quad: a millimeter-wave polarimeter for...

QUAD: A MILLIMETER-WAVE POLARIMETER

FOR OBSERVATION OF THE

COSMIC MICROWAVE BACKGROUND RADIATION

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF PHYSICS

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

James R. Hinderks

August 2005

c© Copyright by James R. Hinderks 2005

All Rights Reserved

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I certify that I have read this dissertation and that, in my opinion, it

is fully adequate in scope and quality as a dissertation for the degree

of Doctor of Philosophy.

Prof. Sarah E. Church Principal Adviser




Prof. Giorgio Gratta




Prof. Steven Kahn

Approved for the University Committee on Graduate Studies.

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Abstract

This thesis describes the design and performance of the QUaD experiment and

presents some of its earliest results. QUaD is a millimeter-wavelength polarime-

ter designed for observing the Cosmic Microwave Background (CMB). QUaD was

commissioned at the MAPO observatory at the Amundsen-Scott South Pole Station

in the Austral Summer of 2004/2005, achieved first light in Feb 2005, and began

science observation in May.

QUaD observes the CMB with an array of 31 polarization-sensitive Neutron

Transmutation Doped (NTD) germanium bolometers split between two frequency

bands centered at 100 and 150 GHz. The telescope is a 2.6 m on-axis Cassegrain

design with beam sizes of 6.3′ and 4.2′ at the two respective observing frequencies.

The resolution and scan strategy are optimized to probe the CMB E-mode power

spectrum over a multipole range of 100 to 2500. The performance of the system has

been characterized with commissioning observations and a high signal-to-noise map

of the CMB temperature anisotropy has been made over a ∼ 50 square degree area.

CMB polarization anisotropies, only recently detected, promise a wealth of new

cosmological information. Their observation complements the many successful tem-

perature anisotropy measurements already performed, confirming our basic under-

standing of the early universe and leading to tighter constraints on cosmological

parameters. Furthermore, polarization observations provide a probe of structure

since the last scattering surface and promise unique constraints on inflation through

the imprint of relict gravitational radiation.

Acknowledgements

QUaD has been a collaborative effort since the beginning and I feel privileged to

have spent the past six years working with the talented group of scientists listed in

Table 1.3 – I have learned a great deal from each one of you. This holds especially

true for the Stanford QUaD team with whom I’ve spent innumerable hours in “the

lab.” And of course, building a telescope isn’t much good if nobody puts it to use

and keeps it in shape. So two gold stars to Robert “Do the Dew” Schwartz and Alan

“No Worries” Day for being the best winter-over crew imaginable.

Grad school has certainly been a long process. Throughout, Sarah has been a

terrific advisor and mentor, and has made so many opportunities available to me.

Thanks to the postdocs I worked with in my first two years at Stanford – Brian and

Byron – for teaching me so much about doing physics. Thanks to Keith for teaching

me a great deal about electronics, careful experimental technique, and about knowing

when to just kludge something together. Thanks to Mel for all the great discussions

on cosmology. Thanks to Brad, who was my fellow Church lab grad student for

many years. Working with you was always fun – whether we were in the lab or on

the summit of Mauna Kea. I’ll never forget learning how to install snow chains at

14,000’ or the night we nearly starved to death at South Point. And thanks to Ben

– who has been my partner in crime working on QUaD for the past four years – for

doing so much to make QUaD a success, and for being a great officemate and friend.

Over the years, our lab has been fortunate enough to have a steady supply of

top-quality undergraduates. Seebany, Judy, Marteen, Evan, Kapil, Elizabeth, Ali,

and Tess: thanks for all your hard work and for making lab so much fun. Particular

thanks go to Kapil for his invaluable CAD work on the focal plane and to Evan

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for his excellent senior thesis work on QUaD optical testing (and for his equally

excellent shirts). Also QUaD never would have made it to the Pole on time without

all the packing and shipping help from Tess, in the form of carpentry, manual labor,

chocolate chip cookies, and of course exploding foam.

Acknowledgement is also due to the great people of the Stanford Physics De-

partment who helped make QUaD a success. Thanks to Dana for her indispensable

organizational and administrative help. The extremely talented group of machinists

who actually built much of the QUaD receiver – John, Mehmet, Matt, and Karl-

heinz – deserve special recognition. And finally, thanks to Stewart, Joel, and Khoi

for keeping the Varian building running smoothly, dealing with our endless stream

of deliveries, and keeping the stock room filled with the assorted cable ties, resistors,

and other random bits that saved the day on many occasions.

A few more random words before wrapping this up. To Mike Z, thanks for the

inspirational music and all the cowbell – it was hot. To Angiola, thanks for letting

me try “one more test,” and for not leaving me on the floor by the water fountain. I

wish you hadn’t stolen that towel though. To Ben, thanks for your awesome Dremel

skills. To Cara, thanks for the jokes, the laughter, the offbeat news, and the stories

about Speedy. Thanks to Dave and Becky for introducing me to the Earthquakes, to

Hilton for always knowing where the free food was and to Phil for sending presents

to cheer us up at the South Pole. Special thanks to Sarah, Mel, and Ben for all your

helpful comments on this document. Best of luck to everyone continuing to work on

QUaD, especially Ed, the team’s newest member.

Finally, I arrive at the most important people – my family. Mom and Dad, thanks

for instilling in me a love of science and of learning. I owe everything to the two of

you. To my four amazing grandparents, thanks for all your love over the years. To

the Suns, thank you for welcoming me into your wonderful family, and in particular

thanks to Christina for providing me with a place to live over the last half year while

I wrote this dissertation. And finally to Stephanie: it must be true love when you’re

willing to spend weekend afternoons in the machine shop wearing safety goggles or

in the lab inhaling solder fumes just to be with your husband. Thanks for being the

best thing in my life.

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Contents

Acknowledgements vii

1 Introduction 1

1.1 Cosmology and the Cosmic Microwave Background . . . . . . . . . . 2

1.1.1 Origin and History of the CMB . . . . . . . . . . . . . . . . . 2

1.1.2 The Modern Cosmological Picture . . . . . . . . . . . . . . . . 3

1.1.3 CMB Temperature Anisotropies . . . . . . . . . . . . . . . . . 7

1.2 The Polarization of the CMB . . . . . . . . . . . . . . . . . . . . . . 12

1.2.1 Stokes Parameters . . . . . . . . . . . . . . . . . . . . . . . . 12

1.2.2 Origins and Characterization of CMB Polarization . . . . . . . 14

1.2.3 Existing Measurements . . . . . . . . . . . . . . . . . . . . . . 22

1.3 The QUaD Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.3.2 Science Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 Experiment Description 31

2.1 The South Pole Observing Site . . . . . . . . . . . . . . . . . . . . . 31

2.2 The DASI Mount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.3.2 Lenses and Cold Stop . . . . . . . . . . . . . . . . . . . . . . . 34

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2.3.3 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.3.4 Corrugated Feeds . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.3.5 Polarization Sensitive Bolometers . . . . . . . . . . . . . . . . 40

