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Measurements of the Cosmic Microwave Background radiation polarization anisotropy at 40Ghz and 90Ghz with the Q/U Imaging ExperimenT (QUIET)

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THE UNIVERSITY OF CHICAGO
MEASUREMENTS OF THE COSMIC MICROWAVE BACKGROUND RADIATION
POLARIZATION ANISOTROPY AT 40GHZ AND 90GHZ WITH THE Q/U IMAGING
EXPERIMENT (QUIET)
A DISSERTATION SUBMITTED TO
THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES
IN CANDIDACY FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
DEPARTMENT OF PHYSICS
BY
ALISON REBECCA BRIZIUS
CHICAGO, ILLINOIS
AUGUST 2011
UMI Number: 3472815
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent on the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 3472815
Copyright 2011 by ProQuest LLC.
All rights reserved. This edition of the work is protected against
unauthorized copying under Title 17, United States Code.
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
c 2011 by Alison Rebecca Brizius
Copyright All rights reserved
to my mother and sister
and
to Bruce
ACKNOWLEDGMENTS
First and foremost, I am profoundly indebted to my advisor, the late Dr. Bruce Winstein,
whose intelligence, tenacity, inspiration and humor made this dissertation (and QUIET)
possible. And, I am grateful to Paolo Privitera for stepping in to advise me and see me
through the completion of this work.
I also thank Akito Kusaka. I could not have managed without his constant and invaluable
assistance, guidance, patience and years of answering what must have seemed an unending
stream of questions. Dorothea Samtleben, Osamu Tajima and Dan Kapner were most generous with their time, knowledge, advice and support. Colin Bischoff, Keith Vanderlinde and
Immanuel Buder were great lab-mates and friends.
QUIET is a large collaboration and as such I am grateful each of you, though I don?t
have the space to mention you all by name. I appreciate your contributions and enjoyed the
privilege of working with you (as well as the good times on top of a mountain).
Cristobal, Rodrigo, Ricardo, Jose, Freddy y Carlos, gracias por toda su ayuda, su trabajo,
y por hacerme sentir siempre bienvenida.
To my friends in Chicago who have seen me through the highs and lows of this process,
I wouldn?t have made it without you.
I extend particular and heartfelt thanks to Leonard and Pamela Schaeffer who have
inspired and supported me in my entire educational career. And finally, but not least, I
thank my family for their unwavering support through this entire process.
iv
ABSTRACT
The polarization of the Cosmic Microwave Background (CMB) contains a wealth of untapped information that will enable us to probe the structure and dynamics of the early
universe. The Q/U Imaging ExperimenT (QUIET) was designed to measure these CMB polarization anisotropies at angular scales of 25 < ` < 1000, primarily targeting the predicted
B-mode signal generated by primordial gravitational waves sourced by inflation. Although
the B-mode signal has eluded detection thus far, discovery of such a signal would provide a
?smoking-gun? for inflationary theories.
Operating between October of 2008 and December of 2010 on the Chajnantor plateau
in the Atacama Desert in Chile, QUIET acquired over 10,000 hours of data in two observing seasons. QUIET employed two arrays of coherent receivers, with central frequencies at
Q-Band (43 GHz) and W-Band (94 GHz). This thesis describes the design and implementation of QUIET, including the construction and characterization of the W-Band receiver,
observations with both receivers, and reports initial results from the first season Q-Band
observations.
v
TABLE OF CONTENTS
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
1 INTRODUCTION . . . . . . . . . . . . . . . . .
1.1 Thesis Scope . . . . . . . . . . . . . . . . . .
1.2 The Big Bang Model . . . . . . . . . . . . .
1.3 The CMB . . . . . . . . . . . . . . . . . . .
1.3.1 Temperature Isotropy of the CMB . .
1.3.2 Temperature Anisotropy of the CMB
1.4 Inflation . . . . . . . . . . . . . . . . . . . .
1.4.1 Problems with the standard model .
1.4.2 Single Field Slow Roll Inflation . . .
1.5 CMB Polarization . . . . . . . . . . . . . . .
1.5.1 Stokes Parameters . . . . . . . . . .
1.5.2 Thomson Scattering . . . . . . . . .
1.5.3 E & B Mode Polarization . . . . . .
1.6 Measurements of CMB Power Spectra . . . .
1.7 Foregrounds . . . . . . . . . . . . . . . . . .
1.7.1 Diffuse Galactic Emission . . . . . .
1.7.2 Compact Radio Sources . . . . . . .
1.7.3 Gravitational Lensing . . . . . . . . .
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1
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2 QUIET PHASE I INSTRUMENT . . . . . . . . . . . . . . . .
2.1 Telescope Mount and Deck Platform . . . . . . . . . . .
2.2 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Mirrors . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Platelet Array . . . . . . . . . . . . . . . . . . . .
2.2.3 Septum Polarizer Orthomode Transducer . . . . .
2.2.4 Differential Temperature Assemblies . . . . . . .
2.2.5 Ground Screen & Sidelobes . . . . . . . . . . . .
2.3 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 300K Stage . . . . . . . . . . . . . . . . . . . . .
2.3.2 80K Stage . . . . . . . . . . . . . . . . . . . . .
2.3.3 20K Stage . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Temperature Monitoring and Thermal Regulation
2.4 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.5
2.4.1 Components of a QUIET Module
2.4.2 An Ideal Module . . . . . . . . .
2.4.3 Detector Characterization . . . .
2.4.4 Sensitivity & Optimization . . . .
Electronics . . . . . . . . . . . . . . . . .
2.5.1 Protection Electronics & Cabling
2.5.2 Electronics Enclosure . . . . . . .
2.5.3 Bias & Monitoring Electronics . .
2.5.4 DAQ System . . . . . . . . . . .
2.5.5 Receiver Control Software . . . .
2.5.6 Telescope Control . . . . . . . . .
3 OBSERVATIONS . . . . . .
3.1 Site . . . . . . . . . . .
3.2 Field Selection . . . . .
3.3 Scan Strategy . . . . .
3.4 Observing Seasons . .
3.4.1 Q-Band Season
3.4.2 W-Band Season
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. 88
. 88
. 91
. 95
. 99
. 99
. 100
4 CALIBRATION . . . . . . . . . . . . .
4.1 Calibrators . . . . . . . . . . . . .
4.2 Beam Profile and Window Function
4.3 Pointing . . . . . . . . . . . . . . .
4.4 Responsivity . . . . . . . . . . . . .
4.5 Detector Polarization Angle . . . .
4.6 Instrumental Polarization . . . . .
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5 ANALYSIS FRAMEWORK . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 TOD Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Noise model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Data Quality Statistics & Cut Fractions . . . . . . . . . . . . . . . .
5.2.1 Cut Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Map Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Power-Spectra Estimation . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Temperature Data Analysis . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Temperature Data Selection Efficiency & Filtering . . . . . . .
5.5.2 Temperature data Map-making & Power-Spectra Estimation
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6 ANALYSIS VALIDATION . . . . . .
6.1 Null Tests . . . . . . . . . . . .
6.1.1 Null Tests in Pseudo-C`
6.2 The Null Suite . . . . . . . . .
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6.3
6.4
6.5
6.2.1 Evaluation of the Null Suite . .
Blind Consistency Checks . . . . . . .
6.3.1 Data Selection Consistency . . .
6.3.2 Patch Consistency . . . . . . .
Analysis Validation Results . . . . . .
Validation of the Temperature Analysis
7 Q-BAND RESULTS . . . . . . . . . . .
7.1 Polarization Power Spectra . . . . .
7.1.1 Consistency with ?CDM . .
7.2 Constraints on Primordial B modes
7.3 Comparison to Other Experiments
7.4 Foreground Analysis . . . . . . . .
7.4.1 Compact Radio Sources . .
7.4.2 Galactic Synchrotron . . . .
7.5 Systematic Effects . . . . . . . . . .
7.6 Temperature Power Spectra . . . .
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8 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
A MODULE ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
A.1 Unequal Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
B FIRMWARE . . . . . . . . .
B.1 VME I/O . . . . . . . .
B.2 Master Clock Generation
B.3 ADC . . . . . . . . . . .
B.4 Housekeeping . . . . . .
B.5 LVDS . . . . . . . . . .
B.6 Snapshot . . . . . . . . .
B.7 Data Streams . . . . . .
B.8 Blanking Mask . . . . .
B.9 Phase Switching . . . . .
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191
192
193
193
194
195
196
196
198
198
C ADC NONLINEARITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
D DATA SELECTION CRITERIA . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
D.1 Final Q-Band Polarization Cuts . . . . . . . . . . . . . . . . . . . . . . . . . 207
D.2 Final Q-Band Temperature Cuts . . . . . . . . . . . . . . . . . . . . . . . . 209
E Q-BAND TEMPERATURE CES BINNING . . . . . . . . . . . . . . . . . . . . . 212
F TT ITERATIVE MAP MAKER . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
viii
G NULL TESTS THRESHOLDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
G.1 Polarization Nulls Test Thresholds . . . . . . . . . . . . . . . . . . . . . . . 216
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
ix
LIST OF FIGURES
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
Spectrum of the Cosmic Microwave Background . . . . . . . . . . . . . . . .
Maps of the Cosmic Microwave Background Temperature Anisotropy . . . .
Temperature Power Spectrum of the Cosmic Microwave Background . . . . .
Illustration of acoustic oscillations giving rise to peaks in the temperature
power spectrum of the CMB . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagram of Stokes Parameters . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagram of the Thomson Scattering of a Quadrapole Anisotropy . . . . . . .
Diagram of E-mode and B-mode Patterns . . . . . . . . . . . . . . . . . . .
Electron in a velocity field . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagram of CMB Polarization via Gravity Waves . . . . . . . . . . . . . . .
Measurement of the TE power spectrum of the CMB . . . . . . . . . . . . .
Measurements of the EE and BB Power Spectra of the Cosmic Microwave
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Illustration of Expected Foreground Levels: Synchrotron, Free-Free and Thermal Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Foreground Maps: Synchrotron, Free-Free and Thermal Dust . . . . . . . . .
Overview of the QUIET instrument. . . . . . . . . . . . . . . . . . . . . . .
Three axis rotation of the QUIET telescope mount . . . . . . . . . . . . . .
Solid model of corrugated horn and image of the W-Band platelet array . . .
Septum polarizer schematic diagram . . . . . . . . . . . . . . . . . . . . . .
Photograph and engineering diagrams of the Septum Polarizer OMT . . . .
Photograph of the Differential Temperature Assembly . . . . . . . . . . . . .
Schematic diagram of a differential temperature assembly . . . . . . . . . . .
Images of the Lower and Upper Ground Screens . . . . . . . . . . . . . . . .
Raytracing diagram of sidelobes terminating on the Ground Screen . . . . .
Diagram of the W-Band 91 element cryostat. . . . . . . . . . . . . . . . . . .
Photographs of the W-Band cryostat . . . . . . . . . . . . . . . . . . . . . .
Temperature variation of the electronics enclosure . . . . . . . . . . . . . . .
Images of the QUIET Q-Band and W-Band modules with septum polarizer
OMTs attached . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Detectors in the Q-Band & W-Band arrays . . . . . . . . . . . . . . . . . . .
Photograph of module interior and module component schematic . . . . . . .
Algebra of Module Signal Processing . . . . . . . . . . . . . . . . . . . . . .
Bandwidths and band centers for the diodes in the W-Band array . . . . . .
Diagram showing the linear extrapolation of Trec . . . . . . . . . . . . . . .
Diagram of the wire grid used to optimize the detector sensitivity . . . . . .
Sample average and double demodulated time streams and their noise power
spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic diagram of rotating plate calibrator . . . . . . . . . . . . . . . . .
RMS module sensitivity and bandwidth as a function of iteration of optimization algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
5
6
7
8
14
16
17
18
19
21
22
24
26
30
32
35
36
37
38
39
40
42
43
44
48
49
50
51
54
62
64
65
67
68
69
2.23
2.24
2.25
2.26
2.27
2.28
2.29
Sensitivity of each diodes in the W-Band array for a single observation . . .
Knee frequency and single diode sensitivity distributions for the W-Band array
Photographs of electronics boards and cables . . . . . . . . . . . . . . . . . .
Connection diagram for the protection, bias and monitoring electronics . . .
Diagram of components in the Electronics Enclosure . . . . . . . . . . . . . .
Enclosure temperature during the W-Band observing season . . . . . . . . .
Sample 800 kHz timestream and illustration of clocking signals . . . . . . . .
70
71
72
75
76
77
82
3.1
3.2
3.3
Atmospheric Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Data Selection Efficiency as a function of PWV . . . . . . . . . . . . . . . . 90
Precipital Water Vapor, Humidity and Wind Speed throughout the QUIET
observing seasons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4 The CMB and Galactic patch locations . . . . . . . . . . . . . . . . . . . . . 93
3.5 Patch Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.6 Constant Elevation Scan in azimuth, elevation and deck rotation. . . . . . . 96
3.7 Sample CES observations of Patch CMB-1 . . . . . . . . . . . . . . . . . . . 97
3.8 Distribution of Parallactic Angles . . . . . . . . . . . . . . . . . . . . . . . . 98
3.9 Week of observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.10 Cumulative operational time with the Q-Band and W-Band receivers . . . . 100
4.1
4.2
4.3
4.4
4.5
4.6
Maps of Taurus A using Q-Band Central Array Element . . . . . . . . . . .
Beam profile and window function . . . . . . . . . . . . . . . . . . . . . . . .
Map of Jupiter, Beam Profile and Window Function for Differential Temperature Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observations of the Moon with all detectors . . . . . . . . . . . . . . . . . .
Measurements of Tau A . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Total Intensity and polarization plots of the Moon . . . . . . . . . . . . . . .
5.1
5.2
5.3
5.4
5.5
5.6
Analysis Flow Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Flow Chart of TOD processing and filtering . . . . . . . . . . . . . . . . . .
noise power spectrum and noise model fit for a single CES-diode . . . . . . .
Sample CES timestream and noise power spectrum before and after filtering.
Azimuthally binned structure in a single CES-diode . . . . . . . . . . . . . .
Distributions and cut thresholds for data quality statistics used for polarization data selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7 Inverse noise weighted polarization maps for all patches . . . . . . . . . . . .
5.8 Distributions and cut thresholds for data quality statistics used for temperature data selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Striping in TT maps with poor cross-linking . . . . . . . . . . . . . . . . . .
5.10 Distribution of CES Array Orientation for Temperature Sub-Maps . . . . . .
6.1
6.2
6.3
109
109
110
111
113
114
118
119
122
123
124
143
144
145
146
146
Polarization Null Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Sample Null Power Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Null Test Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
xi
6.4
6.5
6.6
6.7
6.8
6.9
6.10
Sample ?2 Histogram of Null Suite Results . . . . . . . . . . . . . . . .
Power-spectra differences across iterations of the data selection criteria
Polarization Null Suite Results . . . . . . . . . . . . . . . . . . . . . .
Null-Suite Statistics: ?null and PTE for final iteration of the null suite
Temperature Null Maps . . . . . . . . . . . . . . . . . . . . . . . . . .
Temperature Null Suite ?2 distributions . . . . . . . . . . . . . . . . .
TT ?null Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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157
159
161
162
165
166
166
7.1
7.2
EE, BB, and EB power spectra shown for each patch individually . . . . . .
EE, BB, and EB power spectra from each QUIET pipeline, all four patches
combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Likelihood curve as a function of EE power amplitude, q . . . . . . . . . . .
Likelihood curve as a function of the tensor to scalar ratio, r . . . . . . . .
QUIET EE power spectrum and BB upper limits compared to other experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systematic uncertainty estimates for EE, BB, and EB power spectra . . . . .
Patch CMB-2 temperature map compared to WMAP . . . . . . . . . . . . .
QUIET temperature map for patches CMB-1, CMB-2 and CMB-3 . . . . . .
CMB temperature power spectra: TT, TE, and TB . . . . . . . . . . . . . .
170
7.3
7.4
7.5
7.6
7.7
7.8
7.9
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171
173
174
175
178
181
181
182
C.1 Illustration of missing codes in ADC generating glitch pattern in data timestream204
C.2 ADC glitch pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
C.3 Plots of ADC nonlinearity glitch and correction . . . . . . . . . . . . . . . . 206
xii
LIST OF TABLES
1.1
?CDM Cosmological Parameters . . . . . . . . . . . . . . . . . . . . . . . .
3.1
3.2
3.3
3.4
Patch Locations and Integration Times . . . . . . . . .
Noteworthy Events in the Q-Band Observation Season
Noteworthy Events in the W-Band Observation Season,
Noteworthy Events in the W-Band Observation Season,
4.1
Regular Calibration Observations . . . . . . . . . . . . . . . . . . . . . . . . 105
5.1
5.2
5.3
5.4
Total Hours Observed and Data-Selection Efficiencies . . . . . . . . . . .
Number of CES-diodes rejected by various cuts . . . . . . . . . . . . . .
Azimuth and Deck Bins . . . . . . . . . . . . . . . . . . . . . . . . . . .
Number of CES-diodes rejected by various cuts for Temperature Analysis
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130
132
134
140
6.1
6.2
6.3
6.4
6.5
6.6
Null Test Suite, Part I . . . . . . . . . . . . . . . . . . . . . . . . . . .
Null Test Suite, Part II . . . . . . . . . . . . . . . . . . . . . . . . . . .
Null Suite ?2 Probability To Exceed by Patch . . . . . . . . . . . . . .
The 29 null tests included in the temperature analysis null suite. . . . .
The 5 Null Tests used for temperature-polarization correlation analysis
Probabilities to Exceed for the TT, TE and TB null suites. . . . . . . .
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153
154
162
164
167
167
7.1
7.2
CMB-Spectra Band Powers from QUIET Q-Band Data [1] . . . . . . . . . . 172
Systematic Effects for EE, BB & EB Spectra . . . . . . . . . . . . . . . . . . 179
B.1
B.2
B.3
B.4
QUIET
QUIET
QUIET
QUIET
Firmware
Firmware
Firmware
Firmware
Input/Output
Modules . . .
Modules . . .
Modules . . .
Table
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9
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191
200
201
202
E.1 CES groupings into MCES for mapmaking . . . . . . . . . . . . . . . . . . . 212
G.1
G.2
G.3
G.4
Polarization Null Tests Thresholds Part I . . . . . . . . . . . . . . . . . . . .
Polarization Null Tests Thresholds Part II . . . . . . . . . . . . . . . . . . .
Polarization Null Tests Thresholds Part III . . . . . . . . . . . . . . . . . . .
Thresholds for Temperature Null Tests where different than those for the
polarization null tests: Part I of II . . . . . . . . . . . . . . . . . . . . . . . .
G.5 Thresholds for Temperature Null Tests where different than those for the
polarization null tests: Part II of II . . . . . . . . . . . . . . . . . . . . . . .
xiii
217
218
219
219
220
CHAPTER 1
INTRODUCTION
1.1
Thesis Scope
This thesis describes a precision measurement of the polarization of the Cosmic Microwave
Background (CMB) made using the Q/U Imaging ExperimenT (QUIET). QUIET was designed to measure CMB polarization anisotropies at low angular scales (25 < ` < 1000), in
search of B-modes signals produced by primordial gravity waves.
QUIET employed two arrays of coherent detectors that operated on a telescope located
on the Chajnantor plateau in the Atacama Desert in Chile. The Q-Band receiver contained
an array of 19 pseudo-correlation polarimeters operating with a central frequency of 43 GHz
while the W-Band receiver array comprised 90 polarimeters operating at 94 GHz. The
thesis will emphasize the contributions of the author to the project, describing the design
and performance of the W-Band receiver which was integrated in Chicago, the deployment
and operation of both receivers and the telescope, and the data analysis and results from
the Q-Band receiver. Although the description of the instrumentation will focus on the WBand receiver while the data analysis will focus on the Q-Band results, both receivers share
a common design and similar data analysis framework.
We begin in �by discussing the motivation for such a measurement, providing background for the theoretical underpinnings of the experiment. The telescope and W-Band
receiver are described in detail in � Observations with both the Q-Band and the W-Band
receivers are discussed in �while �is devoted to calibration of the Q-band data. Data
selection and analysis are treated in � and the suite of analysis validation tests is described
in � Results of the Q-Band data analysis and estimates of systematic effects are reported in
� Finally, �summarizes the results of the Q-Band data analysis and describes prospects
for the W-Band analysis and future experiments.
1
1.2
The Big Bang Model
The prevailing theory for the evolution of the universe, known as the ?Big Bang? model, posits
that the universe began in an extremely hot dense state and has been expanding and cooling
ever since. There are several key cosmological observations that support the Big Band model,
including Hubble?s law, the distribution of galaxies, the abundance of primordial elements,
and the CMB.
Hubble?s Law: The first key observation, made by Edwin Hubble [2], is that there is a
proportional relationship between the distance to a galaxy and its redshift: v = H0 D, where
v is the velocity of the galaxy, D is the co-moving distance to the galaxy, and H0 is Hubble?s
constant.1 In other words, all galaxies are moving away from us and the ones that are farther
away have higher apparent velocities; the distance between galaxies is increasing.
Further, the measured distribution of galaxies is isotropic and homogeneous; the universe
looks largely the same in all directions. Measurement of the interaction between the Cosmic
Microwave Background radiation (see �3) and matter in distant galaxies provides evidence
that the CMB has been uniformly cooling for billions of years [4]. This is only possible
with metric expansion2 of the universe, thus Hubble?s law supports the theory that space is
undergoing metric expansion as the Big Bang model suggests.
Distribution and evolution of Galaxies: A second set of observations that support the
Big Bang model are distribution of galaxies and the ages of the stars within them. Galaxies
with older stars are found to be farther away than younger ones supporting the fact that the
universe is expanding. In addition, the formation of galaxies and large-scale structure in the
universe can be explained within the Big Bang model framework [5]. Qualitatively, as the
1. While Hubble was the first to notice this relationship, he miscalculated the value of Hubble?s constant.
km
Current measurements place it at 70.4+1.3
?1.4 sM pc [3] as opposed to his initial estimate of 500.
2. In metric expansion is the expansion of space itself; the distance between all points increases with time.
2
universe expands, it cools to a point where it becomes matter dominated instead of radiation
dominated. At this point gravitational forces which attract particles become stronger than
the radiation pressure pushing them apart. Small fluctuations in the matter density of the
early universe are the seeds of the galaxies we see today.
Abundance of primordial elements: The Big Bang model also can be used to describe
and predict the abundance of light elements in the universe (D, He3 , He4 , etc.). The
formation of these elements can be described by nuclear processes in the rapidly expanding
and cooling first minutes of the universe [6]. There is a limited time during which the
temperature and density of the early universe were sufficient for nuclear fusion. Currently,
Big Bang Nucleosynthesis is the only theory that can explain and predict these elemental
abundances.3
A fourth key prediction of the Big Bang model is the existence and specific properties of the
Cosmic Microwave Background radiation.
1.3
The CMB
The Big Bang model posits that 13.75 � 0.11 [3] billion years ago the universe began in an
extraordinarily hot, dense, compact state and then cooled as it expanded. Roughly 380,000
years after the Big Bang, the universe finally reached the point where it had expanded and
cooled enough that matter and photons could decouple. This period also is referred to as the
time of ?recombination? as the universe was cool enough to allow electrons and protons to
combine to form neutral hydrogen. Before decoupling the universe was a hot ionized plasma
where the mean free path of photons was low compared to the Hubble radius.4
3. In fact, only a single value needed ? the ratio of photons to baryons ? to calculate these elemental
abundances.
4. The Hubble radius (RH = c/Ho ) is the distance beyond which objects in the region of the Universe
surrounding an observer recede from the observer at a rate greater than the speed of light, due to the
3
Known as the ?surface of last scattering?, this was the moment when the universe became
transparent. Before this time, the universe was opaque to observations. This relic radiation
? the Cosmic Microwave Background (CMB) ? exists all around us today and provides a
unique window on the structure and evolution of the universe.
Although the CMB was first predicted by Gamov in 1948 [7] it was not detected until
1965 by Penzias and Wilson [8]. Operating a radio horn antenna at the Crawford Hill
Observatory, they discovered a mysterious source of extra noise that later turned out to be
the CMB.
1.3.1
Temperature Isotropy of the CMB
The CMB is a nearly uniform background radiation. In fact, it is the most perfect blackbody
yet found in nature with a peak temperature of 2.725� 0.002 K. The temperature spectrum
of the CMB is found to be perfect blackbody spectrum to one part in 100,000 (or ? 10礙).
For a perfect blackbody, the total intensity is
I(?, T )d? =
1
2h? 3
d?
h?
3
c
e kT ? 1
(1.1)
where h is Planck?s constant, k is Boltzmann?s constant, ? is frequency and T is temperature.
The spectrum was measured to high precision by the Far Infrared Absolute Spectrometer
(FIRAS) instrument on the COsmic Background Experiment (COBE) satellite (see Figure
1.1)[9].
1.3.2
Temperature Anisotropy of the CMB
Although the CMB is nearly isotropic, there are small anisotropies indicating that the universe was not in perfect thermal equilibrium at the time of decoupling. These anisotropies
expansion of the Universe.
4
Figure 1.1: CMB blackbody spectrum as measured by COBE FIRAS [9]. The black line is
an ideal blackbody spectrum at 2.725 K. Errors bars are plotted at the 100? level.
were first measured by COBE-DMR, the differential microwave radiometer also on the COBE
satellite [10]. Figure 1.2 shows a full-sky temperature map of the CMB as measured the
Wilkinson Microwave Anisotropy Probe (WMAP) [3]. The baseline 2.725 K has been removed to reveal the small anisotropies. The power and scale of these anisotropies have
precise predictions for the structure of the universe. In order to extract more quantitative
information from these maps, it is conventional to decompose the power on the sky into
angular multipoles. Further details of the calculation of this angular multipole power spectrum are given in �6. Figure 1.3 shows the temperature power spectrum of the CMB as a
function of angular scale as measured by WMAP [11].
Upon inspection of the temperature power spectrum, one will immediately notice that it
is not a flat spectrum; there are characteristic angular scales with more power than others.
To understand the cause of these peaks, let us return the hot photon-baryon plasma that
existed before moment of last scattering. Here there are two competing forces: gravitational
5
Figure 1.2: Full-sky maps of the CMB temperature anisotropy as measured by WMAP, 7-yr
data [12]. Top: Maps in Q-Band (40 GHz) and W-Band (90 GHz), the observing frequencies
used in QUIET. The saturated red band is the foreground signal created by our galaxy. Bottom: Foreground removed map made using the Internal Linear Combination (ILC) method
[13]. The overall 2.725K signal and the dipole signal created by the motion of the earth
relative to the CMB have been removed.
attraction and photon pressure. Primordial density fluctuations in the plasma will create
areas that are slightly over-dense. The stronger gravitational forces in these over-dense
regions will attract yet more radiation-coupled matter. At some point the area will become
sufficiently dense that the radiation pressure will dominate pushing the photon-baryon fluid
to rarefy. In effect, ?acoustic? oscillations are set up. The amplitude of the oscillations
depend on relative abundances of baryons and photons. The pattern of the oscillations at
the moment of decoupling can be see in the CMB. Each mode will have had a different
amount of time to oscillate depending on when it entered the causal horizon.5 Peaks in the
5. Points that are farther apart than the time it would take for light to travel from one to the other are
outside the causal horizon.
6
Figure 1.3: Temperature power spectrum of the CMB temperature anisotropy as reported
by WMAP 7-yr release [11]. The red line is calculated using the ?CDM model. The gray
band as low ` is uncertainty due to cosmic variance.
power spectrum occur where a mode had completed an integral number of half-oscillations.
Figure 1.4 illustrates the correspondence between the modes of the acoustic oscillation and
the peaks in the power spectrum.
A staggering amount of information can be extracted from the precise details of the CMB
temperature power spectra. Lambda Cold Dark Matter (?CDM ), is frequently referred to
as the standard model of Big Bang cosmology. It is a six-parameter model given by baryon
density (?b ), dark matter density (?c ), dark energy density(?? ), the optical depth of reionization (? ), scalar spectral index (ns ), the Hubble constant ( Ho ), and the amplitude of the
curvature fluctuation (?2R ). Tuning this model to be consistent with the CMB power spectrum and other cosmological observations6 constrains the possible values of these parameters
and therefore describes our universe. For example, the first peak of the CMB temperature
power spectrum tells us that the universe is close to spatially flat and constraints on the
second peak and third peak give us the levels of baryonic matter, dark matter and radiation
in the early universe. For a full description of information that can be extracted from the
6. Astronomical abundances of elements, the accelerating expansion of the universe, large-scale structure
in the universe, etc.
7
Figure 1.4: Illustration of acoustic oscillations in primordial photon-baryon plasma giving
rise to peaks in the temperature power spectrum of the CMB. Since the spectrum (top)
measures power, the amplitude, not the sign of the oscillation is relevant; both overdense
and rarefied regions will produce a peak in the power spectrum. Figure adapted from [14].
CMB see [15] and references therein. Using the ?CDM model, one also can derive other key
values such as the age of the universe (to ). Table 1.1 lists the current tightest constrains on
cosmological parameters given by a combination of measurement of the temperature power
8
spectrum and other cosmological measurements.7
Table 1.1: ?CDM Cosmological Parameters determined by the WMAP 7year results [16]
Parameter
Value
+0.056
100?b
2.249?0.057 � 0.016
2
?c h
0.1120 � 0.0056
0.727+0.030
??
?0.029
?
0.088 � 0.015
ns
0.967 � 0.014
2
?R
2.43 � 0.11 � 10?9
to
13.77 � 0.13 Gyr
Ho
70.4 � 2.5kms?1 Mpc?1
The goal of extracting this information about the structure and evolution of the universe with greater and greater precision has occupied scientists for more than two decades;
measurement of the CMB has created an era of ?precision cosmology.?
7. Other measurements include distance measurements from the Baryon Acoustic Oscillations (BAO) in
the distribution of galaxies, the Hubble constant (H0), and high-redshift Type Ia supernovae.
9
1.4
Inflation
While the Big Bang model has a broad range of evidence supporting it, several outstanding problems in cosmology remain, including the horizon, flatness, and magnetic monopole
problems. Attempts to resolve these problems led to the development of a complementary
theory known as inflation [17, 18, 19, 20]. Inflation suggests that the universe underwent a
brief period of exponential expansion. This inflationary period is thought to have occurred
between 10?36 and 10?33 seconds after the Big Bang, but during that time the universe expanded by more than a factor of 1026 in size. In addition to resolving the issues mentioned
above, inflation provides a compelling explanation for the origin of structure in the Universe
[e.g. 21, and references therein]. Although all cosmological data collected thus far, including measurements of CMB anisotropies, support the paradigm of inflation, the underlying
fundamental physics responsible for inflation is unknown.
The problems in the standard Big Bang cosmology model that motivate the development
of inflationary theories are described in �4.1. One of the simplest examples posited to
explain the mechanism of inflation ? single field slow-roll inflation ? is discussed in �4.2.
1.4.1
Problems with the standard model
While the ?CDM model provides a solution that describes much of the current conditions
and observable history of the universe, there are three major problems that are unresolved
unless one posits a period of inflation.
Horizon Problem: When we look at the CMB we see that globally, the universe has
a mostly uniform temperature with only small anisotropies, and temperature-polarization
(TE, �6) correlations are seen at large angular scales (& 7? ). Since the CMB is a snapshot
of the universe at the time of recombination, if only known standard model physics is used,
light would only have had time to cross an amount of space that subtends a few degrees on
10
the sky. Parts of the sky that are separated by more than a few degrees would not have had
time to exchange information; they were out of the range of causal contact. So how is the
universe at equilibrium over much larger distances?
Before inflation, there wasn?t a plausible physical mechanism that could explain this
contradiction. The horizon problem can be answered by inflationary theory. If the universe
were once very small and then expanded at superluminal speeds stretching space-time, then
regions that were originally in causal contact would be separated by huge distances after
inflation. The observable universe has large scale structure, including uniform temperature,
because there was a time in the past when it was able to equilibrate, before inflation pushed
many regions out of causal contact. Further, inflation can explain the origin of the primordial
fluctuations in the CMB. What were originally quantum fluctuations, were inflated to sizes
many orders of magnitude larger and frozen into the pattern we see in the CMB today.
Extreme Flatness of Space: This is a ?fine-tuning? problem. Some of the parameters
of the universe, like the matter and energy density, affect the flatness or curvature of space.
There is a critical value required for a flat universe and the density of the universe is very close
to this value and measured to high precision by WMAP (?k = 1 ? ? ? = ?0.0023+0.0054
?0.0056 ,
crit
where ?k is the spatial curvature density, ? is matter density, and ?crit is the critical density
required for flat space) [16]. Even a small deviation in either direction would result in a
universe with spatial curvature. With the rapid expansion of inflation the curvature of space
would have been diluted, explaining its extreme geometric flatness.
Absence of Magnetic Monopoles: Grand unification theories predict the existence of
magnetic monopoles [22]. Monopoles should have been produced in abundance at the high
energies that existed in the early universe. However this particle is yet to be discovered.
Searches have placed upper limits on the abundances observed to be less than 1 in 1029
[23]. The rapid expansion of inflation soon after production of monopoles would dilute the
11
abundance of monopoles to be so rare that we wouldn?t expect to have a high probability of
observing one today.
1.4.2
Single Field Slow Roll Inflation
While inflationary theories solve the major cosmological problems described above, Standard Model particle physics cannot explain the mechanism of inflation. Thus a number of
phenomenological approaches have been employed. One of the simplest approaches is to use
a model with a single scaler field with potential energy. Following [24], let us postulate a
potential V (?) where ? is a scalar field, the inflaton field, that can be thought of as an order
parameter that gives the change in inflationary energy. This potential will create a constant
negative-pressure vacuum energy density causing space to expand exponentially. The potential needs to be chosen such that scalar field slowly returns to its potential minimum, at
which point inflation ceases. In this framework, inflation can only occur if the scalar field
satisfies ?slow-roll? conditions expressed with two parameters ? and ? where
m2Pl V 00
m2Pl V 0 2
,? =
=
16? V
8?
V
(1.2)
where mPl is the Planck mass. The slow-roll conditions dictate that the slow-roll parameters
be small (?, ? << 1). Inflation ends when the slow-roll conditions are violated, ?, ? ? 1.
During inflation, fluctuations in ? can generate scalar perturbations. Tensor perturbations of the metric (gravity waves produced during inflation) can also be generated. These
perturbations create corresponding anisotropy patterns in the CMB. The power spectra of
the scalar (PS ) and tensor (PT ) perturbations at the end of inflation can be expressed as:
PS (k) '
?
3
2
16? ? H2
, PT (k) '
k=aH
where H is the Hubble parameter, H = 8?2 V (?).
3mPl
12
H2
4? 2 m2P l
(1.3)
k=aH
Although inflationary models will generically produce both scalar and tensor perturbations the amplitudes of each are model dependent. In order to distinguish between them, it
is useful to consider a single parameter ? the tensor to scalar ratio, r. Since there is no a
priori prediction for the slow-roll parameters and therefore the potential, the amplitude of
gravitational wave background cannot be predicted in a model-independent manner. There
is a critical value (rcrit ), however, that will allow us to distinguish between theories. For
large-field models8 , r > rcrit . If, on the other hand, r < rcrit , small-field models are correct.
In many attractive slow-roll models, the energy scale of inflation, V 1/4 can be written as,
r 1/4
V 1/4 = 1.06 � 1016 GeV
rcrit
(1.4)
where rcrit ? 0.01 [25].
While scalar and tensor perturbations can generate temperature anisotropies in the CMB,
the signal from tensor perturbations decays quickly when the physical scale of the gravity
wave perturbations become smaller than the Hubble radius. At large angular scales, however,
tensor perturbations can create a unique signature in the polarization of the CMB. It is this
signal that we aim to detect.
1.5
CMB Polarization
The CMB is partially polarized, but the CMB polarization signal is orders of magnitude
smaller than the signal from the temperature anisotropies. While the small size of the
polarization signal makes precise measurement difficult, the potential reward is great since
detection of the ?B-mode? polarization (�5.3) would provide evidence of primordial gravity
waves. Analysis of the B-mode signal would allow us to probe times far earlier and energy
scales far greater than those we can reach through other means.
8. Coincidentally, for large-field models, the energy scale ends up being near the Grand Unification Scale
in particle physics, although it is actually determined by the Planck scale ? 1.22 � 1019 GeV .
13
1.5.1
Stokes Parameters
There are several ways to describe the polarization of a radiation field. For CMB measurements, stokes parameters are most often used. The four stokes parameters, unpolarized
intensity (I), linear polarization (Q & U), and circular polarization (V), completely define
that polarization at any point on the sky. Using two cartesian bases offset by 45? , (x,y) and
(a,b), the stokes parameters are calculated as:
I = |Ex |2 + |Ey |2 = |Ea |2 + |Eb |2 ,
(1.5)
Q = |Ex |2 ? |Ey |2 = 2Re(Ea Eb? ),
(1.6)
U = 2Re(Ex Ey? ) = |Ea |2 ? |Eb |2 ,
(1.7)
V = 2Im(Ex Ey? ) = 2Im(Ea Eb? )
(1.8)
where E is the amplitude of the electric field. Figure 1.5 illustrates the Stokes parameters.
The CMB is not expected to be circularly polarized, so measurements will concentrate on I,
Q & U.
Figure 1.5: Diagram of the Q, U and V stokes paramaters defined in Equations 1.6 to 1.8.
Adapted from [26].
14
1.5.2
Thomson Scattering
Thomson scattering ? the scattering of electromagnetic radiation off of a free charged particle
? is the mechanism through which the CMB was partially polarized. Heuristically, the electric
field of an incident wave causes a charged particle to oscillate and in turn emit radiation.
This emitted radiation will be of the same frequency, radiating most strongly in the direction
normal to motion of the incident wave and polarized in the direction of the charged particle?s
motion. The polarization and intensity of the scattered radiation is dependent on the incident
radiation as described by the differential Thomson scattering cross-section:
d?T
=
d?
2 e
? � ?0 2
me c
(1.9)
where ? is the incident polarization direction and ?0 is the polarization direction of the
scattered radiation.
If there is unpolarized radiation isotropically incident on an electron, the scattered radiation will be net unpolarized. If, however, there is a quadrapole anisotropy in the intensity of
the radiation field incident on an electron and perpendicular to the line of sight, the scattered
radiation will be linearly polarized as shown in Figure 1.6.
Before decoupling, the primordial plasma was optically thick (the mean free path of photons was low). Photons incident on a free electron from locations at different temperatures
would only be possible once recombination had begun and the plasma became optically thin
enough, which occurs near the end of decoupling. However, since decoupling was in progress,
there were fewer and fewer free electrons so polarized radiation could only have been produced during a very short time at the end of decoupling. As a result, the polarization fraction
is . 1%.9
9. Determined from rough ratio of temperature power spectrum to E-mode power spectrum (see Figures
1.3 and 1.11).
15
Figure 1.6: Thomson Scattering of photons off of a free electron when the incident radiation
field has a quadrapole anisotropy in intensity (temperature). In this case, linearly polarized
radiation is produced propagating in the x? direction by the difference in temperature from
the unpolarized radiation incident from the y? and z? directions. Adapted from [27].
1.5.3
E & B Mode Polarization
It is convenient to decompose the polarization on the sky into two patterns. Here we use
an analogy to electromagnetism. E-modes are patterns that are entirely composed of the
radial, or the curl-free component of the polarization. B-modes measure the divergencefree component. Figure 1.7 provides an illustration of E-mode and B-mode patterns. This
decomposition can be used to distinguish between the possible sources of CMB polarization.
There are three mechanisms that can create quadrapole anisotropies in the CMB: scalar,
vector and tensor perturbations.10 Vector perturbations are damped by expansion and only
10. A useful way to describe the sources of the quadrapole anisotropy is to decompose it into l = 2 spherical
harmonics. The scalar and tensor fluctuations correspond to the m = 0 and m = 2 modes, respectively. The
16
scaler and tensor perturbations survive. While both scalar and tensor perturbations can
create an E-mode pattern, tensor perturbations ? primordial gravity waves ? can create
B-mode patterns as well.
Figure 1.7: Diagram of E-mode (curl-free) and B-mode (divergence-free) patterns in a field
of polarization vectors.
Scalar perturbations:
As discussed in �3.2, the density perturbations in the photon-
baryon plasma that existed just prior to recombination induced acoustic oscillations in the
plasma. As the plasma in a particular location oscillates between dense/hot and rarefied/cold
it creates a velocity distribution that is 90? out of phase with the density oscillation. From the
perspective of an electron in the plasma, the incident photons are blueshifted or redshifted
by different amounts in different directions creating an apparent quadrapole anisotropy (see
Figure 1.8). Scalar perturbations can only create E-mode polarization [28]. A scalar perturbation has no ?handedness?; it cannot induce polarization with a curl component.
