger integration time at 150 GHz (due to more feeds) and the slightly
different coverage pattern at the two rotation angles (due to the asymmetric focal
plane resulting from non-functioning feeds). These hit maps result from 37 day’s
data taken between May 17 and July 8, 2005. Trail field hit maps are identical to
those shown above.
75% overlap allows for days to be missed due to bad weather or telescope problems
without creating dead areas in the map. For the first season, the same two deck
rotation angles (-3° and 57°) have been used for all observations. Observations at
additional angles will likely be made next season.
The following summarizes the key points of the observing strategy, highlighting
the notation necessary to understand the maps presented in the next section:
• The observing region is divided into two adjacent, equal-area fields, labelled
lead and trail. Each is approximately 5° wide on the sky.
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CHAPTER 6. FIRST OBSERVATIONS
182
• Each field is observed at two deck rotation angles, -3° and 57°.
Figure 6.2 shows the integration time per pixel achieved after the first complete pass
over the observing region.
6.2
F irst M aps
6.2.1
Tem perature Maps
Temperature maps of the observation region are formed by combining the smaller
maps that are produced each day (one per PSB, per field, per deck angle, per day).1
For this analysis, the daily individual-PSB maps were first combined into full-field
maps (one per PSB, per field, per deck angle). The relative gains of the PSBs were set
using data from the elevation nods. An overall calibration (Section 5.2.3) was then
applied to the field maps. The two field maps from each feed horn (corresponding
to orthogonal PSB detectors) were then combined into an equal number of sum and
difference maps.
The raw maps (especially the sum maps) show low frequency noise from atmo­
spheric emission and ground contamination (Figure 6.3). These effects cause correla­
tions in the time-ordered data which our azimuth-based scanning strategy translates
into horizontal stripping in the map domain. High-pass filtering the maps with poly­
nomial removal suppresses the large-scale contamination resulting from these effects
while preserving small-scale structure from the CMB.
Eight field temperature maps can then be formed by combining the data from
the individual feeds using the measured feed offsets (Section 5.1.2). The eight maps
(Figure 6.4) correspond to the two fields at the two frequencies and the two deck
rotation angles. The integration time per pixel for these maps is given by the hit
maps in the previous section.
1Thanks to B. Rusholme for providing the daily individual-PSB maps used in the analysis in
this chapter.
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6.2. FIRST MAPS
183
Lead (R aw )
-2000
-4000
-2000
-4000
-300
Trail (P oly)
Figure 6.3: Polynomial filtering (right) compared with lead/trail differencing (left)
for removing large scale contamination. This data is from a single feed horn (100-01).
The data on the left is completely raw, having had only a mean subtracted from each
row. The data on the right is high-pass filtered by removing a third-order polynomial
from each row. The field difference map (lead - trail) resulting from each data set is
shown in the bottom row. Field differencing only removes structure due to ground
contamination whereas polynomial filtering effectively removes contamination due
to both ground and atmosphere. After polynomial filtering (right), field differencing
(bottom right) offers no further improvement. The color scale is in units of /zK.
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CHAPTER 6. FIRST OBSERVATIONS
184
1 0 0 GHz
lead/dk-3
0
I
2
3
4
lead/dk+57
1 5 0 GHZ
trail/dk-3
5
0
1 2
3
4
trail/dk+57
leod/dk-3
5
0
1 2
3
4
lead/dk+57
trail/dk—3
5
0
1 2
3
4
5
troil/dk+57
Figure 6.4: QUaD CMB temperature maps made from the first pass over the field
(37 day’s worth of data). The eight maps correspond to the two fields (lead / trail)
at the two frequencies (100 / 150 GHz) and the two deck rotation angles (57° and
-3°). The integration time per pixel is given by the hit maps in Figure 6.2. The x
and y axes are RA and DEC offsets in units of real degrees on the sky. Two quasars
are visible in the lead field and one, in the trail field. Each map has been filtered
with row-wise removal of a third-order polynomial. The horizontal stripes on either
side of the quasars (most visible in the trail field) are an artifact of not masking out
the source when performing the polynomial fit.
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6.2. FIRST MAPS
QUAD 100 GHz, iro-h5.2Sd50
185
QUAD 150 GHz. irc-h5.25d50
(z o fb e ts k y (deg)
WMAP lyr, irohS.2Sd50
az off»M »ky (deg)
az offset sky (deg)
Figure 6.5: QUaD CMB temperature maps compared with B2K and WMAP for
the entire observing region (lead plus trail fields). The QUaD maps (top) axe in
Volts whereas the B2K and WMAP maps are in iiK. Cross correlating these maps
is used to derive a calibration in fiK /V for QUaD. This factor has been used to
calibrate all the other QUaD maps presented in this chapter. Unlike previous maps
in this chapter, these have been smoothed with a beam-sized Gaussian point spread
function (PSF). Figure courtesy of J. Kovac.
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CHAPTER 6. FIRST OBSERVATIONS
186
Several general conclusions can be made regarding these maps. The agreement
between the maps indicates that they are signal dominated. Despite the fewer num­
ber of pixels, the 100 GHz temperature maps are of better quality than the 150 GHz
maps due to less contamination from atmospheric emission. This emission causes
correlation between adjacent samples, resulting in the visible striping of the 150 GHz
maps. The polynomial filter removes this striping on large scales, but on small scales
it cannot be removed without also filtering out the desired CMB signal. The weather
deteriorated as the run progressed, resulting in the increased striping seen at the bot­
tom of the field.
Combining information from all the channels of a given frequency for both fields
and both deck rotations results in the maps seen in Figure 6.5. As a confirmation
that the structure we are seeing is the CMB, the figure also shows the same region
as observed by B2K and WMAP. Note the qualitative agreement among the maps.
The QUaD map shown here (as with all QUaD maps in this Chapter) is, however,
extremely crude - the data from the 37 days of observation have been combined with
no correction for daily drifts in atmospheric opacity (r) or instrumental gain drifts.
Additionally, the QUaD map is only minimally processed (polynomial removal from
each row). Detailed comparison among the experiments should be reserved until
QUaD produces a final map.
A more quantitative indication of QUaD’s performance can be obtained by con­
sidering the two maps of each field from the different deck rotation angles (Figure
6.6). In the absence of noise, these maps should be identical. Thus an estimate of
the signal-to-noise ratio can be computed by comparing the RMS of the map formed
by summing the two deck rotations to the analogous difference map.