2.3.6 The Focal Plane . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.4 Cryogenics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.4.1 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.4.2 Sub-Kelvin Refrigerator . . . . . . . . . . . . . . . . . . . . . 48

2.4.3 The Science Core . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.4.4 Thermometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3 Readout Electronics 57

3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.1.1 Bias Generator . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.1.2 Load Resistor Boxes . . . . . . . . . . . . . . . . . . . . . . . 61

3.1.3 Focal Plane Wiring . . . . . . . . . . . . . . . . . . . . . . . . 63

3.1.4 JFET Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.1.5 Lockin Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.1.6 The Data Acquisition System . . . . . . . . . . . . . . . . . . 70

3.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.2.1 Functionality Tests . . . . . . . . . . . . . . . . . . . . . . . . 71

3.2.2 Noise Performance . . . . . . . . . . . . . . . . . . . . . . . . 77

3.2.3 Channel Capacitance . . . . . . . . . . . . . . . . . . . . . . . 85

3.2.4 Microphonics . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.2.5 Radio Frequency Interference . . . . . . . . . . . . . . . . . . 91

4 Receiver Characterization 93

4.1 Bolometer Characterization . . . . . . . . . . . . . . . . . . . . . . . 93

4.1.1 Bolometer Model . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.1.2 Load Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.2 Optical Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 100

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4.2.1 Optical Testbed . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.2.2 Spectral Bands . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.2.3 Optical Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.2.4 Responsivity and Time Constants . . . . . . . . . . . . . . . . 110

4.2.5 Cosmic Rays and Impulse Response . . . . . . . . . . . . . . . 113

4.3 Polarization Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.3.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

4.3.2 Derivation of the Expected Signal . . . . . . . . . . . . . . . . 120

4.3.3 The Measurement Setup . . . . . . . . . . . . . . . . . . . . . 123

4.3.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 124

5 Instrument Performance 131

5.1 Optical Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.1.1 Raster Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.1.2 Feed Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.1.3 Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.1.4 Time Constants . . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

5.2.1 Atmospheric Transmission . . . . . . . . . . . . . . . . . . . . 144

5.2.2 Routine Gain Calibration . . . . . . . . . . . . . . . . . . . . 149

5.2.3 Absolute Calibration . . . . . . . . . . . . . . . . . . . . . . . 155

5.3 Sensitivity and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.3.1 Optical Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.3.2 Noise Equivalent Power . . . . . . . . . . . . . . . . . . . . . . 163

5.3.3 NET and NEQ . . . . . . . . . . . . . . . . . . . . . . . . . . 174

6 First Observations 177

6.1 Survey Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

6.1.1 Field Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 177

6.1.2 Observing Strategy . . . . . . . . . . . . . . . . . . . . . . . . 179

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6.2 First Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

6.2.1 Temperature Maps . . . . . . . . . . . . . . . . . . . . . . . . 182

6.2.2 Polarization Maps . . . . . . . . . . . . . . . . . . . . . . . . . 190

6.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

A Focal Plane Temperature Control 197

B Commissioning QUaD 201

B.1 Receiver Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

B.2 Foam Cone Installation . . . . . . . . . . . . . . . . . . . . . . . . . . 202

B.3 Secondary Installation and Alignment . . . . . . . . . . . . . . . . . . 204

B.4 Ground Shield Extension . . . . . . . . . . . . . . . . . . . . . . . . . 205

B.5 Receiver Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

C Calibration Source Hardware 209

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List of Tables

1.1 QUaD key numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.2 QUaD timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.3 The QUaD collaboration . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.1 QUaD channel table . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.2 Warm electronics testing noise budget . . . . . . . . . . . . . . . . . . 82

3.3 Electronics noise budget . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.1 Bolometer parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.2 Average spectral band properties. . . . . . . . . . . . . . . . . . . . . 104

4.3 Average optical efficiencies . . . . . . . . . . . . . . . . . . . . . . . . 108

5.1 Measured beam parameters . . . . . . . . . . . . . . . . . . . . . . . 140

5.2 Estimated QUaD optical loading . . . . . . . . . . . . . . . . . . . . 160

6.1 Temperature map noise . . . . . . . . . . . . . . . . . . . . . . . . . . 187

6.2 Single-feed polarization map noise . . . . . . . . . . . . . . . . . . . . 190

6.3 Polarization map noise . . . . . . . . . . . . . . . . . . . . . . . . . . 192

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List of Figures

1.1 WMAP CMB temperature map . . . . . . . . . . . . . . . . . . . . . 4

1.2 Annotated CMB temperature power spectrum . . . . . . . . . . . . . 8

1.3 WMAP CMB temperature power spectrum . . . . . . . . . . . . . . . 9

1.4 Detector orientations for measuring Q and U . . . . . . . . . . . . . . 12

1.5 CMB polarization originates from anisotropic Thompson scattering . 14

1.6 Local quadrupole patterns . . . . . . . . . . . . . . . . . . . . . . . . 15

1.7 E and B Fourier modes . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.8 E and B hot spots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.9 Random E and B patterns . . . . . . . . . . . . . . . . . . . . . . . . 19

1.10 Predicted CMB power spectra . . . . . . . . . . . . . . . . . . . . . . 20

1.11 WMAP TE correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.12 Existing E-mode polarization measurements . . . . . . . . . . . . . . 23

1.13 Panoramic view of the QUaD telescope . . . . . . . . . . . . . . . . . 25

1.14 QUaD predicted E-mode spectrum . . . . . . . . . . . . . . . . . . . 28

1.15 QUaD predicted temperature spectrum . . . . . . . . . . . . . . . . . 29

2.1 QUaD general assembly . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2 QUaD optical path . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3 QUaD pixel schematic . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.4 Cold optics schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.5 Average spectral bands . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.6 Feed horns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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2.7 Feed horn beam pattern . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.8 PSB module and absorber . . . . . . . . . . . . . . . . . . . . . . . . 41

2.9 Pixel position and orientation . . . . . . . . . . . . . . . . . . . . . . 43

2.10 Horn and PSB mounting . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.11 The receiver core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.12 The QUaD cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.13 Three-stage fridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.14 Example fridge operation . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.15 A fridge cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.16 Focal plane CAD rendering . . . . . . . . . . . . . . . . . . . . . . . 52

2.17 Focal plane temperature . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.18 Installing the focal plane in the receiver . . . . . . . . . . . . . . . . . 56

3.1 Electronics overview schematic . . . . . . . . . . . . . . . . . . . . . . 57

3.2 Bias generator schematic . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.3 Cold electronics overview . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.4 Load resistor board . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.5 The focal plane bowl . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.6 JFET membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.7 JFET box CAD model . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.8 Lockin card schematic . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.9 Lockin amplifier box photo . . . . . . . . . . . . . . . . . . . . . . . . 68