Vector perturbations:
Vorticity in the plasma could theoretically cause varying veloc-
ity gradients in much the same way the scalar perturbations do: quadrapole anisotropies
resulting from doppler shifts in the plasma. This is expected to be a negligible signal since
vorticity would be damped out in most inflationary models [29].
vector, or m = 1 modes, are not produced to leading order in perturbation theory and will not be relevant
here.
17
Figure 1.8: Velocity field of an overdense region in the plasma creates an apparent quadrapole
anisotropy in the CMB. An electron in the plasma sees plasma moving toward it from all
directions, but with varying speed. The relative velocities create a quadrapole anisotropy
in the redshift of the incident radiation. Left: reference frame of the density perturbation
Right: reference frame of the electron. Adapted from [14].
Tensor perturbations:
Gravity waves are tensor perturbations predicted to have been
generated during inflation. Gravity waves moving through the primordial plasma during
recombination would stretch and compress space in orthogonal directions (see Figure 1.9).
As space stretches, so too will the wavelengths of photons propagating through it creating a
quadrapole anisotropy.
Tensor perturbations are not constrained to be symmetric like scalar perturbations.
While gravity waves also produce E-modes, they are the only predicted source of B-mode
patterns in the polarization of the CMB.11 Measurements of a B-mode signal would be
evidence of inflation.
1.6
Measurements of CMB Power Spectra
For measurements of the temperature anisotropy of the CMB, the power as a function of
angular scale on the sky can be decomposed in terms of spherical harmonics.
11. B-mode signals can be generated by forground sources (see �7.3).
18
Figure 1.9: Polarization through gravity waves. As a gravity wave passes through the surface
of last scattering (plane of the page), space and therefore photons propagating through
it are alternately stretched and compressed. Depending on direction of the gravity wave
propagation with respect to the line of sight either an E-mode or B-mode signal can be
produced.
T (n?) =
X
a`m Y`m (n?)
(1.10)
`m
where Y`m is the spherical harmonic and a`m is the amplitude of the signal and n?. The linear
polarization can be decribed as a spin-2 field, where we can write the Stokes parameters in
terms of spin-2 spherical harmonics �Y`m (n?) [30, 11].
Q(n?) + iU (n?) =
X
a2,`m (2 Y`m (n?))
(1.11)
`m
B
where aE
`m and a`m are the E & B mode amplitude calculated as:
aE
`m
=?
aB
`m = ?
a2,`m + (?1)m a?2,`?m
2
a2,`m ? (?1)m a?2,`?m
2i
(1.12)
(1.13)
For any given angular scale, `, there are 2`+1 independent functions of m. The two-point
correlation function of the angular power as a function of ` can be defined as:
19
?Y
C`XY = haX
`m a`m i
(1.14)
where X, Y are power in temperature (T) or polarization (E or B). From measurements of
the temperature and polarization of the CMB six independent power spectra: C`T T , C`EE ,
C`BB , C`T E , C`T B and C`EB can be calculated.
Over the last two decades, the TT power spectrum has become increasingly well-constrained
(see Figure 1.3) by WMAP [11] and a combination of many other experiments [e.g. 31, 32,
33, 34, 35].
E-mode polarization has now been detected by many experiments [e.g., 36, 37, 38, 39,
40, 41, 42] as well. However, before QUIET, only BICEP had accurately measured E-mode
polarization in the region of the first acoustic peak [43].
When temperature and E-mode measurements are combined, they are able to constrain
the cross-power spectrum C`T E (Figure 1.10). TE measurements [e.g., 37, 33, 34, 11, 32, 43]
are consistent with predictions. The peaks in the temperature and E-mode polarization
spectra are expected to be out of phase by 90? .12 The expected anti-correlation at ` = 150
and peak at ` = 300 confirm they are purely adiabatic oscillations [13] as expected from
inflationary models. TE also provides information constraining the thickness of the surface
of last scattering, and gives new information on the epoch of reionization.13
Signals from B-modes remain unmeasured. Figure 1.11 shows the upper limits placed on
the BB spectrum thus far. BICEP also reports the best limit on r coming from cosmological
B-modes: r < 0.72 at the 95% confidence level [43]. A new generation of experiments aims for
good sensitivity in this range of r. Establishing the existence of primordial B-modes would
12. Velocity gradients in the plasma (which is out of phase with the density fluctuations) produced the
E-mode polarization so the polarization spectrum is directly out of phase with the temperature anistropy
spectrum.
13. Reionization is the era from roughly one billion to 150 million years ago 6 < z < 20 when structure
had formed that was energetic enough to reionize neutral hydrogen, but before the matter density of the
universe had decreased due to expansion decreasing the frequency of scattering interactions.
20
Figure 1.10: Measurement of the TE power spectrum of the CMB as measured by WMAP
[11] and QUaD [32]. Gray line is the ?CDM model.
both verify an important prediction of inflation and provide access to physics at an incredibly
high energy scale. The most stringent limit to date is r < 0.20 at the 95% confidence level
[16] set by a combination of CMB?temperature-anisotropy measurements, baryon acoustic
oscillations, and supernova observations, but cosmic variance prohibits improvements using
only these measurements.
By parity arguments TB and EB are expected to be zero. They are still useful to
compute as a test of residual contamination in the data, however, since foreground signals
and systematic effects could produce a non-zero signal. Further, if a signal were in fact found
and systematics/foregrounds could be ruled out, it would be evidence of new physics.
1.7
Foregrounds
One major problem encountered in attempts to measure CMB polarization is the existence
of contamination in the measurement from astrophysical sources. CMB photons are not the
only source of polarized radiation in the sky. Collectively, these sources of contamination are
known as foregrounds as they lie between us and the surface of last scattering. The primary
source of foreground contamination comes from the galaxy. This diffuse galactic emission can
21
Figure 1.11: Current best measurements of the EE angular power spectra and upper limits
on the possible BB power. Including DASI [37], BOOMERANG [33], MAXIPOL [44], CBI
[34], CAPMAP [35], WMAP [11], QUAD [32], and BICEP [43]. The gray line in the EE plot
is the ?CDM model. In the lower plot the solid gray line is the total expected B-mode signal
from primordial gravity waves, assuming r = 0.2 (left) and gravitational lensing (right).
be broken into three components or sources: synchrotron, thermal dust, and free-free. These
will be described in �7.1. Two other foregrounds are considered, extragalactic compact
22
radio sources (�7.2) and gravitational lensing (�7.3). Like diffuse galactic emission, compact radio sources emit polarized light that can contaminate the CMB signal. Gravitational
lensing distorts the existing CMB signal. Although these foregrounds provide interesting
science in their own right, they will only be considered as contaminations of the CMB signal
for the purposes of this experiment.
1.7.1
Diffuse Galactic Emission
The most prominent foreground is emission from material lying in the disk of our own Galaxy.
Diffuse Galactic emission includes three components: synchrotron and free-free radiation and
emission from thermal dust. Figure 1.12 shows the expected levels of contamination from
diffuse galactic emission. As one can see, in temperature, synchrotron emission dominates
at frequencies below 60 GHz while emission from dust particles becomes dominant at higher
frequencies. In polarization, the foreground minimum is shifted up to be closer to 80 GHz.
This varying spectral index allows us to distinguish these components by observing at multiple frequencies. Currently, however, none of these foregrounds is well known, either in the
exact form of their frequency dependence or their spatial distribution on the sky. While
foreground emission is a concern in measurements of the temperature anisotropy and the Emode polarization, it is expected to present a much larger problem for B-mode polarization
measurements. In fact, galactic emission may limit our ability to detect B-mode polarization
from primordial gravity waves.
Galactic Synchrotron Emission: Synchrotron radiation is generated by the acceleration
of relativistic electrons spiraling through the galactic magnetic field. The emission varies as a
power-law spectra, decreasing with frequency. The current best measurement of synchrotron
emission, constrains the spectral index, ?, to the range ?3.13 ? ? ? ?2.41 [46]. Recent
measurements suggest that there is spatial structure to polarized Galactic synchrotron emis23
Figure 1.12: Estimates of the possible size of sources of contamination in temperature from
diffuse galactic emission including, synchrotron and free-free radiation and emission from
thermal dust. The microwave bands are over-plotted as is the power level of the CMB
temperature anisotropy. The Q-Band and W-Band are used in QUIET. Figure adapted
from [45].
sion which depends on Galactic latitude [47]; the properties of synchrotron emission may
be significantly different between the galactic plane and high latitudes. The synchrotron
emission will be partially linearly polarized perpendicular to the alignment of the galactic
magnetic field. The mean polarization fraction varies across the sky; from 2%-4% in the
galactic plane and rising to over 20% at high latitudes [48].
Thermal Dust Emission: Galactic dust, heated by ambient thermal radiation, emits
blackbody radiation. This radiation can be polarized because the dust grains are orthogonally aligned to the galactic magnetic field and thus emit preferentially in the direction
perpendicular to the galactic magnetic plane. The spectra of thermal dust emission roughly
follows a power law that increases with frequency (1.5 ? ? ? 2). However, other effects such
as local magnetic conditions, turbulence and dielectric properties of the dust grains can also
effect the polarization [49]. Emission from thermal dust is fractionally polarized at the level
24
of 1% near the Galactic center and rising to 6% at the anticenter [48].
There is a a second source of dust foreground ? emission from ?spinning dust.? Spinning dust is theoretically generated by the electric dipole of rapidly spinning (10-60 GHz)
nanometer-scale dust grains [50]. The existence of spinning dust would explain the anomalous microwave emission (AME) observed by numerous experiments in the 10 - 60 GHz range.
Emission from spinning dust is subdominant to both synchrotron and thermal dust emission
but with a peak from 20-40 GHz [51, 52], it?s spectral index is different than that of thermal
emission.
Free-Free Radiation: Free-Free radiation is thermal Bremsstrahlung radiation generated
when electrons are deflected by ionized gas in the intracluster medium (ICM). It is known
as free-free because the electron is ?free? before and after the interaction with the charged
particle that is deflecting it. Like synchrotron, the spectrum of free-free radiation falls off
with increasing frequency (? ? ?2.1). Free-free emission is a sub-dominant foreground
for polarization measurements because the process produces unpolarized radiation. While
Thomson scattering of an apparent quadrapole created at the edges of an HII region in the
ICM can create polarization, this contribution should be negligible [53].
Full sky maps of the synchrotron, thermal dust, and free-free emission as fit by WMAP
[46] are shown in Figure 1.13. These template maps were used to determine the regions of
minimal foregrounds in which QUIET observes.14
14. Actually, due to the timing of our patch choice decision, a slightly earlier [54], but consistent version
of these maps were used.
25
Figure 1.13: Full sky foreground maps from the WMAP 7yr release [46]. Left: synchrotron
emission, Middle: free-free emission, and Right: emission from thermal dust. Maps are
shown for both Q-Band and W-Band. Note that the synchrotron and free-free components
are stronger in Q-Band, while thermal dust dominates in W-Band.
1.7.2
Compact Radio Sources
Compact radio sources, commonly called ?point sources?,15 can be polarized and thus contribute a spurious signal to polarization measurements of the CMB. They primarily contaminate high-` measurements. Their rms contribution roughly scales as `, assuming a random
distribution. However, their effect is expected to be sufficiently diluted on the angular scales
of interest ( ? ` < 1000) that only the brightest sources need be removed [55]. They could,
however, be a significant source of contamination in high-` polarization measurements.
Although a few surveys exist (e.g. NRAO VLA Sky Survey at 1.4GHz [56]), most are
at low frequencies and would require extrapolation of the polarization and flux to higher
frequencies where the majority of CMB experiments operate. Additional observations are
needed. Currently, the WMAP 7 year point source catalog [46] is the most extensive full-sky
compilation of point sources in the relevant frequency range, although their information is
15. They are so named due to the fact that they are mostly much smaller than the angular size of the
instrument?s beam which is detecting them.
26
much more precise for temperature than for polarization measurements.
The current method for dealing with point source contamination is to mask the known,
bright sources from our maps before calculating the angular power spectra. The details are
described in �3. We can then put limits on contributions from unresolved and unmasked
point sources. These are subdominant effects for QUIET which will be described further in
�4.1.
1.7.3
Gravitational Lensing
While most of the polarization foregrounds are created by intervening sources emitting radiation, gravitational lensing distorts the existing CMB photons. As CMB photons propagate
through the universe, they can be deflected from their original path by large concentrations
of matter in their path. This deflection can modify the existing pattern of both temperature
and polarization patterns in the CMB, but it is of much greater concern in the latter case.
Gravitational lensing can distort the expected E-mode pattern in the CMB into a B-mode
pattern. Consider a patch of CMB with an E-mode (radial) pattern. If you lens this E-mode
pattern, deflecting each element slightly, then the resulting pattern will have a slight B-mode
(non-radial) component. This lensing B-mode signal will be stronger than many predicted
values of the B-mode signal generated by gravity waves from inflation, especially at high `
(see Figure 1.11). At low-`, however, the gravity-wave B-mode signal could still be dominant
depending on the size of r. We can only theorize about how much of a problem the lensing
signal may be.
QUIET is one of two current-generation CMB polarization experiments to observe at frequencies suitable for addressing synchrotron contamination, making observations at 43 GHz
(Q-band) and 95 GHz (W-band) and with sufficient sensitivity to begin to probe primordial
B-modes. The other is Planck [57]. Most planned or operating CMB polarization experi-
27
ments employ bolometric detectors which generally observe at frequencies & 90 GHz. For
QUIET, the other possible contaminations described above are expected to be at a sufficiently low level that they can be masked (point sources) or neglected.
28
CHAPTER 2
QUIET PHASE I INSTRUMENT
The QUIET instrument includes a telescope mount, two receivers, optics, ground shielding
and electronics. The instrument is illustrated in Figure 2.1. The two receivers, hereafter
called the Q-Band and W-Band receivers, share a common design with only minor modifications due to the different frequency bands in which they operate. The Q-Band receiver
contains a 19-element array of detectors that are sensitive to 43 GHz radiation, while the
W-Band receiver contains a 91-element array of detectors that operate at 94 GHz. Each
receiver was mounted sequentially on the same platform and used a common ground screen,
and telescope mirrors. While the electronics boards and software used to power and control
the receivers were common in design, the two receivers did have distinct electronics enclosures. The W-Band receiver and its associated electronics were integrated and characterized
in Chicago and will be the primary focus of this chapter ? values provided will be for the
W-Band receiver unless otherwise specified.
QUIET combines several unique features to achieve a very low level of contamination in
the multipole range where a primordial?B-mode signal is expected. These include compact
polarization-sensitive modules based upon High?Electron-Mobility Transistor (HEMT) amplifiers (�4.1), a new time-stream ?double-demodulation? technique (�4.2), Mizuguchi?
Dragone (MD) optics (�2.2), natural sky rotation (�3), and frequent rotation about the
optical axis (�3)
The telescope mount and deck platform are described �1. The optical chain from the
sky to the detectors will be addressed in �2, including the telescope mirrors, platelet array,
septum polarizers, and ground screen. The design and components of the cryostat that houses
and cools the detectors is discussed in �3. The detectors are described in �4 including
efforts to characterize and optimize their performance. The electronics are treated in �5,
including biasing and protection electronics, telescope control system, thermal regulation
29
Figure 2.1: Overview of the QUIET instrument. The cryostat (6) and 1.4-m telescope
mirrors (3,4) are enclosed in a rectangular comoving absorbing ground screen (8); in this
figure its walls are transparent. The telescope, cryostat and electronics (7) are mounted on
a single platform (1) attached to the deck bearing (9), which allows rotations around the
instrument?s optical axis. The telescope sled (2) and cryostat mounting collar (5) attach the
mirrors and cryostat to the deck platform. Telescope control electronics (10), walkways (11),
and an optical pointing telescope (12) also are attached to the deck platform [1].
and monitoring electronics and the data acquisition system.
2.1
Telescope Mount and Deck Platform
The QUIET telescope, electronics, receiver and ground screen all are mounted on a ?deck
platform? as shown in Figure 2.1 (#1). The deck platform is bolted to the deck bearing of
a telescope mount (#9 ) which originally was built for a previous experiment, the Cosmic
Background Imager (CBI).1 The deck also supports smaller components, including walkways
(#11) for easy access to all components on the deck,2 telescope control electronics (#10, �5)
and an optical pointing telescope (#12 shows its mount, see �3 for further description).
1. CBI operated from January 2000 through May 2008 making CMB observations at 30 GHz [58, 59, 60].
2. The deck platform is roughy 15ft above the ground when the telescope is stowed, pointing at the zenith.
30
The telescope mirrors and the cryostat are attached to the deck platform with a ?sled?
mounting structure. This sled (#2) provides mounting points for the mirrors and the cryostat mounting collar (#5), and features a rigid and stable structure to maintain telescope
alignment, a low center of gravity to minimize torque on the mount motors, and a clear optical path [61]. The sled rails and tensioning turnbuckles provide stability when the assembly
is tilted forward (cryostat elevated above mirrors or vice versa) or laterally.
The deck platform, telescope sled, cryostat, mirrors, electronics and ground-screen were
first integrated during a trial-assembly. As each piece was designed and built at a different
institution, it was vital to confirm that all parts met specifications and interfaced appropriately. Necessary modifications were made during the trial-assembly and the entire deck
structure was balanced to minimize stress on the mount motors. The structure then was disassembled and shipped to the Chajnantor Observatory (see �1), where it was reassembled
and installed on the CBI mount.
The mount provides three axis rotation of the entire deck platform. Figure 2.2 shows
the rotation axes of the mount ? azimuth, elevation and deck rotation. The azimuth drive
allows 450? of rotation (from ?185? to +265? where 0? is due North and East of North is
the positive rotation direction). The azimuth gear is mounted on top of the conical base
structure and is driven by pinion gears attached to two large electric motors.
The elevation drive consists of a jackscrew that pushes against the highest point on the
baseplate under the deck platform to ?tip? the telescope. The base plate is hinged above the
azimuthal drive and opposite to the jackscrew. The upper elevation limit, defined by the
telescope deck platform resting on baseplate of the mount, is 88.96? . The software limit is
set to 87? .3 As the deck platform is ?tipped up?, decreasing elevation, the amount of torque
required to hold it steady increases since the center of mass of the deck platform is shifting.
This torque is also dependent on the balance of deck platform. The weight and balance of
3. In W-Band , the Cloudsat satellite emits strongly at 90 GHz and passes near the zenith daily [62]. An
upper limit of 87? in elevation avoids the satellite.
31
Figure 2.2: Mount has three-axis rotation. Azimuth rotation and the azimuth drive are
shown in green. Rotation about the optical pointing axis (dotted line) of the telescope,
known as deck rotation, is shown in blue. Motion in elevation, shown in red, is driven by
a jackscrew that separates two hinged plates. The upper plate supports the deck platform
and the deck rotation drive.
the QUIET deck platform define the lower elevation limit which is set at 43? (software) and
40.35? (hardware). The combination of a limit switch and hydraulic brake stop the telescope
from moving beyond the lower elevation limit and possibly tipping over.
The deck drive is mounted on top of the plate that moves in elevation. It?s range of
motion is the same as that of the azimuth drive (450? of rotation, +185? to ?265? ). The
deck drive consists of a bearing rotated using three friction drive wheels. Deck rotation is
rotation about the optical pointing axis of the telescope and thus is useful in the mitigation
of systematic effects (see �3 and �5).
Rotation in azimuth and deck are limited by the extension of the cable wraps. Within
the base of the mount and below the deck platform there are wraps of cables connecting the
power, data, and cryogenic lines to the receiver and electronics and held taut by a tensioner
32
spring. Software and hardware limit switches, overlap switches, and optical encoders on the
azimuth and deck drives protect the telescope from driving beyond the full extension of the
cables.
The entire mount and telescope are enclosed within a protective dome (canvas over steel
support structure, visible at the bottom of Figure 2.8) that is open during observations, but
can be closed for maintainence or bad weather.
2.2
Optics
The first element in the QUIET optical chain is a 1.4-m side-fed Dragonnian dual-reflective
telescope (�2.1) [63, 64]. After being focused by the telescope mirrors, radiation is directed
into a platelet array of corrugated conical feedhorns (�2.2). Radiation from each feedhorn
enters a septum polarizer (�2.3) which separates left and right circularly-polarized components (L and R) into two waveguide ports which mate to a QUIET polarimeter module
(�4).
2.2.1
Mirrors
The QUIET antenna consists of two mirrors in a classical side-fed Dragonnian configuration (see #3,4 in Figure 2.1) [64]. The primary parabolic mirror and the secondary concave
hyperbolic mirror, which focus incident radiation, are oriented such that they satisfy the
Mizuguchi condition [63] in order to minimize cross polar response. The combination of a
large diffraction limited focal plane, high gain and low sidelobe response with low cross polar
response make the side-fed Dragonnian configuration preferable to other antenna configurations (e.g. Cassegrain or dual offset classical Gregorian antennas) [65, 66].
Each mirror was attached to the telescope sled at three points. Each of the three mounting
panels has two hexapod turnbuckles with ball joints, permitting adjustment of the mirror
orientation along three axes (x,y,z) at each of the three attachment points. Six tooling balls
33
are installed on the outer rim of each mirror. Precise measurement of the distance between
these 12 points allowed us to align the mirrors to the required geometric configuration with
a precision of < 150祄 for both the Q-Band and W-Band arrays. The telescope was aligned
manually at the beginning of each observation season and then the turnbuckles were locked in
place and checked periodically throughout the season to ensure that they had not loosened.
The mirrors are fabricated from aluminum plates with the reflective surface profile
(paraboloid, hyperboloid) cut in to one side and a light-weighting honeycomb structure
cut into the back. Each mirror is 1.4 m in diameter along the minor axis with a 2 cm rim
[61]. The beam profile is characterized in �2. The W-Band Full Width Half Maximum
(FWHM) beamsize is 12.0 2 � 0.03 (27.0 3 in Q-Band ) [67, 1]. A ray-tracing diagram showing
the beam path into the receiver is shown in �2.5 when sidelobes are discussed.
2.2.2
Platelet Array
Each of the detectors in the W-Band array needs to be coupled to the antenna. Traditionally,
coupling is accomplished via a corrugated horn. The taper of the horn creates a gradual
transition, impedance matching free space to the waveguide that feeds the signal into the
detectors. Corrugated horns feature wide bandwidth (> 25GHz for QUIET W-Band horns)
and high gain (> 26dB). Further the symmetric Gaussian beam, minimal cross-polarization
(< ?30dB), and small sidelobes and low spill-over offered by a conical corrugated horn design
are crucial in mitigating systematic effects that may be induced by instrumental polarization
(see �2 and �5) [68, 69].
Individually machining or electro-forming corrugated horns is expensive for large arrays.
Instead, QUIET uses a platelet array; it is the first CMB experiment to do so. Each horn is
made by drilling progressively smaller holes in a series of thin aluminum plates (Al6061T6A).
The plates are then stacked and diffusion-bonded together to form horns. In this way, the
pattern of holes for each of the 91 feedhorns was machined into each plate allowing the entire
34
Figure 2.3: Left: Solid model of a single corrugated feed in the platelet array. Adapted from
[68]. Right: W-Band 91 horn platelet array. The W-Band array is 42.8 cm wide (point-topoint) and 12.9 cm tall [70].
array to be built at once. Figure 2.3 shows a cross-section of a single horn in the platelet
array and an image of the finished W-Band array. While the 19 horn Q-Band platelet
array was made of 103 individual platelets, the W-Band platelet array is actually made of a
combination of 13 individual platelets each with one corrugation and 5 thicker blocks with
18 corrugations milled into each block. The W-Band array is 42.8 cm wide (point-to-point)
and 12.9 cm tall. Even after the array was light-weighted (the screw holes that allow the
array to be bolted down to an interface plate (see �3) were widened), it still weighed 20 kg.
Weight is one drawback to using a platelet array as it provides a significant thermal load on
the cryostat when the array must be cooled down to cryogenic temperatures (roughly 25 K).
The array has a hexagonal field of view measuring 7? across ( W-Band horns 40-50), with
0.7? spacing between neighboring beams in W-Band and 1.75? spacing in Q-Band.
2.2.3
Septum Polarizer Orthomode Transducer
The circular waveguide output port of each feedhorn in the platelet array is coupled into
a septum polarizer via a circular-to-rectangular waveguide transition that propagates all
polarization states (linear and circular). The septum polarizer is a type of orthomode tranducer (OMT) that separates incident radiation into its left and right circularly polarized
35
components (L = Ex + iEy , R = Ex ? iEy ).
Figure 2.4: Left: Schematic diagram of a septum polarizer, Right: propagation of EM modes
through the septum polarizer. Adapted from [71].
The QUIET OMT is composed of two parts: a stepped septum polarizer block, and a
splitter. The septum polarizer block was made by dividing two halves of a square waveguide
with a thin stepped septum (8mil width) and is based on the design described in Bornemann,
1995 [72]. The stepped septum induces a 90? phase shift between orthogonal modes of
the incident radiation; the mode that is perpendicular to the septum (T E10 ) propagates
unimpeded while the mode that is parallel to the septum (T E01 ) bends around the septum
(see Figure 2.4).
The splitter couples the OMTs closely-spaced, undersized output ports to the polarimeter
module. It consists of stepped transitions to WR-10 waveguide followed by pairs of E-bends
that separate the outputs to the spacing of the module inputs. The OMT was machined out
of aluminum 6061 and bolted to both the interface plate (input) and the module (output).
Figure 2.5 shows a W-Band OMT and a diagram of its component parts.
In W-Band the OMTs are tuned for minimum return loss at 95 GHz. The waveguide
cutoff frequency is 79 GHz, but performance deteriorates below 88 GHz due to detuning of
wavelength-dependent features in the OMT. The effective bandwidth is 17 GHz (88 GHz to
105 GHz) [73].
Ideally, the septum polarizer would perfectly separate and transmit the left and right
circular polarization components of the incident radiation to the module. There is, however,
36
Figure 2.5: Panel a: W-Band septum polarizer OMT [70], Panel b: diagram of the OMT,
Panel c: split view of the septum polarizer block with an enlarged view of the the septum,
Panel d: split-view of the splitter revealing the waveguide separating the outputs to the
spacing necessary to mate with the QUIET module. Panels c and d are the top and bottom
halves of panel b [73].
a small amount of differential loss and cross talk between the transmission of Ex relative
to Ey in the OMT. These terms will generate a small amount of instrumental polarization
known as I ? Q/U leakage. An example of how I ? Q/U leakage is generated in the
module is given in 2.4.2; the algebra describing the effects of the OMT differential loss and
cross talk in the detector time-streams appears in Appendix A. Methods for mitigating this
leakage are described in �3 and the systematic error due to instrumental polarization is
evaluated in �5
2.2.4
Differential Temperature Assemblies
We dedicated a small subset of the array to make a differential measurement of the CMB
temperature instead of the CMB polarization. In W-Band, six elements on the outer edge of
the array were converted into three ?differential temperature assemblies.? A single differential
temperature assembly was installed in the Q-Band receiver. A differential temperature
measurement requires that the temperature be compared between two points on the sky,4
T A , and T B . We accomplished this measurement by coupling radiation from neighboring
feeds in the platelet array to the same module in a construction that is functionally similar
4. An alternative method would be to compare a measurement of the sky to a know calibration source.
37
to that used in WMAP [74]. The septum polarizer OMTs of two neighboring detectors were
each replaced with an X-Y OMTs and Magic-Ts, which were then coupled together as shown
in Figure 2.6.
Figure 2.6: Photograph of one of the three differential temperature assemblies used in the
W-Band array [70].
A block diagram of the differential temperature assembly is shown in Figure 2.7. For
each of two neighboring feeds in the platelet array, A & B, radiation is coupled into the
circular input port of an X-Y OMT (OMTA , OMTB ). As its name suggests, an X-Y OMT
splits incident radiation into Ex and Ey linear polarizations. In the differential temperature
A,B
assembly (hereafter called a TT assembly), Ex,x is coupled (via waveguide) from OMTA(B)
to the Magic-T (a four port hybrid coupler) on the neighboring optical chain, Magic-TB(A) .
A,B
Ey,y is coupled directly from the other port of the X-Y OMT into the Magic-T in the same
optical chain (see Figure 2.7). In the configuration used in QUIET, the two output signals
are the sum and difference of the input signals respectively. Thus, the input signals to the
modules are EyA + ExB , EyA ? ExB for one module and EyB + ExA , EyB ? ExA for the other.
This configuration results in four simultaneous measurements of the temperature difference
between two points (A & B) on the sky. The signal path inside the module is described in
�4.2.
38
Figure 2.7: Schematic diagram of a differential temperature assembly. The inputs of two
neighboring horns in the platelet array are coupled such that both modules measure the
differential temperature between two point on the sky.
2.2.5
Ground Screen & Sidelobes
Although the telescope mirrors were designed to minimize it, a small fraction of the beam
will spill over the edges of the mirrors creating diffuse sidelobe response at large angles from
the main beam. Further, some contaminating signals could make their way into the beam via
multiple reflections. While these sidelobes cannot be eliminated, steps were taken to mitigate
their effect on the data. The amount of contamination will vary depending on where the
beams terminate (sky, ground, etc.).5 Since we are measuring the anisotropies in the CMB,
and modulating the signal via scanning of the telescope (�3), a constant contamination
signal is much preferable to a variable one. Thus, a co-moving ?ground screen? is placed
around the mirrors and receiver to screen out contamination from the ground. This allows
the sidelobes to terminate on a constant ? 280K signal.
5. The sky is ? 10K while the ground is ? 280K.
39
Figure 2.8: Lower and Upper Ground Screens. Courtesy Simon Radford [75].
There are three major parts to the ground screen, the bottom, lower and upper ground
screens (see Figure 2.8, BGS not shown). The primary part is the lower ground screen
(LGS), which is a large box that sits over the mirrors. It has a circular hole cut on one
side through which the cryostat window is inserted. There are large panels on either side
that allow access to the mirrors and cryostat after installation of the ground screen. There
is a large rectangular whole on top through which the beam exits the LGS and to which
the upper ground screen (UGS) attaches. The bottom ground screen is actually a set of
six smaller pieces that fit together in a jig-saw pattern to cover what would be the floor
of the box that is the LGS and a collar that covers the gap between the cryostat and the
wall of the LGS. These pieces were designed to be individually removable so that we could
maintain access to the cryostat and the space under the telescope sled that houses the deck
drive encoder and the cable wrap. The UGS is a telescoping cylinder that is meant to be
extended during observations, but retracted during bad weather to allow the protective dome
to close. The interior walls of the ground screen are sheets of Aluminum 6061 with a layer
of Emmerson Cummings HR10 Eccosorb attached and sealed with a sheet of microwavetransparent polyethelene foam (Volara) which is used for weather proofing. It is important
that water and ice don?t build up in the Eccosorb layer as they are polarized. While there is
no active temperature regulation on the ground screen, the exterior walls are painted white
40
to minimize radiative loading and 26 thermometers, spread throughout the groundscreen,
were implanted under the Volara sheeting and used to monitor the temperature.
Originally, only the lower and bottom ground screen were planned. While diffuse sidelobes terminate on the ground screen, two distinct sidelobe features were revealed during
simulations and data taking. Simulations performed on the QUIET optics [76] predicted
that the upper ground screen was necessary to absorb a sidelobe feature that was otherwise
missed, known as the triple-reflection sidelobe. Unfortunately the upper ground screen was
not completed until several months into the W-Band observing season. As predicted, contamination was found in this sidelobe in the Q-Band and part of the W-Band data when the
triple reflection sidelobe scanned over the sun. Strategies to excise this contamination from
the data are described in �2.
When the UGS was installed in January of 2010, a series of dedicated measurements
were performed with a polarized noise source to identify and map the sidelobes. Maps made
before and after installation of the UGS show the UGS successfully blocks the triple reflection
sidelobe. This test also revealed two additional sidelobes. The second (or ?spillover?) sidelobe,
which comes directly into the receiver over the top edge of the LGS near the top of the
secondary mirror, was also found in the data. Installation of the UGS has also removed this
second sidelobe. A final sidelobe that was discovered during these measurements revealed
that part of a panel of the BGS had come out of place. The hole was patched, the data were
flagged and will be addressed in the W-Band analysis. An illustration showing the major
sidelobes is shown in Figure 2.9.
2.3
Cryostat
The minimize instrumental noise, we cooled the detectors, OMTs and platelet array to
roughly 25 K. They were placed in a cryostat which was held at low pressure (< 10礣orr) and
cooled using two Gifford-McMahon dual-stage refrigerators (CTI Cryogenics Cryodyne 1020).
41
Figure 2.9: Raytracing diagram of sidelobes terminating on the Ground Screen. Adapted
from [77].
Each refrigerator was driven by a water-cooled compressor (CTI model 9600). Water cooling
was used since air cooling is inefficient at high altitudes. The compressors were attached to
the base of the mount, rotating with the azimuth drive, but not in elevation or deck since
they should remain upright during operation for efficient cooling. High purity Helium is
used as the coolant gas in the refrigerators. Helium lines connecting the compressors to the
refrigerators ran up through the deck cable wrap to the cryostat which was mounted on the
telescope sled.
The cryostat is cylindrical in design, 26.4375? in height, with a total outside diameter of
28.5? and weighing approximately 500 lbs [78]. Figure 2.10 shows a cut-away of a solid model
of the W-Band cryostat. Microwave radiation enters the cryostat through a window, passing
through an IR-blocking filter and into the corrugated horns of the platelet array. From
the platelet array radiation enters the septum polarizer OMTs, is split into left and right
circularly polarized components and enters the detectors. The radiation is then processed by
42
the detectors (�4). Detector biasing and data collection signals to and from the electronics
pass into and out of the cryostat via connectors on an access panel attached to the the
baseplate of the cryostat.
Figure 2.10: Solid model of the W-Band 91 element cryostat. Major components are labeled
[79].
The cryostat can be divided into three main sections ? the 300K stage, the 80K stage and
the 20K stage. The temperatures in the names of each stage are meant to be descriptive,
indicating the rough range of temperature achieved. The final temperature of each stage
depends on the performance of the refrigerators and the thermal load generated by incident
radiation, the level of vacuum, the power dissipated from the detectors when they are biased,
and the mass of the components (platelet array etc.). The three stages are physically connected by insulating G10 support rings. With its high tensile strength and low low thermal
conductivity, G10 is an excellent material to support weight while providing a thermal break
between stages. Figure 2.11 provides three views of the W-Band cryostat in various states
of disassembly.
43
Figure 2.11: Pictures of the W-Band cryostat. Left Top: the coldhead of one of the refrigerators is thermally strapped to the interface plate which supports the platelet array.
Right: Partially assembled cryostat. Left Bottom: Assembled cryostat ready for detector
optimization tests [70].
2.3.1
300K Stage
The 300K stage consists of the parts of the cryostat that remain at ambient temperature,
including the outer shell and the window. The outer shell of the cryostat is a vacuum vessel
that can be separated into four pieces ? a support ring, the base with access panel, a lower
ring and a window holder. The four pieces are joined by O-rings to maintain a vacuum seal.
The lower ring connects the window holder to the stainless steel (SS) support ring. The
window holder attaches the window to the top of the cryostat. All internal components of
the cryostat are supported on the stainless steel support ring (1? thick) that has six mounting
?ears? that attach the cryostat to the mounting collar when it is mounted on the telescope.
Alternatively, it can be attached to a cart that allows 360? of rotation of the cryostat for
assembly and lab-testing. The base provides attachment points for a vacuum pressure gauge,
a vacuum pump, both refrigerators and an access panel. The access panel allows access to
the 80 K stage and houses the hermetic connectors that pass the electric connections into
44
and out of the cryostat. Flexible printed circuits (FPCs), carrying all bias, control and data
read-out signals, are epoxied into hermetic connectors to maintain a vacuum seal (�5.1).
The QUIET window is made of expanded-Teflon coated ultra high molecular weight
polyethylene (UHMW-PE). The UHMW-PE was chosen as it was both transparent to microwaves and strong enough to withstand vacuum pressure (5500lbs of force) [80]. The
window measures 22? in diameter so as to provide an unobstructed field of view for all 91
horns in the platelet array.
Expanded teflon was added to the UHMW-PW as an antireflection coating in order to
improve signal transmission through the window. The index of refraction of UHMW-PE is
1.52 and expanded teflon has an index of refraction of 1.2. The teflon was adhered to the
UHMW-PE using a thin layer of LDPE between the two which has a lower melting point.
The materials were pressed and heated while under vacuum to fuse them without creating
air pockets. The total thickness of the window is 0.2976? (0.25? of UHMW-PE coated with
a layer of 0.0213? expanded teflon on each side with two sheets of 0.005? LDPE used for
adhesion).6
In addition to reflection, some small amount of adsorption and cross polarization may be
induced due to the curvature of the window (it bows roughly 2? at the center, under vacuum)
and variable thickness due to the curvature. In W-Band, the predicted transmission through
the three layer window (UHMW-PE + LDPE adhesion layer + Teflon) is 98.3% (98.8% in
Q-Band ) [79]. The measured effect of the window is included in the beam calibration (�2).
2.3.2
80K Stage
The 80K stage is an intermediate level connected to the first stage of the dual-stage refrigerators. The 80K plate, IR Blocker and a radiation shield are all mounted on the 80K stage
which is connected to the SS support ring via the lower G10 ring. The first stages of the
6. For comparison, in W-Band
?
4
? 0.03100
45
refrigerators are thermally strapped to an aluminum plate and maintain a temperature of 80
? 110K. The plate has an access hole in the middle, through which the FPCs pass to reach
the detectors on the 20K stage. The FPCs are thermally strapped to the 80K stage to sink
heat. The aluminum plate also supports and cools a radiation shield. The shield, a thin
metal cylinder covered in layers of aluminum coated mylar insulation, surrounds the 20K
stage and reflects radiative loading from the 300K outer shell. The IR blocker is attached to
the top of the radiation shield, between the window and the top of the platelet array. While
the window is transparent to microwaves, it also is transparent to, and generates, infrared
radiation. A 4? thick disk of polystyrene (3 flbt3 density) that is transparent to microwaves
but not to IR radiation, is used as a filter to reduce radiative loading on the 20K stage.
2.3.3
20K Stage
The 20K stage, or cold stage, is attached to the second stage of the refrigerators (often called
?coldheads?). The coldheads are thermally strapped to an interface plate (IFP) that supports
the focal plane. The platelet array bolts to the top of the IFP and the OMTs attach to the
bottom. The IFP contains waveguide transitions between each horn of the platelet array
and the corresponding OMT (or TT assembly). The IFP is thermally separated from the
80K stage with a second G10 ring.
Although the cryostat is pumped to vacuum (< 10礣orr pressure) when it is first cooled,
some small amount of air remains and some air will eventually diffuse through the window
as well; vacuum leaks also are possible and occurred in the W-Band season. If not removed,
these cryogens (nitrogen, oxygen, argon, etc.) will freeze and build up on the on the coldheads
since they are the coldest points in the cryostat. To absorb residual gas in the cryostat,
activated charcoal is attached to the coldheads and the IFP. A buildup of cryogens on the
coldheads decreases the performance of the refrigerators. The charcoal absorber allows us
to continue to run for months at a time without the need for repeated vacuum pumping.
46
2.3.4
Temperature Monitoring and Thermal Regulation
There are eleven silicon diode thermometers (LAKESHORE DT-470) monitoring the temperature in the cryostat. Six are attached to the OMTs bolted to modules in array locations
09, 22, 28, 45, 59 and 62. The diode attached to module 45 is in the center of the array,
midway between the two coldheads. Two thermometers are attached to the platelet array,
two are attached to the interface plate and one is located on the 80 K plate.
In order to thermally regulate the temperature in the cryostat, two additional thermometers and two power resistors are connected to the coldheads and attached to a cryogenic PID
(CPID) temperature controller (Cryo-con 32B). Figure 2.12 shows the temperature of the
detector in the center of the array (module 45) throughout the observing season and the
maximum temperature change that occurred during each observation. The spikes in temperature indicate times when the cryostat was warming up or cooling back down to operating
temperature. An example of an unexpected warm-up would be when we lost power due to
a generator failure. A steep rise in the temperature followed by blank space is illustrative
of the fact that the compressors, which drive the refrigerators, would fail immediately with
a generator failure, but there is a backup battery (UPS, �5) that protects the detector
electronics for a short time after a power failure allowing safe shutdown procedures for the
detectors. Other reasons for a large temperature variation include a coldhead failures, or a
slow vacuum leak, both of which occurred in the W-Band season.
One of the coldheads was more efficient than the other. The temperature regulation
setpoints for each coldhead were set at 21.5K and 24K respectively. There were several times
during the season, however, when the coldhead behavior changed necessitating a change in
the CPID setpoints. These changes are enumerated in the list of noteworthy events that
occurred during the W-Band observing season (�4). During routine observations, the
average maximum temperature drift during an observation was 0.74K.