In order to find the signal-to-noise per beam-sized pixel, rather than per 1.2
arcmin map pixel, the pixelized map is first smoothed by convolving with a beam­
sized Gaussian point spread function (PSF). The RMS noise per pixel (AT) for the
map is computed as
AT2 = {M g) - ( Mtj) 2
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(6.1)
187
6.2. FIRST MAPS
Table 6.1: RMS noise in pK for deck angle difference maps (Example maps for the
lead field are shown in Figure 6.6). The measured noise level is compared with the
expected noise based on the receiver sensitivity and the integration time. The noise
level in the “beam-sized pixel” column is determined after convolving the maps with
a 6.3' (4.2') Gaussian point spread function at 100 (150) GHz.
Beam-sized pixels
1.2' pixels
Field
lead
trail
Band
Measured
Expected
Measured
Expected
100
150
100
150
57
75
57
76
50
35
50
35
11
25
11
24
6.5
7
6.5
7
where Mij denotes the pixelized map. The symbol < > denotes a hit map weighted
average as
(M y) =
(6.2)
where Hij (the hit map) gives the integration time per pixel (Figure 6.2).
Returning to the maps of Figure 6.6, the sum map is assumed to contain sig­
nal (the CMB) plus noise (receiver and atmospheric) while the difference map, only
noise. Applying the above procedure to these maps estimates the signal-to-noise per
beam-sized pixel as ~ 6 and ~ 3 at 100 and 150 GHz respectively. These figures
were computed using the top half of the field because of the generally poorer weather
conditions during the second half of the run (bottom half of the field) and the bright
point sources in this region. These results show that after 37 days of observation,
QUaD has already made a high signal-to-noise detection of the CMB temperature
anisotropy (something it was not designed to do). The lower signal-to-noise of the
150 GHz map results from the higher atmospheric noise at this frequency. Atmo­
spheric noise is much less of a problem for polarization measurements since it is
unpolarized.
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CHAPTER 6. FIRST OBSERVATIONS
188
The noise level of the deck angle difference maps (Figure 6.6, right) can be com­
pared to the value expected based on the receiver sensitivity (Section 5.3) and the
integration time (Figure 6.2). Table 6.1 summarizes the results for both fields, both
frequencies, and for two different pixel sizes. For the finer 1.2' pixels, the 100 GHz
is close to the expected value whereas the 150 GHz channels show considerable ex­
cess noise due to atmospheric contamination. The results for the beam-sized pixels
confirms the presence of residual correlated structure (atmosphere and ground), es­
pecially at 150 GHz, that keeps the noise from integrating down as expected. This
contamination limits QUaDs ability to measure the CMB temperature power spec­
trum on large angular scales.
Fluctuations in atmospheric emission is the dominant contribution to the residual
contamination in the temperature maps; however, several systematic effects exist
that also result in differences between the maps made at the two deck angles. The
following list describes these effects and how the the final pipeline will deal with
them.
• Gain mismatches - Rotating the receiver in deck angle changes the effective
elevation of each feed resulting in gain difference due to the change in atmo­
spheric loading. Various calibration data including the cal source observations
and elevation nods can be used to correct for this.
• Pointing offsets - There is a small pointing offset between the two deck angles
which causes a shift between the two maps. Pointing cross observations taken
before each observation can be used to quantify this effect.
• Elliptical beams - The elliptical beams cause each pixel in the two deck rota­
tions to probe slightly different areas of the sky. The shapes of the beams are
known from periodic RCW38 beam maps and daily row cal observations.
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6.2. FIRST MAPS
189
Figure 6.6: Deck rotation jackknives. QUaD observes each field at two deck rotation
angles, dkl = 57° and dk2 = —3°. In the absence of noise, these two maps should
be identical. This figure shows the maps formed by summing and differencing these
two data sets. Each map above includes all channels for the given frequency. At
100 GHz, the difference map is dominated by receiver noise. At 150 GHz, residual
atmospheric contamination remains in the difference map. The signal-to-noise ratio
estimated from these maps is ~ 6 and ~ 3.0 at 100 and 150 GHz respectively. Note
the maps shown in this figure are all for the QUaD lead field.
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190
CHAPTER 6. FIRST OBSERVATIONS
Table 6.2: RMS noise in fiK per beam-sized pixel for single-feed polarization maps
(Examples shown in Figure 6.7). At each frequency, the median noise of the available
feeds (9 at 100 GHz and 15 at 150 GHz) is given. The standard deviation, in
parenthesis, indicates the channel-to-channel scatter. Before computing the noise, a
different order polynomial filter is applied to the map. The rightmost column gives
the expected noise (also in nK) based on the receiver sensitivity. Note that despite
their higher sensitivity, the expected noise per beam on the 150 GHz channels is
larger due to their smaller beam size.
Frequency
(GHz)
100
150
6.2.2
Polynomial Filter Order
1st
30 (3)
64 (14)
2nd
29 (3)
47 (7)
3rd
28 (3)
43 (5)
4th
27 (3)
41 (5)
Expected
5th
27 (3)
40 (5)
26
37
Polarization Maps
Polarization maps are formed by PSB differencing which removes the common-mode
signal resulting from unpolarized atmospheric emission. This frees them from much
of the low frequency contamination that plagues the temperature measurements.
Figure 6.7 shows example PSB sum and difference maps for a single feed at each
frequency. Applying the noise analysis presented in the previous section to the
single-feed, PSB difference maps results in Table 6.2. With sufficient filtering, de­
tectors at both frequencies meet the expected sensitivity within the (of order 10%)
calibration uncertainty. At 100 GHz, first-order filtering is sufficient whereas at least
second-order filtering is needed at 150 GHz. This is again due to the higher level of
atmospheric contamination at the higher frequency. More sophisticated processing
in the final pipeline should result in better gain matching within PSB pairs, increas­
ing the common-mode rejection so that only first order filtering is required at both
frequencies. Note that the expected RMS from the CMB polarization signal is ~ 5
/jK
per pixel so that these single-feed maps are receiver-noise dominated (per pixel).
The feeds on the QUaD focal plane are each in one of two angular orientation
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6.2. FIRST MAPS
191
A + B (150)
7
A - B (150)
a i ^ s'i ».v -
7
■A.
/, * * , • ..;^ .p*1* i
6
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o
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1-300
Figure 6.7: Single-feed temperature (left) and polarization (right) maps for the lead
field. A and B denote the maps formed from the two halves of a PSB pair. The sum
map (left) gives the total intensity (Stokes J ) as measured at each map pixel. The
difference map (right) gives Stokes Q as defined by each PSBs coordinate system.