3.10 Measured spectrum of bias generator . . . . . . . . . . . . . . . . . . 71

3.11 Lockin card filtering detail . . . . . . . . . . . . . . . . . . . . . . . . 72

3.12 Lockin 475 Hz LP filter measured response . . . . . . . . . . . . . . . 73

3.13 Lockin 20 Hz LP filter measured response . . . . . . . . . . . . . . . 74

3.14 Lockin 20 Hz LP filter measured response (impulse method) . . . . . 75

3.15 Electronics noise testing setup . . . . . . . . . . . . . . . . . . . . . . 77

3.16 Lockin box noise spectra . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.17 Amplifier noise vs. source resistance . . . . . . . . . . . . . . . . . . . 80

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3.18 Bias noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.19 Electronics stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.20 Bolometer readout including stray capacitance . . . . . . . . . . . . . 86

3.21 Measured QUaD channel capacitance . . . . . . . . . . . . . . . . . . 87

3.22 Attenuation resulting from stray capacitance . . . . . . . . . . . . . . 88

3.23 Microphonic response . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.24 Microphonic response . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.25 Warm RF filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.1 Bolometer thermal and electrical models . . . . . . . . . . . . . . . . 94

4.2 Load curves example . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.3 Bolometer resistance vs. temperature . . . . . . . . . . . . . . . . . . 97

4.4 Measuring Q from load curves . . . . . . . . . . . . . . . . . . . . . . 98

4.5 The QUaD optical testbed . . . . . . . . . . . . . . . . . . . . . . . . 102

4.6 Laboratory optical testing with QUaD . . . . . . . . . . . . . . . . . 103

4.7 QUaD spectral bands . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.8 Optical efficiency with loadcurves . . . . . . . . . . . . . . . . . . . . 106

4.9 Optical efficiency histograms . . . . . . . . . . . . . . . . . . . . . . . 109

4.10 Responsivity curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.11 Lab time constant measurements . . . . . . . . . . . . . . . . . . . . 112

4.12 Cosmic ray impulse response . . . . . . . . . . . . . . . . . . . . . . . 114

4.13 Model QUaD impulse response . . . . . . . . . . . . . . . . . . . . . 115

4.14 Aligning the polarizing grid for testing . . . . . . . . . . . . . . . . . 116

4.15 Polarizing grid mounted on receiver window . . . . . . . . . . . . . . 117

4.16 Polarization response from two horns . . . . . . . . . . . . . . . . . . 118

4.17 Measured PSB orientations . . . . . . . . . . . . . . . . . . . . . . . . 119

4.18 Measured PSB angle and orthogonality . . . . . . . . . . . . . . . . . 120

4.19 Measured cross-polar leakage . . . . . . . . . . . . . . . . . . . . . . . 121

4.20 Cross-polar leakage in QUaD vs. the testbed . . . . . . . . . . . . . . 126

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5.1 Azimuth encoder while mapping . . . . . . . . . . . . . . . . . . . . . 132

5.2 Telescope RA/DEC while raster mapping . . . . . . . . . . . . . . . . 133

5.3 Elevation jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.4 RCW38 maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.5 Measured feed positions . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.6 RCW38 from every feed . . . . . . . . . . . . . . . . . . . . . . . . . 138

5.7 Predicted beam pattern . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.8 Time constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.9 Skydip data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

5.10 QUaD tau vs. 350 micron tipper . . . . . . . . . . . . . . . . . . . . 145

5.11 Tau vs. time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.12 Calibration source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.13 Calibration source data . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.14 Elevation nod example . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.15 A/B ratios from three calibration techniques . . . . . . . . . . . . . . 154

5.16 dB/dT evaluated for QUaD bands . . . . . . . . . . . . . . . . . . . . 155

5.17 Receiver loading vs. time . . . . . . . . . . . . . . . . . . . . . . . . . 161

5.18 Receiver loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

5.19 NEP breakdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

5.20 Total NEP versus bias . . . . . . . . . . . . . . . . . . . . . . . . . . 167

5.21 Responsivity curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.22 Average responsivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.23 Atmospheric noise time-ordered data . . . . . . . . . . . . . . . . . . 170

5.24 Power spectrum of QUaD noise in NEP units . . . . . . . . . . . . . 172

5.25 NEP distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

5.26 NET distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

6.1 QUaD 2005 field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.2 Hit maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

6.3 Map filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

xviii

6.4 QUaD CMB temperature maps . . . . . . . . . . . . . . . . . . . . . 184

6.5 QUaD temperature maps compared with B2K and WMAP . . . . . . 185

6.6 Deck rotation jackknives . . . . . . . . . . . . . . . . . . . . . . . . . 189

6.7 Single-feed polarization maps . . . . . . . . . . . . . . . . . . . . . . 191

6.8 Stokes Q maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

6.9 Simulated Stokes Q maps . . . . . . . . . . . . . . . . . . . . . . . . 195

A.1 Focal plane temperature control schematic . . . . . . . . . . . . . . . 198

A.2 The effect of focal plane temperature control . . . . . . . . . . . . . . 199

B.1 Installing the foam cone . . . . . . . . . . . . . . . . . . . . . . . . . 203

B.2 Installing the receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

B.3 The receiver room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

xix

Chapter 1

Introduction

The Big Bang theory is the cornerstone of modern cosmology. It holds that the

universe began in an extremely hot, dense, and homogeneous state, and that it has

expanded into the cool, clumpy universe we observe today. An abundance of obser-

vations support this model. The first piece of evidence is Hubble’s 1929 discovery

that all galaxies appear to be receding from us with a recession velocity proportional

to distance. The next major piece of evidence came in the late 1940s when Gamow

showed that a hot Big Bang could explain the observed abundances of light elements

in the Universe. The strongest piece of evidence in support of the Big Bang, was

the 1965 discovery of a nearly uniform background glow of thermal radiation, now

known as the Cosmic Microwave Background (CMB).

Today, observations of the CMB are still providing some of the most fruitful data

in the field of observational cosmology. This introduction gives an overview of the

CMB, briefly describing its physical origin and observable properties. The chapter

concludes with a summary of QUaD, a recently fielded experiment that will advance

the state of the art in CMB observations. A detailed description of the design and

characterization of the QUaD experiment forms the bulk of this thesis.

1

2 CHAPTER 1. INTRODUCTION

1.1 Cosmology and the Cosmic Microwave Back-

ground

1.1.1 Origin and History of the CMB

Penzias and Wilson discovered the CMB while trying to determine the origin of an

unknown source of “noise” in a microwave radiometer at Bell Telephone Laborato-

ries in Holmdel, New Jersey [Penzias and Wilson, 1965]. They found what appeared

to be an isotropic background consistent with a thermal source at approximately

3 K. Systematic investigation ruled out a terrestrial source for this signal. Discus-

sion with other researchers – notably Dicke, Peebles, and Wilkinson at Princeton –

led to the realization that this was likely the CMB [Peebles, 1993]. Their pioneer-

ing observations led to Penzias and Wilson being awarded the 1978 Nobel Prize in

Physics.