47
Figure 2.12: Left: Mean temperature of the sillicon diode thermometer attached to module
45. The mean is calculated for each data file (CES, �3). Module 45 is located at the
center of the array, farthest from both coldheads. Right: Temperature excursion across a
single CES as measured by at module 45. The average temperature drift within a single
observation is 0.74K
2.4
Detectors
Large focal plane arrays are achieved through the miniaturization and packaging of a pseudo
correlation polarimeter (Gaier et al., 2003). In the CAPMAP (Cosmic Anisotropy Polarization Mapper) experiment, the precursor to QUIET, a single 90GHz pseudo correlation polarimeter was roughly 45cm in length and assembled from individually packaged microwave
components joined by waveguide [81, 82, 35, 41]. In contrast, each QUIET ?module? is a
complete pseudo-correlation7 receiver including low-noise amplifiers, phase switches, hybrid
couplers and detector diodes packaged into a 3.2cm � 2.9cm housing (5.1cm � 5.1 cm in
Q-Band ). Each module simultaneously measures linear polarization (Q & U Stokes parameters, �5.1) as well as providing a measure of the total power (Stokes parameter I).
The pseudo-correlation technique used in the QUIET modules has several advantages.
Phase switching the signal in one of the two amplifier chains at 4 kHz modulates the signal to
a frequency higher than the 1/f knee frequencies of the atmosphere, amplifiers, and detectors
7. QUIET?s pseudo-correlation polarimeters detect linear polarization by adding left circular and right
circular components of incident radiation rather than multiplying linearly polarized components as is done
in a traditional correlation polarimeter.
48
diodes suppressing these sources of noise. Phase modulation of the signal in the second
amplifier chain at 50Hz allows double demodulation which cancels out spurious instrumental
polarization that can arise if there are transmission differences between the two phase states
in either of the two phase switches. Simultaneous measurements of the Q & U Stokes
parameters within the same detector provide immunity to systematic effects including gain
fluctuations in the amplifiers.
Figure 2.13: Images of the QUIET Q-Band and W-Band modules with septum polarizer
OMTs attached to the waveguide ports on the top of each module. The modules are divided
into groups of seven that share an attachment board (�5.1) that provides the interface
between the module pins and the bias and read-out electronics. Courtesy Ross Williamson
[83]. Left: Image of five of the 19 elements in the Q-Band array. Right: the entire WBand array (TT-assemblies not shown) [70].
The QUIET Q-Band and W-Band receivers contain arrays of 19 and 90 detectors respectively. Figure 2.13 shows an image of both Q-Band and W-Band modules and OMTs.
The modules are divided into groups of seven that share an attachment board (�5.1). The
board provides the interface between the module pins and the bias and read-out electronics.
Figure 2.14 provides a diagram of the disposition of the modules populating the Q-Band and
W-Band arrays. Six modules in the W-Band array and two modules in the Q-Band array are
dedicated to differential temperature measurements. These differential-temperature modules
provide calibration data for the telescope pointing, beams, and sidelobes, as well as data that
allows us to constrain the temperature power spectrum of the CMB.
49
Figure 2.14: Detector numbering in the Q-Band and W-Band arrays. Color groupings
indicate that the modules share a module attachment board (MAB) and therefore share
biasing and read-out electronics. These groupings are useful for array assembly and wiring.
At the top of each panel, the different MAB configurations required to tesselate the arrays are
shown. Three configurations of MAB are used in Q-Band, while five are needed for W-Band.
Blue shading indicates the TT-assemblies. Gray indicates a single unpopulated element in
the W-Band array, left empty due to interface constraints imposed by the geometry of the
TT assemblies.
The components of a QUIET module are described in �4.1. and the theory of operation
processing for an ideal module is treated in �4.2. Characterization of the performance of
the modules and methods of optimizing module performance are treated in �4.3 and �4.4
2.4.1
Components of a QUIET Module
A module has two input ports for RF signal and 27 pins for input from DC electronics and
signal readout. An image of the interior of a QUIET module and a schematic diagram of
the components are shown in Figure 2.15.
50
Figure 2.15: Left: W-Band module with the housing lid removed to reveal its component
parts. Adapted from [84]. Right: Diagram of module components. Color coding indicates
corresponding parts in the image and diagram.
Low Noise Amplifiers: Left and right circularly polarized radiation enters the module
from the OMT via two 50? stripline coupled input ports and is directed into low noise
amplifiers. QUIET uses InP High Electron Mobility Transistors (HEMTs). The HEMTs are
manufactured as Monolithic Microwave Integrated Circuits (MMICs) [85]. There are three
stages of amplification in each of the two legs of the module, two before the phase switch
and one after. Each of the six MMICs has a 4-stage cascaded design, a wide bandwidth
(65-110 GHz for the 1st stage and 80-110 GHz for the second and third stages), and more
than 20dB gain referred to the waveguide input ports [86].
Each MMIC has two gates and one drain line which bias two transistors in the amplifier.
The optimal gate voltages and drain voltages/currents for the transistors in the LNAs vary
from chip-to-chip so it is necessary to individually tune the biases of each MMIC LNA to
minimize amplifier noise and phase match the amplifiers in both legs while maintaining
sufficient gain. To reduce the number of bias lines connected to each module, the gate lines
of two of the three MMICs are tied together. There are two types of W-Band modules, one
51
has the gate lines of the second and third stages tied together, while the second type has
the first and second stage gate lines tied. Because detector development was proceeding in
parallel with array integration, both versions of the module were tested and included in the
W-Band array. On average, the W-Band LNAs have a noise temperature of roughly 60 K
(30 K in Q-Band).
Phase Switches: There is a phase switch in each leg of the module. Each of the phase
switches can be operated independently. A phase switch consists of two PIN diodes (P-type,
Intrinsic Semiconductor, N-type) each leading to a stripline with a different path length. In
normal operation, one of the two diodes is forward biased (in a low-resistance state), while
the other is reverse biased (in a high-resistance state). The impedance difference effectively
blocks one path and the signal travels through the other. The path length of one stripline
is ?/2 longer than the other inducing a 180? phase lag when the signal travels that path.
Switching between the two paths modulates the phase of the signal in that leg.
It is also possible to have both of the diodes forward or reverse biased at the same time. If
both diodes are unbiased, the signal is attenuated by more than 20dB. Turning both diodes
on also heavily attenuates the signal since if both paths are open, the signal is split and
recombined with one half 180? out of phase creating destructive interference. Turning the
phase switches off is useful for diagnostic purposes and done periodically during observation
to check the detector offset levels.
Bandpass Filters: Bandpass filters are used to minimize contributions to the detector
noise from signals out of the band range where the module has good sensitivity and to inhibit
oscillations. Filters are placed between the phase switches and the third-stage amplifiers
and before all four of the detector diodes. They are 5-7 pole coupled line filters designed
to attenuate a known out-of-band spike in the first stage amplifiers at roughly 61GHz as
well as other possible sources of out-of-band noise [86]. They also should block standing
52
waves (oscillations) that could occur between the components at out-of-band frequencies
destabilizing the module performance.
Hybrid Coupler: The output signals from the third stage LNAs in both legs enter the
two input ports of the hybrid coupler. The hybrid coupler consists of a 180? coupler, power
splitters and a 90? coupler connected in series. The coupler uses a 90? Lange coupler with
Schiffman, self-coupled delay lines [86, 87]. The first stage of the coupler sums and differences
the signals from legs A and B of the module by adding a 180? phase shift to one of the legs.
The two outputs of this stage each pass through a 3dB power splitter before they are rectified
by a detector diode. As will be shown in �4.2, the signals on these two detector diodes
correspond to the 盦 Stokes parameters. The other halves of the signal are directed to
the input ports of a 90? coupler which again sums and differences the signals but with a
90? phase shift on each leg, such that the outputs have total phase shifts of 90? , and 270? .
These signals also are rectified by detector diodes whose outputs correspond to the 盪
Stokes parameters.
Detector Diodes: The four outputs of the hybrid coupler are each filtered by a bandpass
filter and then the RF power is rectified by GaAs beamlead detector diodes (Agilent HSCH9161). The diode can be modeled as a non-linear resistor with an IV curve given by:
I(V ) = Is (e?V ? 1)
(2.1)
where ? is a temperature-dependent constant and Is is the saturation current [87]. The
change in DC voltage across the diode for a given input RF power is proportional to the
junction resistance of the diode Rj .8
While the diodes don?t require bias at room temperature, they do require bias at cryogenic
8. Rj is given by dV /dI, evaluated at V = V0 .
53
temperatures; the unbiased junction resistance is ? 1019 ? at 13K. With a forward bias of
30礎, however, the resistance drops to roughly 200? giving a voltage sensitivity of ? 17
mV/礧 [88, 89]. To allow RF signals to terminate on the detector diode, it is capacitively
coupled to the stripline from the hybrid coupler and to the module ground (the diode floats
free from the module ground). The diode is biased via two input/output pins in the module.
The voltage drop across the diode, corresponding to the incident RF power, also is read
out on these lines. The DC offset voltage caused by biasing the diode is subtracted on the
PreAmplifer board (�5.3) before the signal is digitized.
2.4.2
An Ideal Module
Figure 2.16: Diagram of module components and the corresponding algebra of RF signal
processing that occurs in the module.
To describe how a QUIET module measures polarization, we first consider an ideal module. The two legs of the module will be denoted by A & B. Figure 2.16 shows the algebra
describing the module signal processing combined with the schematic diagram of the module
54
components. The inputs to the module are the left and right circularly polarized components EL and ER of the incident radiation which can be expressed in terms of the x and y
components of the electric field as
EA = EL = Ex + iEy
(2.2)
EB = ER = Ex ? iEy .
(2.3)
For simplicity, we will consider the three stages of MMIC LNAs in each leg together,
adding an overall gain of g to each leg. The non-ideal case, where the legs have different
gain factors (gA , gB ) is treated in Appendix A. We will also neglect the noise added by the
amplifiers and the possible phase length mismatch induced between the amplifiers in the two
legs. Switching the phase switch in leg B between 0? and 180? , modulates the RF signal in
that leg, multiplying the signal by � Imbalance in the phase switch transmission, or phase
length mismatch, also are neglected. These, and other systematic effects also are treated in
. After amplification and phase switch modulation, the electric field amplitudes in each
leg are
EA
= gEL
= g(Ex + iEy )
(2.4)
EB = 眊ER = 眊(Ex ? iEy ).
(2.5)
The first stage of the hybrid coupler adds the signals from the two legs with phase shift
? and a?b
? ). The power splitter divides
of 0? and 180? (summing and differencing them ? a+b
2
2
the RF power in half and the detector diodes rectify the power such that the signals seen by
the so-called ?Q1? and ?Q2? detector diodes are
55
|EQ1 |2 = |(EA + EB )|2 = |g(EL � ER )|2
(2.6)
|EQ2 |2 = |(EA ? EB )|2 = |g(EL ? ER )|2
(2.7)
Using the identity |C1 � C2 |2 = |C1 |2 + |C2 |2 � 2Re(C1? C2 ), we find that
? E )2 )
|EQ1 |2 = (|gEL |2 + |gER |2 � 2g 2 Re(EL
R
|EQ2 |2
(2.8)
= 2g 2 (Ex2 + Ey2 ) � 2g 2 (Ex2 ? Ey2 )
(2.9)
= 2g 2 (Ex2 + Ey2 ) ? 2g 2 (Ex2 ? Ey2 ).
(2.10)
0 and E 0
The second hybrid coupler adds an overall phase of �? to the two legs (EA
B
? ), differenced ( a?b
? ), and rectified
after the first hybrid coupler) which are then summed ( a+ib
2
2
giving
0 + iE 0 )|2
|EU 1 |2 = |(EA
B
(2.11)
= |(gEL � ER ) + i(gEL ? ER )|2
(2.12)
= 2g 2 (Ex2 + Ey2 ) ? 2g 2 Re(Ex Ey? )
(2.13)
0 ? iE 0 )|2
|EU 2 |2 = |(EA
B
= 2g 2 (Ex2 + Ey2 ) ? 2g 2 Re(Ex Ey? ).
56
(2.14)
(2.15)
Recalling that the Stokes parameters are defined as
I
= Ex2 + Ey2
(2.16)
Q
= Ex2 ? Ey2
(2.17)
U = 2Re(Ex Ey? ),
(2.18)
The outputs of the four detector diodes can be written as
|EQ1 |2 = 2g 2 (I � Q)
(2.19)
|EQ2 |2 = 2g 2 (I ? Q)
(2.20)
|EU 1 |2 = 2g 2 (I ? U)
(2.21)
|EU 2 |2 = 2g 2 I � U).
(2.22)
The signal is modulated between I + Q(U) and I ? Q(U) times a gain factor at the phase
switching frequency, 4kHz. The signal contains a DC offset proportional to the total power
of the incident radiation (I) and a switching component proportional to Q or U. When the
data are demodulated in the electronics (�5.4), the DC offset is removed and the signals
are [+Q, ?Q, ?U, + U] times a gain factor for the four diodes respectively. If, instead of
demodulating, the output is averaged, the signals correspond to I times a gain factor for all
four diodes.
Here we considered switching the phase switch in a single leg at 4 kHz and demodulating
the signal. In the the final configuration used for data collection, both phase switches were
used ? one switching at 4 kHz, and the other at the much lower frequency of 50 Hz. The data
were then demodulated a second time, or ?double-demodulated?. This is done to eliminate
possible systematic effects namely, instrumental polarization which can be caused if there
57
is an imbalance in the phase switch transmission between the two states. This double
demodulation is also described in Appendix A.
TT modules: Although a total power signal is measured by every detector by averaging
the two phase states, this measurement suffers from large 1/f noise. The TT-assemblies make
use of the phase switching in the modules to modulate the temperature signal, decreasing
the noise and allowing a measurement of the CMB temperature.
By switching the septum polarizer OMT used in the polarization modules to a hybrid-T
configuration, the input to leg A of a single module is ExH1 + EyH2 and the input to leg B is
ExH1 ? EyH2 where H1, 29 are the signals from the two neighboring horns in the TT assembly
(see �2.4). Following the same signal processing, the output on the ?Q1? diode will not be
a measure of the Q stokes parameter, but
2
EQ1 2 = g ExH1 + EyH2 � g ExH1 ? EyH2 H1 2 H2 2
H1 2 H2 2
2
2
= 2g
Ex + Ey � 2g Ex ? Ey ,
(2.23)
(2.24)
where the offset (first term) is the average temperature between the two points on the sky
measured by the two horns and the modulated signal (second term) is a measure of the
temperature difference between the two horns. The demodulated signal on the Q diodes is
Q1 = 2g 2 (ExH1 )2 ? (EyH2 )2
H2
2
H1
2
2
Q2 = 2g (Ey ) ? (Ex ) .
(2.25)
(2.26)
Although this is technically a measure of the difference between the Ex linear polarization
9. Here we have changed notation of the horns from horn A,B used in �2.4 to H1, H2 so as not to
confuse the horns with the legs of a module.
58
in horn H1 and the Ey linear polarization in horn H2, it can be treated as a difference in the
unpolarized temperature as long as the radiation in the two horns is largely unpolarized. This
is true for the CMB (the polarization fraction of the CMB is <1%) and the atmosphere which
is effectively unpolarized. This distinction will become noticible, however, when observing
a strongly polarized source such Taurus A which is used as a calibration source for QUIET
(see �1).
2.4.3
Detector Characterization
To ensure that the QUIET modules are working properly, it is necessary to characterize
their performance. Here we define several statistics used to quantify the performance of the
modules including the sensitivity, noise equivalent temperature, bandwidth and isolation.
Derivations of these values can be found in Appendix A.
A relation, known as the ?Radiometer Equation? [90], describes gives detector sensitivity.
Following [77], the sensitivity defined in terms of minimum detectable signal for a radiometer
per unit time is given as
Tsys
?T = ?
? BW
(2.27)
where ? is the integration time, Tsys is the system temperature and the bandwidth, BW, is
defined as,
R
( Gd?)2
BW = R 2
,
G d?
(2.28)
where G is the gain and ? is frequency. The system temperature is a combination of the
noise temperature,10 Trec , of the components in the receiver (amplifiers, waveguide, etc.)
10. Noise temperature is proportional to the power spectral density of the noise, T = P/(kB BW ) where
P is the power, kB is Boltzman?s constant and BW is the bandwidth.
59
and the temperature of the measured signal or load 11 on the receiver, Tload :
Tsys = Trec + Tload
(2.29)
By measuring the bandwidth and Tsys , one can determine the sensitivity of a detector.
The sensitivity also can be measured directly by calculating the signal-to-noise ratio of a
receiver measuring a known signal. During detector development, the QUIET modules appeared to violate this relation ? measured sensitivities did not match those naively calculated
with the radiometer equation. However, after consideration of the specific architecture of the
QUIET modules and systematic effects (Appendix A, [91, 92]) we can write a QUIET-specific
version of the radiometer equation giving the signal to noise for a single Q diode
Q ?
S
=
? BW
N
Tsys
R
|( 2gA gB ei? d?)|2
BW = R
2 + g 2 )2
d?(gA
B
R
( 2g g cos(?)d?)2
= R A B2
2 )2
d?(gA + gB
(2.30)
(2.31)
(2.32)
where gA and gB are the gains in the two legs of the module, ? is an additional function
accounting for the phase difference that can be induced between the legs in the LNAs and
R
we define Q such that 2gA gB sin(?) = 0 (see Appendix A). If gA = gB and ? = 0,
Equation 2.32 is equivalent to the traditional bandwidth formula given by Equation 2.28;
satisfying these two conditions defines ideal isolation between the amplifiers in the two legs
of the module. The module makes two independent measurements of Q and two of U, so
?
the module measures Q with a S/N that is a factor of 2 larger than that given in Equation
2.30 and simultaneously measures U with the same sensitivity.
11. During observations Tload is roughly TCM B (3K) plus Tatmosphere (5K -10K).
60
Bandwidth & Isolation: Bandwidth is directly measured using a narrow band signal
generator that operates from 0-20GHz in combination with a multiplier that up-converts the
frequency to W-Band. A horn broadcasts the multiplier output with a linear polarization.
The signal is then directed into the receiver feedhorns and swept through a range of frequencies about the expected band center of the modules (typically from 80 to 110 GHz, centered
at 95 GHz). The horn can be aligned with the Q or U polarization axes of of the detector
to measure the bandwidth for the signal at each detector diode. If it is aligned along the Ex
axis then the average and demodulated signals are proportional to the gains associated with
the DC offset term I and the modulated term Q in Equation 2.19, but this time taking the
phase difference ? into account and assuming alignment along the Q direction.
Q1demod ? 2gA (?)gB (?) cos ?(?)
2 (?) + g 2 (?) .
Q1average ? gA
B
(2.33)
(2.34)
These terms are thought of as the ?Demodulated Gain? and ?Average Gain.? Extending to
the U diodes, the cos ? term is phase shifted by 90? in the hybrid coupler giving a term of
sin ? instead
U 1demod ? 2gA (?)gB (?) sin ?(?)
2 (?) + g 2 (?) .
U 1average ? gA
B
(2.35)
(2.36)
The module bandwidth can be calculated by integrating the signal across the band following Equation 2.32. While the bandwidths were measured frequently during module testing
and array integration, the values are dependent on the tuning of the module biases. These
biases were optimized to maximize detector performance (�4.4). The bandwidths and band
61
centers for the modules in the W-Band receiver were measured at the end of the W-Band observing season and are shown in Figure 2.17. The average central frequency is measured to
be 94.5 GHz � 0.8 GHz, with an average bandwidth of 10.7 GHz � 1.1 GHz [93]. The QBand average center frequency is 43.1 � 0.4 GHz, and the average bandwidth is 7.6 � 0.5 GHz
[1].
Figure 2.17: Distribution of bandwidths and band centers for the diodes in the W-Band array
[93]
The phase difference ? rotates the axis along which the detector is sensitive to polarization. The sensitivity of the detector is not decreased if ? is constant as a function of
frequency, but it can be tuned by adjusting the bias values of the MMIC LNAs. We can
define an isolation statistic as
isolation [dB] = 10 log10
2 + g 2 ? 2g g cos ?
gA
A B
B
!
2 + g2
gA
B
gavg ? gdmd
= 10 log10
.
gavg
(2.37)
(2.38)
Perfect isolation occurs when hen gavg = gdmd or gA = gB and ? = 0.
Noise Temperature: The temperature or total power intensity measured by the modules
is a combination of the input signal and the intrinsic noise temperature of the detector
62
(Tsys = Trec + Tload ). In order to extract the receiver noise temperature, Trec , we measure
Tsys for two values of Tload and then extrapolate to a load with zero temperature (known as
a ?Y-factor? measurement). We use the average response of the detector timestream which
is the same for all four diodes. We will use the Q1 diode below. Returning to the ideal
condition where (gA = gB ), we see that
2 + g 2 )I = (g 2 + g 2 )(T
Q1avg = (gA
rec + Tload )
B
A
B
(2.39)
For QUIET, loads were made using a container holding a blackbody absorber (Eccosorb)
immersed in a liquid cryogen bath. For the W-Band array, liquid nitrogen (LN2) and liquid
Argon were used with boiling points of 77K and 87K respectively. Zotefoam, a microwave
transparent, thermally insulating foam, was used for the container window. Using TLN 2 and
TLAr as the two load temperatures, we can calculate Trec using
T
? Y TLN 2
Trec = LAr
Y ?1
(2.40)
where
Y =
Q1avg,LAr
Qavg,LN 2
(2.41)
Here we are using a linear extrapolation which assumes that the receiver response is linear
with temperature, which is true for the low atmospheric temperatures at which we observe
(? 10K). The LNAs and detector diodes exhibit saturation, however, when Tload becomes
large. The compression of the detector response can be determined using a third, room
temperature (? 300K) load as shown in Figure 2.18. Single module Trec measurements are
made in a test cryostat with a variable cold load (Tload ? 30K), but this is an impractical
method of testing for large detector arrays and the cost of large-scale loads using separate
cryostats or cryogens with lower boiling points (e.g. 3He) were prohibitive. The test still
63
can be used to provide an upper limit on Trec .
Figure 2.18: Diagram showing the linear extrapolation of Trec given two values of Tload .
The black line shows compressed response of the module to high temperature signals. Green
shows the measurement of Trec using LN2 and LAr. Red shows the naive extrapolation of
Trec using a Tload that saturates the detector. Adapted from [14].
2.4.4
Sensitivity & Optimization
In order to maximize the sensitivity of the detector array, it is necessary to tune the MMIC
LNAs for maximum gain, minimum Trec , a wide bandwidth and good isolation (? ? 0).
Each module has 10 bias lines that control its LNAs and the optimum bias configuration
varies from chip to chip. The best way to improve the module performance is via direct
optimization of the module sensitivity. Sensitivity can be measured by injecting a modulated
polarized signal and comparing the signal amplitude to the detector noise.
During lab testing of the W-Band array, this was achieved by rotating a sparse wire
grid in front of an unpolarized, cryogenic, blackbody load. The wire grid partially linearly
polarizes the incident radiation from the load. Radiation with an electric field orthogonal
64
to the wire is allowed to pass while the parallel component is scattered. Spacing of the
wires allows tuning of the polarization signal size; the sparser the wire grid, the smaller the
polarization fraction of the radiation. For laboratory measurements using a 77 K load and
12.7mm wire-to-wire spacing the amplitude of the signal was ? 2 K.
The wire grid and load are made large enough that the entire array is illuminated simultaneously. Figure 2.19 shows the configuration of the wiregrid and load with respect to the
cryostat window. The load was used in lab testing, but once the receiver arrived at the site
of observations, the load was replaced with Tsky (? 10K) via a metal plate that reflected
the signal into the cryostat. Final optimization was done once the receiver was installed on
the telescope. The wire grid attaches directly to the cryostat window, so the array could be
optimized after installation on the telescope.
Figure 2.19: Left: Two configurations of the wire grid used to optimize the detector sensitivity. The wire grid is attached to the cryostat window and rotated. The signal terminates
either on a 77K blackbody load or the sky depending on which configuration is used. Right:
Polarized signal (real data) as detected by the four diodes in a module as the wire grid is
rotated [94]. The relative phase between the signals is a measure of the relative polarization
detector angles.
65
Figure 2.19 also shows the polarization signal from the wiregrid for the four diodes of a
single module. Rotation of the wire grid modulates the polarization signal at two times the
rotation frequency. The signal is maximum in a given channel when the linear polarization
is aligned with the polarization axis of the detector. If the linear polarization is aligned with
the Ex axis of the module, the signal in the Q1 diode will be maximized, the Q2 diode signal
will be minimized and the U diode signals will be zero. While detector angles used for the
final analysis are calculated primarily from measurement of the moon (see �5), the wiregrid
data provides a cross-check and a measure of the relative polarization angles between the
modules and diodes within a module.
The amplitude of the sinusiod gives the signal size. The noise is obtained by taking the
fourier transform (FFT) of the data and measuring the white noise level. Figure 2.20 shows
the timestream and its noise power spectrum for a single observation with a single diode.
The average and double-demodulated streams are both plotted to show the reduction in
noise due to demodulation.
The noise power spectrum is modeled as having a pink or ?1/f ? component (noise from
amplifiers, electronics, atmosphere, etc.) and a white component (Johnson noise and shot
noise in the electronics)
fknee ?
(2.42)
P? (?) =
1+
?
?
where B is the white noise level, in units of 礙 s, fknee is the knee frequency (where the
B2
power is two times the white noise level), and ? is the slope of the 1/f component of the
noise power spectrum. The noise used for the signal-to-noise calculation is the white noise
level measured from 10Hz to 25Hz.
The expected signal size for the wire grid depends on where all the reflected rays terminate
and thus is difficult to calculate exactly. In order to determine the absolute sensitivity of
the W-Band receiver in the lab, we used a rotating metal plate instead of the wire grid to
66
Figure 2.20: Sample average and double demodulated time streams and their noise power
spectra. Note the noise suppression in the double demodulated stream. The scan frequency
of the telescope is shown in green for reference.
generate modulated, polarized signals of known amplitude. Reflection of incident radiation
off of a metal plate also will result in a partially polarized signal given by
p
P = 2 6???0 (cos(? ? sec(?))(Tplate ? Tload )
(2.43)
where, ? is the angle of inclination of the plate, ? is the radiation frequency, ? is the
resistivity of the metal plate, and 0 is the permitivity of free space. A diagram of the set-up
is shown in Figure 2.21. Given an aluminum plate, a load temperature of 77 K, and ? = 45?
generates a signal of a few hundred millikelvin. Varying the plate metal (Aluminum, Stainless
Steel) or the load temperature using different cryogens (LN2, LAr) can be used to confirm
results or measure compression in the detector response. A derivation of the polarized signal
generated by this calibrator is given in [14]. This calibrator was to optimize the sensitivity
of the Q-Band modules and is described in [79]. While a version of it, named ?the optimizer?,
was used for optimization of the W-Band modules in early lab tests, it was replaced with
the wiregrid in later tests as the wiregrid proved more convenient, reliable and portable.12
For optimization of the detector performance, only maximization of the signal-to-noise is
necessary, not absolute sensitivity, so the wiregrid could be used. The rotating metal plate
12. The optimizer?s geometry required a much larger load to illuminate the array than the wiregrid configuration. The larger loads proved unwieldy to rotate and less stable over the 12+ hours of optimization
required for W-Band .
67
was then used to measure the absolute sensitivity after optimization in the lab. The final
absolute calibration of the detector is found using astronomical sources and is described in
�1.
Figure 2.21: A schematic diagram of the rotating plate/load calibrator used to measure
the absolute sensitivity of the modules in the lab. Radiation from the blackbody load is
reflected off of the metal plate generating a partially polarized signal of known amplitude.
The calibrator is then rotated, modulating the polarized signal.
Optimization of the W-Band receiver is accomplished using a downhill simplex search
algorithm that iterates through the possible values for the 10 LNA biases in a given module,
calculating the signal to noise at each point from the rotating wire grid signal. The algorithm
is robust and generic enough that other values also can be optimized with the method (e.g.
Trec , isolation, bandwidth). Figure 2.22 shows the sensitivity and bandwidth as a function
of iteration in the optimization algorithm for a subset of modules. Optimizations of each
detector run in parallel; the optimization of the entire array is completed in approximately
twelve hours.
Figure 2.23 shows the range of sensitivities of each diode in the W-Band array for a
68
Figure 2.22: Left: Half of the RMS sensitivity over all diodes as a function of iteration for the
Down Hill Simplex (DHS) optimization using all ten biases of the LNAs in a given module.
Right: Average effective bandwidth over all diodes as a function of iteration for the DHS
optimization. A subset of modules is shown [95].
single observation. The distribution of knee frequencies and sensitivities for each diode
throughout the season are shown in Figure 2.24. The median knee frequency was 13mHz
?
and the median per diode sensitivity was 1.48mK s. Combining all diodes, the total array
?
sensitivity is 70礙 s.
69
Figure 2.23: Sensitivity of each diodes in the W-Band array as measured for a single observation. Smaller circles indicate diodes with off-scale values. Blank squares are non-functional
modules.
2.5
Electronics
The QUIET electronics provide an interface to the modules; they protect them electrically,
provide bias to active components, monitor their values, and amplify and digitize the output signals. The electronics also synchronize the receiver data stream with the telescope
data stream, thermally regulate the cryostat and electronics enclosure and drive the telescope. Protection electronics and cabling are described in �5.1. The electronics enclosure
is discussed in �5.2 and the bias and monitoring boards are addressed in �5.3. The
data acquisition system and the receiver control software are described in �5.4 and �5.5
respectively. The telescope control software is briefly addressed in �5.6
70
Figure 2.24: Knee frequency and single diode sensitivity distributions for the W-Band array
for the W-Band observing season (before data
? cuts are applied). Median fknee = 13mHz
and median per diode sensitivity is 1.48礙 s.
2.5.1
Protection Electronics & Cabling
The protection electronics and cabling are responsible for connecting the module, located in
the cryostat, to the bias and readout electronics located in the electronics enclosure. The
W-Band receiver contains 90 modules with delicate components which require more than
2,100 bias and readout lines. The signal chain from the modules to the electronics box is
described below including the module attachment boards, flexible printed circuits, auxiliary
interface boards and cables.
Module Attachment Boards: The module attachment boards (MABs) are printed circuit boards that provide an interface between the electronics and modules as well as passive
protection circuitry to protect the sensitive components in the modules. Seven modules
attach to a single MAB. Each module has 27 pins on the base that connect to components
inside and each is attached to the MAB by inserting the pins into spring sockets on the
board. Ten pins connect to the gate and drain lines of the LNAs to provide bias voltage and
current. Four pins connect to the two phase switches to bias and switch them. Eight pins
are dedicated to biasing and making differential measurements of the signals on the detector
diodes. One pin is ground (return line for MMIC gates and drains and phase switches) and
71
Figure 2.25: Photographs of the protection electronics and cables (FPCs). Panel A: MABs
(green) attached to the modules (gold) in the cryostat. The modules are attached to the
OMTs (silver) which are bolted to the interface plate. Along the left side of the image, the
TT assemblies are visible [84]. Panel B: After the OMT/module/MAB sets are installed in
the interface plate, the FPCs are connected to the MABs using Hirose connectors. The TTassembly MABs are coated in electrical tape (white); there is very little clearance between
them and the 80K plate [70]. Panel C: The FPCs are grouped into sets of 5, divided by
MAB, and epoxied into hermetic connectors to allow them to pass out of the cryostat while
maintaining vacuum [70]. Panel D: Once outside the cryostat, the FPCs are shielded and
attached to the AIBs. The AIBs are bolted to the outside of the access panel on the base
of the cryostat. AIB cables (not shown) plug into the Harting 150 pin connectors on the
AIBs and connect to the electronics box in the electronics enclosure, located adjacent to the
cryostat on the mount (see Figure 2.1) [70].
four pins are unused.
Bias signals enter the MAB via five 40-pin Hirose connectors (two for connections to
the LNAs, two for detector diodes and one for phase switches) that attach flexible printed
circuits to the board. Signals are routed from Hirose connectors, through passive protection
circuits and then to the module pins. Detector diodes are biased, but have no protection
circuitry. The module component protection circuitry [96, 97] is described below:
Phase Switch protection: The phase switches can draw nearly 1mA of current during
regular operation but are very sensitive to damage from transients. A one-pole RC
low-pass filter with 200? of resistance and a 1000pF capacitor to ground filters the
phase switch lines. The filter has a 3dB attenuation frequency of roughly 800kHz,
well above the phase switch frequency of 4kHz. In addition, a voltage clamp (-3.0V
72
to +1.43V) is created with two diodes and one blue LED. The LED turns on sharply
at ? 1.5V. The phase-switch diodes never need more than 0.9V forward bias, and the
reverse bias voltage from the phase-switch board is -2V.
LNA drain protection: The MMIC drain lines are protected by a -0.715V to +1.5V voltage clamp using a red LED and a switching diode. The W-band drains never need
more than 1V. A 1礔 capacitor to ground protects against transients.
LNA gate protection: Protection on the gate lines consists of a 5.12:1 voltage divider, a 1
礔 capacitor close to the module pin to protect against transients, and a voltage clamp,
using a green LED to limit forward voltages, and a switching diode to limit reverse
voltages. The voltage range for the gate line is limited to -0.715V to +2.0V. After
the voltage divider, the clamp limits voltage to -0.140V to +0.392V. During normal
operation, a gate needs, at most, 0.35V, which requires that the bias board output up
to 1.785V.
Due to the array shape, there are five different MAB configurations in W-Band (three in
Q-Band) needed to complete the tessellation (see Figure 2.14). Panel A of Figure 2.25 shows
the MABs attached to the modules in the array.
Flexible Printed Circuits: To reduce the thermal conductivity and keep cabling manageable, we use flexible printed circuits (FPCs.) Each FPC is 32? in length with a high
trace density ? 40 conductors with a 0.5mm pitch with resistances of 5? [98]. The FPCs are
grouped into sets of five (2 LNAs, 2 PreAmp, and 1 Phase Switch) that connect to a single
MAB and are sealed into custom-made hermetic connectors with Stycast-epoxy such that
one end of each cable is outside the cryostat while the other is inside, attached to an MAB.
Auxiliary Interface Boards and Cables: While the MAB circuitry protects against
transients during testing of the modules at room temperature and during array integration,
73
once the modules are cooled, the resistance, capacitance, and diode thresholds of the components on the MAB change necessitating a second set of passive protection circuitry that
remains at room temperature. Protection circuitry identical to that on the MAB also is
included on the Array interface boards (AIBs).
In addition to providing a second layer of protection to the modules, the AIB boards and
cables connect the FPCs to the electronics boards in the electronics enclosure. Figure 2.26
shows a schematic cabling diagram for the electronics. The ends of the FPCs that remain
outside the cryostat connect to the AIBs via Hirose connectors. The AIBs are divided by
the electronics board to which they attach; multiple FPCs connect to a single AIB. There
are five Phase Switch AIBs, each connecting to a single phase switch board in the electronics
box and three FPCs connecting to three MABS. There are seven of each of the MMIC and
PreAmp AIBs, each connecting to two FPCs. Signals from the electronics boards connect
to the AIBs via 150-pin Harting connectors. AIB cables are made of two 80-pin shielded
ribbon cables with 150-pin female Harting connectors on either end.
The AIBs are attached to the access panel on the bottom of the cryostat and covered
with a weatherproof enclosure. The humidity inside the AIB enclosure is monitored.
2.5.2
Electronics Enclosure
The majority of the QUIET electronics are housed in a weatherproof enclosure for protection
from dust and snow as well as for thermal regulation. The electronics enclosure is an insulated
box (54? tall � 25? wide � 25? deep) that is mounted adjacent to the base of the cryostat
on the deck platform. Figure 2.27 shows a schematic diagram of the placement of the major
components of the electronics within the enclosure.
The electronics box is mounted in the enclosure such that the backplane of the electronics
box is as close as possible to the base of the cryostat, minimizing the length of the AIB cables.
The electronics box is a custom crate with a 6U-standard sized backplane; it houses the
74
Figure 2.26: Connection diagram for the protection, bias and monitoring electronics.
module bias boards (7 PreAmplifier boards, 5 Phase Switch boards and 7 LNA bias boards)
and the Housekeeping board (monitoring). All signals to/from the array pass through the
electronics box. The boards are powered by trays of linear power supplies installed lower in
the enclosure. Bias, housekeeping and phase switching control signals are sent to the bias
boards via a low volt differential signals (LVDS) from the master ADC board in the VME
crate. Housekeeping values are also read-out via the LVDS cable from the electronics box
backplane to the master ADC board. Signal lines from the module are amplified by the
preamplifier boards and then sent to the ADC boards to be digitized. HD-78 cables with
twisted-shielded pairs connect the differential detector diode signals from the PreAmps to
the ADC boards. Each cable carries the signals from 1 MAB (7 modules) to 1 ADC board.
75
Figure 2.27: Diagram of components in the Electronics Enclosure
Since each PreAmp board biases and amplifies the signal from two MABs of modules, two
ADC boards are connected to each PreAmp.
A VME crate holds the 13 ADC boards that digitize and readout the amplified detector
diode signals from the PreAmps. The crate also includes cards for timing synchronization
(see �5.4) and a crate controller PC that runs the basic interface software to the ADC
boards for data collection and control commands.
A rack mounted PC runs the receiver control software (�5.5) and stores the data before
it is transferred to a RAID array in the control room and then backed-up offsite. The data
acquisition (DAQ) system is described in �5.4
The 21 electronics boards are powered by 84 independent, 5V, linear floating power
76
regulators manufactured by Acopian. They are grouped into three trays separated by which
boards they power. The preamp power supply tray also powers the housekeeping board.
The electronics enclosure is thermally regulated using a PID controller (Omega model
CNi16D22-EI) connected to a strip heater mounted above the electronics box and a large
fan that controls airflow into and out of the enclosure. The fan intake is filtered to prevent
the buildup of dust in the enclosure. A thermocouple was mounted in the electronics box
near the LNA bias boards (the most temperature sensitive of the electronics boards) and the
temperature was regulated using that as the reference point. Two rack mounted fans above
and below the electronics box maintain constant airflow past the bias boards. Enclosure
temperature regulation was a challenge in W-Band because of the large number of boards
and power supplies dissipating heat and the poor air conductivity at the site (5080m). The
regulation point was set to 35? C in the winter (April to November) but then was raised
to 40? C during the summer (November to April). The warm PID (WPID)13 was able to
maintain temperature to within 2.2? C as shown in Figure 2.28.
Figure 2.28: Electronics enclosure temperature during the W-Band observing season. The
electronics were thermally regulated with a setpoint of 35? C during the winter (April November) and 40? C during the summer (November to April). The average maximum
excursion of the enclosure temperature during a single observation (CES, �3) as measured
in the electronics box (MMIC Board 3) was 2.2? C. Variation of the enclosure temperature
is one statistic evaluated during data selection (see �2).
13. Named the warm PID to distinguish it from the PID regulating the temperature on the 20K cold stage
in the cryostat (CPID)
77
There are three points of access into the enclosure. A full-length door opens on the side
opposite to the cryostat to allow access to the electronics box, VME crate, power trays, PC,
etc. A small access panel was installed in rear of the box to allow access to the peripheral
controls and the power cords for the electronics. The AIB cable weatherproofing attaches
to an access panel in the enclosure at the same height as the cryostat base to minimize the
AIB cable length.
The electronics enclosure also houses interface boards for peripheral components, including the Q-Band noise source, thermometers monitoring the groundscreen temperature, and
a cryostat pressure sensor. Ethernet controlled power strips and the CPID control system
also are installed in the enclosure.
2.5.3
Bias & Monitoring Electronics
The active components in each module require biasing for operation. Three types of electronics bias boards were built, divided by function ? boards to power the LNAs in the modules,
boards to control the phase switch bias driving the phase switching, and preamplifiers to bias
the detector diodes and amplify the signal before passing it to the data aqusition system.
Further, one board ? housekeeping ? was dedicated to monitoring the bias values and phase
states on all of the bias boards and electronics and cryostat temperatures.
LNA Bias Board: The LNAs in each module require 6 gate voltages and three drain
voltages/currents to power all three stages of the HEMTs. Seven amplifier bias boards that
can each power the LNAs in 14 modules (2 MABs) bias the array. Only 6.5 boards are
needed to power all 90 modules in the array; half of one board is unused, but available as
a spare. The gate voltage is controlled by a voltage source combined with a voltage divider
giving an output voltage range of -0.45V to 1.7V.