Note, the sum and difference maps are actually formed as (A+B)/2 and (A-B)/2
respectively in order to retain the calibration of the individual maps. These maps
are for a single field (lead), a single deck rotation angle (dk=57°), and a single feed
at each frequency.
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CHAPTER 6. FIRST OBSERVATIONS
192
Table 6.3: RMS noise in pK for combined polarization maps (Figure 6.8). In contrast
to the temperature data, QUaD is meeting the expected noise levels in polarization
for both frequencies and pixelizations. The target noise levels are ~ 2 higher than
for the temperature maps because these results are for a single deck angle (rather
than the average of both) and because each feed only measures either Q or U.
Band
100
Deck
57
Stokes
Q
U
-3
Q
U
150
57
Q
U
-3
Q
U
1.2' pixels
Measured Expected
84
87
129
123
87
83
123
125
79
73
78
69
77
73
73
69
Beam-sized pixels
Measured Expected
11
11
17
16
11
11
17
16
16
14
14
16
14
16
14
15
groups (Figure 2.9) differing by 45°. Ignoring the small orientation angle errors
(Figure 4.18), the two groups can be assumed to measure either pure Stokes Q or
U respectively. Combining (as a hit map weighted average) the single-channel maps
(Figure 6.7) of the feeds from each group results in Q and U maps for each field
at each deck rotation angle. Figure 6.8 shows example Q maps at both frequency
bands. For comparison, Figure 6.9 shows the results of applying the same mapping
pipeline to simulated, uncorrelated Gaussian random noise (using the real hit maps
to determine the “integration” time per pixel).
Table 6.3 quantifies the measured and expected noise levels in the combined
polarization maps. Unlike in the temperature maps (Table 6.1), QUaD is meeting
the expected noise level at both frequencies for both pixelizations. No differences
are seen in the results for two fields or the two deck rotation angles. The agreement
between the measured and expected results shows that the sensitivity of the QUaD
receiver to CMB polarization is consistent with the estimates of Section 5.3.
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6.2. FIRST MAPS
6.2.3
193
D iscussion
This chapter has presented initial QUaD data with an eye towards verifying the op­
eration of the receiver, especially with regards to noise performance and systematic
effects. Atmospheric emission and ground pickup contaminate the raw temperature
maps, but row-wise polynomial filtering is shown to reduce the severity of these con­
taminants. This allows a high signal-to-noise measurement of the CMB temperature
anisotropy to be made at both frequency bands, although the noise limit set by the
receiver sensitivity is not met at either observing frequency.
In contrast, the filtered PSB difference (polarization) maps are shown to integrate
down spatially and with time as expected, reaching the expected per-pixel noise level
set by the receiver sensitivity. This indicates an absence of systematic effects, (atmo­
spheric emission, ground pickup, astrophysical foreground contamination, leakage of
the CMB temperature signal) that would prevent QUaD from reaching the science
goals outlined in Section 1.3.2. In particular, this lends confidence in the predicted
CMB power spectrum of Figure 1.14.
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194
CHAPTER 6. FIRST OBSERVATIONS
Figure 6.8: Combined Stokes Q maps for both frequency bands and both fields at
deck = 57°. Unlike the CMB temperature maps, these polarization maps are largely
free from residual contamination.
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6.2. FIRST MAPS
e
Q
195
Lead
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5
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3
-100
4
Figure 6.9: Simulated combined Stokes Q maps for both frequency bands and both
fields. These maps were generated using the same analysis pipeline that produced
Figure 6.8 except a Gaussian random number generator provide the input.
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196
CHAPTER 6. FIRST OBSERVATIONS
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Appendix A
Focal Plane Temperature Control
The focal plane temperature control subsystem attempts to maintain the focal plane
at a constant temperature during observations. The temperature reference comes
from a sensitive thermistor located on the focal plane which is AC biased and read
out using a cryogenic bridge circuit and the same warm lockin amplifier cards as for
the bolometers. Figure A.l shows a block diagram of the system and a detail of the
bridge circuit.
The bridge circuit operates by comparing the resistance of the thermistor, R ~
3 Mfi, to that of a fixed reference resistor, R q = 3.3 Mfl. The thermistor is a “type
D” NTD germanium chip made by Haller-Beeman.1 The two load resistors have the
larger value R l = 10 M fl The temperature set point is determined by changing the
ratio of the bias voltage for the two halves of the bridge circuit. Labelled “bias+”
and “bias-” in Figure A.l, the two biases are sine waves with the same frequency
as the bolometer AC bias. They are in phase and have independently adjustable
amplitude.
A warm lockin amplifier differences and demodulates the voltages from the two
sides of the bridge providing the error voltage input to an SRS-SIM9602 PID (pro­
portional integral derivative) control unit. The PID unit adjusts the heater output
current to null the error signal. The heater current flows through three 10 kf2 metal
film resistors wired in parallel and arranged symmetrically on the underside of the
1www.haller-beeman.com/thermis.htm
2Stanford Research Systems, Inc. www.thinkSRS.com
197
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APPENDIX A. FOCAL PLANE TEMPERATURE CONTROL
198
heater
current
bias+
Bias
Gen.
PID
QUaD
Receiver
biaserror
demodulator reference
biasbias+
error
Warm
lockin
amplifier
Figure A.l: (top) The focal plane temperature control system, (bottom ) Detail of
the thermistor readout bridge. The dashed line indicates the receiver.
focal plane bowl. Because the system cannot cool the focal plane, the set point is
required to be several mK above the natural fridge operating temperature. This al­
lows the PID to smooth over changes in temperature due to, for example, changes in
telescope elevation and the small natural drift upwards in temperature that occurs
with time as the fridge depletes the condensed He-3. Figure A.2 contrasts the tem­
perature stability of the focal plane with and without temperature control enabled.
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199
F ocal P la n e T em perature Control
0.254
2>
0.252
3
2Q)
CL
E
I-a> 0.250
Q
LL.
E n a b le d
D is a b le d
0.248
0
10
5
15
H o u rs
Figure A.2: Temperature control stabilizes the temperature of the focal plane. The
data plotted here is the DC level of one of the dark bolometers (PSB 150-01C). The
calibration from Volts to Kelvin was obtained by correlating the bolometer signal
with the focal plane GRT. The “disabled” data was taken on April 8, 2005 and the
“enabled” data, on April 10, 2005. In both cases, the telescope was raster-mapping
a source while this data was taken. The steps seen in the data are digitization noise.