The existence of a thermal background radiation at a few Kelvin as a consequence

of the Big Bang had been predicted as early as 1948 by Gamow. The reasoning is as

follows: several seconds after the Big Bang, the universe was composed of a dense

plasma of electrons, protons, and photons. Thompson scattering tightly coupled the

photons with the matter, maintaining thermal equilibrium as the universe expanded

and cooled. However, when the Universe was approximately 400,000 years old, it had

cooled sufficiently that the electrons and protons combined to form hydrogen atoms,

and Thompson scattering no longer coupled the photons to the matter. After this

event, known as recombination or decoupling, the photons free streamed, growing in

wavelength with the expanding Universe.

The CMB photons that we observe today have been travelling for approximately

14 billion years. During this journey, their wavelength has expanded by a factor

of one thousand leaving them in the microwave regime. Throughout the expansion,

they have maintained a thermal energy distribution with the temperature decreasing

as one over the expansion factor. Experiments during the late 1960s confirmed the

spectral shape and measured a temperature of a few Kelvin. The definitive spectral

1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND 3

measurement came from the FIRAS (Far Infrared Absolute Spectrophotometer) in-

strument onboard the COBE (Cosmic Background Explorer) satellite [Mather et al.,

1994]. The data give a superb fit to a blackbody spectrum with a temperature of

T0 = 2.726K. These CMB observations confirmed the basic picture of the the early

universe as a hot, dense plasma, providing tremendous support for the Big Bang

model.

The early universe was remarkably uniform, as evidenced by the isotropy of the

CMB. However, the structure that we see today in the form of clusters of galaxies

suggests that minute inhomogeneities must have existed even at the earliest times.

Measuring these tiny fluctuations was a great experimental challenge. In 1992, more

than 25 years after the first CMB observations, the DMR (Differential Microwave

Radiometers) instrument on the COBE satellite finally found anisotropies in the

CMB temperature at the low level of one part in 105 [Smoot et al., 1992]. A flurry

of experiments followed, measuring the anisotropies with higher angular resolution

and better sensitivity (although only over small regions of sky). The first-year data

release of the Wilkinson Microwave Anisotropy Probe (WMAP) satellite in 2003

marked another experimental milestone. The satellite produced all-sky maps at five

frequencies with sub-degree angular resolution. Figure 1.1 shows a map from one of

the frequency bands.

1.1.2 The Modern Cosmological Picture

Overview

Observations of the CMB, combined with evidence from other types of cosmological

observations, have led to a consistent description of the universe. The following list

summarizes the key tenets of the emerging cosmological picture:

Spatial Flatness The universe is “flat” which means that Euclidean geometry ap-

plies even on cosmological scales. This is in contrast to the “open” universe

models that were favored even a decade ago in which initially parallel beams of


Figure 1.1: CMB temperature anisotropies. This is the W band (94 GHz) all-skymap from the WMAP satellite [Bennett et al., 2003]. The red swath across themiddle is foreground emission from our Milky Way galaxy. Away from the Galacticplane, the structure is caused by anisotropies in the CMB. The characteristic sizesof the hot and cold spots leads to constraints on cosmological parameters.

light would eventually diverge. The strongest evidence for a flat universe comes

directly from measurements of the CMB temperature anisotropies [Spergel

et al., 2003].

Dark Matter Only a small fraction (∼ 10%) of the matter in the universe is nor-

mal, or baryonic. This means that the bulk is in an unknown form, termed

dark matter. The best constraints on the total matter content come from ob-

servations of large scale structure in the universe [Percival et al., 2002]. The

limit on the baryon fraction comes from microwave background observations

[Spergel et al., 2003].

Dark Energy The bulk (∼ 75%) of the energy density of the universe resides in

a completely unknown form termed dark energy. The dark energy appears to

be in the form of an energy field with negative pressure. If the pressure is less

than the negative of one third of the total energy density, then the theory of


general relativity predicts that the expansion of the universe should accelerate

with time, rather than decelerate. The most direct evidence for dark energy

comes from observations of high-redshift supernovae [Perlmutter et al., 1999,

Riess et al., 2001, Knop et al., 2003].

Inflation The theory of Inflation posits that the universe expanded by a factor of

∼ 1050 in the first ∼ 10−35 seconds after the Big Bang [Guth, 1981]. This rapid

initial expansion naturally resolves the following weaknesses with the standard

Big Bang model.

• The Flatness Problem - The Big Bang model offers no explanation as to

why the universe would have precisely the critical energy density required

for spatial flatness. In the inflationary model, the present-day horizon

only subtends a tiny fraction of the total universe. Over this limited

scale, the universe appears flat irrespective of curvature that may have

been present in the initial, pre-inflationary universe.

• The Horizon Problem - The isotropy of the CMB temperature on the

largest angular scales presents a problem for the standard Big Bang model.

These regions would not have been in causal contact prior to decoupling

and consequently would not have thermalized. In the inflationary sce-

nario, all these regions were in causal contact before the exponential ex-

pansion, explaining the uniform temperature we see today.

• The Monopole Problem - Particle physics predicts the existence of exotic

particles such as magnetic monopoles that are not observed today. The

rapid expansion of inflation allows these particles to have existed in the

pre-inflationary universe while explaining their scarcity today.

• The Origins of the Initial Perturbations - The Big Bang model postulates

that the anisotropies in the CMB (and the structure we observe in the

local universe) resulted from initial perturbations of the primordial plasma

on all spatial scales. Inflation naturally explains their origin – even the


largest began as tiny quantum fluctuations in the initial universe and were

stretched to cosmological scales during the period of rapid expansion.

Because of these explanations, inflation is an extremely attractive theory. Cur-

rently, however, very little is known about the nature of the inflaton field that

is believed to have driven such a rapid expansion. Further observations of

the CMB, especially its polarization, offer the best hope for elucidating this

mechanism.

Observable Properties of the CMB

The CMB has three observable properties:

• Frequency Spectrum - As previously discussed, the frequency spectrum of the

CMB has been measured to exquisite precision, and it has been found to be

the most pristine example of purely thermal radiation in the universe.

• Temperature Anisotropy - Since it has a thermal spectrum, the intensity of

the radiation can be characterized as a temperature at each point on the sky.

Analysis of the temperature distribution on the sky has led to tight constraints

on many of the cosmological parameters. More detail on this analysis will be

provided in the next subsection.

• Polarization Anisotropy - Observations have shown the CMB to be partially

polarized (Section 1.2.3). It is hoped that future measurements of the polar-

ization pattern on the sky by experiments such as QUaD will lead to tighter

constraints on the cosmological parameters by breaking degeneracies inherent

in the temperature spectrum alone. However, the ultimate goal of CMB polar-

ization studies is to observe and characterize the unique polarization imprint

predicted to arise from inflation. This signature is extremely faint, lying at

least several orders of magnitude below the already faint CMB temperature

anisotropies; however, the potential scientific reward is great. QUaD will cer-

tainly be only one of many experiments needed to fully realize it.


1.1.3 CMB Temperature Anisotropies

Anisotropies

Anisotropies in the CMB begin as density variations in the primordial plasma. Over-

dense regions tend to collapse under the influence of gravity. However, radiation

pressure from the tightly coupled photons resists the collapse. Competition between

these two forces results in oscillations in the plasma. After the photons decouple

at recombination, the radiation pressure is gone, the acoustic oscillations stop, and

the overdense regions collapse under gravity. The photons free-stream, with hotter

photons emanating from overdense regions and cooler photons from rarified regions.