In the first version of the amplifier board that was used during the Q-Band season, the
78
drains were current biased using a current source. The first stage LNAs have a maximum
current of 25mA. The second and third stages used up to 50mA combined since their drain
inputs were biased in parallel. Unfortunately, the transistors used in this circuit had large
temperature coefficients (up to 1.5% per degree) [99]. A short-term fix was implemented
on the board by replacing the transistor feedback with a compensating thermistor circuit to
improve the temperature coefficient, and tightly regulating the electronics enclosure temperature.
For W-Band the current sources for the drain bias lines were replaced with voltage sources
to better tune the LNA performance and the op amp driving the drain circuit was replaced
to improve the stability with respect to temperature changes. The drain voltage range for
the new board was -0.04V to 1.14V.
Phase Switch Bias Board: Each phase switch is controlled by two diodes (�4); one is
forward biased while the other is reverse biased, choosing which path the RF signal takes
through the phase switch. When phase switching, the forward and reverse biases are swapped
sending the RF signal down the opposite path (with a phase length that varies by 180? with
respect to the initial path). The phase switch board provides forward voltages that range
between 0 and 2.5V. The reverse bias voltage is held constance at -1.8V.
The phase switching circuit on the board is a double pole double throw (DPDT) switch.
As the phase switch transitions from one state to the other, the RF power moves from
full power to zero power and back to full power (in the other path). This creates a sharp
transition spike in the raw 800kHz data (see Figure 2.29). An RC filter (R = 470?, C =
1000 pF) protects the phase switch diodes from transients. It also defines the time it takes
to switch between the two phase switch states. The filter is tuned to minimize transition
time (which must be blanked out of the data stream because of the transition spikes) but
have a strong enough filter to protect the diodes from fast transients. The turn-on delay
time plus transition time is roughly 15祍.
79
Each phase switch bias board can drive the phase switches in 21 modules (3 MABs).
Five boards are required for the W-Band array; four boards are completely used as well as
one third of the fifth board. Each board allows separate switching frequencies for the phase
switch in each leg of a module; we switch one leg of each module at 50Hz and the other at
4kHz, as described in �4. Each phase switch bias board provides 2 pairs of clocking lines
(PCLK0a/b and PCLK1a/b). The ?a/b? designations correspond to the two phase switches
in a single module. PCLK0 controls the switching frequency of even numbered modules
while PCLK1 controls odd-numbered modules so they could be switched in different legs.14
This functionality was used during testing only; during observation all modules are switched
in the same configuration.
PreAmplifier Board: Seven PreAmplifier (PA) boards are used in the W-Band array.
Each board biases the detector diodes of 14 modules (2 MABs) and amplifies their signals
before sending them to the analog-to-digital converters for readout. The detector diodes
require zero bias when warm, but still need to be biased at cryogenic temperatures. After
the diode is biased, the DC offset created by biasing the diode is subtracted from the signal
so that a diode with zero RF power incident on it will have a roughly 0V signal. In practice,
the offset can only be reduced to within �mV due to the resolution of the bias bit settings.
The detector diodes are biased and the offsets are removed with the module LNAs and phase
switches turned off so the voltage on the diode when the module is on reflects the power
of the RF signal only. During data-taking, regular offsets are taken (phase switches turned
off) to monitor any change in the bias offset level caused by changes in temperature of the
detector diodes or pre-amplifier boards. The board has three stages of amplification with
a combined gain of ? 13015 [77]. Referred to the preamp input, the noise of the back end
14. This scheme was developed before double demodulation was implemented, when only one phase switch
in a given module was switched at one time. At that point, balance of the phase switch diode transmission
was very important and added flexibility in choice of switching leg/module combinations was desired.
15. A factor of ? 65 comes from preamplifier circuits plus a factor of two at the input to the ADC
80
electronics (preamp plus ADC), with a cold, biased detector diode at the preamp input, is
?
about 8 nV / Hz which is subdominant to the front-end noise.[100]. There is a three-pole
filter to limit the bandwidth of the preamp output signal such that is doesn?t significantly
exceed the sampling Nyquist frequency (400 kHz) [101].
Housekeeping Board: There is one housekeeping (HK) board in the electronics. The
board monitors temperatures inside the cryostat and in the electronics enclosure. It also
monitors the module biases on the bias boards. On the LNA bias boards, the gate voltages,
drain voltages and currents are monitored. The forward bias currents are monitored on the
phase switch boards. The board multiplexes through the monitored values taking a measurement of a new channel every 2ms. Since there 1,774 monitored values in W-Band each
channel is sampled at roughly 3.5Hz (491 values for Q-Band give a 1Hz sampling rate). To
take care not to contaminate the bias lines with noise from HK digital signals, opto-isolators
are used to avoid sharing ground between the HK and the other bias boards. Further, the
MUX address is only changed during phase-switch transitions, when the data are masked
out anyway.
2.5.4
DAQ System
The QUIET Data Acquisition (DAQ) system consists of 14 Analog-to-Digital Conversion
(ADC) boards housed in a 6U Weiner series 6000 Versamodule Eurocard (VME) crate, a crate
computer (GE vmivme-7700) that controls the software interface to the ADC boards, a Time
Code Reader (TCR, Symmetricom TTM635VME) that is used to synchronize the receiver
data to the telescope data, and a rack mounted PC housed in the electronics enclosure. The
receiver control software, which is described in �5.5, is split between this PC and the VME
crate PC.
81
ADC Boards & Firmware: The ADC board accepts the output of the preamplifier
board ? amplified and offset-removed voltages from the RF rectifing detector diodes in the
modules ? and digitizes it at a sampling rate of 800kHz. Each ADC board has 28 channels16
(7 modules � 4 diodes per module) that are digitized using analog-to-digital converters
(AD74674) with 18-bits. The ADC samples the data using a Successive Approximation
Register (SAR) which holds the value and conducts a binary search to find the appropriate
bit value.
Figure 2.29: Left: Sample 800 kHz timestream. The large spikes are the 4-kHz phase
switch transitions. Blue and green timestreams indicate the polarization is modulated by
each transition. The shaded region at each transition is not included when the data are
demodulated to 100 Hz. Right: Diagram of ADC clocks used to blank, average, demodulate
and downsample the data into average, demodulated and quadrature timestreams.
Each ADC board also contains an Altera Field Programmable Gate Array (FPGA). One
of the 14 ADC boards is a master board (only the control functionality ? firmware operating
on the FPGA ? not the actual ADC circuits, is used). The master board?s firmware generates
the clocking signals to synchronize data collection across the 13 ADC boards which take
data, controls housekeeping data collection and sends control commands to the phase switch,
preamp and LNA bias boards to set bias levels and phase switch states. It also synchronizes
the phase switching with data collection and masking of phase switch transitions. While these
control and data processing functions are outlined below, further details of the firmware are
16. The boards are built with 32 channels but only 28, corresponding to the 7 modules on a single MAB,
are used.
82
found in Appendix B.
Data Streams: The firmware installed on the FPGAs of each of the other 13 (slave) ADC
boards controls the ADC chips on each board, collecting 800kHz samples from each channel.
A sample 800kHz timestream from one detector diodes is shown in Figure 2.29. The 4kHz
phase switching can be seen in the data as 8kHz spikes (spiking occurs at the phase switch
transitions ? and ?). The firmware masks out the phase switch transition spikes using an
adjustable mask. The 14 samples around each 4kHz transition are blanked out, corresponding
to a loss of 17.5祍 per every 125祍 of data; 14% of the data are lost to phase switch transition
masking. The signal then is digitally demodulated and averaged at 4kHz and downsampled
to 100Hz. In the demodulated stream, samples are differenced according to their phase switch
state; the average stream is created by summing all samples regardless of the phase state.
A third, quadrature, timestream also is created by demodulating the data at 4kHz, but 90?
out of phase with the demodulation clock (see Figure 2.29). The quadrature stream should
have the noise properties of the demodulated stream, but with the signal subtracted out,
providing a useful systematic check to monitor potential contamination and understand the
detector noise properties.17 The 100Hz samples of all three timestreams for all 28 detectors
diodes are then saved to the FPGA memory as 32-bit integers and readout by the VME PC
in 4Hz (25 sample) frames. Because the other phase switch in each module is switching at
50Hz, every other 100Hz sample will be in the same phase state and the 50Hz demodulation
can be done in post-processing.
Timing: In order to synchronize the telescope and receiver data streams, a time code
reader (TCR) was installed in the VME crate. The TCR accepts an IRIG-B formatted
signal from the GPS receiver in the control room. This signal also is sent to the telescope
control system (�5.6). The TCR communicates with the VME PC via the backplane to
17. This quadrature stream was implemented in W-Band only.
83
assign an absolute timestamp to each 4Hz data frame from the ADC boards. The TCR also
outputs synchronized 10MHz and 1Hz clocking signals that are input to the master ADC via
the timing auxiliary board which contains a buffer circuit that converts the TTL signal from
the TCR to an LVDS signal for the ADC. The 10MHz and 1Hz clocks are used to generate
the data collection, downsampling, demodulation, phase switching, housekeeping, and bias
electronics control clocks.
The data collection is synchronized across all boards by a set of clocking signals generated
in the FPGA on the master ADC board. Synchronized 10MHz, 800kHz 4kHz, and 100Hz
clocks are sent to each board via the VME backplane. Direct probing of the clock signals on
each board indicates that the clocks are synchronized to better than 10ns. The FPGA clock
frequency is 40MHz.
Housekeeping: Housekeeping data are digitized on the housekeeping board which is controlled by FPGA on the master ADC board over the LVDS lines. The housekeeping data
are read out via a single line that is multiplexed. To remove the possibility of receiver data
contamination from this multiplexing, changing the MUX address, digitizing, and reading
out are only done during the masked-out time when the phase state is changed. Housekeeping data are sampled at 500Hz. The samples are accumulated in 125-sample frames which
are read out with the receiver data at 4Hz. The multiplexing scheme is controllable via the
ADC. During normal operation, the ADC cycles through all available HK values but it has
the ability to sample a subset at a higher frequency or collect 500Hz data on a single HK
channel (used for diagnostic purposes).
Snapshot: The ADC also includes the functionality to record 800kHz data directly, without downsampling. This is called a ?snapshot? because only 1024 samples can be buffered
due to the limits of the FPGA. These data are continuously collected and overwritten until
a ?freeze? command is sent, at which point they are read out to disk. The clocking signals
84
for demodulation, phase switching, masking and downsampling also are packaged in a free
channel and read out with the receiver data. During observations, a snapshot is recorded
once every 10 minutes and archived in case it is needed for debugging purposes during data
analysis.
In earlier versions of the firmware, a highspeed (800kHz) timestream was enabled. Due to
FPGA constraints only four channels (a single module) could be read out at once. This mode
of operation was useful during the module and electronics testing phase. It was discarded
in favor of a quadrature timestream for the W-Band observing season when there was no
longer a need to retain it.
LVDS Bias Control: All bias boards (LNA bias, Phase Switch, PreAmplifier) are controlled via low voltage differential signals (LVDS) passed from the FPGA on the master ADC
board to the electronics box backplane. Desired bias values for the phase switches, detector
diodes, and LNA gate and drains are stored in the FPGA memory as well as sent to the bias
boards. The phase switch state also is set and stored in the firmware and the commanded
clocking signals are sent to the phase switch board via the LVDS cable.
2.5.5
Receiver Control Software
The receiver control software (RCS) is a suite of programs that control the interface between
the user and the receiver electronics. It includes an adc server, a bias server, a data compilation program, a peripheral server, and several larger programs that automate tasks such as
biasing the zeroing the PreAmplifer offsets after the detector diodes are biased. RCS runs
on the PC mounted in the electronics enclosure and on the VME crate controller PC in the
ADC VME crate.
ADC server controls the interface to the ADC boards and runs on the VME crate computer. Three types of data from the ADC are collected at 4Hz: downsampled (100Hz) data,
85
snapshot data (800kHz) and housekeeping data (500Hz MUXed). The 100Hz data include
the average, demodulated, and quadrature timestreams.
Bias server sends commands to the ADC boards requesting the phase switch mode,
adjusting the blanking mask for the downsampled timestreams, setting HK MUX addresses
and setting the bit values to send to the bias boards to bias the modules. Bias server can
also query the ADC firmware for the current settings and resolve competing requests to the
ADC between adc server and bias or status commands.
Peripheral server handles the interface to the warm and cold PID temperature regulators,
and collects data from the cryostat pressure sensor, the Q-Band noise source and the external
thermometers monitoring the groundscreen temperature.
Data Compilation merges data from the downsampled time streams, housekeeping, bias
and phase switch status and peripheral data with the telescope pointing data and writes it
to disk in one second frames.18 W-Band produces roughly 20GB of data per day.
2.5.6
Telescope Control
The telescope control system, CBI control,19 predated QUIET and is fully described in
[102]. The telescope control system uses a combination of a Tracker software program that
computes trajectories and, a commercial programmable multi-axis controller (PMAC) that
drives the azimuth, elevation and deck motors. CBI control collects encoder positions, on-site
weather station information such as windspeed and temperature, and executes predefined
trajectories using Tracker such as stowing the telescope, tracking a source, or executing a
custom QUIET scan (�3).
The data stream from the telescope was synchronized with that of the receiver using a
18. Telescope pointing and radiometer data were not integrated in data compilation in the Q-Band season
and were instead integrated in data processing due to the rush to deploy and the pre-existing telescope
control software
19. CBI control was written for CBI when the mount was built.
86
common IRIG-B signal from a GPS receive located in the control room. The synchronization
of the telescope and receiver data streams wasn?t perfect, however. During data analysis a
25msec offset was discovered between the telescope and receiver data. Up to 10msec of this
offset can be attributed to the fact that the receiver data is integrated over 5 millisecond
intervals (100Hz sampling) and the timestamp is attached at the end of each sample, while
the encoders are sampled and stamped instantaneously. The origin of the remaining offset
is traced to the FPGA on the ADC, but the exact source of the delay is unknown. We rely
on the fact that it is very stable (constant to less than 1ms precision) throughout the season
and is compensated for during analysis (�.
87
CHAPTER 3
OBSERVATIONS
The QUIET experiment consisted of two observing seasons. In May of 2008, the telescope and
Q-Band receiver were sent to the Chajnantor Observatory in northern Chile. After several
months of shipping, assembly, and commissioning tests, the Q-Band observation season
began in October 2008 and lasted eight months. The Q-Band receiver was decomissioned in
June of 2009. The second or W-Band observing season commenced science observations in
September 2009 and was completed sixteen months later on December 23, 2010.
The physical site of the telescope and common weather patterns at the site of observations
are described in �1. The choice of sky patches observed and the observation strategy
employed are discussed in �2 and �3, respectively. The major events that occurred during
each of the two observation seasons are noted in �4.
3.1
Site
The Chajnantor Observatory is located on the Chajnantor plateau in the Atacama desert
in northern Chile (67? 450 4200 W, 23? 010 4200 S). QUIET makes use of existing infrastructure
at the observatory which was originally built for a previous experiment, the Cosmic Background Imager (CBI).1 Facilities at the site include the telescope mount (described in �1),
a protective dome, diesel generators, a machine shop, a laboratory, and a control room.
QUIET shares the plateau with the Atacama Cosmology Telescope (ACT), Atacama Large
Millimeter Array (ALMA) and the Atacama Pathfinder EXperiment (APEX).2 Favorable
observing conditions on the plateau ? high altitude (5,080 m), extreme dryness, low horizon
(6? ? 8? ) and accessibility of the site ? have made it an increasingly popular destination
1. CBI operated from January 2000 through May 2008 making CMB observations at 30 GHz [58, 59, 60]
2. The Atacama Submillimeter Telescope Experiment (ASTE) and NANTEN2 are located nearby on the
Pampa la Bola valley.
88
for CMB experiments.The site is remote enough that interference or contamination from
terrestrial microwave sources is minimal, but accessible enough (a few hours by car) that
supplies are readily available. The low horizon decreases the likelihood of contamination from
ground pick-up. The altitude and dry climate mitigate the absorption of CMB radiation by
atmospheric water vapor and oxygen.
Figure 3.1: Atmospheric opacity (left vertical axis) and Equivalent Blackbody (EBB) zenith
Temperature (right vertical axis) as a function of frequency on the Chajnantor Plateau
(5000 m) as calculated from the ATM model [103]. The QUIET Q-Band and W-Band frequency ranges are overlaid in blue bands. Colored lines represent different PWV levels in
the atmosphere. Adapted from [104].
Figure 3.1 shows the atmospheric opacity3 and equivalent blackbody sky temperature
as a function of frequency for several possible values of precipital water vapor (PWV). The
opacity is calculated using the ATM atmospheric model [103] assuming an approximate
altitude of 5000 m. As shown in Figure 3.1, the atmospheric temperature is more strongly
dependent on frequency in Q-Band but more susceptible to changes in PWV in W-Band.
The median values of the PWV measured during the observation seasons were 1.2 mm
3. At a given radio frequency, atmospheric attenuation is characterized by the zenith opacity, ? . The
intensity of radiation transmitted through the atmosphere from a celestial source to an observer is I(? ) =
I0 e?? A where I(? ) is the received radiation intensity, Io is the unattenuated radiation intensity, and A is
the airmass [105].
89
and 0.95 mm for Q-Band and W-Band respectively. The PWV is determined using values
from the APEX weather monitor, located less than one kilometer from the site [106].
The effective atmospheric temperature as calculated from QUIET data is 9 K at 40 GHz
(Q-Band) and 5 K at 90 GHz (W-Band). These temperatures are comparable to those
measured at the South Pole4 and better (lower) than those at the Caltech Submillimeter Observatory (CSO), two sites where several other CMB experiments are located [e.g.,
43, 32, 107, 108, 109, 110].
Of greater concern than the overall atmospheric temperature are the possible atmospheric
fluctuations. These have been found to be acceptably low 5 for average observing conditions,
although they worsen in bad weather. Data quality statistics that are used to identify and
cut regions of bad weather out of the data are described in �2.1. The fraction of usable
data for each season as a function of PWV is shown in Figure 3.2.
Figure 3.2: Data selection efficiency as a function of PWV at the site for Q-Band and WBand. The final data selection criteria are used for the Q-Band data while only preliminary
cuts are applied to the W-Band data since that analysis is still in progress.
QUIET observes 24 hours a day, year round unless unforeseen events such as telescope
mount malfunctions, generator failures, snow and winds storms, interrupt the observations.
4. Actually, at 90 GHz the effective atmospheric temperature is slightly lower on Chajnantor (5 K) than
at than the south pole (? 7 K)
5. In W-Band the average level of atmospheric fluctuation corresponds to roughly 1% of the white noise
level [104, 111].
90
The average PWV, wind speed and humidity are monitored throughout the season and shown
in Figure 3.3. Unlike the PWV, which is taken from APEX, the humidity and windspeed are
monitored by an on-site weather station. Observations are suspended when the windspeed
rises above 15 m/s or the average humidity rises above 90% for more than an hour which
usually indicates snow. High winds can also cause physical damage to the mount if it is
in operation. There is a strong diurnal variation to the wind patterns on the Chajnantor
Plateau. They often rise during afternoons (occasionally halting observations for an hour or
so) and then fall off again in the evenings. The incongruously named ?Bolivian winter? occurs
in the Chilean summer (January ? March) when snow storms come in over the mountains
from the east (Bolivia) and accumulate snow at high altitudes. While we observed through
this season, data quality varied and observing efficiency suffered as we typically had to shut
down operations for several days roughly two to three times a year for prolonged storms.
3.2
Field Selection
We divide our observations among four CMB fields, referred to henceforth as ?patches.? The
number, size and location of patches to observe were determined by balancing the conflicting
requirements of maximizing observation time and efficiency while minimizing the number of
patches and the foreground contamination in each patch.
To maximize observation time we operate 24 hours a day. This required that there be
a sufficient number of patches so that one is always available to observe. To be available, a
patch must be above the telescope?s lower elevation limit of 43? and not so high in elevation
that it would become too wide in azimuth to observe efficiently. The distance in azimuth that
the telescope must move to cover a patch of the same size on the sky is proportional to the
cosine of elevation. Since the telescope has limited speed, it takes more time to scan across
the patch as it rises in elevation; at ? 75? a scan will take nearly three times longer than it
would at 45? and thus the scan is less efficient (see �3). These elevation requirements limit
91
Figure 3.3: Top: PWV, Middle; Wind Speed, Bottom: Humidity measured throughout
the Q-Band (blue) and W-Band (blue) observing seasons. Black lines indicate observations
limits. Observations must be suspended if the humidity reach the limits. Observations can
and usually do continue if the PWV rises above 4 mm but the data will likely be cut.
the declination (Dec.) of a possible patch (?55? . Dec. . ?35? ) while the desire to evenly
distribute patches throughout the day and night means that they should have a broad range
of right ascensions (R.A.).
Limiting the number of patches that we observe allows us to spend more time observing
each patch. The more time spent on a given patch the more we are able to integrate down
the noise in the measurement of that patch to improve the sensitivity. The sensitivity of the
measurement improves as the square root of the observing time (�4). Further, we want to
choose patches that are ?clean? ? have minimal foreground contamination. Once the range
92
60�
30�
12h
14h
16h
18h
20h
22h
0h
2h
4h
6h
8h
0�
-30�
CMB-2
CMB-1
-60�
CMB-3
G-2
CMB-4
G-1
0
mK
2
Figure 3.4: The CMB and Galactic patches, in equatorial coordinates, superimposed on a
Q-band all-sky WMAP 7-year temperature map [112]. Note that the Galactic-plane temperature signal saturates the color scale. Patch G-2 is the Galactic center [1].
of possible patches was chosen through R.A. and Dec. constraints, the specific positions of
each patch were chosen to minimize foreground emission using WMAP 3-year data [112].
The area of each patch is approximately 225 deg2 . Figure 3.4 indicates their positions on the
sky and Table 3.1 lists their center positions and total integration times.
In addition to the four CMB patches, we observed two galactic patches. Patch G-2 is
the galactic center while patch G-1 is a region slightly offset from the galactic center in the
galactic plane. Observing these patches allows us to constrain the spectral properties of
the polarized low-frequency foregrounds with a high signal-to-noise ratio. As bright sources,
they also were helpful as check of pointing (�3) and TT performance. Figure 3.5 shows
the elevation of the four CMB patches and two galactic patches throughout a typical day?s
observations.
The galactic patches have the added benefit of filling in the time between the setting of
93
Patch
CMB-1
CMB-2
CMB-3
CMB-4
G-1
G-2
Total
Table 3.1: Patch Locations and Integration Times
R.A.
Dec.
Q-Band Hours
W-Band Hours
(J2000)
CES CES Diodes CES CES Diodes
h
m
?
0
12 04
?39 00
905
56, 062
1, 773
606, 275
h
m
?
0
05 12
?39 00
703
43, 598
1, 096
374, 930
00h 48m ?48? 000
837
51, 795
984
336, 440
22h 44m ?36? 000
223
13, 808
473
161, 784
h
m
?
0
16 00
?53 00
311
23, 058
502
171, 548
h
m
?
0
17 46
?28 56
85
6, 899
250
85, 464
3, 064
195, 220
5, 078 1, 736, 444
Note. ? The central equatorial coordinates and integration times for each observing patch. G-1 and G-2
are Galactic patches. CES indicates a single observation or Constant Elevation Scan (see �3). A CES
Diode is a single observation with a single detector diode; it is the unit of data used for data selection (see
�2).
patch CMB-1 and the time when CMB-4 rises. Although patch G-2 is an exception to the
declination limits imposed when choosing the patches ? at a declination of ?28? 560 , it rises
to nearly 80? in elevation (see Figure 3.5) ? we chose to observe it anyway as it is the galactic
center. To avoid high elevations, we observed it only when it was rising or setting, but not
during transit. A special, smaller scan also was implemented for patch G-2 part way through
the Q-Band season.6 As seen in table 3.1, CMB-4 has markedly fewer hours of observation
time than the other patches. The time of day during which patch CMB-4 is available overlaps
with that of CMB-3. Patch CMB-3 was prioritized as it is a cleaner patch. CMB-3 was also
chosen such that it partially overlaps with the field the BICEP collaboration has chosen to
observe [43]. This is an added benefit, since it creates the opportunity to directly compare
results.
6. With a scan width of 5? in R.A. instead of the usual 7.5? , the telescope was able to observe the patch
when it was closer to the upper elevation limit.
94
Figure 3.5: Patch elevations at the site during a typical 24 hour period. The solid lines
represent the elevations of the four CMB patches while the dotted lines denote the two
galactic patches observed. The gray box separates night from daytime observations and the
black line shows the elevation limit for the telescope. Note that continuous coverage can be
achieved with these four CMB patches, and two galactic patches.
3.3
Scan Strategy
QUIET uses a drift and scan strategy. The telescope is slewed to a point that is ahead of
the patch but on it?s path. Once there, the telescope slews back and forth across the sky
in azimuth while maintaining a constant elevation. This azimuthal scan continues until the
patch has drifted past the telescope, at which point the telescope is repointed (either to a
new patch, or ahead of the same patch) and the process, known as a Constant Elevation
Scan (CES), repeats. An example of the telescope?s motion in azimuth, elevation and deck
angle (rotation about the optical pointing axis of the telescope) during a single CES is
illustrated in Figure 3.6. Since each QUIET patch is roughly 15? x 15? in size, a typical
95
CES begins by pointing 7.5? ahead of the patch in R.A. and an scanning an average of 15?
in azimuth for 1.25-1.5 hours until the patch has drifted through 15? . Figure 3.7 shows a
series of several CES in azimuth and elevation as a patch rises and sets. The azimuth drive
of the telescope has a average speed of 4.54? /s , a maximum speed of 6.3? /s, a maximum
acceleration of 4.5? /s2 and a jerk of 2.25? /s3 . Combining the azimuthal speed and patch
size, we get typical scan periods ranging from 10 seconds at 45? to more than 20 seconds
65? . At the beginning of each CES, a series of mini sky-dips are performed for calibration
and are further described in �1.
Figure 3.6: The motion of the telescope in azimuth, elevation and deck rotation is shown
for a single Constant Elevation Scan(CES). Each CES involves slewing to a point ahead of
the patch and then slewing back and forth in azimuth while staying at a constant elevation
and deck angle. At the beginning of each CES, a series of mini sky-dips are performed for
calibration.
Scanning the telescope modulates the signal from the sky, converting CMB angular scales
into frequencies in the detector time streams. Since QUIET targets large angular scales, fast
scanning is critical to ensure that the polarization modes of interest appear at frequencies
higher than the atmospheric and instrumental 1/f knee frequencies (see �4). Maintaining
96
constant elevation during a scan ensures constant atmospheric column depth, minimizing
atmospheric fluctuations.
Figure 3.7: Right: Typical series of CES following the rise and setting of a patch. The black
line indicates the patch center while the azimuthal scan is shown in blue and the elevation of
the telescope is shown in green. Note that as the elevation of the patch increases, the scan
must increase in azimuth to cover the patch.
Diurnal sky rotation and weekly deck rotations provide uniform parallactic-angle7 coverage of the patches, and ensure that peripheral regions are observed by multiple polarimeters.
As discussed in �2.3, an effect know as I ? Q/U leakage can induce a spurious polarization
signal. Since it is an instrumental effect, the spurious signal is fixed in the reference frame
of the instrument. By varying the parallactic angle during the observation season ? rotating
the patch with respect to the instrument (diurnal sky rotation) or rotating the instrument
with respect to the sky (deck rotation) ? we can average out this leakage. The amount of
parallactic angle coverage determines the degree to which we suppress the leakage. Figure
7. Parallactic angle gives array orientation on the sky. It is defined as the angle between two great circles
on the sky: the first is drawn between the optical pointing axis of the telescope and the zenith, the second
is drawn between the optical pointing axis and the north pole.
97
3.8 shows the distribution of parallactic angles throughout the Q-Band and W-Band observation seasons for all four CMB patches. The array orientation is calculated based on
the mean azimuth, elevation, and deck angle during each CES. Five deck angles (?150? ,
30? , 75? , 120? , and 165? ) were used in the Q-Band season while W-Band used nine (the five
used in Q-Band plus ?120? , ?105? , ?60? , and ? 15? ).8
Figure 3.8: Parallactic Angle (?) coverage throughout the Q-Band and W-Band seasons
separated by patch. The distribution is more even in W-Band due to the increased number
of deck rotations throughout the season. The array orientation is calculated from the mean
azimuth, elevation, and deck angle during each CES. 2? is plotted since polarization is
periodic in two times the parallactic angle.
In addition to the four CMB patches and two galactic patches, several calibration sources
(discussed in detail in �1) are observed on an intermittent schedule. Some like the moon
or Taurus A are observed daily when available and others (e.g. Jupiter) are observed only
weekly. Figure 3.9 shows a sample week of observations. Note that patches CMB-1, 2, & 3
dominate the schedule with calibrations and galactic patch observations filling in the gaps.
8. A deck angle of 120? was used briefly during the W-Band season when there were problems with the
azimuth drive while scanning at low elevations. It was chosen to maximize the balance of the deck, decreasing
the likelihood of further telescope stalls.
98
Figure 3.9: A week of observations with the W-Band receiver. Observations are dominated
by patches CMB-1, CMB-2, CMB-3. Blank space indicates wind storms.
3.4
Observing Seasons
After several months of test integration at Caltech, the Q-Band receiver, mount platform
and telescope were packed and shipped to Chile. They arrived by ship six weeks later and
were assembled and installed over several weeks in the late summer of 2008. Once the
platform, telescope, electronics, ground screen, and cryostat were re-assembled at the site,
they were installed on the existing mount and observed for eight months. The cryostat and
electronics were replaced with those of the W-Band receiver in the summer of 2009 which
then operated for sixteen months. Figure 3.10 shows the integrated observation times for
both seasons. While the W-Band season was longer, observing efficiency was high during
the Q-Band season for reasons discussed in �4.2.
3.4.1
Q-Band Season
Observations with the Q-band receiver officially commenced on October 24, 2008. Collecting 3,458 hours of data, the receiver operated until June 13, 2009. Of these data, 77% are
observations of the CMB, with 12% of the observing time used for Galactic fields, 7% for calibration sources, and 4% cut due to obvious instrumental problems such as lack of telescope
motion. Our full-season operating efficiency9 is 63%.
Table 3.2 lists the noteworthy events in the Q-Band observing season. These are events
9. Operating efficiency is the fraction of total time in the season that the telescope was operating ?
telescope was scanning and data was being collected.
99
Figure 3.10: Comparison of the operational time (time when telescope is scanning and data
is being collected) for the Q-Band and W-Band seasons. No data selection cuts are applied
and calibration observations are included. The plateaus indicate downtime for storms or
mechanical failures.
that cause a major change in the state of the instrument and may include anything that
causes lost data, changes in calibration or damage. The record of these event is used during data selection to ensure that all changes are accounted for and contaminated data are
rejected.
The most notable events in the Q-Band season include changes in bias boards and cabling
made while hunting glitches in the data (�5 and �2), several weeks lost to mount and
generator failures that required us to purchase and install a new generator and the discovery
that the deck encoder had slipped out of alignment due to loose bolts (see �3).
3.4.2
W-Band Season
In June 2009, the Q-Band receiver and accompanying electronics enclosure were removed
from the mount and replaced with corresponding W-Band components. After installation
100
Table 3.2: Noteworthy Events in the Q-Band Observation Season
Description
Dates
Slew Near Sun
01/19/09
Generator Failure
11/18/08, 02/18/09
Bias Array On/Off
12/29/08
Snow/Wind Storm
01/04/09
Telescope Stall
01/24/09, 01/26/09, 01/27/09, 01/30/09, 02/01/09
Blown ADC Fuse
01/22/09, 01/07/09
Failure of data archiving
02/16/09
Data Cable Swap
01/09/09 ? 01/15/09
Mount failures
10/31/08-11/07/08, 01/04/09 ? 01/10/09
Telescope Maintenance
01/11/09
PreAmp Board Swap
11/28/08, 11/30/08
Begin Double Demodulation
10/22/08
Phase Switch Diode Broken
12/27/08, 02/17/09
Groundscreen found Open
12/09/08
New generator installed
12/19/08
Thermal Cycling
12/19/08
Phase Switches Fixed
12/19/08, 01/27/09
Add Eccosorb to Noise Source
01/30/09
Cables tied to reduce dk slips
01/29/09
Deck encoder bolts tightened
01/28/09
Holiday Shut down
01/28/09 ? 01/04/2010
of the new electronics and cryostat, the deck platform was rebalanced to account for the
increased weight of the W-Band electronics and the mirrors were re-focused to account for the
slightly different position of the phases center of the W-Band receiver. The W-Band receiver
collected 7,567 hours of data giving an operating efficiency of 62.9%.
The W-Band season was marked by far more noteworthy events than the Q-Band season.
First, this is due to the fact that the telescope mount was nearing the end of its life and as such
required more frequent maintenance as parts wore out. Second, we suffered failures of both
of the cryostat cold heads in the W-Band receiver during the season. These failures had to
be diagnosed and then the cold heads had to be replaced in the open air on the mount which
drastically increased the difficulty of and time required to complete the operations. Later in
the season an intermittent leak in the cryostat vacuum appeared. Although it was suspected
101
to have been near the window, it was never identified. As it couldn?t be found, periodically
we would have to re-attach vacuum pumps to the cryostat to improve the vacuum. Further,
the combination of a vacuum leak and failing cold heads required more frequent variation
in the cryostat temperature regulation (CPID) parameters. A delivery of un-weatherized
fuel froze the fuel lines in both the primary and back-up generators forcing observations
to halt until the ambient temperature rose above freezing (roughly 1 week). In January,
observations were halted to install the Upper Ground Screen and perform dedicated sidelobe
measurements (�2.5). Further, due to a bad batch of capacitors the linear power supplies
that powered the PreAmplifier boards periodically faile during the season. They too had to
be replaced on the mount. Tables 3.3 and 3.4 list the major difficulties encountered during
the observation season that either caused us to lose observation time or caused changes to
the system that could have possible systematic effects.
102
Table 3.3: Noteworthy Events in the W-Band Observation Season, Part I
Dates
Description
ADC Fuse Blown
03-04-10
Azimuth Limit
10/30/10, 11/15/10, 11/20/10, 11/23/10, 12/01/10,
Switch Slippage
12/13/10, 12/15/10
Bias Array Up/Down
08/14/10, 08/26/10, 09/09/10, 09/21/10, 10/06/10
CPID changes in
setpoint / parameters
Cryostat Modifications
Deck slipped off bearing
Diagnose & Replace Cold Head
Dome Ripped
Earthquake
Generator Failure
Internet Outage
JPL Biases
MAB01 Pwr. Cord Failure
MAB Offset Failure
Modify Groundscreen
Telescope Stalls
in Az/El/Dk
Pumped on Cryostat
RAID Faliure
Replace Failed Cold Head
Replaced Linear
Power Supplies
08/17/09, 11/18/09, 11/19/09, 11/26/09, 04/25/10
07/05/10, 07/29/10, 07-31/10, 08/05/10, 08/19/10
10/23/10, 10/26/10, 11/10/10, 11/11/10
11/28/10, 11/30/10
05/30/10, 06/02/10
07/28/10
09/26/09 ? 10/19/09
05/17/10
02/27/10
08/20/09, 11/16/09, 11/17/09, 06/03/10
07/18/10 ? 07/24/10, 11/07/10
09/07/10
08/26/10
11/28/10 ? 11/30/10
08/17/09
07/06/10, 05/24/10, 01/30/10
11/08/09, 11/21/09, 11/25/09, 11/26/09, 12/08/09
12/17/09, 12/13/09, 03/13/10, 04/07/10, 04/08/10
05/21/10, 07/16/10, 09/26/10, 09/29/10, 10/31/10
11/19/10, 12/15/10
05/02/10, 05/17/10, 06/19/10, 08/05/10, 08/19/10
09/11/10, 09/16/10, 09/29/10, 10/02/10, 10/05/10
11/08/10
03-02-10
08/01/09 ? 08/06/09
08/14/09, 01/31/10, 05/26/10, 05/30/10
06/10/10, 06/30/10, 07/10/10, 12/13/10
103
Table 3.4: Noteworthy Events in the W-Band Observation Season, Part II
Description
Dates
Remove UGS
12/17/10
Sidelobe Measurements
01/27/10 ? 01/30/10
Slew Near Sun
11/18/09
Snow/Wind Storms
Telescope Failures
/Maintenance
Thermal Cycling
Turn Off Rx 28,42 (Broken)
UGS Installation
UGS Failure
UPS/VME Failure
WPID change in
setpoint / parameters
08/08/09, 11/04/09 ? 11/07/09, 05/17/10 ? 05/20/10
05/22/10, 05/29/10 ? 05/03/10, 02/25/10 ? 03/01/10
09/01/10 ? 09/03/10, 09/12/10, 09/25/10, 09/27/10
09/30/10, 10/01/10 ? 10/04/10, 10/06/10 , 10/09/10
10/12/10 ? 10/13/10, 11/15/10
08/04/09, 09/09/09 ? 09/15/09, 11/11/09 ? 11/12/09
11/27/09, 12/07/09, 12/14/09, 12/16/09, 12/29/09
12/31/09, 01/01/10, 01/06/10, 02/05/10, 02/08/10
02/15/10, 02/17/10, 03/21/10 ? 03/29/10, 04/07/10
04/08/10, 05/09/10 ? 05/12/10, 08/06/10, 09/28/10
10/04/10, 10/10/10, 10/15/10, 10/19/10
10/26/10, 10/27/10
07/24/10, 06/03/10, 06/19/10, 05/28/10, 05/30/10
05/03/10, 05/20/10, 09/11/10, 09/16/10, 11/08/10
09/11/10, 09/16/10, 1/08/10
08/07/09
01/26/10
11/20/10
10/31/09 ? 11/01/09, 11/03/09, 11/05/09
11/29/09, 12/04/09, 04/18/10
05/19/10, 10/30/10, 11/10/10
104
CHAPTER 4
CALIBRATION
Measurements of calibration sources account for 7% of the observations in the Q-Band season.
The raw module timestreams are converted into polarization power spectra using observations of a combination of astronomical and instrumental sources as well as the atmosphere.
are combined and used to convert. Descriptions of the calibrators used are found in �1
and the beam profiles (�2), the pointing model (�3), detector responsivities (�4), and
detector polarization angles (�5) required to calibrate the detectors are described below.
Instrumental polarization is also measured and described in (�6).
4.1
Calibrators
Primary calibrations are made using observations of astronomical sources including the
Moon, Taurus A, Jupiter, Venus, and RCW38, and atmospheric modulation known as ?skydips?. Additional calibration measurements also are made using two instrumental calibrators
? a broadband polarized noise source and a sparse wire grid. Table 4.1 lists the astronomical
calibration sources and their observation frequencies. Each is described briefly below:
Table 4.1: Regular Calibration Observations
Source
Schedule
Duration (min.)
sky dips every 1.5 hours
3
Tau A
every 1?2 days
20
Moon
weekly
60
Jupiter
weekly
20
Venus
weekly
20
RCW38
weekly
20
Taurus A: The supernove remnant Taurus A (Tau A, or the Crab Nebula) has a strongly
emitting, rotating, neutron star pulsar at its center. Tau A is a commonly used cal105
ibration source for CMB as in the microwave region it is the among the brightest
polarized objects. Tau A has a polarized flux of 22.12 � 0.60 Jy at 40.64 GHz [113].
Unfortunately, due to the declination of Tau A (22? ), at the QUIET site it is only
available for roughly 1.5 hours per day, Tight raster scans are used (narrow azimuth
scans stepped in elevation). Because of the small signal size and low availability of
Tau A, observations are performed on one module at a time instead of the full array.
The raster scans are repeated at several deck angles to modulate the signal (see �4).
It is used primarily as an absolute polarization calibrator, but measurements of the
relative detector polarization angles are also obtained.
Moon: The moon is useful for calibration as its strong polarized emission1 and availability
make calibration observations efficient and easily scheduled. A full array drift scan
similar, but smaller in width than that used for CMB observations is used to observe
the moon. The moon is radially polarized, giving a quadrapolar polarization pattern
and primarily is used to measure the detector angle for each diode, but the I ?Q/U,
and relative detector gain are also measured.
Sky-Dips: At the beginning of each CES, a ?sky-dip? calibration is made, consisting of three
elevation scans with 4? amplitude. The atmospheric depth increases from zenith to
the horizon, thus the sky temperature will vary with a scan in elevation. will cause
the sky temperature to change as sin1 el . Thus, the voltage measured by the modules?
detector diode average (Total Power) timestreams as a function of elevation is given
by:
Vi = Gav
Tz
+ ? + ?ti
sin eli
(4.1)
where Gav is the average gain ([mV /K], Tz is the zenith sky temperature,2 , ? is the
1. For a QUIET module, a one second observation can give a measurement with S/N > 1000[77].
2. This varies as a function of PWV and frequency, see Figure 3.1.
106
receiver system temperature (incorporating the atmospheric sky model [103], and ? is
a linear drift in the detector timestream (this compensates for the large 1/f noise in
the average timestream) [114]. Sky dips are used to determine the relative detector
responsivities and the I?Q/U leakage. Large sky-dips also were performed during
end-season calibrations; they scanned in elevation from 43? ? 87? .