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200
APPENDIX A. FOCAL PLANE TEMPERATURE CONTROL
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Appendix B
Commissioning QUaD
QUaD was commissioned at the South Pole during the 2004/2005 summer season by
ten intrepid team members who deployed for periods ranging from several weeks to
the entire season. Completing this enormous task under the severe time constraint
imposed by the onset of winter, required a Herculean effort from everyone. In ad­
dition to the dedicated QUaD team, we were also fortunate to have the help of the
South Pole Station’s superb science support and construction personnel.
Despite being one of the most remote locations on the planet, the station offers
an extensive infrastructure that make it very attractive as an observing site. In
addition to the basic necessities, the station operates a liquid nitrogen plant and
maintains a store of liquid helium with a cryogenic expert on-call for immediate
assistance when needed. A fully-equipped machine shop in the MAPO building is
staffed by professional machinists dedicated to supporting astronomical research.
Several electronics shops offer components and test equipment for troubleshooting
and repairs. Although packages take several weeks to be delivered, the vast quantity
of parts and scraps accumulated over the stations many years in operation ensures
that ample spares can usually be obtained or constructed when needed. Perhaps
the biggest drawback to the remote location is that communication with the out­
side world, including data transfers, is limited to approximately half the day when
connections can be made via satellite.
201
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202
APPENDIX B. COMMISSIONING QUAD
The following list includes some of the major tasks that were accomplished during
the commissioning period:
B .l
R eceiver T estin g
Upon unpacking the receiver, we performed a cool down without the focal plane.
This run tested the cryostat and the fridge to ensure they had survived the long
journey from California. Successfully cycling the fridge was cause for celebration
since any damage to the cryogenic systems would likely have resulted in losing the
entire observing season.
Just prior to shipping, we had changed all the filtering on the 100 GHz feeds
(to broaden the band) and installed several freshly minted PSBs. In fact, the final
PSB modules were hand-carried to the Pole and installed on the focal plane during
the cryogenic test run. Both to ensure that nothing had broken during shipping,
and to characterize all of the new detectors, our next run was dedicated to receiver
testing. We measured the optical efficiency, cross-polar leakage, PSB orientation,
the spectral bandpass for each feed, and the noise level for each detector. Most of
the results described in Section 4.2 are from this period of intense testing.
B .2
Foam C one In sta lla tio n
The crate containing the foam cone was designed to just fit in the cargo hold of the
LC-130 cargo planes that service the Pole. Unfortunately, this made it too large
for any commercial cargo planes except a special version of the Boeing 747. This
complicated the shipping arrangements resulting in significant delays. We were all
greatly relieved when the enormous box finally arrived at the Pole.
The cone is made of two layers of Zotefoam in the form of overlapping sectors
which are bonded together with adhesive. Fiberglass collars at the top and bottom
clamp the layers securely together. The cone is not particularly heavy, but handling
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B.2. FOAM CONE INSTALLATION
203
Figure B.l: Installing the QUaD foam cone. The crane arm is just visible in the
upper right corner. The two workers visible inside the ground shield guided the
cone onto the telescope primary mirror (not visible), which was pointed towards the
zenith.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX B. COMMISSIONING QUAD
204
it is extremely awkward due to its large size. Installing it onto the primary mirror
required the assistance of one of the station’s skilled crane operators and his crew.
Figure B .l shows the cone in mid-air, partway along its journey to its final resting
place atop the primary mirror. Once on the mirror, the cone was aligned relative
to the hole in the primary mirror. It was secured to the primary mirror guard ring
with fiberglass bolts through a flange on the cone’s bottom collar.
B .3
Secon dary In sta lla tio n and A lign m en t
Before installing the secondary mirror, extensive testing of the mechanical stability
of the foam cone was performed using a custom laser measuring system. A cornercube reflector and plane mirror mounted near the vertex of the cone combined with
three lasers allowed measurement of the x, y, and z position of the vertex as well
as tip and tilt. Tests were performed with the telescope at different elevation and
theta angles. The initial results were extremely puzzling. After a change in telescope
position, the cone would show a quick “step” change in its position followed by a very
slow drift. The drift was eventually traced to thermal expansion as the cone reached
a new equilibrium temperature distribution reflecting its new position relative to the
sun. This effect was compounded by the black tarp we had covered it with in order
to make the laser spots more visible.
The secondary mirror was intended to be attached to the foam cone via a motor­
ized hexapod mount that would allow convenient and accurate position and focus
corrections throughout the season. However, nagging mechanical problems made this
option less attractive. We were forced to completely abandon this option when static
electricity destroyed its control processor and the spare. In the end, we mounted the
secondary to the foam cone’s top cap using three l/2 ”-13 threaded rods. Nuts were
used to set the focus and then locked in place for the season.
Once the secondary was mounted, we performed the final alignment relative to
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BA. GROUND SHIELD EXTENSION
205
Figure B.2: Lifting the cryostat into the receiver room as seen from above.
the primary using an articulated measuring arm (Romer SOOOi)1. We rigidly mounted
the base of the arm to the telescope and then touched the probe at the end of arm
to the mirror surfaces. Extremely high resolution encoders at the joints allow the
position of the probe to be measured in three dimensions to better than
0.01 m m
with respect to the base. An array of data points were taken over the primary and
secondary surfaces which were then fit to their known functional forms. Adjustments
were then made to the mounting screws to bring the surfaces into alignment.
B .4
G round Shield E x ten sio n
With the original DASI ground shield, the top of the primary mirror would have
been able to “see” the ground when the telescope was tipped to low elevation angles.
This was deemed unacceptable and a plan was developed to extend the ground
1ROMER CimCore, 51170 Grand River Avenue, Wixom, MI 48393
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APPENDIX B. COMMISSIONING QUAD
206
shield by approximately four feet. Raytheon engineers designed and manufactured
the extension panels.
The panels were intended to arrive mid-season for installation by a construction
crew; however, a string of bad weather combined with large shipments of highpriority building materials for the new station meant they just barely arrived with
enough time left to install them before station closing.
B .5
R eceiver In stalla tio n
We performed the difficult task of mounting the receiver onto the telescope a total
of three separate times during the commissioning period. The first time was im­
mediately after unpacking, before the first cool down. At this point, the cryostat
and fridge still had their protective shipping hardware installed, and were least sus­
ceptible to physical damage from rough handling. The goal of this first installation
was to perform mechanical fit checking, to determine the best routing of the cryogen
refill lines, and to develop a reliable installation procedure. During future installa­
tions, the cryostat would be under vacuum and filled with liquid cryogens - so a safe
and reliable procedure was essential. For the second installation, the receiver was
cooled and fully operational. This run was mainly for testing microphonic response
while driving the telescope. The final installation was a few days before the end of
the season, just after the foam cone and secondary mirror had been installed and
mounted.