Figure 1.1 shows an all-sky map of CMB temperature anisotropies from the 2003

data release of the WMAP satellite. This is the best measurement of the CMB

temperature anisotropies currently available. The random pattern confirms that

oscillations were present at all scales in the early universe; however, there is a char-

acteristic size to the hot/cold spots of roughly 1 where the temperature contrast is

greatest. This results from the largest mode that just had time to complete one rar-

efaction/compression cycle before decoupling. Smaller modes oscillate proportionally

faster, so a harmonic series of modes exist, each of which ends at a compression or

rarefaction. These show up on the sky as a series of preferred sizes to the hot/cold

spots.

The Power Spectrum

Structure in CMB maps is more conveniently discussed in terms of the angular power

spectrum. The power spectrum is found by making a spherical harmonic expansion

of the observed spatial temperature distribution as

T (θ, φ) =∞∑

=2

∑m=−

amYm(θ, φ) (1.1)


Figure 1.2: Example CMB Temperature power spectrum with the key features la-belled. (Figure courtesy of M. Bowden)

where the = 1 dipole term is omitted because the intrinsic CMB dipole is obscured

by the apparent dipole resulting from Earth’s motion with respect to the reference

frame defined by the CMB. For a given scale , the fluctuations are evenly distributed

among the available orientations m = −,− + 1, . . . , with no preferred direction.

The power at a given is then defined as an average over the 2 + 1 possible values

of m as

C ≡1

2 + 1

∑m=−

|am|2 =⟨|am|2

⟩. (1.2)

It is a property of the spherical harmonics that the zeros are spaced at the approxi-

mate interval ∆θ ≈ 180/ (see eg. Peebles [1980]). This associates an angular scale

with each value.

Figure 1.2 shows an example power spectrum with some of the key features

annotated. The most prominent feature is the series of peaks beginning around

∼ 200. These arise from the previously discussed modes of oscillation that are

extremal at decoupling. The first peak represents a mode that just had time to

maximally compress before decoupling. Peaks at increasing alternately correspond


Figure 1.3: The status of measurements of the CMB temperature anisotropy powerspectrum. This figure is from Bennett et al. [2003].

to modes that reached maximum rarefaction and compression. Above ∼ 1000, the

power is reduced as the angular scale of the fluctuations approaches the thickness

of the “surface” of last scatter. The region between ∼ 10 < < 200 corresponds

to modes that enter the horizon before decoupling, and begin collapsing but do not

reach maximal compression. Fluctuations on the largest angular scales ( <∼ 10) do

not enter the horizon and do not collapse. However, they still produce temperature

anisotropies (and thus non-zero power in the power spectrum) through the Sachs

Wolf effect. Here denser regions appear colder because photons that climb out of

their gravitational potential well appear redshifted. This gravitational redshift effect

occurs on all angular scales, reducing the effective temperature of the anisotropies.


Current Measurements

Figure 1.3 shows the current state of the art in CMB temperature measurements.

Below ∼ 800 the highest quality data comes from the first data release of the

WMAP satellite. This is an on-going all-sky survey at five frequency bands from 23

to 94 GHz. Several experiments have measured the high- region of the spectrum.

The two shown here are from CBI (Cosmic Background Imager), an interferom-

eter operating from Chile, and ACBAR (Arcminute Cosmology Bolometer Array

Receiver), a bolometer-based instrument observing from the South Pole.

Cosmological Parameters

Our knowledge of the Universe on its largest scale is given in terms of a small

number of measurable values known as cosmological parameters. The following lists

those that most influence the shape of the CMB power spectrum; these describe the

density, composition, and expansion rate of the universe.

• Ω0 - The total energy density of the universe in units of the critical density.

• h - The Hubble constant, in units of 100 km/s/Mpc.

• Ωb - The fractional density of baryonic matter in the universe.

• Ωm - The fractional density of matter (including baryonic and dark).

• ΩΛ - The fractional density of dark energy (note: ΩΛ + Ωm = Ω0).

The precise shape of the CMB power spectrum, in particular the location and

relative heights of the acoustic peaks, probes these parameters. For example, the

location of the first peak in space probes the horizon size at decoupling, measuring

the geometry of the universe on the largest possible scale. This directly leads to con-

straints on Ω0. As a second example, adding mass in the form of baryons (increasing

Ωb) allows the plasma to fall deeper into the potential wells before rebounding due


to photon pressure. This enhances the compressional (odd-numbered) peaks in the

power spectrum relative to the rarefactional (even-numbered) peaks.

Inflationary theories make predictions about the spatial power spectrum of the

primordial potential fluctuations that eventually give rise to the observed CMB

anisotropies. There are three possible types of metric perturbations that each evolve

separately:

Scalar modes correspond to the fluctuations in the gravitational potential that

give rise to the CMB temperature anisotropy power spectrum.

Vector modes arise from rotation motions in the plasma. They are not enhanced

by gravitational collapse and so are damped relative to scalar and tensor modes

as the universe expands. They are thus expected not to leave an observable

imprint on the CMB and will not be discussed further.

Tensor modes distort the metric in an analogous manner to a background of gravi-

tational radiation. These contribute to the CMB temperature and polarization

spectrum; however, their contribution to the temperature spectrum is swamped

by the scalar modes.

The following parameters describe the power spectrum of the initial perturbations:

• A - The amplitude of the scalar perturbations.

• ns - The spectral index of the scalar perturbation spectrum. The currently

favored value of ns = 1 describes a scale-invariant spectrum in which pertur-

bations of all wavelengths have equal power.

• dns/dlnk - This describes a “running” spectral index that varies with scale.

• r - The ratio of the amplitude of the tensor to the scalar perturbation spectrum.

Measuring these parameters constrains theories such as inflation that predict the

initial spectrum of perturbations. In particular, measurement of a non-zero value of


x

x y+x y-y

Q Detector U Detector

Figure 1.4: The geometry for Q and U detectors described in eqs. 1.7 and 1.8.

r provides a direct test of the inflationary model. Current observations limit r to be

less than 0.71 [Spergel et al., 2003], but no theoretical lower limit exists.