Jupiter: The effective temperature of Jupiter as seen by the Q-Band receiver is roughly
51mK. Jupiter is a convenient bright source for the absolute gain calibration of a the
differential temperature assemblies as it is unpolarized. With its small angular size,
5000 , it is also a useful ?point? source that can be used for beam mapping (QUIET?s
Q-Band beam FWHM is 270 .3).
Venus, & RCW38: RCW38 is an ionized HII star forming region with a total power flux of
140Jy, but less than 0.09% polarization. It is useful only for total power (temperature)
measurements [115]. Venus is also a bright, unpolarized source. They are used as
responsivity calibrators for the differential temperature receivers, supplementing the
measurements of Jupiter.
Wire grid: The wire grid is described in �4.4. It was mounted to the Q-Band cryostat
window during final calibrations after the observation season ended but before the
receiver was decommissioned. Rotation of the wire grid modulates a polarized signal
(?2K) allowing us to measure the relative detector polarization angles.
Noise Source A broadband RF noise source was installed under the secondary mirror midway through the Q-Band observing season. It was used as a monitor of relative responsivity. It was flashed (chopped on and off) for 30s at the beginning of each CES.
The noise source was composed of a broadband noise diode amplified by two MMIC
amplifiers; the output was chopped using a pulsing noise diode at 2 Hz giving an output signal of ? 30 礧 [116]. It was coupled to a rectangular horn and installed in
107
the bottom ground screen approximately 15? from the main beam. The gain of the
MMIC LNAs varies with a thermal coefficient of roughly 0.2%/K. The noise source
was enclosed and thermally regulated to 0.5 K. A mechanical switch blocked RF in
the off state with better than 50 dB isolation. The noise source was controlled, and
monitored by peripheral server (�5.5).
4.2
Beam Profile and Window Function
Determination of the beam profile and window function is described in detail in [69]. The polarization beams are obtained from maps created using measurements of Tau A. Differentialtemperature beams (edge horns in the array) are measured from Jupiter observations. The
average FWHM for the beams across the array is 27.0 3. The central horn and edge horns
are relatively well-measured and thus have a FWHM uncertainty of 0.0 1 while other, less
frequently measured horn have a 1.0 5 uncertainty on their beamwidths [1].
Details of the beam mapping are given in [69]: the beams are modeled as a sum of six
even Gauss-Hermite terms
m
h
?
?2 X
a2i H2i ( )
bs (?) = exp(? 2 )
?s
2?s
(4.2)
i=0
where H2i are the Hermite polynomials of order 2i (even), and the amplitude coefficients
a2i are the fitting parameters and ?s is the symmetric gaussian beam size. This is done to
account for the non-Gaussian beam shape at large angles3
Beam window functions are computed from the beam profiles; both are shown in Figure
4.2. Deviations between the beam profile and window function of the central horn and a
horn of the differential temperature assembly modules (at the edge of the array) are shown in
Figure 4.3. The uncertainty accounts for statistical error and differences between polarization
3. Angles greater than twice the beam size or ? 0.4? [69].
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and differential-temperature beams, as described in � 7.5 [1].
Figure 4.1: Maps of Tau A as measured by the four detector diodes of the module RQ09 ?
the central element in the Q-Band array [117].
Figure 4.2: Left panel: Beam profile from Tau A observations with the central feed horn.
The data are overplotted with the expansion in Gauss-Hermite polynomials described in the
text. Right panel: Beam window function with fractional uncertainties shown in red [1].
4.3
Pointing
The global pointing model is generated from physical models of the 3-axis mount, the detector
array and the telescope in combination with observations of calibration sources. Observations
of the Moon with the central feed horn in the array are combined with observations of Jupiter
and Venus with the differential-temperature assembly on the outer edge of the array. Optical
pointing observations are taken regularly with a co-aligned star camera and used to monitor
109
Figure 4.3: Left panel: Map of Jupiter using the RQ17Q1 detector diode of the differential
temperature assembly. Central panel: Residual differences between the beam profile of the
central horn (RQ09 made using Tau A) and the horns of the differential temperature assembly
(made using Jupiter). The lines represent the measurement using the different detector
diodes of the modules of the differential temperature assembly. Right Panel. Residuals in
the measurement of the window function[118].
the time evolution of the pointing model. Except for the time when the deck encoder was
slipping (described below), the pointing module was stable. Mean pointing solutions from
the start and end of the season were less than 10 . apart [1].
In the mount model, five corrections are applied to the compensate for the difference
between the encoder values for the array pointing and the actual physical pointing [102, 77]:
Deck Encoder Offset: During the first two months in the season, a mechanical problem
with the deck-angle encoder created pointing shifts in the data. The problem was
subsequently repaired. To correct the pointing, different offsets were applied to the
deck encoder values for four distinct periods during the season. Based on pointing
observations of the Moon and other astronomical sources, we verify that these encoder
shifts are ? 1.88? [77].
Deck Flexure: The deck bearing is subject to some flexure as the telescope tilts in elevation
due to the large uneven distribution of weight on the deck platform. The flexure
increases for lower elevations.
Azimuth Tilt: Offsets between the zenith and the rotation axis of the azimuth mount can
cause small elevation changes during azimuth scanning.
110
Elevation Sag: Likewise, the azimuth of the telescope will change during elevation scans if
the elevation axis is not perpendicular to the plane of the azimuth drive (and horizon).
Array Collimation: If optical axis of the telescope (as defined by the central element of
the array), is correctly aligned with the deck drive?s rotation axis, the deck can rotate
while aiming at the same point. If there is a misalignment, the telescope will instead
trace out a small circle. Array collimation is measured using observation of calibration
sources with the central horn. Corresponding offsets are applied to the other horns by
combining the known offset of the central horn with the horn array model.
Figure 4.4 shows observations of the moon for all detectors; these observations (and those
of Jupiter for the TT modules) were used to determine relative pointing among the horns
with an RMS pointing error of 3.0 5[1].
Figure 4.4: Observations of the Moon with all detectors. The moon response is fit to a
Gaussian beam and the central values are used to determine the pointing offsets between
the central horn and the others in the array.
111
4.4
Responsivity
A responsivity model for each detector channel is generated by combining measurements of
the absolute polarized responsivity using Tau A, measurements of the total power responsivity using regular mini sky dips and measurements of the enclosure temperature variation.
Combined, these three measurements provide a conversion of the average and demodulated
signals from voltage to temperature units for every diode in every CES.
Responsivities as measured by regular sky-dips taken at the beginning of each CES can
vary by up to 10% per day[1]. This is primarily due to thermal variations in the bias
electronics caused by weather. A correction factor is applied to each detector diode channel.
Observations of Tau A at multiple deck angles will modulate the polarized flux as the
detector polarization axes align with the direction of the polarized flux. Given a known
absolute polarized flux for TauA ? 5 mK signal at 43GHz4 ? the amplitude of the modulation
is fit to determine the absolute responsivity of the channel (see Figure 4.5). A typical
responsivity is 2.3 mV K?1 , with a precision from a single set of observations of 6% [114].
Since Tau A is rarely available, however, observations with non-central horns in the array
were infrequent (1-2 observations /horn for the season) while the central horn observed Tau
A every few days. Thus, the absolute responsivity was calculated for the central horn and
extrapolated to the other horns using the more frequent relative gain calibrations of the
sky-dip measurements.
The absolute responsivity for the differential-temperature modules is calculated from
measurements of Jupiter [119], Venus [120] and RCW38; all three agree within errors.
Finally, a dedicated set of calibration measurements were carried out at the end of the
season in which the electronics temperature was varied while taking repeated sky-dips. This
data confirmed the responsivity model which was further validated by comparison to measurement of the responsivity using the Moon, wiregrid, and broadband noise source. Mea4. Scaled to Q-band using a spectral index of ?0.3476
112
Figure 4.5: Output of the four detector diodes of the central module (RQ09) as a function
of deck angle while observing Tau A. The set of observations (all four deck angles combined)
took roughly 20 minutes; yet errors are already smaller than the point size plotted here.
The top and bottom plots show the response of the 盦 diodes respectively while the middle
plots give ?U . Figure courtesy of O. Tajima.
113
surements agree within 2%-6% [1].
4.5
Detector Polarization Angle
Measurements of the radial polarization5 of the moon are used to determine the detector
polarization angles. In the ?Q? detector diodes of a module (measuring the Q Stokes parameter) the polarization appears as a quadrapole. Simiilary, the ?U? diodes measure another
quadrapole, but ideally rotated by 45? with respect to the Q quadrapole. These quadrapoles
are used to determine the detector polarization angles. Detailed treatment of the fitting procedure and results is given in [77]. Eighteen full array moon observations taken throughout
the season are fit and averaged for each diode. Figure 4.6 shows contour maps of the moon
in both total power (intensity) and demodulated (polarization) timestreams as measured by
the ?U1? diode of the central module (RQ09). The polarization angles are stable, changing
by < 0.? 2, except during the period with the deck-angle?encoder problem mentioned above.
Figure 4.6: Left: Map of the total power (I) measurement of the Moon from one detector diode (RQ09U1) Right: Map of the polarization of the Moon with the same detector
diode. The amplitude of the quadrupole polarization is ? 400 mK. The dotted line gives the
orientation of the detector polarization angle. Contours spacing is 100 mK, with negative
contours indicated by blue lines and positive contours indicated by red. [1]
5. The moon is modeled as a dielectric disk, thus emitted light is preferentially polarized along the radial
direction [77]
114
As a check, the detector angles are also calculated using fits to the Tau A data [121], and
determination of the relative phases between the detectors using the rotation of the sparse
wire grid (�4.4)[122]. Both methods are less precise than the measurements obtained from
the Moon observations. In each case, the differences between the detector angles determined
by the secondary method and the Moon are described by a standard deviation of ? 3? [77].
However, we find a mean shift between the Tau A-derived and Moon-derived angles of 1.? 7.
Errors are estimated in �5 and found to be small.
4.6
Instrumental Polarization
Instrumental imperfections can induce I?Q/U leakage generating spurious polarization signals in the data. One example of this leakage, caused by imbalance in the phase switches,
is eliminated by double demodulation (�4.2). I?Q/U leakage is also produced by imperfections in the septum polarizers (�2.3) [92]. A fraction of the power input on one port
of the module is reflected back because of a bandpass mismatch to the septum polarizer,
and a fraction of the reflected power re-enters the other port. This cross-talk generates the
dominant monopole term of the leakage.
A second septum polarizer imperfection, known as differential loss, generates I?Q only
leakage. Ideally, inputs to the OMT (parallel and perpendicular to the septum) would be
transmitted with equal power to the output ports. Imperfections with the septum (see 2.2.3)
can cause different amounts of loss of each signal at the output ports, resulting in added
power in Q. U signals (at 45? with respect to the septum) are unaffected.
We measure this leakage by measuring the module responses to temperature changes.
Estimates of the leakage are obtained using sky dips, observations of the Moon, Tau A,
and the galactic center as well as variations from the weather[77, 114, 69]. The average
magnitude is 1.0% (0.2%) for the Q (U) diodes. The discrepancy in the Q and U averages
was predicted from measurements[73] of the properties of the septum polarizers and using
115
calibration observations.
116
CHAPTER 5
ANALYSIS FRAMEWORK
QUIET follows a technique of blind analysis in analyzing the data. This means that all data
selection, map-making and power spectra estimation are performed without looking at the
final result. A suite of analysis validation tests are performed to determine if the data are
contaminated and if the results from each patch are consistent. These validation tests are
described in � If the validation tests fail, indicating residual contamination in the data,
the data selection criteria, choice of filtering and unit of cross-correlation used in power
spectrum estimation are all evaluated and modified if necessary. The process is repeated
until the validation tests are passed.
QUIET data analysis employs two parallel pipelines (pipelines A and B) to calculate CMB
power spectra. In addition to the analysis validation tests and blind analysis framework,
independent pipelines provides an additional check for systematic effects that may be intrinsic
to the framework of one pipeline. As will be shown in � the results from our two pipelines
are in excellent agreement.
Pipeline A is based on the pseudo-C` analysis framework, first described by [123], which
is used by numerous experiments [124, 125, 43, 42, 126]. An advantage of the pseudoC` framework is computational efficiency, which is critical for completing the more than
30 iterations of the data selection criteria calculations of the null-test suite used during
analysis validation tests. For the same reason, this pipeline is used for the systematicerror evaluations found in Section 7.5. Pseudo-C` analysis also enables us to perform cross
correlation, making the resultant power spectra immune to possible misestimation of noise
bias. This pipeline made all analysis choices in accordance with a strict (blind) analysis
validation policy described in � 6.
Pipeline B implements a maximum-likelihood (ML) framework [e.g., 127, 128], which
has a long history of use by CMB experiments [e.g., 129, 130, 40, 41]. This framework
117
yields minimum-variance estimates of the power spectra, naturally accounts for E/B mixing, and directly provides the exact CMB likelihood required for estimation of cosmological
parameters, without the use of analytical approximations. Assuming that the noise and contaminations in the data are well understood and accounted for in the calculation of the noise
bias, it produces unbiased maps with full noise-covariance matrices, useful for comparisons
with other experiments. However, this approach also is computationally more expensive than
the pseudo-C` framework. Thus a reduced set of analysis validation tests were performed.
Details of the pipeline B analysis can be found in [79]. Analysis with Pipeline A?s pseudo-C`
framework is described here.
Figure 5.1: Analysis Flow Chart: Data goes through TOD processing and filtering, data
quality statistics are calculated and cut criteria are chosen. Then maps are made and both
blinded and null power spectra are calculated for analysis validation tests. If the data fail
the validation tests, we reevaluate the cut criteria and if necessary define new data quality
statistics or modify the filtering. The process is repeated until the data pass the validation
tests, at which point the results are unblinded.
The analysis can be divided into four major components: i) time ordered data (TOD)
processing and filtering, ii) data selection, iii) map making and power spectrum estimation,
iv) analysis validation tests and systematic error estimates. Figure 5.1 provides an overview
of the flow of the analysis. TOD processing, calculation of TOD noise parameters and
filtering are described in �1, �1.1 and �1.2 respectively. Data selection criteria and
final data selection efficiency ?how much data is retained ? are described in �2 and �2.1.
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Methods of map-making and power spectra estimation used in the pseudo-C` framework
adopted in pipeline A are described in �3 and �4. Analysis of the temperature data
followed much the same framework as the polarization data; data selection efficiency and
differences in the analysis methodology (namely filtering and map-making) are described in
�5. Analysis validation is described in 6 and systematic effects are quantified in �5.
5.1
TOD Pre-Processing
To prepare the TOD for map making, we execute a series of pre-processing and filtering
steps. The telescope pointing data and the polarization data are synchronized, calibrated and
demodulated. Then three filter are applied to the polarization TOD to remove contamination
from atmospheric and detector 1/f noise and ground pickup. A diagram of the steps involved
in TOD processing and filtering is shown in Figure 5.2.
Figure 5.2: The flow of data through the preliminary TOD processing and filtering are shown.
Polarization TOD processing is shown in blue and telescope pointing data processing is shown
in red. Filtering of the TOD is shown in green. Dotted lines indicated that input from the
scan data is necessary for the filtering of the polarization TOD, but the scan data is not
modified.
All TOD processing and filtering are done performed on every CES-diode. The steps
119
involved in TOD processing include:
Type-B glitch correction: The first data-processing step is to correct for a small nonlinearity that was discovered in the analog-to-digital converter (ADC) system. The
non-linearities occur every 1024 bits; roughly 14% of the data are affected. The effect
was measured across the dynamic range of the ADC chip for each channel and the
glitch size and spacing were measured. The measurement of the glitches and the data
correction algorithm applied are treated in Appendix C. The success of the correction
is used as a data selection criteria (�2). Systematic uncertainty from this effect is
estimated in � 7.5.
Timing Synchronization: Next, the receiver data are synchronized with the telescope
pointing. This includes correction of a small timing offset between the two data streams
described in �5.4. The 100Hz receiver data lags behind the telescope pointing data
by 2.5 samples (25 milliseconds). Because the timing offset is a non- integer number
of samples, the timestamps and telescope encoder information are interpolated to line
up with the radiometer samples.
ADC ? V: Each 100 Hz sample read out of the firmware on the ADC board is created by
accumulating 6880 samples of 800 kHz data (8000 samples - 1120 which are masked
out). The data are converted from ADC counts to Volts by dividing by Nsamp = 6880,
multiplying by the dynamic range of the ADC (4V) and dividing by the number of
bits in the ADC (Nbits = 1218 ).
Apply Gain Model: A model of the detectors? polarized responsivities (gain) converts the
data from Volts into thermodynamic temperature [mK]. The gain model is described
in �4.
Apply Pointing Model: The corrections to the telescope pointing data are applied using
the pointing model described in �3.
120
Double Demodulation: The 100Hz receiver data are double-demodulated to 50Hz differencing the demodulated samples from ? and ? clock states (�4.2). The telescope
pointing data are also downampled to 50Hz by averaging the two samples.
5.1.1
Noise model
In the pseudo-C` method, the full noise covariance matrix is not calculated (as it is in the
ML method). A spherical harmonic transformation is applied to the map instead. This
creates a biased ?pseudo-power spectrum? C?` . Monte Carlo (MC) simulations are used to
correct the bias and estimate the uncertainty of the final result. This allows us the ability
to test, and if necessary employ, a wide range of filtering schemes. Instead of attempting
to account for filtering effects on the noise-covariance matrix, they are accounted for in the
Monte Carlo Simulations. Simulated data with noise is processed through the same filters
as the real data and the filter effects can be determined easily.
The noise properties of the data need to be measured to be used for the noise model
in the MC simulations. After pre-processing, the time streams for each detector diode in
each CES are Fourier-transformed and their noise power spectra are fit to the noise model
described in �4.3. Three parameters are fit: the amplitude of white noise, the 1/f knee
frequency, and the power-law slope of the 1/f noise.1 Figure 5.3 shows the Fourier transform
of a single CES for a single diode.
A small fraction of the noise spectra contain features not accounted for in the noise
model such as high frequency narrow spikes (& 6 Hz) or scan synchronous signals. The
beam sidelobes (see � 2.2.5) scanning across features on the ground create a narrow spike
at the scan frequency. Certain slowly changing weather patterns can also create a broader
peak around the scan frequency. To prevent these features from biasing the noise model, the
1. White-noise correlations among detector diodes in the same module are also taken into account in the
noise model and described in [77, 79]
121
Figure 5.3: Fourier transform of a single CES for a single diode (CES 419.4, module 1, U2
diode). The binned data are shown in blue, the noise model fit is shown with the red dashed
line. Gray regions ? ? > 4.6Hz and small region around the scan frequency ? are masked
when the data are fit. This CES was chosen as an example of data with a strong scan
synchronous signal and high frequency noise that that could skew the fit if not masked. The
green dashed line indicated the scan frequency.
fit excludes a region around the scan frequency as well as frequencies above 4.6 Hz. These
excluded regions are shown in Figure 5.3 as well. Once the noise properties are modeled,
contaminations are removed by filtering.
.
5.1.2
Filtering
Three filters are applied to the TOD to remove high frequency noise, atmospheric fluctuations
and detector 1/f noise, and scan synchronous signals. These were chosen from the results
of many runs of the null-test suite (see � 6.1).
High Frequency Cutoff: To remove the high-frequency narrow spikes, we apply a low-pass
filter that turns on at 4.5 Hz, and cuts signals off sharply above 4.6 Hz. For QUIET?s
122
Figure 5.4: TOD (top) and its fourier transform (bottom), for a single CES-diode, before
(left) and after (right) filtering. The region attenuated by the high frequency cutoff filter is
shown with a gray box. The green line indicates the scan frequency.
beam size and scanning speed a low-pass filter of 4.5?4.6 Hz results in a minimal loss
of sensitivity to the CMB.2
Linear Azimuth Filter: To suppress contamination from linear scan synchronous signals,
we subtract a linear function from each telescope half scan (left-going or right-going).
The linear function is fit to the signal as a function of azimuth (not time). This
will remove signals from atmospheric fluctuations or some types of ground-pickup.
Additionally, it will act as a high-pass filter attenuating detector 1/f noise below two
times the scan frequency. The linear azimuth filter removes modes below twice the
scan frequency (45 mHz to 100 mHz depending on patch position, see �3). QUIET is
incapable of measuring CMB modes that would appear as a linear function in single
azimuthal half-scan, so discarding them is acceptable.
2. The signal is already significantly attenuated due to the beam size at frequencies & 5 Hz.
123
Azimuth Binned Structure Subtraction: This filter is designed to eliminate signal from
ground emission. Signals from the beam sidelobes terminating on the ground will not
necessarily have a linear shape and thus won?t be removed by the linear function
subtraction. To remove ground contamination, the data are binned in azimuth (20
bins), averaged over an entire CES for one diode. Any structure that remains is
removed by subtracting the mean value of each bin from the data in that bin. Figure
5.5 shows a CES diode with particularly bad scan-synchronous structure.
Figure 5.4 shows the TOD and its fourier transform, for a single CES-diode, before and
after filtering. Time varying, non-linear, scan synchronous signals will not be removed by
any of the three filters. They will show up as residual ?broad bump? in the power around
the scan frequency. They are cut during data selection (�2).
Figure 5.5: CES TOD binned in Azimuth.
124
5.2
Data Quality Statistics & Cut Fractions
Data quality statistics were developed to identify contaminated data and remove it from the
data set. After a baseline data set was identified, eleven selection criteria were chosen (although many more were investigated). More than 33 iterations of the data selection criteria
and cut thresholds were investigated before the data set passed analysis validation tests (�
and the analysis was complete. The final data set was chosen when these statistics showed
negligible contamination and were little affected by changes to the cuts. The fundamental
unit of data used for analysis is the double-demodulated output of one detector diode for a
single CES, referred to as a ?CES-diode.? Several additional cuts remove entire CES. The
data selection criteria, cut thresholds and amount of data cut by each are described below.
Baseline Cuts: Of the 3,458 hours of data collected in the Q-Band observation season,
2,797 were CMB observations. The first step in data selection is to identify and remove
data in this set with known problems. Channels known to be defective are cut as well as
observations where the mount stalled, or the receiver was not in its operating configuration
(i.e. broken electronics, or different electronics used for debugging). Many of these cuts
remove data due to events listed in the noteworthy events table 3.2. CES shorter than
1000-s also are discarded, which are mainly caused by partial or incomplete observations.
Observations occasionally ended early either because they were halted (e.g. due to high
winds or telescope stall) or the runs were scheduled such that the patch set before a full
observation could complete. In principle this data can be recovered and used, but its noise
properties are not well sampled due to the short duration; the gain would be marginal. These
cuts remove 129 hours of data, establishing a baseline data set with 2,668 hours of CMB
observations. The specific baseline cuts are listed below:
? Reject any CES with duration < 1000 seconds.
? Cut Module 4, diode Q1, which consistently has a lot of high frequency noise.
125
? Cut Module 8, diode U2, which is broken (shorted).
? Cut Module 16 which has an unreliable gate bias connection.
? Cut runs3 0329 through 0341 because the preamp configuration was different. One
board was swapped out during ADC non-linearity debugging effort.
? Cut run 398 because Ground Screen door came open during observation
? Cut CES 0529.1 because the receiver was turned off.
? Cut runs 0563 through 0593 because alternate AIB cables were used (also changed
during ADC non-linearity debugging).
? For CES 0632.4 and runs 0633 through 0635, cut modules 7-9, 12, 13, and 16. ADC
board 2 was not working (blown fuse).
? Cut CES 759.0 because dome maintenance occurred during observation
? Cut CES 654.0, run 937, CES 951.0, 953.1, 953.2, 953.3, 954.0, 955.0, 955.1 and 1413.0
for mount stalls.
? Cut CES 980.0 because the receiver cryogenic temperature was still stabilizing
Weather Cuts: Two weather cuts remove data taken during bad weather. Bad weather
can be separated into two components, the atmospheric opacity increases raising the sky
temperature and atmospheric fluctuations increase. Fluctuations can introduce unstable
scan synchronous signals with 1/f type power spectrum and the increased sky temperature
will increase the white noise for the timestream.
As atmospheric emission is unpolarized, the average or total power (TP) data stream is
used as an atmospheric monitor. Weather is a ?global? effect ? it should be detected by all
3. Runs include all CES in a row that observe the same patch
126
functioning modules in the array during the same CES. This can help distinguish weather
contamination from other sources that would appear only in a single or small sub-set of
modules in the array. Two statistics are calculated from the 10-s RMS fluctuations of the
TP data streams averaged across the array.4 The 10-s timescale was chosen as it is close to
the average half-scan period and thus sensitive to atmospheric fluctuations.
The statistic R10 is defined as the maximum value of the aggregate 10 second rms over
95 , is defined to be 95th percentile value (i.e. the
the entire CES. A second statistic, R10
maximum value after excluding the highest 5%). Cut thresholds are set at 150 mK for R10
95 , significantly higher than the value expected for good weather (45mK
and at 80 mK for R10
95 exceeds the defined threshold, then the entire CES is
[131, 77]). If either of R10 or R10
95 is
excluded from the analysis. R10 targets short periods with jumps in the noise level. R10
more sensitive to long periods of bad weather.
Sun Sidelobe Cut: The sun can introduce contamination into the data if the beam sidelobes (�2.5), pass over the Sun while the telescope is scanning. Unlike ground pick-up,
which is constant during a CES and so filtered out of the data, sun contamination, varies
during the CES, as the sun drifts through the sidelobe region under sidereal motion. Sunsidelobe contamination cannot be filtered, so a specific data cut was developed to remove
contaminated CES. The position of the triple reflection and spill-over sidelobes are calculated for every CES. If the sun enters the area around the sidelobe position during the CES,
its is cut. The regions cut are defined in terms of ? and ? coordinates measured with respect
to the optical axis of the beam (see �3). For the triple reflection sidelobe, the region with
44? < ?s < 60? and 120? < ?s < 180? is cut. Two regions are cut for the second sidelobe:
60? < ?s < 65? and ?90? < ?s < 0? plus 44? < ?s < 60? and ?75? < ?s < ?15? . The
location of the spillover sidelobe is individually calculated and cut for each module[132].
4. Only modules connected to ADC-1 (Module 0-6) are used since the modules connected to the other
two ADC boards show anomalous TP noise. Demodulated timestreams are not effected.
127
TOD Glitch Cuts: CES-diodes are removed if they have sufficiently large glitches or
spikes in the TOD. The data are evaluated on three timescales: 20 ms (1 sample), 100 ms (5
samples), and 1 s (50 samples). For each of the three statistics, data is summed for the given
interval (1,5 or 50 samples) ? a running boxcar sum is used. If the absolute value of the
most discrepant interval of the summed data stream is > 6? from the mean, the CES-diodes
is cut.
TP-Demod Linearity Cut: We cut individual CES-diodes that show deviation from the
expected linear relationship between the demodulated and TP signals. This cut removes
data with residual ADC non-linearity. As described in �1, a correction is applied to the
TOD to compensate for the known nonlinearity in the ADC chips. For a small number of
CES-diodes, the correction does not completely remove the effect. These diodes also have
increased 1/f noise and are removed by the 1/f knee cut as well. Data with poor thermal
regulation of the electronics or cryostat or sudden shifts is the DC level are also removed by
this cut. The cut is applied at a loose level (only > 10? deviations are cut).
Filtered ?2 Cuts: Next, we reject CES-diodes with poor agreement between the filtered
data and the noise model ? indicating contamination in the data. Further, the noise model
is used to generate simulated timestreams for the Monte Carlo simulations. Including data
that do not fit the noise model will lead to systematic differences between the actual and
simulated data. The ?2 statistics are calculated after the data are filtered to pick up residual
contamination that survives the filtering. It is calculated between the noise model and the
filtered data for three frequency ranges: a narrow range (only 40 Fourier modes) about
the scan frequency, from twice the scan frequency to 1 Hz, and from 1 Hz to 4.6 Hz. Each
frequency range is sensitive to different features in the data.
Any CES-diode with a ?2 statistic greater than 5 in the 40 modes around the scan
frequency is cut from the data analysis. Excess power near the scan frequency usually
128
falls into two categories: a sharp peak caused by constant scan synchronous signals (e.g.
ground pick-up) or a broad bump caused by time-varying scan synchronous signals (e.g. bad
weather). Data with a ?2 > 3 for both the < 1Hz and > 1Hz regions are cut. Some of
the unfiltered diode spectra have spiking at higher frequencies (removed by the low-pass
filter), but problems between 1Hz and 4.6 Hz are rare as reflected by the cut fractions for
this criteria. Data with a high ?2 for frequencies below 1Hz indicates contamination that
survived the azimuthal binning and each azimuth scan linear filters.
1/f Knee Frequency Cuts: We cut CES-diodes that have higher than usual 1/f knee
frequencies as calculated by the noise model (see �4.3). This cut eliminates bad weather
periods (atmospheric fluctuations due to I ? Q/U leakage) as well as enclosure temperature
drifts. The median 1/f knee frequency for the array for the season is 5.5 mHz but it varies
from diode to diode. Cut uses separately defined threshold for each diode. By calculating
the mean and standard distribution of the 1/f knee frequencies for each diode over the whole
season of data after baseline cuts are applied and the worst outliers removed. For each diode,
the threshold is set at 5? above the mean of the distribution after the worst 0.15% of outliers
are excluded.
Azimuthal Slope Cut: Cutting data when there are large variations during the CES in
the azimuthal slopes of the double-demodulated time streams helps to eliminate bad weather
periods. The statistic is calculated by dividing the data into 2.5 minute segments and taking
the difference to the mean of the average slope over those 2.5 minutes.
Other possible selection criteria investigated for contamination but not used in the final data
selection set, include double demodulated statistics, map ?2 , TOD Gaussianity, pre-filtered
FFT ?2 to noise model, Housekeeping(temperature variation of electronics bias boards, Atmospheric characteristics (PWV,windspeed, humidity etc.). Some were accounted for in null
tests, others were redundant with existing selection criteria (did not uniquely cut any data),
129
Table 5.1: Total Hours Observed and Data-Selection Efficiencies
Patch
Total Hours A % B % Common %
CMB-1
905
81.7 84.3
76.7
CMB-2
703
67.3 70.0
61.2
CMB-3
837
56.0 61.4
51.4
CMB-4
223
70.6 74.2
65.9
All Patches
2668
69.4 72.9
64.2
Note. ? Selection efficiencies for each pipeline. ?Common? gives the efficiencies if both sets of cuts were
applied.
still others were rejected in favor of more direct statistics (pre-filtered FFT ?2 ? Post-Az
filtered ?2 ).
5.2.1
Cut Efficiency
Cut efficiencies, defined as the fractions of CES-diodes accepted for the analysis, are given for
both pipelines in Table 5.1. The percent of data retained after cuts are given and compared
the efficiencies in pipeline B which uses slightly different data selection criteria([79]). The
majority of data selected by one pipeline are also selected in the other indicating agreement
on what constitutes ?clean? vs. ?contaminated? data. While each pipeline applies its own
cuts uniformly to all four patches, the efficiencies among patches are non-uniform because
of differences in weather quality. Diurnal variation in the weather results in difference in
weather cut fractions; patch CMB-1, observed in the calm cool nights, has higher efficiency
than CMB-3 which was most often observed in the afternoons when higher temperatures
and high winds were prevalent.
The number of CES-diodes cut by each data selection criterion are broken down by patch
and given in Table 5.2.1. Many cuts remove overlapping data sets (e.g. a CES with bad
weather may be cut by the weather, 1/f knee frequency, and ?2 cuts). Cut percentages are
provided for the total data cut if only the given criterion is applied as well as the ?uniquely?
130
cut case where no other cut removes a given CES-diode. Patch CMB-1 has the highest
efficiency while patch CMB-3 has the worst.
5.3
Map Making
After data selection criteria are applied and the data are filtered, the TOD for all diodes
are combined to produce polarization (Q and U ) maps for each of the QUIET patches. The
maps use a HEALPix (Hierarchical, Equal Area, and isoLatitude Pixelization) Nside = 256
pixelization which corresponds to pixel size of ? 0.05 square degrees [133].
Q and U maps are made by summing samples of the demodulated data, di into pixels
determined by the telescope pointing information. Samples are weighted by their inverse
variance which is calculated from the white-noise amplitudes ?i of the data determined
using the noise model (see �4.3).
Following [77], the inverse noise weighted Stokes parameters, Q? and U? for a pixel are
given by
X 1
di cos (2?i )
?i2
i
X 1
U? =
d sin (2?i )
2 i
?
i
i
Q? =
(5.1)
(5.2)
where i are the samples that hit the pixel, ?i , are the position angles of the detector diode
polarization axes (�5) for the sample. If the samples are independent, the inverse variances
131
132
of CES-diodes that are cut by this criteria but no others.
38922
7860 (20.19%)
7550 (19.40%)
8294 (21.31%)
8407 (21.60%)
3356 (8.62%)
9459 (24.30%)
11325 (29.10%)
7655 (19.6%)
5805 (14.91%)
4559 (11.71%)
4680 (12.02%)
5588 (14.36%)
5801 (14.90%)
3355 (8.62%)
10425 (26.78%)
17125 (44.00%)
56.00%
CMB-3
a
b Number
38006
4154 (10.93%)
3720 (9.79%)
4216 (11.09%)
4216 (11.09%)
877 (2.31%)
4913 (12.93%)
6535 (17.19%)
3958 (10.41%)
4143 (10.90%)
2076 (5.46%)
2170 (5.71%)
2887 (7.60%)
2979 (7.84%)
1746 (4.59%)
4644 (12.22%)
12432 (32.71%)
67.29%
Total Cut
of CES-diodes, out of the entire baseline data set, cut by each criteria.
46915
1550 (3.30%)
1054 (2.25%)
1550 (3.30%)
2238 (4.77%)
400 (0.85%)
2518 (5.37%)
4057 (8.65%)
1614 (3.44%)
1566 (3.34%)
1230 (2.62%)
1258 (2.68%)
1170 (2.49%)
1526 (3.25%)
1342 (2.86%)
2266 (4.83%)
8581 (18.29%)
81.71%
Baseline data set
Weather cut R10
95
Weather cut R10
Weather cut total
Filtered ?2 < 1Hz
Filtered ?2 > 1Hz
Filtered ?2 near scan freq.
Filtered ?2 total
Knee frequency
Sun cut
Glitch, 1 sample (20ms)
Glitch, 5 samples (100ms)
Glitch, 500 samples (1sec)
Glitch cut total
TP-Demod Linearity
Slope Statistic
All cuts
Passing cuts
CMB-2
a Number
CMB-1
Criteria
14718
1388 (9.43%)
1574 (10.69%)
1760 (11.96%)
1533 (10.42%)
333 (2.26%)
2252 (15.30%)
2623 (17.82%)
1469 (9.98%)
669 (4.55%)
429 (2.91%)
447 (3.04%)
671 (4.56%)
706 (4.80%)
638 (4.33%)
2806 (19.07%)
4321 (29.36%)
70.64%
CMB-4
?
256 (0.55%)
0 (0%)
399 (0.85%)
777 (1.65%)
131 (0.28%)
782 (1.67%)
1831 (3.90%)
343 (0.73%)
1358 (2.89%)
7 (0.01%)
10 (0.02%)
23 (0.05%)
715 (1.52%)
665 (1.41%)
361 (0.77%)
?
?
CMB-1
?
164 (0.43%)
0 (0%)
450 (1.18%)
566 (1.49%)
61 (0.16%)
950 (2.50%)
1768 (4.65%)
389 (1.02%)
3469 (9.13%)
1 (0.002%)
1 (0.002%)
20 (0.05%)
104 (0.27%)
379 (1.00%)
253 (0.67%)
?
?
?
235 (0.60%)
105 (0.27%)
695 (1.79%)
495 (1.27%)
98 (0.25%)
572 (1.47%)
1290 (3.31%)
370 (0.95%)
2436 (6.26%)
5 (0.01%)
3 (0.008%)
19 (0.05%)
93 (0.24%)
285 (0.73%)
819 (2.10%)
?
?
Uniquely Cut b
CMB-2
CMB-3
Table 5.2. Number of CES-diodes rejected by various cuts
?
66 (0.45%)
75 (0.51%)
249 (1.69%)
222 (1.51%)
27 (0.18%)
154 (1.05%)
424 (2.88%)
115 (0.78%)
286 (1.94%)
0 (0%)
0 (0%)
6 (0.04%)
14 (0.10%)
104 (0.71%)
443 (3.01%)
?
?
CMB-4
of the pixels are defined as [77]:
X 1
cos2 (2?i )
2
?i
i
X 1
(UU)?1 =
sin2 (2?i )
2
?i
i
X 1
(QU)?1 =
cos (2?i ) sin (2?i )
2
?
i
i
(QQ)?1 =
(5.3)
(5.4)
(5.5)
Diode noise correlations and filtering mean that the samples are, in fact, correlated,
biasing in the unweighted maps. Fortunately, these biases rre eliminated during power
spectrum estimation.
Figure 5.7 shows full season inverse noise weighted maps of Q? and U? for all four patches.
Edge pixels are observed less frequently and thus have higher variances so they are de? may seem an arbitrary choice, it is important to note,
weighted. While showing maps of Q/U
however, that where we have good pixel coverage (i.e the central region of the maps) there
are many values of ?i so the inverse noise weighting matrix is roughly diagonal (Q?U??1 ? 0)
and can be approximated as a scalar inverse weighting. Thus, the central region of the maps
effectively shows scalar inverse weighted Q and U maps.
Masking Compact Sources: Although QUIET patches were chosen to minimize contamination from foregrounds, several compact radio sources exist in our patches. Two polarized
sources, Centaurus A (CenA) and Pictor A (PicA), are masked from the maps. Cen A, a
galaxy with ? 330礙 polarized emission5 [115], is located on the outer edge6 of patch CMB-1
(see Figure 5.7). Pic A, a jet galaxy with ? 330礙 polarized emission is located closer to
the center7 of patch CMB-2. Both are removed using circular top-hat masks with radii of
5. Signal size detected by a Q-Band module
6. R.A. of 13h25m27.62s and Dec. of 43d01m8.8s
7. R.A. of 5h19m49.7s and Dec. of 45d46m44.5s
133
2? and 1? , for Cen A and Pic A respectively by given pixels in those regions weightings of
zero). Cen A extends over several degrees and thus a larger mask is applied. As it is very
near the edge of the patch where coverage is low, the region is already de-weighted and very
little sensitivity is lost.
Sub-maps: In addition to full season maps, sub-maps were made based on divisions of
array orientation in azimuth and deck angle. These sub-maps are used for cross-correlation
during power spectrum estimation (see �4). The azimuth was divided into ten bins ranging
from 108? to 252? and the deck angle ranges in steps of 45? , ranging from 30? to 330? creating
60 possible sub-maps for each patch. Azimuth is defined in terms of the central azimuth
value for the central horn in the array for the CES. The azimuth and deck ranges were
determined by the locations of our patches during the observing season. Tables 5.3 give the
azimuth and deck ranges of the bins. The same binning is used for all patches, which means
that not all divisions are populated for patches CMB-3 and CMB-4.
Table 5.3: Azimuth and Deck Bins
Deck Bin
1
2
3
4
5
8
Azimuth Bin Azimuth Range [? ]
0
108 - 130
1
131 - 139
2
140 - 149
3
150 - 166
4
167 - 191
192 - 209
5
6
210 - 223
7
224 - 231
8
232 - 236
9
237 - 252
134
Deck Angle [? ]
30
75
120
165
210
330
5.4
Power-Spectra Estimation
QUIET uses the MASTER (Monte Carlo Apodized Spherical Transform Estimator) method
of calculating the power spectra [123, 134]. It it is based on a pseudo-C` technique that takes
account of effects induced by the data processing, including the effect of the instrumental
beam, experimental noise, and filtering of the TOD stream, using Monte Carlo (MC) simulations. Following [123, 77], the pseudo power spectrum C?` can be calculated by the direct
spherical harmonics transform of a partial sky map,
C?` =
`
X
1
|a`m
? |2 .
2` + 1
(5.6)
m=?`
where a`m
? are the spherical harmonic coefficients calculated to account for the finite size of
the observed patch on the sky [135].8 They are given by
a?`m = ?
X
? (i)
Ti Wi Y`m
(5.7)
i
where ? is the solid angle of a pixel, Ti is the measured temperature for each pixel, and Wi
is a weighting function ? inverse noise variance is chosen for QUIET. Here we have used the
simpler case of temperature which we will extend to the case of polarization below.