The physical installation procedure went as follows. First, we hoisted the cryostat
from the laboratory floor through the narrow entrance port into the receiver room
(around 20 feet total) using a hand operated winch (Figure B.2). Once the cryostat
was safely inside the receiver room, the real work began. First, we lowered it onto
a wheeled lifting table and pushed it underneath the mounting ring. We then used
the lifting table to raise the cryostat to its full extension which was just over half
the necessary distance. Then, we suspended the cryostat from the mounting ring
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B.5. RECEIVER INSTALLATION
207
Figure B.3: (top) The receiver mounted to the telescope before installation of the
warm readout electronics, (bottom ) The final configuration of the readout elec­
tronics. The real time control computer is mounted on the left. The 19” rack on the
right holds (top to bottom) two power supplies, the focal plane temperature control
unit, and the cryogenic temperature readout. The aluminum boxes hanging from the
cryostat (just beyond the top of the image) house the bias generator and amplifiers.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
208
APPENDIX B. COMMISSIONING QUAD
with cargo straps while the table was lowered and a spacer inserted. We raised the
table again, lifting the cryostat until the six 0.5” diameter mounting bolts passed
through the mating flange on the cryostat. At this point, we engaged the nuts and
raised the cryostat the rest of the way by tightening them. During this lifting, we
had to ensure that the stingers for the cryogen lines were properly aligned with the
cryostat refill tubes and not binding.
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Appendix C
Calibration Source Hardware
The calibration source includes the following hardware items:
Flip m irro r The flip mirror itself has already been described in the text (see Figure
5.12). A small DC servo motor, like the kind commonly found in the steering
mechanisms of remote-controlled cars, drives the up/down motion. Hardware
stops at the limits ensure a repeatable positioning.
Polarizing grid The polarizing grid is a smaller version of the one seen in Figure
4.14. A precision stepper motor and gear train rotates the grid.
B lackbody source The black body source is a copper disk covered in carbonloaded Stycast epoxy. Its absorption properties were verified using an FTS.
The disk has a heater resistor embedded in it in case temperature regulation
was desired. A National Semiconductor LM35 temperature sensor provides a
monitor good to ±0.5° C.
H all effect sw itch A steel vane on the perimeter of the polarizing grid engages a
Hall effect switch once per revolution, providing an home mark. Before flipping
the mirror down, the control system automatically homes the grid, ensuring
that all cal runs begin in the same state.
B a tte ry pack Wires running from the primary up to the cal source inside the
secondary were extremely undesirable since they would introduce scattering
209
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APPENDIX C. CALIBRATION SOURCE HARDWARE
210
that could be polarized. Hence the source was designed from the beginning to
run off of a lithium ion battery pack. However, this gives our “winter-over”
the unpleasant task of venturing into the Antarctic winter and standing on a
ladder to reach inside the foam cone and replace the battery. Fortunately, the
duty cycle of the source is quite low, so a reasonable battery life was obtained
by keeping the system standby current as low as possible. This was achieved
by powering down all the subsystems when not in use.
In frare d link The cal source receives commands and transmits data over an In­
frared data link that is implemented using the same chips that power the IrDA
data links commonly found in laptop computers and hand-held organizers. The
real-time control computer issues commands to the cal source over a standard
RS-232 serial line which links to a custom translator box. The translator box
interfaces with an IR transmitter/receiver located on the bottom edge of the
foam cone which communicates with the corresponding transceiver located just
behind the secondary (see Figure 5.12 for the approximate location of the link).
The protocol for RS-232 side of the link is completely ASCII based allowing
easy stand-alone operation with a terminal emulator program for troubleshoot­
ing. The translator box packages the command strings with a simple header
including a start characters, a string length, and a checksum byte. This has
resulted in an extremely robust and reliable link.
C o n tro l co m p u ter The cal source was designed to be operated by the same control
computer as the hexapod which was destroyed by static electricity late in the
summer season. A replacement system was designed mostly from scratch using
the spare components we had brought with us or were available on station. The
replacement system is based on a PIC16F873 (Microchip Technology Inc.) 8bit microcontroller. The chip’s 4 kB of program memory and 192 bytes of
RAM were filled to capacity by the program needed to interface with all the
subsystems.
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Bibliography
P. A. Ade, C. Tucker, and C. V. Haynes. Filters, Dichroics, Beam Dividers and
Fabry-Perot Plates for Ultra-Low-Background Far Infrared Instruments. In Proc.
Second Workshop on New Concepts for Far-IR Submillimeter Space Astronomy,
March 2002.
D. Barkats, C. Bischoff, P. Farese, L. Fitzpatrick, T. Gaier, J. 0 . Gundersen, M. M.
Hedman, L. Hyatt, J. J. McMahon, D. Samtleben, S. T. Staggs, K. Vanderlinde,
and B. Winstein. First Measurements of the Polarization of the Cosmic Microwave
Background Radiation at Small Angular Scales from CAPMAP. The Astrophysical
Journal Letters, 619:L127-L130, February 2005.
C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S.
Meyer, L. Page, D. N. Spergel, G. S. Tucker, E. Wollack, E. L. Wright, C. Barnes,
M. R. Greason, R. S. Hill, E. Komatsu, M. R. Nolta, N. Odegard, H. V. Peiris,
L. Verde, and J. L. Weiland. First-Year Wilkinson Microwave Anisotropy Probe
(WMAP) Observations: Preliminary Maps and Basic Results. The Astrophysical
Journal Supplement, 148:1-27, September 2003.
R. S. Bhatia, S. T. Chase, S. F. Edgington, J. Glenn, W. C. Jones, A. E. Lange,
B. Maffei, A. K. Mainzer, P. D. Mauskopf, B. J. Philhour, and B. K. Rownd. A
three-stage helium sorption refrigerator for cooling of infrared detectors to 280
mK. Cryogenics, 40:685-691, 2000.
211
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
212
BIBLIOGRAPHY
J. J. Bock. Rocket-borne observation of singly ionized carbon 158 micron emission
from the diffuse interstellar medium. PhD thesis, U.C. Berkeley, 1994.
J. J. Bock, D. Chen, P. D. Mauskopf, and A. E. Lange. A Novel Bolometer for
Infrared and Millimeter-Wave Astrophysics. Space Science Reviews, 74:229-235,
November 1995.