1.2 The Polarization of the CMB

1.2.1 Stokes Parameters

Incoherent, partially polarized radiation such as the CMB can be described by a set

of intensities known as the Stokes parameters. The total intensity of the radiation

is represented by I, which can be decomposed into unpolarized (Iup) and polarized

(Ip) components as

I = Iup + Ip. (1.3)

The degree of polarization, p, is defined as the ratio of the polarized intensity to the

total

p =Ip

I . (1.4)

For linear polarization, as is expected for the CMB, the two intensity quantities Qand U specify the angle, χ, of the electric field of the polarized radiation with respect

1.2. THE POLARIZATION OF THE CMB 13

to the locally-defined x axis as

Q = Ip cos 2χ, (1.5)

U = Ip sin 2χ. (1.6)

Experimentally, Q can be measured as the difference between the intensities mea-

sured by two orthogonal detectors aligned with the local x and y axes as

Q = 〈E2x〉 − 〈E2

y〉 ≡ Ix − Iy. (1.7)

Similarly, U can be measured by differencing detectors aligned with a set of axes

rotated by 45 (here denoted as the x + y and x − y axes) as

U = 〈E2x+y〉 − 〈E2

x−y〉 ≡ Ix+y − Ix−y. (1.8)

The total intensity, I is given by I = Ix + Iy = Ix+y + Ix−y. Figure 1.4 shows the

experimental setup to clarify the geometry used in eqs. 1.7 and 1.8. From, eqs. 1.5

and 1.6, a measurement of the parameters Q and U gives the polarized intensity and

angle as

I2p = Q2 + U2 and tan 2χ = U/Q. (1.9)

Measurements of the Stokes parameters I, Q, and U completely describe partially

linearly polarized radiation. Note that this treatment has omitted the effect of

the fourth Stokes parameter V, which quantifies the degree of circular polarization

present. Since this component is expected to be zero for the CMB, a number of

present experiments (including QUaD) are concentrating on measuring only I, Q,

and U .


e-IncidentCool radiation

IncidentWarm radiation

Partially polarizedscattered radiation

Figure 1.5: Temperature anisotropies lead to polarization via Thompson scattering.Warm radiation is incident on a free electron from the top and bottom while colderradiation comes from the sides. This corresponds to a quadrupole anisotropy in thelocal temperature distribution. The electron does not scatter radiation polarizedalong the line of sight (i.e., the polarization must be perpendicular to the outgoingwavevector) leading to a partially polarized outgoing wave.

1.2.2 Origins and Characterization of CMB Polarization

Origins

It was first noted in 1968 that anisotropies in the local temperature distribution as

seen by an electron at the surface of last scattering would lead to a partially polar-

ized CMB [Rees, 1968]. In the primordial plasma, electrons and photons interact

via Thompson scattering, which has a polarization-dependent cross section. The

differential Thompson cross section, dσT /dΩ, depends on the incident and outgoing

polarization directions (E and E ′ respectively) as dσT /dΩ ∝ |E · E ′|2. In particu-

lar, an electron does not scatter incident radiation polarized along the line of sight.

An isotropic distribution will thus result in an unpolarized scattered wave. How-

ever, a local quadrupole anisotropy, as illustrated in Figure 1.5, results in partial

polarization of the outgoing wave.

Due to the symmetry of the Thompson cross section, only the quadrupole moment

of the local temperature distribution (as seen by a free electron in the primordial


Figure 1.6: (left) An m = 0 pattern arises from a scalar perturbation. (right) Anm = 2 pattern arises from a tensor perturbation. See text for more explanation.Figures from Hu and White [1997].

plasma) leads to a net polarization. In terms of the spherical harmonics Y2,m, there

are three possible quadrupole patterns corresponding to m = 0, m = ±1, and

m = ±2. These patterns have physically distinct origins, arising from scalar, vector,

and tensor perturbations respectively [Hu and White, 1997].

Figure 1.6 (left) shows the local quadrupolar pattern resulting from a scalar per-

turbation. Here we consider a single plane wave (Fourier mode) of the gravitational

potential and a free electron in trough (cold region). Due to the Doppler boost

from its velocity, infalling matter from above and below emits warm radiation to-

ward the free electron in the center. The electron “sees” an azimuthally-symmetric

quadrupole in the local temperature distribution oriented parallel to the wave vector

of the Fourier mode. Analogously, an electron located on a crest sees a quadrupole

perpendicular to the wave vector. Figure 1.6 (right) shows the m = 2 pattern result-

ing from a tensor perturbation. An electron on the crest of a passing gravitational

wave sees space stretched in the plane of the perturbation, resulting in a qualitatively

different quadrupole pattern from the scalar case.

Thompson scattering converts these local temperature anisotropies into partially

polarized outgoing waves. In a coordinate system oriented along the wave vector of


the perturbation (up/down in Figure 1.6), the scalar mode results in a pattern that is

purely Stokes Q (since the polarization direction is always parallel or perpendicular

to the wave vector). The tensor mode results in a mixture of Q and U [Hu and

White, 1997].

The observed polarization pattern on the sky results from the superposition of

the signals from many different scalar and tensor modes with randomly oriented

wave vectors. Because of this superposition, the resulting pattern will contain both

Stokes Q and U components (even if only scalar modes were present). Because of

this mixing, a Stokes parameter description of the all-sky CMB polarization pattern

does not allow an easy separation of the contributions from scalar and tensor modes.

The following subsection introduces a mathematical tool, the E-B decomposition,

designed to accomplish just this.

E and B decomposition

Polarization direction is a spin-2 quantity since it is invariant under rotation by

180. The full CMB polarization pattern on the sky can be expanded in terms of

spin-2 spherical harmonics in an analogous manner as the temperature anisotropies

are expanded in scalar spherical harmonics. Like the scalar spherical harmonics,

the spin-2 harmonics form a complete and orthogonal basis. Linear combinations

of the spin-2 harmonics can be formed that transform as scalars. These are named

“E-modes” after the closely related curl-free pattern of a static electric field. Simi-

larly, linear combinations that transform as pseudo-scalars are named “B-modes” in

analogy with a divergence-free magnetic field. Any full-sky polarization map can be

expanded in terms of these E and B modes. The E/B decomposition was introduced

in Zaldarriaga and Seljak [1997] and Kamionkowski et al. [1997].1 Physically, this

decomposition is useful because scalar perturbations produce only E modes whereas

tensor perturbations produce both E and B modes.

1The latter use the notation of G (grad) and C (curl) modes rather than the now more commonE and B introduced by the former.


E Pattern B Pattern

Figure 1.7: Example E (left) and B (right) Fourier modes. In both cases, the wavevector lies along the x axis running horizontally.


E Pattern B Pattern

E Pattern B Pattern

Figure 1.8: E and B “hot spots” formed from the superposition of eight (properlyphased) plane waves of the form shown in Figure 1.7 evenly distributed in angle Notethat the E mode patterns are invariant under reflection whereas the B patterns arenot.


E Pattern B Pattern

Figure 1.9: E and B patterns generated from the superposition of pure Fourier modeswith random amplitude and wave vector.

Over a small region of sky, the flat sky approximation can be used and the spin-2

harmonics reduce to the mathematically simpler Fourier modes [Bunn, 2002]. Figure

1.7 shows representative E and B Fourier modes. For the E modes, the polarization

aligns parallel or perpendicular to the wave vector, like the polarization pattern

resulting from a scalar density perturbation. For B modes, the polarization aligns at

a 45 angle to the wave vector. A superposition of E and B modes is thus necessary

to create the polarization pattern generated by tensor perturbations.

Figure 1.8 shows how the Fourier modes can be superposed to create characteris-

tic E and B mode patterns. Note that like the scalar perturbations from which they

originate, the E patterns lack a handedness. In contrast, the gravitational waves

that create the B modes do have have a defined chirality which is reflected in the

resulting patterns. Figure 1.9 shows E and B patterns resulting from the superposi-

tion of random Fourier modes. Inspection of the two maps reveals the characteristic

“hotspot” patterns shown in Figure 1.8.