The pseudo-C` spectrum, designated by C?` , is related to the true spectrum C` by:
hC?` i =
X
M``0 F`0 B`20 hC`0 i + hN?` i.
(5.8)
`0
Here B` is the beam window function, describing the combined smoothing effects of the beam
and finite pixel size (� 4.2), and M``0 is a mode-mode?coupling kernel describing the effect of
observing only a small fraction of the sky with non-uniform coverage. It is calculable from the
pixel weights, which are chosen to maximize the signal-to-noise ratio [136]. F` is the transfer
8. spherical harmonic are orthogonal over the full sky, but not necessarily orthogonal on a small patch.
135
function applied due to filtering of the data. F` is found by applying the filters used on the
data to signal-only simulations which are processed through the pipeline to determine their
effects of the power spectra. The term corresponding to noise bias, hN?` i, is also determined
using noise only simulations propagated through the pipeline. More importantly, this terms
is canceled out by employing a cross-correlation technique described below.
By measuring C?` from the data (Equation 5.6), an estimate of the true power spectrum
C` , can be obtained by solving Equation 5.8. We bin the data into 9 ` bins and recover
the true power spectrum C` in nine band powers. The binned estimate, Fb , is found by
processing noiseless CMB simulations through the pipeline and used to obtain Cb .
For the polarization power spectra, equation (5.8) is generalized for the case where C?`
contains both C?`EE and C?`BB as:
?
?
?
hC?`EE i
hC?`BB i
?
?
? X?
?
?=
`0
+
M``
0
?
M``
0
?
M``
0
+
M``
0
??
??
??
F`0 B`20 hC`EE
0 i
F`0 B`20 hC`BB
0 i
?
?
? ?
?+?
hN`EE i
hN`BB i
?
?
?
(5.9)
For polarization, the relation between pseudo-power spectra and true power spectra includes not only coupling between different multipoles, but also coupling between E-modes
and B-modes. The partial sky coverage of QUIET also generates a small amount of E/B
mixing [137], which contributes an additional variance to the BB power spectrum. We incorporate it as part of the statistical error. This mixing can be corrected, but is not treated
in the current implementation of the pipeline because the effect is negligible compared to
instrumental noise of QUIET.9
The errors estimated for power spectra are frequentist two-sided 68% confidence intervals.
A likelihood function used to compute the confidence intervals is modeled following [139] and
calibrated using the MC simulation ensemble of more than 2000 realizations with and without
CMB signal.
9. Code to calculate a B-mode estimator without E/B mixing was developed by Kendrick Smith [138]
and can be implemented if needed in the future.
136
Cross-Correlation: Cross-correlation is used to eliminate noise bias. When dividing the
data into multiple maps, each map will contain the same CMB signal but a different contribution from noise. While the CMB signal is constant, the noise should be uncorrelated from
j
map to map. Cross-correlating theses maps will eliminate the noise component: hN`i N` i = 0.
The cumulative, all season map for each patch can be thought of as a combination of these
P
sub-maps. MT OT = i Mi . Measuring the power spectrum of the cumulative map is equivalent to summing up all possible auto and cross-correlations of the daily maps. Measuring
the power spectrum of each sub-map, measures the auto-correlation for that sub-map. Using
the identity (A + B)2 = A2 + B 2 + 2AB, we can see that calculating the power in the total
map and subtracting power in each individual map removes the auto-correlations, leaving
only the cross-correlated terms. Since the noise is independent, it only contributes to the
auto-correlation, so by subtracting out the auto-correlations, the noise bias is eliminated.
We divide the data into 60 sub-maps based on array pointing (Azimuth and Deck bins,
see Table 5.3) for each of the QUIET patches. Dropping the auto correlations creates only
a small increase in the statistical errors (? 3%) on the power spectra but it ensures that
errors in the noise model will not contribute bias.10
5.5
Temperature Data Analysis
As described in � 2.4, we dedicate one pair of modules to differential-temperature measurements. While these modules are useful for calibration purposes, when combined with our
polarization data they also enable us to make self-contained measurements of the TE and
TB power spectra. The analysis of the temperature data is much the same as that of the
polarization data. In this section we describe the differences between the two analyses, including data selection efficiencies, map-making and binning of the data for cross-correlation
10. This is an updated binning to the day-by-day binning described in [77]. In that configuration a small
bias was discovered which led to a change of binning. See 6.2.1 for further details.
137
when computing the TT power spectrum and the TE and TB cross power spectra.
5.5.1
Temperature Data Selection Efficiency & Filtering
The temperature-sensitive modules, are far more susceptible to atmospheric contamination
than the polarization modules. This results in the drastically reduced data selection efficiencies necessary to ensure that the temperature data passed the analysis validation tests
(�4).
The while the criteria are similar to those used for the polarization analysis, there are
some slight differences. The baseline criteria don?t include those that are specific to the
polarization analysis. Only Q diodes are used as they contain the sensitivity to differential temperature measurements (�4.2). Further, in the temperature analysis the the slope
statistic (2.5 minute average, azimuthal excursion) used the normalized version of the criteria instead of the raw criteria used in the polarization analysis. While both versions of
this statistic cut heavily in to the distribution (see Figure 5.8), it should be noted that this
statistic evaluates the data in the low frequency region (below the scan frequency) where we
we are not sensitive to the CMB signal. This difference in the cuts was motivated by expediency; near the end of the analysis several variations of the slopes statistic were evaluated
simultaneously and one (the raw, unnormalized statistic) was chosen for the polarization
that had only a marginal (but not statistically significant) improvement over the other in
the analysis validation tests. The normalized statistic was left in place for the temperature
analysis, as it had just had passed validation tests in this configuration. The knee frequency
cut used in the polarization data selection is discarded for the temperature analysis. Due to
the increased contamination at low frequencies and near the scan frequency, the fit of the
temperature data to the noise model frequently failed. The knee frequencies of the selected
data set (after other cuts are applied) is checked to confirm that no large outliers in knee
frequency remain in the data set.
138
The TOD processing and filtering proceed the same as for the polarization analysis with
one exception ? the azimuthal filter. For temperature data, a second-order polynomial is fit
and removed from each telescope half scan instead of a linear function. This suppresses the
increased contamination from atmospheric fluctuations in the temperature data.
The final cut fractions for each data selection statistic and patch are given in Table 5.5.1;
the distributions of the data for each selection statistic are shown in Figure 5.8. Although
several iterations of data selection were attempted with loosened cut criteria, these failed
the analysis validation tests. The final analysis, only 12.4%, 6.9%, 6.8%, 18.7% of the data
were retained for patches CMB-1, CMB-2, CMB-3, and CMB-4 respectively. Although patch
CMB-4, has the highest selection efficiency, the total observation time for that patch is the
lowest so the smallest total amount of data is retained (only 178 CES-diodes). Patch CMB4 was excluded from the final analysis because the remaining data did not have sufficient
crosslinking (see �5.2). Further tailoring of the cuts and filtering for these modules would
improve efficiencies, but as will be seen in �6, this amount of data was sufficient for the
purposes of TT,TE and TB analysis.
5.5.2
Temperature data Map-making & Power-Spectra Estimation
For the temperature data, we employ an iterative map maker based on the algorithm described by Wright et al. [140]. As the temperature data is differential, obtaining an absolute
value for any pixel in the map is not straightforward. The modules measure the difference in
temperature between the pixels observed by the two horns in the differential assembly. The
iterative map-making method is described in Appendix . The process involves starting
with an initial guess for the temperature of a pixel in the map and then iterating through
realizations of the map such that for each pixel the new sky map temperature is the average
of all differential observations of that pixel (accounting for the sign of the observing beam)
139
140
of CES-diodes that are cut by this criteria but no others.
2516
512 (20.35%)
492 (19.55%)
540 (21.46%)
2084 (82.83%)
1588 (63.12%)
854 (33.94%)
2146 (85.29%)
220 (8.74%)
1192 (47.38%)
1230 (48.89%)
1297 (51.55%)
1427 (56.72%)
1475 (58.62%)
2214 (88.0%)
2344(93.16%)
6.83%
b Number
2452
268 (10.93%)
240 (9.79%)
272 (11.09%)
2016 (82.22%)
1220 (49.76%)
848 (34.58%)
2071 (84.46%)
368 (15.01%)
661 (26.96%)
709 (28.92%)
941 (38.38%)
992 (40.46%)
1105 (45.07%)
2186 (89.15%)
2281(93.03%)
6.97%
of CES-diodes, out of the entire baseline data set, cut by each criteria.
3028
100 (3.3%)
68 (2.25%)
100 (3.3%)
2129 (70.31%)
1029 (33.98%)
1185 (39.13%)
2261 (74.67%)
136 (4.49%)
539 (17.8%)
559 (18.46%)
716 (23.65%)
770 (25.43%)
686 (22.66%)
2494 (82.36%)
2652(87.58%)
12.42%
Baseline data set
Weather cut R10
95
Weather cut R10
Weather cut total
Filtered ?2 < 1Hz
Filtered ?2 > 1Hz
Filtered ?2 near scan frequency
Filtered ?2 total
Sun cut
Glitch, 1 sample (20ms)
Glitch, 5 samples (100ms)
Glitch, 500 samples (1sec)
Glitch cut total
ADC Nonlinearity
Slope Statistic
All cuts
Percentage passing cuts
Total Cut a
CMB-2
CMB-3
a Number
CMB-1
Criteria
952
92 (9.66%)
104 (10.92%)
116 (12.18%)
649 (68.17%)
468 (49.16%)
292 (30.67%)
683 (71.74%)
12 (1.26%)
271 (28.47%)
285 (29.94%)
311 (32.67%)
355 (37.29%)
462.0 (48.53%)
706 (74.16%)
774(81.30%)
18.70%
CMB-4
?
0 (0.0%)
0 (0.0%)
0 (0.0%)
74 (2.44%)
5 (0.17%)
10 (0.33%)
102 (3.37%)
2 (0.07%)
0 (0.0%)
0 (0.0%)
2 (0.07%)
9 (0.3%)
8 (0.26%)
318 (10.5%)
?
?
CMB-1
?
0 (0.0%)
0 (0.0%)
0 (0.0%)
55 (2.24%)
1 (0.04%)
1 (0.04%)
61 (2.49%)
10 (0.41%)
0 (0.0%)
0 (0.0%)
0 (0.0%)
1 (0.04%)
10 (0.41%)
139 (5.67%)
?
?
?
2 (0.08%)
0 (0.0%)
2 (0.08%)
66 (2.62%)
4 (0.16%)
9 (0.36%)
90 (3.58%)
6 (0.24%)
0 (0.0%)
0 (0.0%)
2 (0.08%)
4 (0.16%)
6 (0.24%)
134 (5.33%)
?
?
Uniquely Cut b
CMB-2
CMB-3
Table 5.4. Number of CES-diodes rejected by various cuts for Temperature Analysis
?
0 (0.0%)
0 (0.0%)
0 (0.0%)
35 (3.68%)
6 (0.63%)
2 (0.21%)
44 (4.62%)
0 (0.0%)
0 (0.0%)
0 (0.0%)
0 (0.0%)
0 (0.0%)
8.0 (0.84%)
75 (7.88%)
?
?
CMB-4
corrected by an estimate of the signal in the paired beam, based on the previous sky map
iteration [74]. The process iterates until user-specified convergence criteria are met. The
methods used to account for diode noise correlations and variable noise among the multiple
CES in the TT iterative map maker are also addressed in Appendix F.
Cross Linking and CES Pairing Iterative map making for differential receivers requires
that each pixel is measured at multiple array pointings or well cross linked. Parallel stripes
are generated through a combination of low frequency fluctuations (e.g. 1/f noise) in the
data and poor cross-linking between pixels. Observations of the same patch at different
arrays orientations (scanning across the patch in different directions, or with several array
orientations) links measurement of multiple pixels, suppressing noise contamination. An
example of noise suppression in a map from improved cross linking is shown in Figure 5.9
Natural sky rotation during a single CES is not sufficient to produce a stripe-free map.
We need to combine the data from multiple CES with different array orientations to make
temperature maps with sufficiently low noise. In order to improve cross linking we divide
the temperature data into only four sub-maps by azimuth and deck angle, rather than the
60 divisions used for polarization analysis. The allocation of CES into four sub-maps are
constrained by three criteria. First, all CES in an Az-Deck bin used for the polarization analysis, are included in a single temperature bin (MCES 11 ) for ease of temperature-polarization
cross correlation. Second, each MCES must contain CES with at least three distinct array
orientations (although more are preferred). Array orientations are divided into bins that
are 7.2? in width.12 Third, the number of possible null tests must be maximized. In a null
test (�1) the data are divided in half bases on some threshold. In order for a null test
to be able to be performed, each half-MCES must meet criteria #2 ? at least three array
11. Each temperature bin is named an MegaCES or MCES because the data from all CES included are
stitched into one timestream that is send to the iterative map-maker
12. 1.75? � 0.2 is the horn separation in the differential temperature assembly.
141
orientations ? once the MCES is divided based on the null test threshold. As is described in
�5, not all of the 42 null tests performed on the polarization analysis could be implemented
for the temperature analysis given this constraint, but the MCES were defined to maximize
the possible null tests for each patch. Figure 5.10 shows the distribution of CES-diode array
orientations in each of the four MCES in each patch. As can be seen in the figure, patch
CMB-4 did not have enough data at distinct array orientations in different az-dk bins to
populate four MCES while allowing any null tests to be performed. Thus, it was discarded
from the analysis.
To calculate TE and TB power spectra, polarization maps are made for these four divisions, plus one additional map that contains all polarization data with pointings not represented in the temperature data.
142
Figure 5.6: Distributions for data quality statistics used for polarization data analysis. Selection criteria values are calculated for all CES diodes in patch CMB-1 after baseline cuts
are applied. Distributions for patches CMB-2,3,&4 are given in Appendix D. Cut thresholds
are shown with black vertical lines. Cut percentages for each statistics are given assuming
that it is the only cut applied. Sun cut distribution is not shown, this is a binary cut (either
the sun is or is not in the sidelobe.)
143
Figure 5.7: Top to Bottom: Maps of patches CMB-1, CMB-2, CMB-3, and CMB-4 respectively. Left and Middle: Inverse noise weighted maps for Q? (left) and U? (middle). Right:
Coverage (inverse noise weighting) map. Red indicates areas that are well observed (low
variance) while blue areas near the edges are. Centaurus A can be seen near the edge of the
patch CMB-1 (top row); the white circle indicates the 2 degree radius region that is masked
for power spectrum estimation. Pictor A can be seen in the Patch CMB-4 map; the white
circle indicates the 1 degree radius masked region. No point sources are masked in patches
CMB-3 or CMB-4.
144
Figure 5.8: Distributions for data quality statistics used in the temperature analysis. Selection criteria values are calculated for all CES diodes in patch CMB-1 after baseline cuts are
applied. Distributions for patches CMB-2,3,&4 are given in Appendix D. Cut thresholds
are shown with black vertical lines. Cut percentages for each statistics are given assuming
that it is the only cut applied.
145
Figure 5.9: Left Panel: map of a single CES at deck of ?15o Middle Panel: map of a single
CES at deck of +30o . Right Panel: MCES with 2 CES in left and middle panels stitched
together. Note the reduction in striping where the CES overlap. Upper left inset shows
coverage overlap between the two CES.
Figure 5.10: Distribution of CES-diode array orientations in each MCES. Patch CMB-4 fails
cross-linking criteria with > 2 MCES and was excluded from analysis.
146
CHAPTER 6
ANALYSIS VALIDATION
The QUIET data analysis follows a policy of not looking at the power spectra until the
analysis passes a set of pre-defined validation tests. Given the strong expectations for the size
and shapes of the polarization power spectra (�6), and the ease with which contamination
in the data set can generate a spurious signal, great care must be taken to mitigate or remove
experimenter bias. The validation tests are used to probe the data for contamination and
consistency without revealing the final result. We conduct this validation in a blind-analysis
framework, making the analysis choices without knowing the result, to reduce experimenter
bias. The data-selection criteria, filtering methods, and the division of data into maps for
cross correlation are all evaluated using the validation tests and refined until the tests are
passed. Only after the analysis is finalized and the following validation tests pass do we
examine the power spectra.
The validation tests consist of three checks for possible systematic effects: a suite of
null tests, comparisons across multiple analysis configurations, and consistency checks on
power spectra between different CMB patches. While these test will identify most sources
of contamination, there are a few systematic effects, such as a uniform shift in the detector responsivity calibration (�4), that cannot be detected by these techniques; they are
addressed in �5.
This section discusses the analysis validation tests used in the Pipeline A analysis.
Pipeline B performed a smaller set of null tests during their analysis. The increased computational requirements of the maximum-likelihood framework used in Pipeline B limited
the number of tests that could be performed and required those tests to be run using lowerresolution maps than for the non-null analysis. For a description of the Pipeline B analysis
null tests see [79].
Null tests, the calculation of null power spectra are discussed in �1. A description of the
147
null suite and methods for evaluating the null suite results are described in �2. The blind
consistency checks performed on the non-null power spectra are discussed in �3. Results of
the final iteration of the null suite are given in �4 and results of the temperature analysis
validation tests are presented in �5
6.1
Null Tests
In normal observations we rely on the variation of noise in the data to allow us to average
out the noise; otherwise, we wouldn?t be able to extract the much smaller CMB signal
from the dominant noise of our detector and the atmosphere. We reverse this feature to
identify sources of contamination. Null tests make use of the fact that while the CMB signal
is constant across observations, sources of contamination will vary. If the same patch is
scanned twice, once when the weather is bad, and again when the weather is good, then
underlying CMB signal will remain the same, but the contamination (in this case the bad
weather) will vary. If we then subtract the two scans, the signal will be differenced away and
only the contamination will remain. In a null, test the data are split into two subsets based
on a selected criterion. Maps, m1 and m2 , are made from each data subset. The power
spectra of the difference map, mdiff ? (m1 ? m2 )/2, are analyzed for consistency with the
hypothesis of zero signal.
The criteria upon which the data are divided are chosen to test for a variety of systematic
effects. If the data selection and filtering (�2.1) have not effectively removed some contamination from the data, the null power spectrum will show the contamination signal. Certain
types of contamination in the data, such as excess noise, are accounted for in simulations
(e.g. by the noise model, �1.2). The point of a null test is to look for possible sources of
contamination that are not included in the model.
Figure 6.1 shows an example of the two maps created for a null test based on one of
the weather statistics (TP 10s RMS 100%). Weather can be thought of as contributing
148
Figure 6.1: Sample polarization maps for null tests. The data has been divided in half based
on the value of the weather-based data selection criteria: TP 10s RMS 100%. The bright
spot in the upper left corner of the map is Centaurus-A. It is masked out of each map when
the power spectrum is calculated.
two forms of contamination to the data: stationary noise, that is accounted for in the noise
model and non-stationary noise that is not included in the noise model. It is the residual
non-stationary component that the data selection may have failed to cut that the null test is
designed to reveal. If the data cuts were successful, the truly bad weather has already been
cut from the data set and the null maps are actually of the better and worse halves of the
remaining data. Any residual contamination due to bad weather should show up in the bad
weather map but not in the good weather map. A sample null power spectrum is shown in
Figure 6.2.
Non-stationary noise (e.g. weather) is not the only type of effect that could induce a nonnull signal. Incorrectly calibrating the gain of a subset of modules would leave a residual
CMB signal in the null map. Also, miscalculation of the telescope pointing could distort the
signal, and instrumental I ? Q/U leakage or ground pick-up could induce spurious signal.
A full list of the null tests performed can be found in �2.
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Figure 6.2: EE null power spectrum for the patch CMB-1 null test between good and bad
weather (TP 10s RMS 100%). The left panel shows the low-` region in detail. The right
panel shows the full null spectrum. Although auto-correlations are dropped in the final
analysis, they are shown during the null test evaluation as a diagnostic; miss-estimation of
the white noise correlation among diodes would show up in the auto-correlation points.
6.1.1
Null Tests in Pseudo-C`
Ideally, we would like to calculate the null power spectrum directly from the null map,
mdiff ? (m1 ? m2 )/2. However, there are some difficulties in doing this directly in a pseudoC` framework. Following Smith, 2009 [141], we describe a few of these difficulties and a
general solution below.
In pseudo-C` pipelines, the sky map, m, is not an unbiased estimator of the underlying
CMB realization, s. Instead, s has been processed by some filter F ,
hmi = F s + N
(6.1)
where N is the noise in the map. As discussed in � we use Monte Carlo (MC) simulations
to compute a transfer function, F , which represents the average effect of the filter on the
power spectrum.
A null test between CES which scan the sky in different directions will generate two
150
half-maps where the signal has been filtered differently,1 and thus, the signal will not cancel
perfectly if we naively subtract the maps. In addition to computing the filter transfer functions of each map (m1 , m2 ) separately, F`11 and F`22 , we need to determine a cross transfer
function F`12 which is computed from cross pseudo power spectrum of the maps m1 ,m2 (See
5.1.2).
We would like to weight the null maps the same as we would the non-null maps. When
we divide the data into two halves, however, the pixel weighting functions for each half map
will have to be different since the sky coverage will not be the same in each half map as in
the total map (e.g. if one pixel is only measured in one map but not the other). We define
the pixel weighting function for null maps as:
1
W (x) = 2
?1 (x) + ?22 (x)
(6.2)
where ?1,2 is the variance of the null half-map m1,2 and x specifies the map pixel.
Given these complications, in a pseudo-C` pipeline, we never actually calculate the power
spectrum of a null map. Instead, we can make use of the fact that (A?B)2 = A2 ?B 2 ?2AB
and calculate the power in the auto and cross correlations of the two half maps (while
calculating the correct transfer functions and weightings for each) instead of the calculating
the power in the difference map. We can we calculate the pseudo power spectrum estimators
for each half-map C?` (m1 , m1 ), C?` (m2 , m2 ) and the cross pseudo power spectrum estimator
C?` (m1 , m2 ). Then, we can construct the null power estimator directly:
C?`null (m1 ) =
C?` (m1 ,m1 )
F`11
+ ?2
C?` (m1 ,m2 )
F`12
+
C?` (m2 ,m2 )
.
F`22
(6.3)
1. The high-pass filter (�1) will filter modes perpendicular to the scan direction as they are measured
slowly through drift of the patch, while modes parallel to the scan direction are measured at higher frequencies.
151
6.2
The Null Suite
The null suite for the polarization analysis consists of 42 tests. Each test targets a possible
source of signal contamination or miscalibration. Tables 6.1 and G.2 enumerate all tests in
the null suite categorized by the type of systematic they probe. Nine tests divide the data
by detector diode or module based on susceptibility to instrumental effects. Instrumental
polarization (I ? Q/U leakage) varies among modules and is systematically larger in Q
diodes (�6). Problems with the biasing electronics or operation of specific module would
also show up in these divisions. Eight tests target residual contamination in the TOD such
as weather. These tests are based on the data quality statistics described in �2. Ten tests
divide the data by environmental conditions such as ambient temperature or humidity. These
tests mainly check for variations in conditions that could cause fluctuations in the detector
responsivity that may not have been accounted for by the responsivity model (�4). Ten
tests target effects that depend on the telescope pointing such as data taken at high or low
elevation. They would reveal problems with the pointing model that introduce errors when
reconstructing the signal on the sky. Five tests divide data based on the proximity of the
main or sidelobe beams to known sources such as the Sun, Moon, Galaxy, and ground pickup. Only 41 null tests are performed for patch CMB-4; one test, patch rising vs. setting, is
dropped because there are no data in one of the subsets.
Null Test Correlations: These are highly independent tests; the data divisions for different null tests are correlated at only 8.8% on average. Independence of the tests is a design
criteria used in the development of the null suite. A large number of highly correlated tests
would dilute the power of the null suite. If we flooded the suite with slightly different versions of a single test that was known to pass, we would effectively de-weight outliers in other
tests. Like the data selection criteria, the tests that make up the null suite went through
several iterations. Figure 6.3 shows the correlation between null tests in an early iteration
152
Table 6.1: The 27 null tests in the polarization null suite based on the instrumental and
environmental contaminations.
Category
Null test
Instrumental
Effects
TOD
Contamination
Environmental
Conditions
Modules on MAB A vs B + C
Modules on MAB B vs A + C
Modules on MAB C vs A + B
The central seven modules vs. the peripheral modules
Modules with high vs. low instrumental polarization
Modules with high vs. low average 1/f knee frequencies
Modules with high vs. low bandpass center frequencies
Q vs U diodes
Diodes with/without abrupt TP level shifts
CES-diodes with more/less excess noise power near the scan frequency
CES-diodes with more/less excess noise power at high freqs. (2?15 Hz)
CES by average responsivity (high vs. low)
CES-diodes by responsivity of each diode compared to its average
CES-diodes with high vs. low non-linearity of double-demod. vs. TP data
Weather quality based on 10-s TP RMS 100% statistic
Weather quality based on 10-s TP RMS 95% statistic
CES-diodes with high vs. low white noise amplitudes
CES with high vs. low ambient temperatures
CES with high vs. low ambient humidity
CES with large vs. small humidity changes
CES with high vs. low bias electronics temperatures
CES with large vs. small bias electronics temperature change
CES with fast vs. slow electronics temperature changes
CES with high vs. low cryostat temperature
CES with large vs. small cryostat temperature changes
The first half of the season vs. the second half of the season
Scan period is an integral multiple of cryostat cold head pumping period
of the null suite. Several null tests in this version of the null suite were highly correlated
to each other as well as others. The most obvious examples are the four null tests that
divided the season into two halves based on different events (AIB cable change, AIB heater
installed, new generator installed, and deck encoder fix). Though the events happened at
different times, all four null tests put October and November CES in the before category
and April and May CES in the after category. The suns annual motion means that a null
test based on the proximity of the sun to patch CMB-1 also would be degenerate with the
153
Table 6.2: The 15 null tests in the 42 tests in the polarization null suite that are based on
array orientation.
Category
Null test
Pointing
Effects
Source
Positions
a
CES at high vs. low elevation
CES with the patch rising vs. setting
Deck angle 30? vs. others
Deck angle divisions offset by 45?
Deck angle divisions offset by 90?
Array orientation offset by 45?
Array orientation offset by 90?
Array orientation offset by 180?
Data from left vs. right-moving telescope scan motion
Accelerating vs. decelerating telescope scan motion
Sun proximity to the main beam
Moon proximity to the main beam
Far sidelobe elevation high vs. low a
Far sidelobe 1 proximity to the Galaxy
Far sidelobe 2 proximity to the Galaxy
Note that because of the orientation of the two far sidelobes a test for one?s sidelobe elevation is degenerate
with a test for the other?s sidelobe elevation
before/after null tests. As a result these tests were removed and replaced with a single test:
first vs. second half of the season. Although steps are taken to maximize the independence
of the null tests, some small amount of correlation always will remain. It is accounted for
using Monte Carlo simulations (�4).
6.2.1
Evaluation of the Null Suite
The Null Suite consists 3,006 null-spectrum points. In each of the four CMB patches, for
each of the 42 (41) null tests, the power is calculated in nine `-bins, for both EE and BB null
power spectra. Outliers are expected in a data set of this size so the results of the null suite
must be evaluated statistically; all points cannot be expected to be within 1? of zero power.
A ?-like statistic is defined to evaluate the null suite results. For the power in each bin, b,
154
Figure 6.3: Map of correlations between null tests analyzed using an early iteration of the
the null suite (NS2). Two null tests that select identical data in each half of each test would
have a correlation of +1. If the data selected in each null test were identical but the halves
were reversed (1st vs. 2nd half of the season ? 2nd vs. 1st half of the season) correlation
would be -1. Note that the tests highlighted in the red box are especially highly correlated
and were removed from the final null suite. Figure adapted from [142].
?null ?
Cbnull
?b
(6.4)
where Cbnull is the null power and ?b is the standard deviation of Cbnull given by MC simulations. We evaluate both ?null and its square; ?null is sensitive to systematic biases in the
null spectra while ?2null is more responsive to outliers. We calculate EB null spectra as well
but they are assigned lesser significance since sources of spurious EB power will also result
in the failure of EE and BB null tests.
To evaluate how well the data ?pass? the null tests, we must understand the expected
155
distribution of the ?2null statistic. There are two small factors that should cause the ?2null
statistic to diverge from a ?2 distribution. The first is the small correlation among the null
tests. Consider the case of two highly correlated tests. If the null power spectrum for one
of the tests registered power at the one sigma level, then this same power would likely show
up in the other test as well (they contain nearly identical data), contributing two sigma to
the sum of ?2null , overweighting the effect. Although the level of correlation among the null
tests is low (8.8%), there is still a small effect.
The second factor is the slight non-Gaussianity of the ?null distribution. Non-Gaussianity
is caused by the small number of modes at low `. The power measured in each `-bin is the
sum of the measured power in spherical harmonic modes with multipoles within a given
range of `. For a large number of independent modes, the central limit theorem tells us that
the statistics will be approximately Gaussian. However, with QUIETs sky coverage, the
lowest ` bins contain a fairly small number of modes (27 modes in bin 25 ? ` ? 74). Further
modes in the lowest ` bins are killed by the filtering (�1) so the number becomes small
enough that the statistics become non-Gaussian. If the power spectrum C` values aren?t
quite Gaussian, this would contribute to a slightly longer tail for the ?2null distribution.
We ran MC simulations of the full null suite to take into account these two features. We
then used the MC results (1024 realizations) to compute the probability to exceed (PTE)
for the total ?2 of the null suite as well as for any outliers. Figure 6.2 shows the ?2null
distribution of EE null power spectra points for patch CMB-1 . The red histogram includes
all ?2null values for the data null result (42 null tests x 9 points in each null spectrum = 378
values). The null suite results also include similar results for 1024 MC realizations of the
data. For each MC realization, the same histogram is calculated. The dark shaded region
indicates the range containing 68% of the MC histogram for each bin in ?2 ; the medium and
light shaded regions contain the 95.4% and 99.7% of the MC histograms, respectively.
156
Figure 6.4: Left: The EE null power spectrum for the patch CMB-3. The red histogram
includes all ?2 values for the data null result (42 null tests x 9 points in each null spectrum
= 378 values). The null suite results also include similar results for 1024 Monte Carlo
realizations of the data. For each Monte Carlo realization, the same histogram is calculated.
The dark shaded region indicates the range containing 68% of the MC histogram for each
bin in ?2 ; the medium and light shaded regions contain the 95.4% and 99.7% of the MC
histograms, respectively. Right: A histogram of the probabilities to exceed for the data ?2
values; for each point, the PTE value is calculated from the Monte Carlo realizations of the
same null test and `-bin
? Bias: The ?null distribution proved useful for identifying and quantifying potential contaminants. During the blind stage of the analysis, a positive bias in the ?null distribution
of 0.1 was identified. This can be thought of as a shift in the mean of the ?null distribution
corresponding to 10% of the statistical errors of each power spectrum point. This bias was
found when we were cross correlating maps made from data divided by time (day-by-day)
instead of using array orientation as the unit of cross correlation (see �4). After detailed
studies, we found that cross-correlation based on the division of data by array orientation
decreased the bias to 0.02 � 0.02 (see Figure 6.7) which is consistent with zero.
Pipeline B finds a shift in the ?null distribution of 0.19. When including auto correlations,
we can see a bias of a similar level (0.21), in pipeline A. The maximum-likelihood technique
employed by pipeline B intrinsically uses auto-correlations so there is no straightforward way
to remove the bias from the Pipeline B framework. However, as will be seen in � the power
spectra from the two pipelines are consistent. Possible systematic bias that remain in the
Pipeline B data is well below the level of the statistical errors.
157
6.3
Blind Consistency Checks
As we refine the data-selection criteria based on the results of the null suite, we use a second
test to monitor changes in the non-null power spectra. Using a blind analysis framework, we
compute the difference of the power spectra between any two iterations of the data selection
without revealing the non-null spectra. We do this by adding a random number that we don?t
know to the measured power in each `-bin and then taking the difference of the two power
spectra. Further, we randomize the sign of the difference to hide the direction of the change;
knowledge of the direction could allow experimenter bias. For example, we don?t expect to
measure power in BB given the sensitivity of the instrument and the integration time in the
Q-Band season. The sign of the difference would tell us which of the two configurations had
lower power.
6.3.1
Data Selection Consistency
Figure 6.5 shows differences in the null power spectra between the final configuration of the
null suite and several intermediate iterations of the data selection. In the early iterations of
the null suite, the data selection criteria were still being developed. Unsurprisingly, these
data sets showed significant failures for the null-test suite. Statistically significant differences between two iterations of the data selection criteria indicate a change in the level of
contamination in the selected data set. Our data-selection criteria are finalized when further
iterations only result in statistically expected fluctuations. Fluctuations in the power spectra
during the final few iterations of the data set are much less than the statistical error of the
final result (shown in blue).
158
Figure 6.5: Power-spectra differences between the final data selection and six of the 32
earlier data-selection iterations, ordered temporally. The lowest-` bin of patch CMB-1 is
shown. The error bars correspond to the expected fluctuations due to the differences in data
selected, which are much smaller than the final statistical errors in this bin (? 0.10 礙2 for
BB). Iterations that are closer to the final data selection have smaller errors. The expected
EE power in this bin from the ?CDM model (gray) and the statistical error on the final
result (black) also are shown for comparison. Adapted from [1].
159
6.3.2
Patch Consistency
The non-null power spectra were compared among the four CMB patches. We computed a ?2
statistic comparing the deviation of each patch?s non-null power spectra from the weighted
average over all patches. ?2p is defined as,
?2p
!
X C i ? 礲 2
b
?
?bi
(6.5)
i,b
where Cbi is the power in the patch i in bin b, ?bi are the errors for each bandpower and the
P i i P i
average of the patch bandpowers is 礲 ?
Cb wb / wb , and the patch weights are given by
i
i
wbi ? 1/? 2 . To determine if non-statistical deviations are present, we computed the expected
distribution of ?2p from 1024 MC simulations and compared them to the total ?2null .
6.4
Analysis Validation Results
When all aspects of the analysis were finalized, the last round of null tests and CMB patch
comparisons were used to validated the non-null?power-spectra results. Figure 6.6 shows a
histogram of the ?2 values for all points from all EE and BB null spectra for all four patches.
EB ?2 distributions are shown as well.
Examinations of various subsets of the null suite, such as EE or BB only, do not reveal
any anomalies. The EB null spectra do not indicate any failure either. The worst outlier in
the null suite is found in the 175 < ` < 225 bin of the EE spectrum for patch CMB-2. The
point is found in the null test based on the galactic latitude of sidelobe 2, with ?2 = 20.6. Of
the MC realizations, 2.93% have an outlier with a larger ?2 in their EE spectrum. Combining
EE and BB, 5.66% of the MC realizations have an outlier with ?2 > 20.6. One point at
this level is not a concern; with a large number of statistics we expect to see a few points
in the tail of the distribution. There are three points in EE and BB with ?2 > 8 (80.1% of
160
Figure 6.6:
polarization
?2null distributions for the EE, BB, and EB null power spectra for the final
null suite are shown for all CMB patches.
MCs have similar points). The total ?2 for all EE points is 375 with 378 degrees of freedom,
giving a PTE of 0.518. For BB, the total ?2 is 420 giving a PTE of 0.094. The combined
EE, BB null suite has a PTE of 0.194.
Figure 6.7 shows the distributions of the ?null statistic and of the PTEs corresponding to
all ?2null values from the full null suite. In pipeline A, the distribution of ?null is consistent
with the expectation from MC simulations. The mean of the ?null distribution is 0.02 � 0.02;
the mean of the MC-ensemble ?null distribution also is consistent with zero. The distribution
of the ?2null PTEs is uniform as expected. Table 6.3 lists the PTEs for the sums of the ?2null
statistic over all bins in each patch. Patch comparison PTEs are 0.16, 0.93, and 0.40 for
EE, BB, and EB, respectively, demonstrating no statistically significant difference among
161
the patches. Complete results for the null suite are given in appendix G along with the
threshold values used to split the data for each null test. The null test outliers are few and
none of the PTEs are too low, and the patches are consistent. The data have passed the null
tests.
Figure 6.7: Null-Suite Statistics. The left panel shows a histogram of the ?null values and
the average of 1024 MC realizations of the pipeline-A null suite (gray histogram). Both data
and MC distributions show similar non-Gaussianity in the ?null statistic. The right panel
shows a histogram of PTEs calculated from the ?2null statistic (outliers from either side of
the upper distribution manifest as low PTEs).
Table 6.3: Null Suite ?2 Probability To Exceed by Patch
Patch
CMB-1
CMB-2
CMB-3
CMB-4
Pipeline A %
44
19
16
68
Pipeline B %
7
43
23
28
Note. ? PTEs calculated from the sums of the ?2null statistics, for EE and BB spectra points, over the
null tests for each patch.
162
6.5
Validation of the Temperature Analysis
A smaller number of null tests are used for the temperature analysis. While there is a large
overlap between the polarization and temperature null suites, several tests in the polarization
null suite are not applicable to the temperature data and others were discarded due to lack
of data with sufficient cross linking. Tests such as Q vs.? U diodes are not useful since
only Q diodes are used in the temperate data analysis. Instead this test is replaced with
analogous tests (e.g. Q1 vs.? Q2 diodes). Most tests that are dropped from the null suite
are removed because they fail to meet the minimum cross-linking requirements established
in � Sufficient cross-linking is harder to maintain in null test because, by definition, each
map only contains approximately half of the original data set. Since the data already are
divided into four MCES for the temperature analysis, they must be divided into eight MCES
for each null test. Null tests based on array pointing are even less likely to be viable since
they often are designed to group data by array orientation, directly conflicting with the
cross-linking criteria. Null tests are less critical for the temperature analysis however, as
the spectra (TT,TE,TB) are used primarily as validation of receiver performance and a
consistency check for the polarization result �1.
Even with these limitations, we are able to run suites of 29, 27, and 23 TT null tests
on patches CMB-1, CMB-2, and CMB-3, respectively. Patch CMB-4 was excluded from
analysis because it lacked the data necessary to perform null tests; any result obtained from
that patch could not be validated. Table 6.4 lists the null tests in the temperature null suite
for each of the three patches included.
Passing the null suite is more challenging with temperature than polarization data since
both the signal and the possible sources of contamination are stronger. Figure 6.8 shows
the maps for the good vs. bad weather null test (the same null test shown in Figure 6.1 for
polarization). Atmospheric fluctuations are stronger in temperature than in polarization.
Consider I ? Q/U leakage. This is instrumental polarization that comes from a small
163
Table 6.4: The 29 null tests included in the temperature analysis null suite.
Patch
Null test
Category
CMB-1 CMB-2
RQ17 vs. RQ18
x
x
Q1 diodes vs Q2 diodes
x
x
Instrumental
Effects
RQ17Q1+ RQ18Q2 vs. RQ17Q1+ RQ18Q2
x
x
Diodes with/without abrupt TP level shifts
x
x
CES at high vs. low elevation
x
x
CES with the patch rising vs. setting
x
?
Pointing
Deck angle divisions offset by 45?
x
x
Deck angle divisions offset by 90?
x
x
Effects
Array orientation offset by 45?
x
x
?
Array orientation offset by 90
x
x
?
Array orientation offset by 180
x
x
Sun proximity to the main beam
x
x
Source
Moon proximity to the main beam
x
x
Far sidelobe elevation high vs. low
x
x
Positions
Far sidelobe 1 proximity to the Galaxy
x
?
Far sidelobe 2 proximity to the Galaxy
x
x
More vs. less excess noise near the scan freq.
x
x
TOD
More vs. less high freq. (2?15 Hz) excess noise
x
x
x
x
Contamination Weather quality: 10-s TP RMS 100% statistic
Weather quality: 10-s TP RMS 95% statistic
x
x
High vs. low white noise amplitudes
x
x
High vs. low ambient humidity
x
x
Large vs. small humidity changes
x
x
High vs. low bias electronics temp.
x
x
Environmental Large vs. small bias electronics temp. change
x
x
Conditions
Fast vs. slow electronics temp. changes
x
x
High vs. low cryostat temp.
x
x
Large vs. small cryostat temp. changes
x
x
First half vs. second half of the season
x
x
CMB-3
x
x
x
x
x
?
?
?
x
x
?
x
x
?
?
?
x
x
x
x
x
x
x
x
x
x
x
x
x
fraction of the temperature or total intensity signal (I) ?leaking? into the Q/U channels (see
�2.3). In the temperature analysis, the total intensity of the differential signal from a
possible source of contamination, such as ground pick-up, would show up in the data.
After several iterations of cuts, filtering and MCES reconfiguration, the data for patches
CMB-1 and CMB-2 passed the temperature validation tests. We calculated the sums of
?2null statistics, yielding PTEs of 0.26 and 0.11 for patches CMB-1 and CMB-2, respectively.
164
Figure 6.8: Sample temperature maps for null tests. The data has been divided in half based
on the value of the weather-based data selection criteria: TP 10s RMS 100%.