M. Born and E. Wolf. Principals of Optics. Pergammon, sixth edition, 1980.
M. Bowden, A. N. Taylor, K. M. Ganga, P. A. R. Ade, J. J. Bock, G. Cahill, J. E.
Carlstrom, S. E. Church, W. K. Gear, J. R. Hinderks, W. Hu, B. G. Keating,
J. Kovac, A. E. Lange, E. M. Leitch, B. Maffei, O. E. Mallie, S. J. Melhuish,
J. A. Murphy, G. Pisano, L. Piccirillo, C. Pryke, B. A. Rusholme, C. O’Sullivan,
and K. Thompson. Scientific optimization of a ground-based CMB polarization
experiment.
Monthly Notices of the Royal Astronomical Society, 349:321-335,
March 2004.
E. F. Bunn. Detectability of microwave background polarization. Physical Review
D, 65(4):043003-+, February 2002.
R. S. Bussmann, W. L. Holzapfel, and C. L. Kuo. Millimeter Wavelength Brightness
Fluctuations of the Atmosphere above the South Pole. The Astrophysical Journal,
622:1343-1355, April 2005.
G. Cahill. The Quasi-Optical Design and Analysis of Sub MM Telescopes. PhD
thesis, NUI Maynooth, 2005.
G. Cahill, C. O’Sullivan, J. A. Murphy, W. Lanigan, E. Gleeson, P. A. R. Ade, J. J.
Bock, M. Bowden, J. E. Carlstrom, S. E. Church, K. Ganga, W. Gear, J. Har­
ris, J. Hinderks, W. Hu, J. Kovac, A. Lange, E. M. Leitch, B. Maffei, O. Mallie,
S. Melhuish, A. Orlando, G. Pisano, L. Piccirillo, C. Pryke, B. Rusholme, A. Tay­
lor, K. L. Thompson, and M. Zemcov. The quasi-optical design of the QUaD
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
BIBLIOGRAPHY
213
Telescope. In Astronomical Structures and Mechanisms Technology. Edited by Antebi, Joseph; Lemke, Dietrich. Proceedings of the SPIE, Volume 5498, pp. 396-406
(2004)-, pages 396-406, October 2004.
J. E. Carlstrom, J. Kovac, E. M. Leitch, and C. Pryke. Status of CMB polarization
measurements from DASI and other experiments. New Astronomy Review, 47:
953-966, December 2003.
K. Coble et al.
Observations of galactic and extra-galactic sources from the
boomerang and sest telescopes. 2003.
B. P. Crill, P. A. R. Ade, D. R. Artusa, R. S. Bhatia, J. J. Bock, A. Boscaleri,
P. Cardoni, S. E. Church, K. Coble, P. de Bernardis, G. de Troia, P. Farese, K. M.
Ganga, M. Giacometti, C. V. Haynes, E. Hivon, V. V. Hristov, A. Iacoangeli,
W. C. Jones, A. E. Lange, L. Martinis, S. Masi, P. V. Mason, P. D. Mauskopf,
L. Miglio, T. Montroy, C. B. Netterfield, C. G. Paine, E. Pascale, F. Piacentini,
G. Polenta, F. Pongetti, G. Romeo, J. E. Ruhl, F. Scaramuzzi, D. Sforna, and A. D.
Turner. BOOMERANG: A Balloon-borne Millimeter-Wave Telescope and Total
Power Receiver for Mapping Anisotropy in the Cosmic Microwave Background.
The Astrophysical Journal Supplement, 148:527-541, October 2003.
Brendan P. Crill. A Measurement of the Angular Power Spectrum of the Cosmic
Microwave Background with a Long Duration Balloon-borne Receiver. PhD thesis,
California Institute of Technology, 2001.
P. C. Farese, G. Dall’Oglio, J. O. Gundersen, B. G. Keating, S. Klawikowski,
L. Knox, A. Levy, P. M. Lubin, C. W. O’Dell, A. Peel, L. Piccirillo, J. Ruhl,
and P. T. Timbie. COMPASS: An Upper Limit on Cosmic Microwave Back­
ground Polarization at an Angular Scale of 20’. The Astrophysical Journal, 610:
625-634, July 2004.
J. Glenn, J. J. Bock, G. Chattopadhyay, S. F. Edgington, A. E. Lange, J. Zmuidzinas,
P. D. Mauskopf, B. Rownd, L. Yuen, and P. A. Ade. Bolocam: a millimeter-wave
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
214
BIBLIOGRAPHY
bolometric camera. In Proc. SPIE Vol. 3357, p. 326-334, Advanced Technology
MMW, Radio, and Terahertz Telescopes, Thomas G. Phillips; Ed., pages 326-334,
July 1998.
A. H. Guth. Inflationary universe: A possible solution to the horizon and flatness
problems. Physical Review D, 23:347-356, January 1981.
Eugene Hecht. Optics. Addison-Wesley, third edition, 1998.
W. L. Holzapfel, T. M. Wilbanks, P. A. R. Ade, S. E. Church, M. L. Fischer, P. D.
Mauskopf, D. E. Osgood, and A. E. Lange. The Sunyaev-Zeldovich Infrared Ex­
periment: A Millimeter-Wave Receiver for Cluster Cosmology. The Astrophysical
Journal, 479:17-+, April 1997.
W. Hu and M. White. A CMB polarization primer. New Astronomy, 2:323-344,
October 1997.
W. C. Jones, R. Bhatia, J. J. Bock, and A. E. Lange.
A Polarization Sensi­
tive Bolometric Receiver for Observations of the Cosmic Microwave Background.
In Millimeter and Submillimeter Detectors for Astronomy. Edited by Phillips,
Thomas G.; Zmuidzinas, Jonas. Proceedings of the SPIE, Volume 4855, pp. 227238 (2003)., pages 227-238, February 2003.
William C. Jones. A Measurement of the Temperature and Polarization Anisotropies
in the Cosmic Microwave Background Radiation. PhD thesis, California Institute
of Technology, 2005.
M. Kamionkowski, A. Kosowsky, and A. Stebbins. Statistics of cosmic microwave
background polarization. Physical Review D, 55:7368-7388, June 1997.