Figure 1.10: The four CMB power spectra for the standard cosmological model (solidlines). Annotations indicate physical processes responsible for key features. See textfor explanation. The dashed lines show the gravitational wave (tensor mode) con-tribution to the E and B spectra (note the roughly equal magnitude of the two)assuming a value of r = 0.1. The dashed-dotted line shows the gravitational lensingcontribution to the B mode spectrum which dominates at small angular scales. Dot-ted lines show the expected change in the spectra resulting from reionization (usingthe WMAP measured value of τ ∼ 0.17). Figure from Carlstrom et al. [2003] andderived using the CMBFAST computer code of Seljak and Zaldarriaga [1996].


The power spectra

The E/B decomposition results in a set of coefficients for the multipole expansion

of the polarization field, Em and Bm, analogous to the am of eq. 1.1 for the

temperature field. In analogy with eq. 1.2, six power spectra can be formed: CTT ,

CTE , CEE

, CBB , CTB

, CEB . The last two of these vanish since the B field has opposite

parity to the T and E fields. The remaining four spectra completely describe the

two-point statistics of the CMB. If, as predicted by inflation, the CMB is a Gaussian

random field then these four power spectra encode all the information that can be

obtained from the CMB.

Figure 1.10 shows simulated spectra. The E-mode spectrum is dominated by

contributions from scalar perturbations, but lies more than an order of magnitude

below the temperature spectrum. Acoustic oscillations in the primordial plasma

lead to peaks in the E-mode spectrum as in the temperature spectrum (Section

1.1.3). The two sets of peaks are out of phase because the polarization spectrum

depends on the velocity rather than the density of the plasma at the surface of last

scatter. The correlation expressed by the TE spectrum reinforces the common origin

(but complicated relationship) of the peaks in the T and E spectra. Gravitational

waves (tensor modes) are seen to contribute roughly equally to the E and B spectra,

as described in the previous subsection; however, in the E spectrum, the scalar

contribution dominates. Scalar perturbations do not generate B modes: hence the

emphasis on measuring the B spectrum for probing inflation.

Two sources of secondary anisotropy, reionization and gravitational lensing, effect

the shape of the spectra. Reionization occurred when a fraction of the neutral

hydrogen in the interstellar medium was ionized, likely due to emission from the

first generation of stars. The resulting free electrons lead to polarization via the

same mechanism of anisotropic Thompson scattering responsible for the primary

polarization signal. Reionization leads to power on large angular scales (low )

corresponding to the larger horizon size at this latter epoch. Gravitational lensing,

resulting from massive objects such as clusters of galaxies between us and the surface


Figure 1.11: The WMAP TE correlation. The lowest- data point is interpreted toresult from reionization. Figure from Bennett et al. [2003].

of last scattering, mix a small fraction of the polarized power between E and B

modes. This mixing occurs at small angular scales where it dominates the expected

B-mode signal. This sets a limit on the values of the tensor scalar ratio that could

be measured even with a perfect instrument of ∼ 10−4 [Knox and Song, 2002]. If the

relict tensor modes lie below this level, they cannot be measured from the CMB.

1.2.3 Existing Measurements

The temperature power spectrum is well-characterized over a broad range of angular

scales as described in Section 1.1.3 and shown in Figure 1.3. Polarization measure-

ments; however, are in their infancy. CMB polarization has been detected by five

experiments (in chronological order): DASI, WMAP, CBI, CAPMAP, and B2K.

The measurements are shown in Figure 1.12. No detection of B modes has yet been

made.


Figure 1.12: Existing E-mode polarization measurements. See text for data refer-ences. Thanks to M. Bowden for her assistance in preparing this plot.

• DASI - The Degree Angular Scale Interferometer was a 13-element interfer-

ometer operating in the frequency range of 26-36 GHz. DASI was located at

the South Pole and observed from 1999-2003. The DASI team made the first

detection of CMB polarization and the first measurement of the E-mode power

spectrum in their second season of operation (the first season as a polarimeter)

[Leitch et al., 2002a], [Kovac et al., 2002]. Polarization observation continued

for a total of three seasons resulting in the reduced error bars shown in Figure

1.12 [Leitch et al., 2005]. QUaD is the successor to the DASI experiment. It

is located at the same site and uses the same telescope mount (Section 1.3.1).

• WMAP - The radiometers onboard the WMAP satellite are inherently po-

larization sensitive. Figure 1.11 shows the measured TE correlation resulting


from the first season of observation [Kogut et al., 2003].

• CBI - The Cosmic Background Imager is an interferometer operating at 26-

36 GHz from the Chajnantor plateau in the Chilean Andes. It has a similar

design to DASI and shares many components, but its larger size allows higher

angular resolution. As with DASI, it initially observed the CMB temperature

and was later modified for polarization measurements. It made observations

with polarization sensitivity from 2002 through 2004 [Readhead et al., 2004].

• CAPMAP - The Cosmic Anisotropy Polarization MAPper is composed of

four 90 GHz correlation polarimeters observing from the Bell Laboratories 7

m telescope at Crawford Hill in Holmdel, NJ [Barkats et al., 2005].

• B2K - B2K was another flight of the successful BOOMERANG experiment

(Crill [2001], Lange et al. [2001]) upgraded with polarization sensitive bolome-

ters (PSBs) [Jones, 2005]. B2K observed the CMB with four 145 GHz PSBs

from an altitude of ∼ 35 km on an 11 day flight over Antarctica. The B2K

measurement of the E-mode spectrum is described in Montroy et al. [2005].

1.3 The QUaD Experiment

1.3.1 Overview

With the exception of CAPMAP, all existing measurements of the E-mode spec-

trum come from temperature experiments that were retrofit for polarization sensi-

tivity. The current data are broadly consistent with the prediction from the standard

cosmological model; however, much greater sensitivity is needed to confirm this in

detail. Further progress requires a new generation of experiments, designed from the

start as polarimeters.

Achieving first light in early 2005, QUaD is the first such experiment to come

online. The name reflects the merger between the DASI team and the former QUEST

1.3. THE QUAD EXPERIMENT 25

Figure 1.13: The QUaD telescope contained within the much larger ground shield.The 2005 winter telescope operator (“winter-over”), Robert Schwartz, sets the scale.

collaboration in 2003. At this time, DASI had recently completed a survey resulting

in the first detection of CMB polarization. The QUEST collaboration was developing

a state-of-the-art millimeter-wave polarimeter and optical system, but had not yet

built a telescope mount. The two groups combined their complementary hardware

by upgrading the DASI mount with the new receiver and chose the name QUaD

(QUEST and DASI) to reflect the merger.

The resulting instrument combines a focal plane array of 31 PSBs with an optical

system that was designed to minimize systematic effects in polarization observations.