No significant outliers were found for these patches. Figure 6.9 shows the histograms of the
?2null distributions for the TT, TE and TB null suites.
However, a 5-? outlier in a single test, dividing the data based on array pointing (array
orientation 0? vs. 90? ), was found in patch CMB-3, implying contamination in its temperature map. The outlier was located in the 75 < ` < 125 bin and with a ?2 per one degree of
freedom of 25.16, none of the MC simulations had an outlier that large. CMB-3 is therefore
excluded from further analysis.
We confirm consistency between the patches CMB-1 and CMB-2 with a PTE of 0.26.
The ?null distribution also was calculated for the temperature data and is shown in Figure
6.10. With a mean value of ?0.03 � 0.04, the ?null distribution is consistent with zero and
MC simulations.
With no significant contamination in TT, EE, or BB spectra, one may be confident that
the TE and TB spectra are similarly clean. For confirmation, however, we calculated TE
and TB null spectra for five null tests that are common to the temperature and polarization
165
Figure 6.9: ?2null distributions for the TT, TE, and TB null power spectra for the final
temperature null suite are shown for patches CMB-1,2 and 3.
Figure 6.10: A histogram of the ?null values for temperature null suite for patches CMB-1
and CMB-2 is shown in red. The average of 512 MC realizations the null suite is shown in
blue. With a mean value of ?0.03 � 0.04, the ?null distribution is consistent with zero and
MC simulations.
166
Table 6.5: The 5 Null Tests used for temperature-polarization correlation analysis
Null test
Category
Instrumental Effects
Diodes with/without abrupt TP level shifts
TOD
More vs. less high freq. (2?15 Hz) excess noise
Weather quality: 10-s TP RMS 100% statistic
Contamination
Environmental
High vs. low ambient humidity
High vs. low bias electronics temp.
Conditions
analyses. These null tests are listed in Table 6.5. These yield PTEs of 0.61 and 0.82 for TE,
and 0.16 and 0.55 for TB, for patches CMB-1 and CMB-2, respectively, with no significant
outliers. Table 6.6 gives the PTE for each patch in the TT, TE and TB null suites. Patch
consistency checks give PTEs of 0.48 for TE and 0.26 for TB. Thus, the TE and TB power
spectra, as well as the TT, passed all validation tests that were performed.
Table 6.6: Probabilities to Exceed for the
Patch TT TE
CMB-1 0.26 0.61
CMB-2 0.11 0.82
CMB-3 0.08 0.55
167
TT, TE and TB null suites.
TB
0.16
0.55
0.02
CHAPTER 7
Q-BAND RESULTS
Once the data selection criteria and analysis methodology (choice of cross-correlation unit,
filtering, etc.) are validated in a blind analysis framework, we compute the final power spectra. Results of the first season of observations with the Q-Band receiver are presented in this
section. The polarization power spectra are presented in �1 for all patches and for patchcombined results for both pipelines. They are evaluated for consistency to the concordance
?CDM model. Limits on the possible power from primordial B-Modes (gravity waves),
given by the tensor to scalar ratio, r, are presented in �2. Comparison to results from
other experiments is shown in �3. Contributions to the power spectra from foregrounds
are addressed in �4 and other systematic effects are evaluated in �5. Temperature and
temperature-polarization cross spectra are shown in �6. Unless otherwise specified, results
presented here were calculated in pipeline A; systematic error analysis was performed using
and null tests were passed in this pipeline.
7.1
Polarization Power Spectra
For each of the EE, BB and EB spectra, the power is computed in nine `-bins. Multipoles
below `min = 25 cannot be measured reliably given our patch size (See 5.4). The bins begin
at `min and are equally spaced with a width of ?` = 50; the first bin is 25 ? ` ? 75 and
the last bin is 426 ? ` ? 475. EE, BB and EB spectra, computed for each of the four
patches, are shown in Figure 7.1 along with the patch combined values. The power in the
first bin of the EE spectrum in patch CMB-1 (red in the plot) shows evidence of foreground
contamination when comparing it to WMAP K-Band results and will be addressed in �4.
A ?2 statistic can be calculated by minimizing the log-Likelihood function to a model
of patch consistency; the model simply assumes that for each ` bin, all four patches should
168
measure the same power. For all patches, spectra and bins, ?2min is given by:
?2min ? ?2 ln Lmin = 82.5.
(7.1)
The likelihood function, L, is normalized such that L = 1 if the central values of the power
measured in the different patches are the same. ?2min follows a ?2 distribution with 81
degrees of freedom1 giving a 43% PTE and confirming patch consistency.
The patch-combined EE, BB, and EB polarization power spectra estimated by both
pipelines are shown in Figure 7.2 and the results from pipeline A are provided in Table 7.1.
The agreement between the results obtained by the two pipelines is excellent, and both are
consistent with the ?CDM concordance cosmology (see �1.1). The errors shown in Figure
7.2 are statistical uncertainties only. Systematic effects are quantified in �5. Errors shown
for pipeline A are 68% frequentist confidence intervals.2 The window and transfer functions
also are also shown for each bin and represent the response in each band to the true C`
spectrum. The correlation between neighboring bins is typically ?0.1; it becomes negligible
for bins further apart.
7.1.1
Consistency with ?CDM
We calculate the consistency between the QUIET EE spectrum and the 7-year best-fit
WMAP ?CDM spectrum [42]. We let the overall amplitude of the EE power spectrum,
q, be the only free parameter and fit the QUIET EE data excluding the point in the first bin
as it has significant foreground contamination (see �7). The amplitude is constrained to
q = 0.87 � 0.10 3 which is consistent with the ?CDM amplitude (q = 1) within 1.3?. Figure
1. 3 spectra measured in 4 patches in 9 bins gives 108 points, 27 (3� i.e. the patch averaged power) of
which are free to move (patches should be consistent) thus we have 81 d.o.f.
2. Pipeline B uses the diagonal elements of the Fisher matrix.
3. q = 0.94 � 0.09 for pipeline B
169
Figure 7.1: CMB power spectra are shown for each patch individually. The patch combined
values are shown in black. Bins have a width of ?` = 50. Black points are placed at the
bin centers. While all points from all patches are calculated for the same bins, the plotted
points are offset slightly from the band centers for clarity. The top, middle and bottom
panels show the EE, BB and EB spectra, respectively. Left panels show the low ` range in
greater detail while right panels give the power computed in all nine bins. In the EE spectra
plot the gray line shows the ?CDM concordance model EE power. The gray dotted lines
in the lower two panels indicate zero-power. The different error bars for each patch mainly
reflect the amounts of time each was observed.
7.3 shows the Likelihood curve as a function of EE power amplitude, q.
The ?2 is given by the log-Likelihood ratio:
??2 ? ?2 ln[L(Cb?CDM )/Lmin ].
170
(7.2)
Figure 7.2: EE, BB, and EB power spectra from each QUIET pipeline, all four patches
combined. The insets show the low-` region in detail. Window and transfer functions for
each ` bin are shown below the corresponding power spectra in black and gray, respectively.
The EE point in the lowest-` bin includes foreground contamination from patch CMB-1. For
this display, pipeline A shows frequentist 68% confidence intervals while pipeline B uses the
diagonal elements of the Fisher matrix; the difference is most pronounced in the lowest-` bin
where the likelihood is the most non-Gaussian [1].
171
Table 7.1: CMB-Spectra Band Powers from QUIET Q-Band Data [1]
` bin
EE
BB
EB
25-75
a
0.33+0.16
?0.11
0.82+0.23
?0.20
0.93+0.34
?0.31
1.11+0.58
?0.52
2.46+1.10
?0.99
+2.1
8.2?1.9
11.5+3.6
?3.3
15.0+6.2
?5.8
+13
21?11
?0.01+0.06
?0.04
0.00+0.07
?0.07
0.04+0.14
?0.12
?0.10+0.11
?0.12
0.24+0.28
?0.25
0.71+0.22
?0.20
0.64+0.53
?0.46
0.18+0.38
?0.38
1.07+0.98
?0.86
?0.52+0.68
?0.69
0.8+1.6
?1.4
0.9+1.3
?1.3
?2.2+2.7
?2.4
0.0+2.0
?2.0
?4.9+5.3
?4.9
3.2+3.9
?3.9
2+11
?10
4.5+8.3
?8.2
76-125
126-175
176-225
226-275
276-325
326-375
376-425
426-475
a
Note. ? Units are thermodynamic temperatures, 礙2 , scaled as C` `(` + 1)/2?.
Patch CMB-1 has significant foreground contamination in the first EE bin.
For EE only (9 d.o.f.), ??2 = 11.1 with a PTE of 27%. Instead, considering ??2 between
the best fit to the QUIET EE spectrum and a hypothesis of zero EE power (q = 0), we find
??2 = 114 demonstrating a more than 10? detection of EE power. Considering the first
peak only (two bins spanning 76 ? ` ? 175), the ??2 between ?2min and zero power in those
two bins is ??2 =44.1 giving a detection with more than 6? significance.
Considering all spectra (EE, BB, and EB) and excluding the first bin of each, ??2 to
?CDM assuming C`EB = C`BB = 0 is 31.6 with 24 degrees of freedom, corresponding to a
PTE of 14%.4 Our results are consistent with ?CDM.
172
Figure 7.3: Likelihood curve as a function of EE power amplitude, q, using the 8 EE bins
with ` ? 76. The ?CDM, EE power spectrum amplitude corresponds to q = 1
7.2
Constraints on Primordial B modes
Measurement of the BB power spectrum at low multipoles (25 ? ` ? 175) is used to constrain
the tensor-to-scalar ratio, r. The definition of r used here is consistent with that used in [43]:
the ratio of the amplitude of primordial?gravitational-waves to the curvature-perturbation
amplitude at a scale k0 = 0.002 Mpc?1 . Our BB measurement is fit to a BB-spectrum
template based on the ?CDM concordance parameters, where r is the free parameter. The
BB power spectrum amplitude is directly proportional to r.5 The likelihood function for r
6
is shown in Figure 7.4. We find r = 0.35+1.06
?0.87 , corresponding to r < 2.2 at 95% confidence.
7.3
Comparison to Other Experiments
The QUIET Q-Band EE power spectrum and limits on BB power are shown in comparison
with other experiments in Figure 7.5. BICEP, QUaD, and WMAP are selected as they are
4. For pipeline B, ?2 =24.3 with a PTE of 45%.
5. The tensor spectral index is fixed to nt = 0
6. Pipeline B obtains r = 0.52+0.97
?0.81
173
Figure 7.4: Likelihood curve as a function of the tensor to scalar ratio, r, using the three
BB bins in the range 25 ? ` ? 175. r = 0.35+1.06
?0.87 , with r < 2.2 at 95% confidence.
the most relevant experiments in our multipole range. QUIET?s detection of the first peak
in EE (> 6? significance in the 76 ? ` ? 175 range) confirms the only other detection of this
peak.7 QUIET?s conservative upper limits on BB lie between those of BICEP and WMAP,
significantly limiting r in our multipole range.
7.4
Foreground Analysis
Two sources of foreground contamination are considered in the QUIET Q-Band analysis,
compact radio sources and galactic synchrotron radiation. Contributions from other sources
described in �7, including thermal and spinning dust, are expected to be negligible and
thus neglected. Compact radio sources are treated in �4.1. Foreground contamination from
synchrotron, detected in the lowest ` bin in the EE power spectrum, is addressed in �4.2.
7. The other detection was made by BICEP [43]
174
Figure 7.5: The top panel shows EE results with 68% C.L. error bars; the bottom panel shows
BB 95% C.L. upper limits. For comparison, we also plot results from previous experiments
[125, 43, 42] and the ?CDM model (the value r = 0.2 is currently the best 95% C.L. limit
on tensor modes).
7.4.1
Compact Radio Sources
Two compact radio sources (CenA and PicA) are masked before the power spectra are
computed (See �3 ).8 To confirm this is sufficient we compute the power spectrum both
with and without the full WMAP source mask [143] applied; no statistically significant
change is found in the CMB spectra. Contribution from sources not detected by WMAP
8. The full WMAP point source mask is applied in pipeline B
175
(below 1 Jy) are estimated from [144]. Their possible contribution is found to be small
(0.003 礙2 at ` = 50 and 0.01 礙2 at ` = 100).
7.4.2
Galactic Synchrotron
The EE band power in the first bin of patch CMB-1 is 0.55 � 0.14 礙2 where the uncertainty
is calculated from the scatter the the MC simulations assuming ?CDM. This is a 3-? outlier
relative to the expected ?CDM band power of 0.13 礙2 (See Figure 7.1). To determine
whether this is a detection of synchroton emission we first consider whether the power in
that bin is consistent with the WMAP 7 K-band (23-GHz) map where contributions from
synchrotron emission are much stronger (See Figure 1.12).
The WMAP 7 K-band map is processed through the pipeline to estimate its bandpower,
QK
C?bKK . A cross spectra, C?b
, is also measured using the QUIET Q-Band data.
KK = 17.4 � 4.7 礙2 ) and the
Significant power is found in both the WMAP K-Band (C?b=1
KQ
K/Q cross-correlated spectra ( C?b=1 = 3.3 � 0.55 礙2 ) in the first ` bin (25 ? ` ? 75). The
KQ
cross correlated power, C?b=1 , confirms that the excess is not due to systematic effects in the
two experiments; it is likely a foreground.
To confirm that the excess power in the first bin of the EE spectrum is consistent with a
synchrotron frequency spectrum, we extrapolate the power as measured in WMAP K-Band
to Q-Band. Using the synchrotron spectral index, ? = ?3.1 (See �7) we find that the
QK
QQ
expected power would be C?b=1 = 2.57 � 0.69 礙2 and C?b=1 = 0.38 � 0.10 礙2 where the
KK [1, 145]. The foreground contamination is consistent with
uncertainties are scaled from C?b=1
synchrotron emission.
QK
KK and C?
The C?b=1
b=1 powers are calculated for every bin in every patch in the EE, BB, and
EB spectra. No significant power is found in any other case, nor is it expected above ` > 75
[146]. Although we neither expected nor detected any BB foreground power, the detection
of the foreground in EE suggests that BB foregrounds might be present at a smaller level.
176
Thus, the limit on r given in �2 is conservative.
7.5
Systematic Effects
Systematic uncertainties are quantified using a set of dedicated simulations. Passing the
analysis validation tests limits systematic uncertainty but to increase confidence in our result
we constrain the level to well below that of the statistical errors. B-modes remain undetected,
thus it is vital to constrain possible systematic effects to be as low as possible as their values
will have implications for future phases of the QUIET experiment.
We simulate possible systematic effects in the TOD or maps, propagate them through
the pipeline and evaluate the excess power. The systematic effects evaluated include possible contamination from miscalibrations (beam, pointing, responsivity, detector polarization
angle) and sources of spurious signal (instrumental polarization and sidelobes seeing the
sun and ground). Uncertainty in the beam window function is evaluated using the difference between beam measurements of the central and edge horns (TT assembly).9 Errors in
the pointing model can distort the signal in the maps leading to underestimates of the EE
power and spurious BB power. Uncertainty in the responsivity includes possible contributions from the overall responsivity error, possible sub-CES time variation of the responsivity,
uncertainty in the atmospheric model used to calculate the atmospheric temperature and
the variation in calculated responsivity from multiple calibration sources (TauA, Moon, Skydips or Wiregrid). E-mode to B-mode leakage can be generated if the polarization axes of
the modules are not well known. Instrumental polarization (I ? Q/U) can create spurious
signals both in the monopole term (from OMT) and in higher order leakage (dipole and
quadrapole terms from differing beam elipticities [1, 69]). Residual ground synchronous signals or instances of far sidelobes seeing the sun could remain in the data although the former
9. The beams are well measured; both are measured to better precision than the difference between the
two (�2)
177
is filtered from the data in TOD processing and the later is cut in data selection. The effects
simulated and the levels of systematic error found for each are given in Table 7.2 for EE, BB,
and EB. Figure 7.6 shows these levels in comparison to both the levels of statistical errors
and expectations from models( ?CDM EE spectrum and the expected B-mode signal given
r = 0.1).
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Figure 7.6: Systematic uncertainty estimates for EE, BB, and EB power spectra. Estimates
for a variety of effects (see text) are shown for the three power spectra. In all cases, they are
well below the statistical errors, which also are shown. In particular, the contaminations to
the primordial?B-mode signal, at multipoles below 100, are below the level of r = 0.1, even
though we do not make a correction for the largest contaminant, the monopole leakage [1].
Other, subdominant effects are also considered including data selection biases and ADC
non-linearities. To ensure that we do not cut so tightly on the data that we bias the results,
we applied our data selection criteria to a suite of noise simulations and evaluated the result.
No bias was found and spurious B-mode signals are limited to . 10?3 礙2 in the low ` region
where any gravity-wave B-mode signal would be expected to peak (` < 100). Systematic
178
179
EB
BB
EE
25-75
76-125
126-175
176-225
226-275
276-325
326-375
376-425
426-475
476-525
25-75
76-125
126-175
176-225
226-275
276-325
326-375
376-425
426-475
476-525
25-75
76-125
126-175
176-225
226-275
276-325
326-375
376-425
426-475
476-525
` Bins
7.09 �
9.80 � 10?3
2.58 � 10?2
3.02 � 10?2
1.32 � 10?1
8.72 � 10?1
2.33 � 100
3.21 � 100
3.03 � 100
1.69 � 100
5.68 � 10?5
1.32 � 10?4
2.08 � 10?4
1.27 � 10?4
4.95 � 10?4
1.16 � 10?3
2.72 � 10?3
1.89 � 10?3
3.83 � 10?3
4.87 � 10?3
1.82 � 10?3
7.96 � 10?3
1.03 � 10?2
7.26 � 10?3
2.10 � 10?2
1.01 � 10?1
1.98 � 10?1
1.92 � 10?1
1.48 � 10?1
5.93 � 10?2
10?4
Pointing
6.52 �
1.48 � 10?2
4.31 � 10?2
4.22 � 10?2
2.14 � 10?1
9.96 � 10?1
2.23 � 100
2.73 � 100
1.89 � 100
8.15 � 10?1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
10?4
Beam
1.60 �
9.50 � 10?2
1.30 � 10?1
7.72 � 10?2
2.79 � 10?1
1.04 � 100
2.05 � 100
2.41 � 100
1.77 � 100
9.04 � 10?1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
10?2
Absolute
Responsivity
4.58 �
1.95 � 10?2
2.41 � 10?2
1.82 � 10?2
5.22 � 10?2
2.40 � 10?1
4.82 � 10?1
5.18 � 10?1
4.15 � 10?1
1.80 � 10?1
2.69 � 10?4
1.25 � 10?4
1.61 � 10?4
1.11 � 10?4
1.50 � 10?4
5.28 � 10?4
9.69 � 10?4
1.31 � 10?3
1.26 � 10?3
2.32 � 10?3
1.05 � 10?4
1.61 � 10?4
3.44 � 10?4
2.19 � 10?4
2.33 � 10?4
1.76 � 10?3
1.57 � 10?3
1.72 � 10?3
2.58 � 10?3
2.42 � 10?3
10?3
2.54 �
1.06 � 10?2
1.36 � 10?2
9.90 � 10?3
3.06 � 10?2
1.38 � 10?1
2.70 � 10?1
2.93 � 10?1
2.23 � 10?1
1.06 � 10?1
1.59 � 10?4
1.78 � 10?3
1.93 � 10?3
1.37 � 10?3
3.83 � 10?3
1.78 � 10?2
3.66 � 10?2
4.09 � 10?2
3.59 � 10?2
1.74 � 10?2
7.47 � 10?3
3.15 � 10?2
3.97 � 10?2
2.91 � 10?2
8.47 � 10?2
3.91 � 10?1
7.91 � 10?1
8.42 � 10?1
6.68 � 10?1
2.89 � 10?1
10?3
3.25 �
8.39 � 10?3
9.85 � 10?3
1.05 � 10?2
8.62 � 10?3
1.01 � 10?2
8.18 � 10?3
1.24 � 10?2
3.33 � 10?2
2.85 � 10?2
2.81 � 10?3
5.79 � 10?3
8.84 � 10?3
9.42 � 10?3
9.80 � 10?3
9.26 � 10?3
7.39 � 10?3
8.95 � 10?3
1.35 � 10?2
2.84 � 10?2
6.21 � 10?4
1.24 � 10?3
1.62 � 10?3
1.64 � 10?3
4.38 � 10?3
6.29 � 10?4
2.47 � 10?3
4.05 � 10?3
5.10 � 10?3
1.38 � 10?2
10?3
Size of Systematic Effect [� K 2 ]
Detector
Total
Polarization
I-Q/U
Responsivity
Angle
Monopole
1.39 �
6.03 � 10?5
2.20 � 10?4
3.16 � 10?4
2.25 � 10?4
1.18 � 10?3
1.34 � 10?3
3.76 � 10?4
2.81 � 10?4
6.86 � 10?4
2.82 � 10?5
5.71 � 10?5
1.19 � 10?4
1.40 � 10?4
1.59 � 10?4
1.34 � 10?4
1.89 � 10?4
1.25 � 10?4
3.29 � 10?4
4.51 � 10?4
2.59 � 10?5
2.42 � 10?4
2.34 � 10?5
1.19 � 10?4
9.10 � 10?5
3.77 � 10?4
6.47 � 10?6
2.68 � 10?4
1.57 � 10?4
9.95 � 10?5
10?4
I-Q/U
Dipole &
Quadrapole
Table 7.2. Systematic Effects for EE, BB & EB Spectra
?5.29 �
1.41 � 10?2
?2.24 � 10?2
9.43 � 10?3
1.84 � 10?2
1.98 � 10?1
9.36 � 10?2
1.74 � 10?1
2.35 � 10?1
?7.11 � 10?2
1.05 � 10?3
1.11 � 10?3
4.18 � 10?4
?1.96 � 10?3
8.89 � 10?3
2.06 � 10?4
1.62 � 10?3
?5.97 � 10?2
?1.62 � 10?2
?1.55 � 10?3
6.92 � 10?3
6.36 � 10?3
7.83 � 10?3
4.22 � 10?3
3.07 � 10?3
3.02 � 10?2
1.58 � 10?1
8.63 � 10?2
4.57 � 10?2
2.33 � 10?2
10?4
Sidelobe
Sun
Signal
1.72 � 10?2
1.00 � 10?1
1.44 � 10?1
9.63 � 10?2
3.82 � 10?1
1.72 � 100
3.86 � 100
4.90 � 100
4.02 � 100
2.10 � 100
3.02 � 10?3
6.16 � 10?3
9.06 � 10?3
9.72 � 10?3
1.38 � 10?2
2.01 � 10?2
3.75 � 10?2
7.30 � 10?2
4.18 � 10?2
3.38 � 10?2
1.04 � 10?2
3.32 � 10?2
4.18 � 10?2
3.03 � 10?2
8.74 � 10?2
4.05 � 10?1
8.30 � 10?1
8.68 � 10?1
6.86 � 10?1
2.96 � 10?1
Total
effects induced by residual ADC non-linearities (Type-B Glitching, ) fall into two possible
categories; they either induce an effect similar to sub-CES time variation of the responsivity
or one similar to I ? Q/U leakage. As both of these effects already have been quantified (see
Table 7.2), ADC non-linearities would simply increase the level of each of these systematics.
Such contaminations are estimated to contribute less than a 3% increase to the leakage
(? 10?4 礙 2 ) and less than a 50% increase in responsivity (< 10?2 礙 2 for EE, < 10?4 礙 2
for BB and EB in the low multipole region below 100).
The possible contaminations from all evaluated systematic effects are well below the
statistical errors. The levels of spurious-B modes are less than the signal of r = 0.1 in
the low-` region. This is the lowest level of BB contamination yet reported by any CMB
experiment.
7.6
Temperature Power Spectra
Although the primary goal of QUIET is to make a precision measurement of the polarization
power spectra of the CMB, some sensitivity to temperature is valued. When combined
with our polarization data, measurements of the temperature power spectrum enable us
to make self-contained measurements of the TE and TB power spectra. Measurements of a
known signal (e.g. the well measured TT power spectrum) with the newly developed QUIET
modules provides an additional check of detector function. The high sensitivity of these
modules also makes them very useful for calibration, pointing estimation, and consistency
checks (see �. Figure 7.7 compares the QUIET temperature map for patch CMB-1 to the
WMAP 7-year Q-band map [112]. Figure 7.8 shows temperature maps for patches CMB1, CMB-2 and CMB-3 made using pipeline A. CMB-3 is shown for interest although it is
excluded from the final analysis since it failed to pass the null suite (�5). Point sources are
visible in the patch CMB-2 map and are masked before the power spectra are calculated.
Figure 7.9 shows the TT, TE, and TB power spectra results for both pipelines. Agreement
180
Figure 7.7: Comparison of QUIET (left) temperature map to the WMAP (right) 7-year Qband map [112] for patch CMB-1. Note: While the WMAP map has been weighted by the
patch coverage of the QUIET data, it has not been processed through the QUIET filtering
(see �1.2), thus the low-` modes remain. For reference, the bottom panel of Figure 7.1
shows the transfer function applied to the QUIET data.
Figure 7.8: QUIET temperature map for patches CMB-1, CMB-2 and CMB-3. Maps are
made using pipeline A. Insets show patch coverage. CMB-3 is shown for interest although it
is excluded from the final analysis since it failed to pass the null suite (�5) Point sources,
indicated by white circles, are visible in the patch CMB-2 map and are masked before the
power spectra are calculated.
with the ?CDM model is good. In particular the first dip in the TE cross-power spectrum
is well measured and consistent with recent measurements by other experiments (see Figure
1.10). These results are a strong demonstration of the raw sensitivity of the QUIET detectors;
the single QUIET differential-temperature assembly produces a high?signal-to-noise map
using only 189 hours (after selection) of observations.
181
Figure 7.9: The three panels show the CMB temperature power spectra: TT, TE, and
TB (top to bottom) as measured by both pipelines (Patch CMB-1, CMB-2 combined).
Measurements are in good agreement with the ?CDM model.
182
CHAPTER 8
CONCLUSIONS
QUIET collected over 10,000 hours of data with the Q-Band and W-Band receivers. The
?
sensitivity of the Q-Band array is 69 礙 s and the W-Band array has a similar sensitivity
?
of 70礙 s. QUIET?s newly-developed pseudo-correlation polarimeters are demonstrated to
have excellent sensitivity and systematic immunity.
Using only the first season of observations (roughly one third of the total data set),
QUIET detects polarization in the EE power spectrum at 43 GHz. We confirm with high
significance the detection of polarization in the region of the first acoustic peak [43] in the
multipole region ` = 76?175. We find no significant power in either BB or EB between ` = 25
and ` = 475 and we measure the tensor-to-scalar ratio to be r = 0.35+1.06
?0.87 . The robustness
of the final results is supported by an extensive suite of null tests, rigorous adherence to a
blind analysis framework and excellent agreement of the results obtained using two separate
pipelines.
As experiments continue to push the limits of their sensitivity in search of B-mode
power, systematic effects and constraints on foregrounds will become increasingly important. Through a series of systematic studies, the possible contaminations in the B-mode
power are limited, for QUIET, to a level smaller than for any other published experiment:
below the level of r = 0.1 for the primordial B-modes. Further, a 3-? detection of synchrotron emission was found in one of our four CMB patches. While the detection is only
in EE, if we assuming a similar level of contamination exists in BB and we extrapolate to
the foreground minimum of about 95 GHz, we would have synchrotron contamination at the
level of r = 0.02.
Analysis of the over 7,500 hours of W-Band data is underway; data selection criteria are
being refined using the null suite. While the results from the first generation of the QUIET
experiment are competitive, a new generation of instruments with larger arrays, detectors
183
with greater sensitivity, low systematics and longer observations will be need to achieve the
sensitivity necessary to detect B-modes with r < 0.1.
184
APPENDIX A
MODULE ALGEBRA
For the following sections, let us redefine the detector diodes that are typically referred to as
[Q1, Q2, U 1, U 2] (describing the signals they measure in the ideal case) as [D1, D2, D3, D4].
Further, recall the Stokes parameters:
I = |L|2 + |R|2
Q = 2 Re(L? R)
U = ?2 Im(L? R)
V
= |L|2 ? |R|2 .
and the useful complex identities:
|A + B|2 = |A|2 + |B|2 � 2 Re(A? B)
(A? � B ? )(A ? B) = |A|2 ? |B|2 ? 2 i Im(A? B).
The two legs of the module are denoted by A & B. The inputs to the module are the left
and right circularly polarized components EL and ER of the incident radiation.
EA = EL = Ex + iEy
(A.1)
EB = ER = Ex ? iEy .
(A.2)
185
A.1
Unequal Gains
In the case of the ideal module, we assumed that the gain was equal in both legs of the
module. Now let?s consider the case gA 6= gB . Again, let us switch only the phase switch in
leg B.
EA
= gA (EL )
= gA (Ex + iEy )
EB = 眊B (ER ) = 眊B (Ex ? iEy ).
(A.3)
(A.4)
The hybrid couplers adds the signals from the two legs, the power splitters divide the RF
power in half and the detector diodes rectify the power giving the outputs:
D1 = |(EA + EB )|2 = |(gA EL � gB ER )|2
(A.5)
? E )2 )
= (|gA EL |2 + |gB ER |2 � 2gA gB Re(EL
R
(A.6)
2 + g 2 )(E 2 + E 2 ) � 2g g (E 2 ? E 2 )
= (gA
A B x
x
y
y
B
(A.7)
2 + g 2 )(E 2 + E 2 ) ? 2g g (E 2 ? E 2 )
D2 = |(EA ? EB )|2 = (gA
A B x
x
y
y
B
(A.8)
0 + iE 0 )|2 = |(g E � E ) + i(g E ? E )|2
D3 = |(EA
A L
R
A L
R
B
(A.9)
2 + g 2 )(E 2 + E 2 ) ? 2g g Re(E E ? )
= (gA
x y
A B
x
y
B
0 ? iE 0 )|2
D4 = |(EA
B
(A.10)
(A.11)
2 + g 2 )(E 2 + E 2 ) ? 2g g Re(E E ? ).
= (gA
x y
A B
x
y
B
(A.12)
Converting into Stokes parameters, the outputs of the four detector diodes can be written
as
186
2 + g 2 )I � 2g g Q
D1 = (gA
A B
B
(A.13)
2 + g 2 )I ? 2g g Q
D2 = (gA
A B
B
(A.14)
2 + g 2 )I ? 2g g U
D3 = (gA
A B
B
(A.15)
2 + g 2 )I � 2g g U.
D4 = (gA
A B
B
(A.16)
which reduce to:
1
D1DM D = gA gB Q
2
1
D2DM D = ? gA gB Q
2
1
D3DM D = ? gA gB U
2
1
D4DM D = gA gB U
2
(A.17)
(A.18)
(A.19)
(A.20)
(A.21)
and
1 2
2 )I
D1AV G = (gA
+ gB
8
1 2
2 )I
D2AV G = (gA
+ gB
8
1 2
2 )I
D3AV G = (gA
+ gB
8
1 2
2 )I
D4AV G = (gA
+ gB
8
(A.22)
(A.23)
(A.24)
(A.25)
(A.26)
when the signal are averaged or demodulated. When the data are demodulated in the
187
electronics (�5.4), the DC offset is removed and the signals are [+Q, ?Q, ?U, +U ] times
a gain factor for the four diodes respectively. Note that when gA = gB = g, we regain the
result for the ideal module. However, this doesn?t matter in Equation A.26; the gain factors
are multiplicative for the Q/U Stokes parameters.
Double Demodulation: One systematic effect, an imbalance in the phase switch transmission between the two phase switch states, can lead to leakage of the total power signal
I into the Q/U signals. This leakage can be eliminated by modulating the phase switch in
the other leg. In the ideal module case, we considered modulation of the phase switch in leg
B. In order to consider simultaneous modulation of the phase switch in leg A, let us denote
the two states of a single phase switch as ? or ?. The signal measured at the Q1 diode can is
defined as Q1AB = Q1?? if the phase switches are both in the ? state. Further let us consider
that in the ? state, the phase switches have a transmission of 1 (perfect transmission) but
in the ? state they have transmission of ?A,B where ? is close to one. Then the signal on
the Q1 diode, when the 4kHz switching in leg B is demodulated, would be
1 2
1
2 )I � 1 g g (1 + ? 2 )Q
(Q1?? ? Q1?? ) = (gB
)(1 ? ?B
B
2
4
2 A B
(A.27)
1 2
1
2 )I ? 1 g g ? (1 + ? 2 )Q
(Q1?? ? Q1?? ) = (gB
)(1 ? ?B
B
2
4
2 A B A
(A.28)
or
depending on the phase state of the phase switch in leg A. The I term no longer cancels when
the signal is demodulated at 4kHz. If the phase switch in leg A is modulated at a slower
frequency however, such as 50Hz, and the signal is demodulated again (difference Equations
2.24 and 2.23), the I term will cancel. The ?double-demodulated? signal, Q1DD will be:
1
Q1DD = gA gB (1 + ?A )(1 + ?B )Q
4
188
(A.29)
and I ? Q leakage will cancel. This can be extended to the other three diodes.
Phase Length Mismatch We also can consider the case of a phase length mismatch in
the legs of the modules. In this case the relative phase difference of ? between the two phase
states will add a multiplicative factor of ei? to one of the legs. Once again, only switching
the phase switch in leg B, we can write
EA
= gA (EL )
= gA (Ex + iEy )
EB = 眊B (ER ) = 眊B ei? (Ex ? iEy ).
(A.30)
(A.31)
Then the output signal on the detector diodes is
D1 = |(EA + EB )|2 = |(gA EL � gB ei? ER )|2
? + ei? E ? E )
= (|gA EL |2 + |ei? gB ER |2 � 2gA gB (ei? EL ER
L R
2 + g 2 )(I) � 2g g ( 1 Q(ei? + e?i? ) ? 1 U(ei? ? e?i? ))
= (gA
A B
B
2
2
1
1
2
2
= (gA + gB )(I) � 2gA gB ( Qcos(?) ? Usin(?))
2
2
1
2 + g 2 )(I) ? 2g g ( Ucos(?) ? 1 Qsin(?))
D2 = (gA
A B
B
2
2
1
2 + g 2 )(I) � 2g g ( Ucos(?) ? 1 Qsin(?))
= (gA
A B
B
2
2
1
1
2 + g 2 )(I) ? 2g g ( Qcos(?) ? Usin(?))
= (gA
A B
B
2
2
(A.32)
(A.33)
(A.34)
(A.35)
(A.36)
(A.37)
(A.38)
(A.39)
which reduce to 14 I when averaged and to the following when demodulated:
189
which reduce to:
1
D1DM D = gA gB (Qcos(?) + Usin(?))
2
1
D2DM D = ? gA gB (Ucos(?) ? Qsin(?))
2
1
D3DM D = ? gA gB (Ucos(?) ? Qsin(?))
2
1
D4DM D = gA gB (Qcos(?) + Usin(?))
2
(A.40)
(A.41)
(A.42)
(A.43)
(A.44)
Other Effects: Above I have presented three of the possible imperfections in the the
module signal processing. There are numerous others including, phase length mismatch
and transmission imbalance generated in the hybrid coupler, complex gain, differential loss
and cross talk between the legs of the module generated via imperfections in the OMT and
OMT/Module interface, and the fact the the frequency dependence of all module components. These effects are treated in [147, 148, 92, 149, 73, 77, 79].
190
APPENDIX B
FIRMWARE
This appendix summarizes the components of the QUIET Firmware, summarizing and supplementing the information found in [150] and describing later modifications made to it. The
QUIET Firmware can be divided into several large components or modules: VME interface,
clock generation and synchronization, data collection, housekeeping, and module biasing and
control. The direct input and output lines to the firmware (FPGA) which are not controlled
via interface with the VME crate computer are listed in Table B.1. The following sections
give detail to supplement the general descriptions of the firmware modules that are provided
in �5.4 and Tables B.2 ? B.4 provide the input and output signals to each module.
Table B.1: QUIET Firmware Input/Output Table. Signals which enter/leave the FPGA
without being processed by the VME I/O program described below are listed here.
Signal
From / To
Internal 20 MHz Clock
Oscillator on Master Board
Internal 16 MHz Clock
VME Crate Computer
External 10 MHz Clock TimeCodeReader via TCR Aux. Board
External 1 Hz Clock
TimeCodeReader via TCR Aux. Board
External Clock Mode
VME Crate Computer
Inputs
Backplane 800 kHz Clock
Master Board via VME Backplane
Backplane 1 Hz Clock
Master Board via VME Backplane
Backplane Clock Mode
VME Crate Computer
SDOUT[31..0]
32 ADC chips on Board
BUSY[31..0]
32 ADC chips Board
Master 800 kHz
VME Backplane (if Master Board)
Master 1 Hz
VME Backplane (if Master Board)
Outputs
SCLK[31..0]
32 ADC chips Board
CNVST[31..0]
32 ADC chips Board
191
B.1
VME I/O
? VME I/O controls the interface between the the user/control software and the other
firmware modules.
? It accepts requests for data transfer from the software and then raises the flag protecting
the memory block from being written to, and then reads out the data.
? It forwards on user-defined control signals and information to the appropriate firmware
modules including phase switch state, mask, bias values, housekeeping MUX, and clock
configuration (i.e. use external, backplane or internal clocks).
? It also forwards user-defined control values to LVDS bias interface, housekeeping and
phase state (but the functionality is only used on the Master ADC board)
? All boards digitize and store snapshot and 100Hz data for readout.
? Each ADC board is accessed via an address base that increments with card slot in the
VME crate:
Slot 0: 0 � 08000000
Slot 1: 0 � 10000000
Slot 2: 0 � 18000000
..
.
Slot 21: 0 � A8000000
? The addresses that are associated with readable/writable memory blocks within each
board?s FPGA are given in the section for each firmware module below.
192
B.2
Master Clock Generation
? Board can operate independently (for debugging) or synchronized with the other boards
by changing the input signal to Master Clock Generation that is used to generate the
firmware internal clocks.
? Address: 0 � 34 controls the use of clocking signals from the VME backplane (0 for
ignore, 1 for use).
? Boards can be designated as the ?master? ADC by adding a set of four jumpers to the
ADC board that connect the outputs ? master 800kHz and master 1Hz? to the VME
backplane.
? All boards, master & slave, accept the master 800kHz and master 1Hz signals to generate the rest of their clocking signals (4kHz, 100Hz, etc.)
? Address: 0 � 38 controls the use of clocking signals from an external source (0 for
ignore, 1 for use). This external clock signal is used by the ?master? ADC board. It
accepts the 10 MHz and 1 Hz Signals from the Time Code Reader which synchronize
the data collection timestamps with those on the telescope motor encoders.
? If neither external nor backplane clock inputs are available, the firmware defaults to
use its own internal 20MHz signal to generate other necessary clocks.
B.3
ADC
? The redundantly named ADC firmware module controls the ADC chips on the ADC
board.
? It uses clocking signals generated in Master Clock Generation, control the conversion
of the 32 possible channels of analog signals from the detector diodes of seven modules
193
(a single MAB)
? The data are sampled at 800 kHz.
? Each channel has a single digital line from each of the ADC chips. The data are
repackaged into a 1024-bit block (32, 32-bit words)
? Only the lower 18-bits are used (we are using 18-bit ADC 7674 chips), but the data
are stored as 32-bits words for simplicity of data processing as 32-bit signed integers
are necessary for the 100Hz, downsampled data that is created in the Data Streams
firmware module.
B.4
Housekeeping
1. Housekeeping Data is digitized on the housekeeping board and read out via a single
digital line which is multiplexed through a user-defined set of 12-bit MUX addresses.
2. The housekeeping values which are to be read out are user-selected. Any combination
between a sampling a single channel at 500Hz or switching between multiple channels,
sampling each at a lower frequency.
3. The MUXing is controlled by writing a 32-but value to Address 0 � 80. Bit 0 of the
value indicates whether to step through MUX addresses provided by the software or
sit at a specific value which is given in bits 1-10.
4. If the HK data is set to MUX through several values, the number of values is stored
at address 0 � 0c and the addresses are stored in a memory block at address 0 � 40000
as 32-bit words where only the lowest 12 bits are used.
5. The MUX is only changed during masked-out 800-kHz samples (at the rising edge
of the 4kHz phase-sw clock), and the digitizing and clocking out is done during the
194
following masked out block (the falling edge of the 4kHz clock).
6. Housekeeping data consists of 16-bit unsigned integers sampled at 500Hz.
7. The samples are buffered by the master ADC in 125-sample packets.
8. Data is stored as a 250-byte memory block at 0xD00000. The memory is divided into
two blocks (as in the radiometer timestreams). One is readout while data is written to
the other.