E. Kirby. Complete Characterization of One QUaD Pixel. Undergraduate Thesis,
Varian Physics Dept., May 2004.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
BIBLIOGRAPHY
215
R. A. Knop, G. Aldering, R. Amanullah, P. Astier, G. Blanc, M. S. Burns, A. Conley,
S. E. Deustua, M. Doi, R. Ellis, S. Fabbro, G. Folatelli, A. S. Fruchter, G. Garavini,
S. Garmond, K. Garton, R. Gibbons, G. Goldhaber, A. Goobar, D. E. Groom,
D. Hardin, I. Hook, D. A. Howell, A. G. Kim, B. C. Lee, C. Lidman, J. Mendez,
S. Nobili, P. E. Nugent, R. Pain, N. Panagia, C. R. Pennypacker, S. Perlmutter,
R. Quimby, J. Raux, N. Regnault, P. Ruiz-Lapuente, G. Sainton, B. Schaefer,
K. Schahmaneche, E. Smith, A. L. Spadafora, V. Stanishev, M. Sullivan, N. A.
Walton, L. Wang, W. M. Wood-Vasey, and N. Yasuda. New Constraints on
Q
m
,
0 - L a m b d a ,
and w from an Independent Set of 11 High-Redshift Supernovae
Observed with the Hubble Space Telescope. The Astrophysical Journal, 598:102137, November 2003.
L. Knox and Y.-S. Song. Limit on the Detectability of the Energy Scale of Inflation.
Physical Review Letters, 89(1):011303—h, July 2002.
A. Kogut, D. N. Spergel, C. Barnes, C. L. Bennett, M. Halpern, G. Hinshaw,
N. Jarosik, M. Limon, S. S. Meyer, L. Page, G. S. Tucker, E. Wollack, and E. L.
Wright. First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observa­
tions: Temperature-Polarization Correlation. The Astrophysical Journal Supple­
ment, 148:161-173, September 2003.
J. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L.
Holzapfel. Detection of polarization in the cosmic microwave background using
dasi. Nature, 420:772-787, 2002.
C. L. Kuo, P. A. R. Ade, J. J. Bock, C. Cantalupo, M. D. Daub, J. Goldstein, W. L.
Holzapfel, A. E. Lange, M. Lueker, M. Newcomb, J. B. Peterson, J. Ruhl, M. C.
Runyan, and E. Torbet. High-Resolution Observations of the Cosmic Microwave
Background Power Spectrum with ACBAR. The Astrophysical Journal, 600:3251, January 2004.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
216
BIBLIOGRAPHY
A. P. Lane. AST/RO: Submillimeter Astronomy. Bulletin of the American Astro­
nomical Society, 30:883, May 1998.
A. E. Lange, P. A. Ade, J. J. Bock, J. R. Bond, J. Borrill, A. Boscaleri, K. Coble,
B. P. Crill, P. de Bernardis, P. Farese, P. Ferreira, K. Ganga, M. Giacometti,
E. Hivon, V. V. Hristov, A. Iacoangeli, A. H. Jaffe, L. Martinis, S. Masi, P. D.
Mauskopf, A. Melchiorri, T. Montroy, C. B. Netterfield, E. Pascale, F. Piacentini, D. Pogosyan, S. Prunet, S. Rao, G. Romeo, J. E. Ruhl, F. Scaramuzzi, and
D. Sforna. Cosmological parameters from the first results of Boomerang. Physical
Review D, 63(4):042001-+, February 2001.
O. P. Lay and N. W. Halverson. The Impact of Atmospheric Fluctuations on DegreeScale Imaging of the Cosmic Microwave Background. The Astrophysical Journal,
543:787-798, November 2000.
C. Lee, P. A. Ade, and C. V. Haynes. Self-Supporting Filters for Compact Focal
Plane Designs. In ESA SP-388: Submillimetre and Far-Infrared Space Instrumen­
tation, pages 81-+, December 1996.
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.
E. M. Leitch, J. M. Kovac, C. Pryke, B. Reddall, E. S. Sandberg, M. Dragovanl,
J.E. Carlstrom, N. W. Halverson, and W. L. Holzapfel. Measuring polarization
with dasi. Nature, 420:763-771, 2002a.
E. M. Leitch, C. Pryke, N. W. Halverson, J. Kovac, G. Davidson, S. LaRoque,
E. Schartmanl, J. Yamasaki, and J. E. Carlstrom. Experiment design and first
season observations with the degree angular scale interferometer. The Astrophys­
ical Journal, 568:28-37, 2002b.
J. C. G. Lesurf. Millimetre-wave Optics, Devices & Systems. Adam Hilger, 1990.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
BIBLIOGRAPHY
217
B. S. Mason, T. J. Pearson, A. C. S. Readhead, M. C. Shepherd, J. Sievers, P. S.
Udomprasert, J. K. Cartwright, A. J. Farmer, S. Padin, S. T. Myers, J. R. Bond,
C. R. Contaldi, U. Pen, S. Prunet, D. Pogosyan, J. E. Carlstrom, J. Kovac, E. M.
Leitch, C. Pryke, N. W. Halverson, W. L. Holzapfel, P. Altamirano, L. Bronfman,
S. Casassus, J. May, and M. Joy. The Anisotropy of the Microwave Background
to 1 = 3500: Deep Field Observations with the Cosmic Background Imager. The
Astrophysical Journal, 591:540-555, July 2003.
J. C. Mather. Bolometer Noise: Nonequilibrium Thoery. Applied Optics, 21:1125—
1129, March 1982.
J. C. Mather. Bolometers: Ultimate Sensitivity, Optimization, and Amplifier Cou­
pling. Applied Optics, 23:584-588, February 1984.
J. C. Mather, E. S. Cheng, D. A. Cottingham, R. E. Eplee, D. J. Fixsen,
T. Hewagama, R. B. Isaacman, K. A. Jensen, S. S. Meyer, P. D. Noerdlinger, S. M.
Read, L. P. Rosen, R. A. Shafer, E. L. Wright, C. L. Bennett, N. W. Boggess,
M. G. Hauser, T. Kelsall, S. H. Moseley, R. F. Silverberg, G. F. Smoot, R. Weiss,
and D. T. Wilkinson. Measurement of the cosmic microwave background spec­
trum by the COBE FIRAS instrument. The Astrophysical Journal, 420:439-444,
January 1994.
P. D. Mauskopf, J. J. Bock, H. del Castillo, W. L. Holzapfel, and A. E. Lange.
Composite infrared bolometers with Si 3 N 4 micromesh absorbers. Applied Optics,
36:765-771, February 1997.
T. E. Montroy et al. A Measurement of the CMB jEE^ Spectrum from the 2003
Flight of Boomerang. 2005.
C. W. O’Dell. A New Upper Limit on the Large Angular Scale Polarization of the
Cosmic Microwave Background Radiation. PhD thesis, University of Wisconsin
Madison, 2001.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
218
BIBLIOGRAPHY
P. J. E. Peebles. The Large-Scale Structure of the Universe. Princeton University
Press, 1980.
P. J. E. Peebles. Principles of Physical Cosmology. Princeton University Press, 1993.
A. A. Penzias and R. W. Wilson. A Measurement of Excess Antenna Temperature
at 4080 Mc/s. The Astrophysical Journal, 142:419-421, July 1965.
W. J. Percival, W. Sutherland, J. A. Peacock, C. M. Baugh, J. Bland-Hawthorn,
T. Bridges, R. Cannon, S. Cole, M. Colless, C. Collins, W. Couch, G. Dalton,
R. De Propris, S. P. Driver, G. Efstathiou, R. S. Ellis, C. S. Frenk, K. Glazebrook,
C. Jackson, O. Lahav, I. Lewis, S. Lumsden, S. Maddox, S. Moody, P. Norberg,
B. A. Peterson, and K. Taylor. Parameter constraints for flat cosmologies from
cosmic microwave background and 2dFGRS power spectra. Monthly Notices of
the Royal Astronomical Society, 337:1068-1080, December 2002.
S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro,
S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y.
Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman,
R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer,
B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M.
Newberg, W. J. Couch, and The Supernova Cosmology Project. Measurements
of Omega and Lambda from 42 High-Redshift Supernovae.
The Astrophysical
Journal, 517:565-586, June 1999.
J. B. Peterson, S. J. E. Radford, P. A. R. Ade, R. A. Chamberlin, M. J. O’Kelly,
K. M. Peterson, and E. Schartman. Stability of the Submillimeter Brightness of
the Atmosphere above Mauna Kea, Chajnantor, and the South Pole. Publications
of the ASP, 115:383-388, March 2003.
L. Piccirillo, G. dall’Oglio, P. Farese, J. Gundersen, B. Keating, S. Klawikowski,
L. Knox, A. Levy, P. Lubin, C. O’dell, P. Timbie, and J. Ruhl. COMPASS: A 2.6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
BIBLIOGRAPHY
219
m telescope for CMBR polarization studies. In A IP Conf. Proc. 616: Experimental
Cosmology at Millimetre Wavelengths, pages 183-186, May 2002.
A. C. S. Readhead, S. T. Myers, T. J. Pearson, J. L. Sievers, B. S. Mason, C. R.
Contaldi, J. R. Bond, R. Bustos, P. Altamirano, C. Achermann, L. Bronfman,
J. E. Carlstrom, J. K. Cartwright, S. Casassus, C. Dickinson, W. L. Holzapfel,
J. M. Kovac, E. M. Leitch, J. May, S. Padin, D. Pogosyan, M. Pospieszalski,
C. Pryke, R. Reeves, M. C. Shepherd, and S. Torres. Polarization Observations
with the Cosmic Background Imager. Science, 306:836-844, October 2004.
M. J. Rees. Polarization and Spectrum of the Primeval Radiation in an Anisotropic
Universe. The Astrophysical Journal Letters, 153:L1+, July 1968.
A. G. Riess, P. E. Nugent, R. L. Gilliland, B. P. Schmidt, J. Tonry, M. Dickin­
son, R. I. Thompson, T. Budavari, S. Casertano, A. S. Evans, A. V. Filippenko,
M. Livio, D. B. Sanders, A. E. Shapley, H. Spinrad, C. C. Steidel, D. Stern,
J. Surace, and S. Veilleux. The Farthest Known Supernova: Support for an Accel­
erating Universe and a Glimpse of the Epoch of Deceleration. The Astrophysical
Journal, 560:49-71, October 2001.
M. C. Runyan, P. A. R. Ade, R. S. Bhatia, J. J. Bock, M. D. Daub, J. H. Goldstein,
C. V. Haynes, W. L. Holzapfel, C. L. Kuo, A. E. Lange, J. Leong, M. Lueker,
M. Newcomb, J. B. Peterson, C. Reichardt, J. Ruhl, G. Sirbi, E. Torbet, C. Tucker,
A. D. Turner, and D. Woolsey. ACBAR: The Arcminute Cosmology Bolometer
Array Receiver. The Astrophysical Journal Supplement, 149:265-287, December
2003.
Marcus C. Runyan. A Search for Galaxy Clusters Using the Sunyaev-Zel’dovich
Effect. PhD thesis, California Institute of Technology, 2002.
D. J. Schlegel, D. P. Finkbeiner, and M. Davis. Maps of Dust IR Emission for Use
in Estimation of Reddening and CMBR Foregrounds. Bulletin of the American
Astronomical Society, 29:1354-1-, December 1997.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
220
BIBLIOGRAPHY
U. Seljak and M. Zaldarriaga. A Line-of-Sight Integration Approach to Cosmic Mi­
crowave Background Anisotropies. The Astrophysical Journal, 469:437-+, October
1996.
G. F. Smoot, C. L. Bennett, A. Kogut, E. L. Wright, J. Aymon, N. W. Boggess,
E. S. Cheng, G. de Amici, S. Gulkis, M. G. Hauser, G. Hinshaw, P. D. Jackson,
M. Janssen, E. Kaita, T. Kelsall, P. Keegstra, C. Lineweaver, K. Loewenstein,
P. Lubin, J. Mather, S. S. Meyer, S. H. Moseley, T. Murdock, L. Rokke, R. F.
Silverberg, L. Tenorio, R. Weiss, and D. T. Wilkinson. Structure in the COBE dif­
ferential microwave radiometer first-year maps. The Astrophysical Journal Letters,
396:L1-L5, September 1992.
D. N. Spergel, L. Verde, H. V. Peiris, E. Komatsu, M. R. Nolta, C. L. Bennett,
M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page,
G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright. First-Year Wilkinson
Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmo­
logical Parameters. The Astrophysical Journal Supplement, 148:175-194, Septem­
ber 2003.
R. V. Sudiwala, M. J. Griffin, and A. L. Woodcraft. Thermal modelling and charac­
terisation of semiconductor bolometers. Int. Journal of Infrared and Mm Waves,
23:545-573, 2002.
A. L. Woodcraft, R. V. Sudiwala, P. A. R. Ade, M. J. Griffin, E. Wakui, R. S. Bhatia,
A. E. Lange, J. J. Bock, A. D. Turner, M. H. Yun, and J. W. Beeman. Predicting
the response of a submillimeter bolometer to cosmic rays. Applied Optics, 42:
5009-5016, September 2003.
M. Zaldarriaga and U. Seljak. All-sky analysis of polarization in the microwave
background. Physical Review D, 55:1830-1840, February 1997.
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