9. The memory blocks are then read out at 4Hz, synchronous to the 100Hz radiometer
timestreams data.
B.5
LVDS
? The MMIC, Phase-Switch, and Preamp Bias circuits are controlled by DACs on the
bias cards. LVDS signals passed from the Firmware on the ADC board are passed
along the electronics box backplane to the specific card and providing the values set.
? All desired bias values are first sent by the software to the LVDS firmware module and
stored in memory.
? Bias are set as 10-bit values stored as 32-bit words where:
Bias Value: stored in bits 0-9
DAC: stored in bits 10-14
Address: stored in bits 15-18
Card: stored in bits 19-23
? Once all bias addresses and values are stored, a second command is sent from the
software, to transfer the bias values from the FPGA internal memory to the addresses
specified.
195
? The bias memory block address is 0 � C00000.
B.6
Snapshot
? Snapshot data allows readout of a small amount of 800kHz data and is used for debugging.
? The data is sent to a single buffer that continuously records data until a?freeze? command is send. This disables writing to the buffer until the data is read out.
? The freeze command is a synchronous, so the position of the 1024 samples relative to
any of the downsampling clocks (mask, 4kHz, 100Hz, 50Hz etc.) is not constant.
? The 800kHz data is 18-bits wide, leaving 14 free bits as all data are stored in 32-bit
words.
? The 50Hz, 100Hz, 4kHz, and Mask clock signals are stored in channel 0, bits 27-31
? The 1024 samples are split into two memory blocks due to the FPGA 65536-byte
transfer block limit.
? Snapshot Address: 0 � 700000
? Freeze flag address: 0 � 30
B.7
Data Streams
? Accumulators are used to downsample the raw, 800kHz data to 100 Hz
? To create the average timestream, an accumulator sums 800kHz samples
? To create the average timestream, a second accumulate sums 800kHz samples while
the 4kHz demodulation clock is high and subtracts samples while the clock is low. The
196
demodulation clock is the same clock sent to the phase switch board to modulate the
signal (operate the phase switch)
? The quadrature timestream is created in the same way as the demodulated timestream
except that a quadrature 4kHz clock is used which is 90? out of phase with the 4kHz
demodulation clock.
? All three of the accumulators are disabled while the mask signal is high ? no samples
taken during phase switch transitions are retained.
? If no mask is applied, each 100Hz sample of all three timestreams (average, demodulated, quadrature) can include 8000 samples. With the final mask, only 6,880 are
retained.
? Storing a maximum of 8,000, 18-bit samples requires 31 bits, while the data are stored
as 32-bit signed (twos-compliment) integers for each of the 32 channels.
? In the demodulated stream, the numbers of unmasked samples during the high and low
4kHz clock states, the 1Hz clock and the 50Hz double demodulation clock are packed
into the 32 free bits (one from each channel).
? After the data are saved to disk, the masking fraction is used in the conversion from
ADC counts to Volts (Total from accumulator / (218 � N samples) and the 50Hz clock
is used to double demodulate the data.
? Data for each timestream are stored in 3200-byte memory blocks (32-bits words for
each 100 Hz sample, 32 words wide (1 per channel) and 25 samples deep)
? Addresses: 0�0000,0�1000,and 0�2000 for Demodulated, Average and Quadrature data respectively.
197
? There are two memory blocks allocated for each of the three data streams. One is
enabled for writing while the other is being read-out to disk.
? The data is read out at 4Hz
B.8
Blanking Mask
? There are 200, 800kHz samples in each 4kHz cycle.
? The blanking mask is 200-bits (0 or 1 depending on whether the sample should be
accepted or masked).
? It is user configurable and saved to memory in the FPGA in 8, 32-bit words.
? Mask Address: 0 � 200000
? The offset of this mask may be offset with respect to the 4 kHz clock to account for any
phase-lag in the transmission from the firmware on the ADC board to the actual phase
switch in the module (via the phase switch board). These delays are also accounted
for in the demodulation clock in the Data Streams module.
B.9
Phase Switching
? Each Phase switch board requires four signals (pckl0a, pckl0b, pckl1a, and pckl1b)
which drive the four phase switch diodes in each module.
? The phase switch diodes can be on (VCC), off (GND), or switching (clock signal).
? Two clocks are used to drive the phase switched: 4 kHz, and 50 Hz. The 90? out of
phase versions of these clocks are also provided (i.e. by applying a logical NOT to each
of the two clock signals from Master Clock Generation.
198
? The phase switch firmware module allows user-defined configurations. A MUXing
circuit is used to set each of the outputs to the phase switch board into any of the
configurations listed above.
? The phase state for the modules are chosen by sending a 32-bit word with each byte
defining the state of a line
? Address: 0 � 10,
199
Table B.2: QUIET Firmware Modules
Inputs
Module
Outputs
Internal 20 MHz Clock
Master 1 Hz
Master 800 kHz
Internal 16 MHz Clock
External 10 MHz Clock
40 MHz Clock
2 MHz Clock
External 1 Hz Clock
800 kHz Clock
External Clock Mode
Backplane 800 kHz Clock
20 kHz Clock
4 kHz Clock
Backplane 1 Hz Clock
Master Clock
Backplane Clock Mode
500 Hz Clock
Generation
100 Hz Clock
50 Hz Clock
1 Hz Clock
Internal Clock Locked
External Clock Locked
Clock Select [1..0]
Version[31..0]
VME data[31..0]
Address[23..2]
Channel Select [31..0]
HK MUX enabled
Average Data[31..0]
Demod Data[31..0]
mask enabled
Quadrature Data[31..0]
mask in[31..0]
HK MUX in[31..0]
4Hz Counter[31..0]
N MUX[31..0]
Snapshot Data[31..0]
Housekeeping Data[31..0]
HK MUX select[31..0]
lvds in[31..0]
lvds output[31..0]
lvds bias done
lvds send[31..0]
VME I/O
4 Hz Tick
4 Hz Clear
External 1 Hz
External Clock Mode
External Clock Locked
Backplane Clock Mode
Internal Clock Locked
lvds ps state[31..0]
vmewrite
lvds dac mask[31..0]
vmeas
lvds in enabled
vmeds
lvds send enabled
Quadrature clock enabled
4 Hz Clear
halt mode
200
Table B.3: QUIET Firmware Modules
Inputs
Module
Outputs
cnvclk
data block[1023..0]
SCLK[31..0]
800 kHz Clock
ADC
SDOUT[31..0]
CNVST[31..0]
CS[31..0]
BUSY[31..0]
data block[1023..0]
Average Data[31..0]
address[16..2]
Demod Data[31..0]
Quadrature Data[31..0]
mask
Quadrature Clock
1 Hz Clock
4 Hz Tick
50 Hz Clock
Data Streams
100 Hz Clock
4 kHz Clock
8 kHz Clock
k
800 kHz Clock
2 MHz Clock
cnvclk
vmeas
data block[1023..0]
Snapshot Data[31..0]
Addresst[16..2]
freeze
50 Hz Clock
4 kHz Clock
Snapshot
800 kHz Clock
cnvclk
mask
Quadrature Clock
vmeas
201
Table B.4: QUIET
Inputs
VCC
GND
4 kHz Clock
NOT 4 kHz Clock
50 Hz Clock
NOT 50 Hz Clock
lvds ps state[2..0]
lvds ps state[10..8]
lvds ps state[18..16]
lvds ps state[26..24]
mask in[31..0]
Quad Mask In[31..0]
4 kHz Clock
800 kHz Clock
20 MHz Clock
CNV Clock
Write Clock (vmeds AND Mask en)
quad wrt clk (vmeds AND quad mask en)
CNV Clock
Address[14..2]
lvds in[31..0]
lvds dac mask[31..0]
lvds send[31..0]
2 MHz Clock
vmeas
start send (lvds send en AND vmeds)
write clock (lvds in en AND vmeds)
HK MUX in[31..0]
HK MUX select[12..0]
N MUX select[31..0]
1 Hz Clock
500 Hz Clock
4 kHz Clock
2 MHz Clock
40 MHz Clock
mask
Address[9..2] (read addr)
Address[13..2] (write addr)
vmeas
write clock (hk mux enable AND vmeds)
Firmware Modules
Module
Outputs
pclk0a
pclk0b
pclk1a
pclk1b
Phase Switch
mask
Quadrature 4 kHz Clock
Blanking Mask
LVDS Control
202
Card Select[21..0]
lvds output[31..0]
lvds bias done
send clock
send bit
MUX address[31..0]
HK Data[31..0]
4 Hz Tick
hk cnv
hk dclk
Housekeeping
APPENDIX C
ADC NONLINEARITIES
The analog to digital conversion of the QUIET data is handled using an Analog Devices
7674 18bit, 800kSPS SAR1 chip. During preliminary Q-Band data analysis, excess noise
was discovered in the data that was traced to a nonlinearity in the transfer function of the
ADC chip caused by missing codes. Figure C.1 illustrates the effect. If the conversion were
perfect, a linear relationship is expected between the input voltage and the output (digital
code corresponding to the input voltage). Instead, there are missing codes in the conversion,
resulting in a discontinuity in the output (see panel a of Figure C.1).
While 800kHz data is collected and digitized, the downsampled and demodulated 100Hz
data stream is used for data analysis. The demodulated data is measuring the difference
between two phase states which each have slightly different voltage levels. If the the two
levels straddle a discontinuity, in can result in a ?jump? in the demodulated signal as shown
in panel b of Figure C.1. Further, there is noise inherent in the signal which will effectively
spread or smooth the discontinuity in the level shift.
Approximately 14% of the data are effected by this ?glitching? in the ADCs. As the
average voltage level (output in Figure C.1) of our time ordered data crosses a discontinuity,
the demodulated datastream (? output) will jump and then return to normal as the discontinuity (or glitch) is passed. This will appear as increased noise or (I ? Q/U) leakage in
the data. We can measure the glitch pattern, however, and correct it recovering most of the
data.
The glitches can be modeled as
F (x; ?) = x +
x?x
A
erf ( ? 0 )
2
2?
(C.1)
1. Successive Approximation Register (SAR) uses a binary search to determine the appropriate conversion
from a continuous analog signal to a discrete digital value
203
Figure C.1: Illustration of missing codes in the digital conversion of the data timestream
leading to discontinuities or ?glitches? in the data. Panel a: analog input vs. digital output
shows nonlinearity in the case of missing codes. Green vertical lines denote the voltage levels
in each of the two phase states of the data as measured at three average voltage levels. Panel
b: Discontinuity creates a ?jump? in the? output or demodulated signal. Panels c & d: noise
in the input signal (Gaussian distributions) ?smears? the signal producing the pattern noticed
in the actual QUIET data (see Figure C.3).
where A is the glitch height, x0 is the glitch location, and ? is the standard deviation
of the input signal. The heights (which can be positive or negative and of varying heights
depending on the missing codes) and spacing between the glitches are measured directly for
each channel 2 (76 in Q-Band and 360 in W-Band ), using an input signal that was swept
through the dynamic range of the ADC (� ). Figure C.2 shows the glitch pattern for a
single channel. The glitches are regularly spaced every 1024 counts (1023.95 � 12). Glitch
height vary from ? 6 ? 130礦 , but follow a regular pattern as shown in Figure C.2. Several
channels deviate from this pattern with wider but constant spacing or variations in glitch
height which necessitate individual corrections for each channel.
2. Here channel is defined as a single detector diode output for a single module.
204
Figure C.2: Demodulated vs. Average (Total Power) data for a single channel where the
input signal was swept through the voltage range of the ADC to map out the glitch pattern.
The glitch heights and positions are fit and used in the glitch correction algorithm. This is a
typical channel; most other channels share this glitch pattern. There are several exceptions,
however, so each channel must be fit separately.
The noise level of the raw 800kHz data (?), however, is more difficult to estimate. In
principle, it could measured directly, but the 800kHz data are not retained. The data are
digitally downsampled to 100Hz in the FPGA on each board and only the downsampled data
are written to disk. While the 800kHz noise level can be determined given the 100Hz noise
level, the filter function of the low pass filters on the preamplifier boards must be taken into
account since they would correlate the data. Further, the measurement of the 100Hz noise
level will be increased by the very glitching for which we are attempting to correct. The
process can further complicated by a single data set with voltage levels the cross multiple
glitches. Thus, we opted to used an iterative algorithm to determine the noise level and
glitch correction for each CES and channel. Details of the correction process are described
in [151, 152, 77].
205
Figure C.3 gives examples of glitching (or lack thereof) in three channels of the QBand data for a single CES. Since each module has a slightly different offset voltage, the
voltage levels of their average datastreams sit at slightly different levels and thus near or
far from different glitch positions. The blue points show the uncorrected 100Hz data stream
while the yellow point show the corrected data. A data selection criteria were established
based on the linearity of demodulated vs. average signal for the corrected data. Data with
residual non-linearity (indicating insufficient or imperfect correction) are eliminated from
the final data set as described in �2.1.
Figure C.3: Demodulated vs. Average (Total Power) data for three channels for a single CES.
Blue points show the 100Hz uncorrected data and the yellow points show the corrected data.
The left panel shows data with no glitching, while the center and right panels show glitches
and different locations. If the correction works the data should show a linear relationship.
206
APPENDIX D
DATA SELECTION CRITERIA
This appendix includes the database queries that selected the final data sets for the polarization (.1) and TT (.2) Q-Band analysis.  contains correspondence tables of the
the cross-correlation units for the temperature analysis which had a larger binning than the
polarization analysis.
D.1
Final Q-Band Polarization Cuts
Below is the mySQL query that selects the final data set used in the Q-Band polarization
analysis.1 Because of the amount of data and different criteria that were used for investigations of data quality, data selection and null tests, it was useful to develop several tables
of data quality statistics and a master table of existing CES. The data quality statistics are
described in �2 and the calculation of each statistic is found in [77]. Comments denoted
by green text and a hash mark.
CES are defined by a run id and a run subid: e.g. 128.0
SELECT DISTINCT
q19_scan.run_id, q19_scan.run_subid,
q19_timestream.module, q19_timestream.diode
Choose and join relevant data tables
FROM q19_typeb
NATURAL JOIN q19_scan
NATURAL JOIN q19_timestream
NATURAL JOIN q19_weather
NATURAL JOIN q19_ces_usable
1. N.B. This is an updated version of the query found in [77].
207
NATURAL JOIN q19_sun_spike
NATURAL JOIN q19_slopes_stats
Choose a patch.
The data base uses old nomenclature for the patches
Names based on patches chosen out of a much larger set of potential
patches evaluated.
The final names used in this thesis are noted in green.
Only one patch is evaluated at a time.
AND (q19_scan.object = ?patch2a?) # Patch CMB-1
# OR
# AND (q19_scan.object = ?patch4a?)
# Patch CMB-2
# AND (q19_scan.object = ?patch6a?)
# Patch CMB-3
# AND (q19_scan.object = ?patch7b?)
# Patch CMB-4
Baseline Cuts:
WHERE
(q19_ces_usable.usable)
AND (q19_scan.duration >= 1000.)
AND (q19_typeb.module < 16)
AND NOT (q19_typeb.module = 4 AND q19_typeb.diode = "Q1")
AND NOT (q19_typeb.module = 8 AND q19_typeb.diode = "U2")
AND NOT (q19_scan.run_id BETWEEN 329 AND 341)
AND NOT (q19_scan.run_id = 398)
AND NOT (q19_scan.run_id = 529 AND q19_scan.run_subid = 1)
AND NOT (q19_scan.run_id BETWEEN 563 AND 593)
AND NOT (((q19_scan.run_id = 632 AND q19_scan.run_subid = 4)
OR q19_scan.run_id BETWEEN 633 AND 635)
AND (q19_typeb.module BETWEEN 7 AND 9 OR q19_typeb.module = 12
OR q19_typeb.module = 13 OR q19_typeb.module = 16))
AND NOT (q19_scan.run_id = 654 AND q19_scan.run_subid = 0)
208
AND NOT (q19_scan.run_id = 759 AND q19_scan.run_subid = 0)
AND NOT (q19_scan.run_id = 937)
AND NOT (q19_scan.run_id = 951 AND q19_scan.run_subid = 0)
AND NOT (q19_scan.run_id BETWEEN 953 AND 955)
AND NOT (q19_scan.run_id = 980 AND q19_scan.run_subid = 0)
AND NOT (q19_scan.run_id = 1413 AND q19_scan.run_subid = 0)
Final Values for data selection criteria:
AND (q19_weather.tp_rms_10sec <= 0.15)
AND (q19_weather.tp_rms_10sec_95 <= 0.08)
AND FKNEE_CUT_15_5(q19_timestream.module, q19_timestream.diode,
q19_timestream.knee_frequency)
AND (q19_timestream.each_az_chisquare_below_1Hz <= 3.0)
AND (q19_timestream.each_az_chisquare_above_1Hz <= 2.5)
AND (q19_slopes_stats.five_min_max_raw <= 25)
AND (q19_timestream.sss_filtered_chisquare_nearscan <= 5)
AND (q19_timestream.glitch2_1sample <= 6.)
AND (q19_timestream.glitch2_100msec <= 6.)
AND (q19_timestream.glitch2_1sec <= 6.)
AND (q19_typeb.chisquare_demodav_corrected <= 10.)
AND (q19_sun_spike.has_spike = 0)
D.2
Final Q-Band Temperature Cuts
Below is the mySQL query that selects the final data set used in the Q-Band temperature
analysis.
209
CES are defined by a run id and a run subid: e.g. 128.0
SELECT DISTINCT
q19_scan.run_id, q19_scan.run_subid
Choose and join relevant data tables
FROM q19_typeb
NATURAL JOIN q19_scan
NATURAL JOIN q19_timestream
NATURAL JOIN q19_weather
NATURAL JOIN q19_ces_usable
NATURAL JOIN q19_sun_spike
NATURAL JOIN q19_slopes_stats
Baseline Cuts:
WHERE (q19_ces_usable.usable)
AND (q19_scan.duration >= 1000.)
AND (q19_typeb.module > 16)
AND (q19_typeb.diode = "Q1" OR q19_typeb.diode = "Q2")
AND NOT (q19_scan.run_id BETWEEN 329 AND 341)
AND NOT (q19_scan.run_id = 398)
AND NOT (q19_scan.run_id = 529 AND q19_scan.run_subid = 1)
AND NOT (q19_scan.run_id BETWEEN 563 AND 593)
AND NOT (q19_scan.run_id = 654 AND q19_scan.run_subid = 0)
AND NOT (q19_scan.run_id = 759 AND q19_scan.run_subid = 0)
AND NOT (q19_scan.run_id = 937)
AND NOT (q19_scan.run_id = 951 AND q19_scan.run_subid = 0)
AND NOT (q19_scan.run_id BETWEEN 953 AND 955)
AND NOT (q19_scan.run_id = 980 AND q19_scan.run_subid = 0)
210
AND NOT (q19_scan.run_id = 1413 AND q19_scan.run_subid = 0)
Choose a patch.
AND (q19_scan.object = ?patch2a?) # Patch CMB-1
# OR
# AND (q19_scan.object = ?patch4a?) # Patch CMB-2
# AND (q19_scan.object = ?patch6a?) # Patch CMB-3
# AND (q19_scan.object = ?patch7b?) # Patch CMB-4
Final Values for data selection criteria:
AND (q19_weather.tp_rms_10sec <= 0.15)
AND (q19_weather.tp_rms_10sec_95 <= 0.08)
AND (q19_timestream.each_az_chisquare_below_1Hz <= 3.0)
AND (q19_timestream.each_az_chisquare_above_1Hz <= 2.5)
AND (q19_slopes_stats.five_min_max_az_normalized <= 650)
AND (q19_timestream.sss_filtered_chisquare_nearscan <= 5)
AND (q19_timestream.glitch2_1sample <= 6.)
AND (q19_timestream.glitch2_100msec <= 6.)
AND (q19_timestream.glitch2_1sec <= 6.)
AND (q19_typeb.chisquare_demodav_corrected <= 10.)
AND (q19_sun_spike.has_spike = 0)
211
APPENDIX E
Q-BAND TEMPERATURE CES BINNING
For the temperature analysis, due to the need to have maps with sufficient cross-linking,
it was necessary to bin the data into larger cross-correlation units that included several
azimuth-deck (az-dk) bins. The data were binned into four MegaCES or MCES. The following table lists the MCES used in the temperature analysis and the az-dk bins that were
included in that MCES. There are different numbers of az-dk bins included in each MCES
because there are varying numbers of CES in each az-dk bin due to the details of patch
position during the season. An attempt was made to equalize the amount of data in each
MCES while maintaining a variety of array orientations to maximize cross-linking. Not all
az-dk bins are listed; some az-dk bins can be neglected since all data in that bin has been
cut due to bad data quality.
Table E.1: CES groupings into MCES for mapmaking
Azimuth-Deck Bins
Patch MCES ID
2000
0-3, 4-1, 4-2, 5-2, 5-4, 6-4, 8-2, 9-1
2001
0-4, 2-1, 2-3, 4-5, 7-2, 7-4, 8-1, 9-3, 9-4
CMB-1
2002
0-1, 0-2, 1-1, 2-2, 2-4, 4-4, 5-1, 6-3, 7-1, 7-3, 7-5, 8-3
2003
1-2, 1-4, 1-8, 2-5, 3-3, 3-4, 4-3, 5-3, 6-1, 6-2, 8-4, 9-2
4000
1-2, 1-4, 2-2, 6-1, 7-1, 7-2, 8-2, 8-4
4001
0-3, 1-8, 4-2, 5-1, 5-3, 6-5, 8-1, 8-3, 9-2
CMB-2
4002
0-2, 0-4, 2-3, 3-2, 3-3, 3-8, 6-4, 7-4, 7-8, 9-3
4003
1-1, 2-1, 3-4, 5-2, 5-4, 6-2, 7-3, 7-5, 8-5, 9-5
6000
1-3, 3-3, 3-8, 5-8, 6-1, 6-3
6001
1-1, 2-3, 3-1, 3-4, 5-4, 7-3
CMB-3
6002
1-4, 2-2, 2-4, 3-2, 4-2, 4-4
6003
1-2, 4-1, 4-3, 5-2, 5-3, 6-2, 6-4, 7-4
212
APPENDIX F
TT ITERATIVE MAP MAKER
For the temperature analysis, the data are binned into MCES that consist of several CES
as described in �5. The iterative map-making procedure for a differential temperature
measurement was established by [140]. Reproducing the derivation from Kusaka, 2010 [153]
the iterative map maker solution is extended to compensate for variable noise among the
CES combined into a single MCES in the temperature data analysis.1
Using the notations found in [140] and [154], we define:
A ? MT N?1 M
(F.1)
B ? MT N?1 d
(F.2)
where M(nt � npix ) , N(nt � nt ), and d(nt � 1) are the pointing matrix, TOD covariance
matrix, and the TOD, respectively, and nt and npix are the length of TOD and the number
of pixels specifying their dimensions. The solution for the maximum likelihood map making
is:
X = lim (A + I)?1 B
?0+
(F.3)
A solution for the iterative solver in in the simple case of N = I is given by [140] as:
Xn+1 = Xn + D?1 [B ? AXn ]
(F.4)
where D is a diagonal matrix whose elements are the number of observations at each pixel
i ), and the equivalent solution but in time order is:
(Nobs
1. This is likely the method used in [154].
213
Xn+1
=
+ d(t)]}
+ d(t)] + ?i,m(t) [Xn
?t {?i,p(t) [Xn
p(t)
m(t)
?t [?i,p(t) + ?i,m(t) ]
(F.5)
where p(t) and m(t) are the pixels where ?+horn? and ??horn? are looking at a given time
of t.
Formalism of QUIET: The purpose here is to write down the solution for N 6= I (method
of [154], not explicitly written out there). For simplicity, we constrain ourselves to the
case of QUIET, where N can be approximated by a diagonal (but not constant) matrix,
Ntt = ? 2 (t), and each row of M is (0,. . . , 0, +1/2, 0,. . . , 0, ?1/2, 0,. . . , 0)2 . In this case, we
define a diagonal matrix A?ii as 3
A?ii ?
1
4
1
X
p(t)=i, or
t?{
}
n(t)=i
? 2 (t)
(F.6)
The coefficient 1/4 is due to the definition of M. As we will discuss later, A? has the
same diagonal elements as A and thus is used as an approximate of A, which is the inverse
of the map noise covariance. Equation 4 is now rewritten as
X(n+1) = X(n) + A??1 [B ? AX(n) ]
(F.7)
The substitution of D by A? is optimal since
A??1 B ' A?1 B = X
(F.8)
A??1 AX(n) ' X(n)
(F.9)
2. The two non-zero elements are not �but �2 just because that is how the calibration is done.
3. One can easily confirm A? becomes D for N ? I and the elements of M are �
214
and thus
A??1 [B ? AX(n) ] ' X ? X(n)
(F.10)
The matrix A is calculated as
Aij =
X
(M T )it (N ?1 )tt Mtj
(F.11)
t
= A?ij ?
1
4
X
t?{p(t)=i ? n(t)=j}
1
1
?
2
? (t) 4
1
X
t?{p(t)=j ? n(t)=i}
? 2 (t)
(F.12)
Note that p(t) 6= n(t) for all t, and thus the second and third terms can be non-zero only
when i 6= j. Therefore,
X
(n)
Aij Xj
=
X
j
(n)
A?ij Xj
j
?
?
1?
(n)
Xn(t)
X
4?
t?{p(t)=i}
? 2 (t)
X
?
(n)
Xp(t) ?
t?{n(t)=i}
? 2 (t) ?
?
(F.13)
On the other hand,
Bi =
1
2
X
t?{p(t)=i}
1
d(t)
?
? 2 (t) 2
X
t?{n(t)=i}
d(t)
? 2 (t)
(F.14)
Substituting Equations (12) and (13) into Eq. (7), we obtain
(n+1)
Xi
=
(n)
1
1
4 ?t ? 2 (t) {?i,p(t) [Xn(t)
(n)
+ 2d(t)] + ?i,n(t) [Xp(t) ? 2d(t)]}
A?ii
215
(F.15)
APPENDIX G
NULL TESTS THRESHOLDS
G.1
Polarization Nulls Test Thresholds
Tables of the threshold values used for the null tests are given below. Tables are provided
for both the polarization and temperature data analyses for the final analysis configurations
and data selection criteria described in �2.
216
217
CES
CES
CES
Scan Period
TOD
TOD
Array orientation 45?
Array orientation 90?
Array orientation 180?
Scan cycle (x1.2 Hz)
Left vs. right moving scans
Accelerating vs. decelerating
Diode
Center frequencies [GHz]
Diode
Diode
Diode
CES
CES
CES
Modules
Modules
Modules
Modules
Modules
Modules
MAB A vs B + C
MAB B vs A + C
MAB C vs A + B
Central 7 vs. peripheral
Instrumental polarization
1/f knee frequencies
Q vs U diodes
Abrupt TP level shifts
Abrupt TP level shifts
Deck angle 30?
Deck angle 45?
Deck angle 90?
Database Value
Null Test
0-6
7-9
10,11,14,15
3,4,8-10,13,14
5,7-10,13-15
1-3,5-7,9,13
1.1, 1.2, 2.1, 2.2, 2.3, 2.4
3.1, 4.2, 4.3, 4.4, 5.4, 6.2
6.3, 6.4, 7.2, 7.3, 7.4, 9.2
9.3, 9.4, 10.1,10.2, 12.2
12.3, 13.2, 13.3, 13.4, 14.4
15.1,15.2,15.2,15.3
Q
0.3, 2.3, 3.2, 6.1, 6.4, 8.4, 9.2,
10.4, 12.3, 14.0, 14.1, 14.2, 14.3
30
-240,-150,30,120
-150,30,75
-180 to -135, -90 to -45
0 to 45, 90 to 135
-90 to 0, 90 to 180
-90 to 90
10s,20s,30s
Left moving half-scans
Accelerating
1st Half
2nd Half
other
others
others
-135 to -90, -45 to 0
45 to 90, 135 to 180
-180 to -90, 0 to 90
-180 to -90, 90 to 180
others
Right moving half-scans
Decelerating
. 7-15
0-6, 10,11,14,15
0-9, 12,13
0-3,6,7,11,12,15
1-4,6,11,12
4, 8, 10-12, 14,15
1.3, 1.4, 3.2, 3.3, 3.4, 4.1
5.1, 5.2, 5.3, 6.1, 7.1, 8.1
8.2, 8.3, 8.4, 9.1, 10.3
10.4, 11.1, 11.2, 11.3
11.4, 12.1, 12.4, 13.1
14.1, 14.2, 14.3
U
others
Table G.1. Polarization Null Tests Thresholds Part I
Table G.2: Polarization Null Tests Thresholds Part II
Null test
Type
Value
Patch rising vs. setting
CES
q19 scan.hour angle
vs. setting
Moon proximity
CES
q19 scan.moon theta
to the main beam
Far sidelobe elevation
CES
q19 scan.sidelobe el
high vs. low
Cryostat
CES
q19 housekeeping.
temperature
RQ17 temp p2t5 mean
Cryostat temperature
CES
q19 housekeeping.
changes
RQ17 temp p2t5 range
Electronics temperature
CES
q19 housekeeping.
mmic1 temp p3t6 mean
Electronics temperature
CES
q19 housekeeping.
change
mmic1 temp p3t6 range
Electronics temperature
q19 housekeeping.
change speed
enclosure temp zigzag fom
Ambient humidity
CES
q19 weather.humidity max
Scan synchronous
CESD
q19 timestream.
signals
scan synchronous signal
High frequency
CESD
q19 timestream.
excess (2?15 Hz)
chisquare 2Hz 15Hz
Average responsivity
CES
AVG(q19 timestream.fiducial gain)
(high vs. low)
Responsivity vs. Avg.
CESD
q19 timestream.fiducial gain
(high vs. low)
Weather 10-s
CES
q19 weather.tp rms 10sec
TP RMS 100%
Weather 10-s
CES
q19 weather.tp rms 10sec 95
TP RMS 95%
CES
ABS(q19 typeb.chisquare
Double-demod.
demodav uncorrected vs. TP data
- q19 typeb.chisquare
demodav corrected)
White noise
DIODE
uK sqrtsec median
amplitudes
1st vs. 2nd half of the season
CES
q19 scan.run id
218
Threshold
0
92.0?
28.5?
19.98 K
0.0536 K
24.63 C
0.321 C
0
31.4 %
0.7
3.0
2.34
gain mean
0.056
0.049
0.1
> 570
1000
Table G.3. Polarization Null Tests Thresholds Part III
Null Test
Type
Database Value
CMB-1
Elevation
High vs. low
Sun proximity
to the main beam
Far galactic sidelobe 1
Far galactic sidelobe 2
Ambient temperatures
Humidity Changes
Threshold
CMB-2 CMB-3
CMB-4
CES
q19 scan.elevation
63.0
63.0
59.0
59.0
CES
q19 scan.sun theta
125.0
88.0
79.0
79.0
CES
CES
CES
CES
q19 scan.sidelobe lat
q19 scan.sidelobe2 lat
q19 atm.air temp med
q19 weather.humidity diff
25.0
32.0
-3.7
6.5
17.0
32.0
-1.5
6.5
35.0
32.0
-1.5
6.5
44.0
15.0
-3.7
3.7
Table G.4. Thresholds for Temperature Null Tests where different than those for the
polarization null tests: Part I of II
Null Test
Database Value
1st Half
2nd Half
RQ17 vs. RQ18
RQ17Q1 vs. RQ18Q2
vs. RQ17Q2 vs. RQ18Q1
Q vs U diodes
Modules
Diode
17
17.1,18.4
18
17.4,18.1
Diode
Q
U
219
220
Electronics temperature
change
White noise amplitudes
CES
CES
CES
CES
CES
CES
CES
CES
CES
CES
CESD
CESD
CES
Elevation High vs. low [? ]
Sun proximity to the main beam [? ]
Moon proximity to the main beam [? ]
Far sidelobe elevation high vs. low [? ]
Far galactic sidelobe 1 [? ]
Far galactic sidelobe 2 [? ]
Ambient humidity [%]
Humidity Changes [%]
Weather 10-s TP RMS 100%
Weather 10-s TP RMS 95%
Scan synchronous signals
High frequency excess (2?15 Hz)
Cryostat
temperature
Cryostat temperature
changes
Electronics temperature
DIODE
CES
CES
CES
Type
Null Test
q19 scan.elevation
q19 scan.sun theta
q19 scan.moon theta
q19 scan.sidelobe el
q19 scan.sidelobe lat
q19 scan.sidelobe2 lat
q19 weather.humidity max
q19 weather.humidity diff
q19 weather.tp rms 10sec
q19 weather.tp rms 10sec 95
q19 timestream.scan synchronous signal
q19 timestream.chisquare 2Hz 15Hz
q19 housekeeping.
RQ17 temp p2t5 mean
q19 housekeeping.
RQ17 temp p2t5 range
q19 housekeeping.
mmic1 temp p3t6 mean
q19 housekeeping.
mmic1 temp p3t6 range
uK sqrtsec median
Database Value
726
0.26
24.38
0.04
66.0
125.7
78.4
35.6
26.6
35.0
24.85
4.77
0.054
0.048
1.37
1.24
19.94
CMB-1
726
0.33
24.79
0.038
63.8
116.5
94.5
25.9
?
30.7
25.2
4.45
0.055
0.049
1.20
1.33
19.65
726
0.33
24.69
0.075
58.9
87.4
95.2
?
?
?
18.0
3.79
0.055
0.048
1.78
1.20
19.92
Threshold
CMB-2 CMB-3
Table G.5. Thresholds for Temperature Null Tests where different than those for the
polarization null tests: Part II of II
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treated in [147, 148, 92, 149, 73, 77, 79].
190
APPENDIX B
FIRMWARE
This appendix summarizes the components of the QUIET Firmware, summarizing and supplementing the information found in [150] and describing later modifications made to it. The
QUIET Firmware can be divided into several large components or modules: VME interface,
clock generation and synchronization, data collection, housekeeping, and module biasing and
control. The direct input and output lines to the firmware (FPGA) which are not controlled
via interface with the VME crate computer are listed in Table B.1. The following sections
give detail to supplement the general descriptions of the firmware modules that are provided
in �5.4 and Tables B.2 ? B.4 provide the input and output signals to each module.
Table B.1: QUIET Firmware Input/Output Table. Signals which enter/leave the FPGA
without being processed by the VME I/O program described below are listed here.
Signal
From / To
Internal 20 MHz Clock
Oscillator on Master Board
Internal 16 MHz Clock
VME Crate Computer
External 10 MHz Clock TimeCodeReader via TCR Aux. Board
External 1 Hz Clock
TimeCodeReader via TCR Aux. Board
External Clock Mode
VME Crate Computer
Inputs
Backplane 800 kHz Clock
Master Board via VME Backplane
Backplane 1 Hz Clock
Master Board via VME Backplane
Backplane Clock Mode
VME Crate Computer
SDOUT[31..0]
32 ADC chips on Board
BUSY[31..0]
32 ADC chips Board
Master 800 kHz
VME Backplane (if Master Board)
Master 1 Hz
VME Backplane (if Master Board)
Outputs
SCLK[31..0]
32 ADC chips Board
CNVST[31..0]
32 ADC chips Board
191
B.1
VME I/O
? VME I/O controls the interface between the the user/control software and the other
firmware modules.
? It accepts requests for data transfer from the software and then raises the flag protecting
the memory block from being written to, and then reads out the data.
? It forwards on user-defined control signals and information to the appropriate firmware
modules including phase switch state, mask, bias values, housekeeping MUX, and clock
configuration (i.e. use external, backplane or internal clocks).
? It also forwards user-defined control values to LVDS bias interface, housekeeping and
phase state (but the functionality is only used on the Master ADC board)
? All boards digitize and store snapshot and 100Hz data for readout.
? Each ADC board is accessed via an address base that increments with card slot in the
VME crate:
Slot 0: 0 � 08000000
Slot 1: 0 � 10000000
Slot 2: 0 � 18000000
..
.
Slot 21: 0 � A8000000
? The addresses that are associated with readable/writable memory blocks within each
board?s FPGA are given in the section for each firmware module below.
192
B.2
Master Clock Generation
? Board can operate independently (for debugging) or synchronized with the other boards
by changing the input signal to Master Clock Generation that is used to generate the
firmware internal clocks.
? Address: 0 � 34 controls the use of clocking signals from the VME backplane (0 for
ignore, 1 for use).
? Boards can be designated as the ?master? ADC by adding a set of four jumpers to the
ADC board that connect the outputs ? master 800kHz and master 1Hz? to the VME
backplane.
? All boards, master & slave, accept the master 800kHz and master 1Hz signals to generate the rest of their clocking signals (4kHz, 100Hz, etc.)
? Address: 0 � 38 controls the use of clocking signals from an external source (0 for
ignore, 1 for use). This external clock signal is used by the ?master? ADC board. It
accepts the 10 MHz and 1 Hz Signals from the Time Code Reader which synchronize
the data collection timestamps with those on the telescope motor encoders.
? If neither external nor backplane clock inputs are available, the firmware defaults to
use its own internal 20MHz signal to generate other necessary clocks.
B.3
ADC
? The redundantly named ADC firmware module controls the ADC chips on the ADC
board.
? It uses clocking signals generated in Master Clock Generation, control the conversion
of the 32 possible channels of analog signals from the detector diodes of seven modules
193
(a single MAB)
? The data are sampled at 800 kHz.
? Each channel has a single digital line from each of the ADC chips. The data are
repackaged into a 1024-bit block (32, 32-bit words)
? Only the lower 18-bits are used (we are using 18-bit ADC 7674 chips), but the data
are stored as 32-bits words for simplicity of data processing as 32-bit signed integers
are necessary for the 100Hz, downsampled data that is created in the Data Streams
firmware module.
B.4
Housekeeping
1. Housekeeping Data is digitized on the housekeeping board and read out via a single
digital line which is multiplexed through a user-defined set of 12-bit MUX addresses.
2. The housekeeping values which are to be read out are user-selected. Any combination
between a sampling a single channel at 500Hz or switching between multiple channels,
sampling each at a lower frequency.
3. The MUXing is controlled by writing a 32-but value to Address 0 � 80. Bit 0 of the
value indicates whether to step through MUX addresses provided by the software or
sit at a specific value which is given in bits 1-10.
4. If the HK data is set to MUX through several values, the number of values is stored
at address 0 � 0c and the addresses are stored in a memory block at address 0 � 40000
as 32-bit words where only the lowest 12 bits are used.
5. The MUX is only changed during masked-out 800-kHz samples (at the rising edge
of the 4kHz phase-sw clock), and the digitizing and clocking out is done during the
194
following masked out block (the falling edge of the 4kHz clock).
6. Housekeeping data consists of 16-bit unsigned integers sampled at 500Hz.
7. The samples are buffered by the master ADC in 125-sample packets.
8. Data is stored as a 250-byte memory block at 0xD00000. The memory is divided into
two blocks (as in the radiometer timestreams). One is readout while data is written to
the other.
9. The memory blocks are then read out at 4Hz, synchronous to the 100Hz radiometer
timestreams data.
B.5
LVDS
? The MMIC, Phase-Switch, and Preamp Bias circuits are controlled by DACs on the
bias cards. LVDS signals passed from the Firmware on the ADC board are passed
along the electronics box backplane to the specific card and providing the values set.
? All desired bias values are first sent by the software to the LVDS firmware module and
stored in memory.
? Bias are set as 10-bit values stored as 32-bit words where:
Bias Value: stored in bits 0-9
DAC: stored in bits 10-14
Address: stored in bits 15-18
Card: stored in bits 19-23
? Once all bias addresses and values are stored, a second command is sent from the
software, to transfer the bias values from the FPGA internal memory to the addresses
specified.
195
? The bias memory block address is 0 � C00000.
B.6
Snapshot
? Snapshot data allows readout of a small amount of 800kHz data and is used for debugging.
? The data is sent to a single buffer that continuously records data until a?freeze? command is send. This disables writing to the buffer until the data is read out.
? The freeze command is a synchronous, so the position of the 1024 samples relative to
any of the downsampling clocks (mask, 4kHz, 100Hz, 50Hz etc.) is not constant.
? The 800kHz data is 18-bits wide, leaving 14 free bits as all data are stored in 32-bit
words.
? The 50Hz, 100Hz, 4kHz, and Mask clock signals are stored in channel 0, bits 27-31
? The 1024 samples are split into two memory blocks due to the FPGA 65536-byte
transfer block limit.
? Snapshot Address: 0 � 700000
? Freeze flag address: 0 � 30
B.7
Data Streams
? Accumulators are used to downsample the raw, 800kHz data to 100 Hz
? To create the average timestream, an accumulator sums 800kHz samples
? To create the average timestream, a second accumulate sums 800kHz samples while
the 4kHz demodulation clock is high and subtracts samples while the clock is low. The
196
demodulation clock is the same clock sent to the phase 
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