QUaD observes in two frequency bands centered near 100 and 150 GHz which align

with windows in the atmospheric transmission function and lie near the minimum

of the expected polarized foreground contamination. The experiment is located at

the Geographic South Pole, the premier site for millimeter-wave observations.

Three tables in this section (1.1, 1.2, and 1.3), summarize the key instrument


Table 1.1: QUaD key numbers.

Primary diameter (mm) 2640Secondary diameter (mm) 450Frequencies (GHz) 100 150Bandwidths (%) 28 27Nominal beam sizes (arcmin) 4.2 6.3Pixels 12 19Available pixels 2005 season1 10 16Sensitivity2 (µK sec1/2) 350 380

1Non-functional pixels will be replaced in the 2005/2006 summer season.2The numbers quoted here are the NEQ per pixel. Section 5.3 defines NEQ and describes how

these numbers were obtained.

parameters, the time line of the experiment, and the people involved. Figure 1.13

shows an overhead, panoramic photograph of the experiment. The section concludes

with a summary of the science goals that we hope to accomplish during our multi-

year observing campaign.

1.3.2 Science Goals

EE Spectrum - QUaD will make the first precision measurement of the E-mode

power spectrum (Figure 1.14). Compared with existing measurements (Fig-

ure 1.12), a three-year QUaD observation will extend the -space coverage

by a factor of two above the recent B2K experiment and reduce the error

bars in this extended frequency range by an order of magnitude relative to

existing measurements from DASI and CBI. Previous measurements have de-

tected polarized power in the CMB at high significance. QUaD will be the

first experiment to convincingly measure the features in the spectrum. The

existence of acoustic peaks in the E-mode spectrum, if detected, will confirm

our understanding of the underlying mechanism generating CMB polarization.

1.3. THE QUAD EXPERIMENT 27

Measuring these spectral features is the primary QUaD science goal.

BB Spectrum - QUaD will place new upper limits on the power in B modes over a

large range of angular scales. A detection of B-modes caused by gravitational

lensing of E-modes may be possible.

Parameter Estimation - The E-mode measurement and B-mode limits place tighter

constraints on the values of cosmological parameters, especially the inflationary

parameters r and ns.

TT Spectrum - QUaD will measure the CMB temperature power spectrum at

high multipoles at two frequencies (Figure 1.15, left). Combining this with

data from ACBAR and CBI may help shed light on the origin of the excess

power seen above ∼ 2000 by CBI [Kuo et al., 2004], [Mason et al., 2003].

Table 1.2: QUaD timeline

1999 Initial concept

2000 ProposalInitial optical design

2001-2002 Optical design finalizedPrimary mirror manufacturedElectronics, focal plane, and cryostat design

2003 Laboratory testing of receiver componentsInstallation of primary mirror on DASI mount

Mar. 2004 Integration and laboratory testing of receiver

Nov. 2004 Commissioning at the South Pole

Feb. 2005 Engineering observations

May 2005 Science observations begin


Figure 1.14: QUaD predicted first-year EE power spectrum. The red points are fromthe first season of observation and the blue points from a three-year survey. Pointswithout error bars represent upper limits. Figure courtesy M. Bowden.

1.4 Thesis Outline

This thesis describes the QUaD instrument, with particular emphasis on the design

and characterization of the receiver. The following list summarizes the main topics

covered in each chapter.

Chapter 1: Introduction and science background

Chapter 2: Instrument description

Chapter 3: Readout electronics description and characterization

Chapter 4: Receiver characterization focusing on the results of laboratory testing

1.4. THESIS OUTLINE 29

Figure 1.15: Predicted QUaD first-year TT power spectrum (red) and three-yearresult (blue). Note that atmospheric 1/f noise limits temperature observation tosmaller angular scales than for polarization.

Chapter 5: Instrument performance based primarily on data from South Pole com-

missioning observations

Chapter 6: First-year survey description and preliminary data


Table 1.3: The QUaD collaboration: People, institutions, and the main institutionalresponsibilities during the design and commissioning phase. Currently, all institu-tions are taking part in the data analysis.

The QUaD Collaboration

Caltech / JPLA. E. Lange, J. J. Bock, J. Kovac

Detectors and JFET Modules

Cardiff University

W. K. Gear, P. A. R. Ade, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo,C. Tucker, M. ZemcovCryostat design, cryogenics, filters design, optical component design and manufac-ture

College de FranceK. M. Ganga

Simulations, software, and science support

National University of Ireland, MaynoothJ. A. Murphy, C. O’Sullivan, G. Cahill

Optical design and modelling

Stanford UniversityS. E. Church, M. Bowden, J. R. Hinderks, E. Kirby, B. A. Rusholme, K. ThompsonReceiver integration and characterization, focal plane design and manufacture, read-out electronics, optical testing

University of ChicagoJ. E. Carlstrom, C. Pryke, E. M. Leitch

Telescope and mount, data acquisition system, receiver installation, optical align-ment, and control system software

University of EdinburghA. N. Taylor, M. L. Brown, P. Castro

Software development and science support

The South PoleR. Schwartz, A. Day, C. Hammock

Telescope and receiver operation and maintenance.

Chapter 2

Experiment Description

This chapter provides a description of the QUaD experiment including the observing

site, the telescope mount, the optics and the cryogenics. Discussion of the readout

electronics (including both the cryogenic and room temperature subsystems) is de-

ferred until Chapter 3.

2.1 The South Pole Observing Site

QUaD is located at the Martin A. Pomerantz Observatory (MAPO), approximately

750 meters from the Geographic South Pole. The precise location (obtained from

a GPS receiver) is 4554’14.8”W, 8959’36.3”S at an elevation of 2785 m. The

observatory is part of the Amundsen-Scott South Pole Station, which is overseen by

the National Science Foundation’s Office of Polar Programs.

This site is unsurpassed for ground-based, millimeter-wave observations, [Lane,

1998, Lay and Halverson, 2000, Peterson et al., 2003, Bussmann et al., 2005]. The

winter precipitable water vapor averages only 0.26 mm due to the inland location,

the high altitude, and the extreme cold temperatures. The atmospheric conditions

are stable over long periods of time with minimal diurnal variation. The six month

“night” during the winter season allows for virtually uninterrupted observation. The

location near Earth’s axis permits deep integrations on small areas since the entire

31

32 CHAPTER 2. EXPERIMENT DESCRIPTION

Figure 2.1: The QUaD telescope (the QUEST receiver and the DASI mount).

southern celestial hemisphere is accessible all year.

2.2 The DASI Mount

The DASI mount provided a robust and stable platform for the successful Degree

Angular Scale Interferometer CMB experiment that observed from 1999 through

2003 [Leitch et al., 2002b]. An independent tripod structure supports the telescope

mount, isolating it from mechanical activity in the surrounding building. The room

just beneath the mount connects via an extension corridor with the MAPO labora-

tory. The entire area, including the interior of the mount itself (the receiver room),

is heated to provide a nearly room-temperature environment for the telescope and

receiver. This key feature meant that mechanical and electronic components of the

2.3. OPTICS 33

QUaD receiver did not have to be designed to cope with the extreme temperatures of

the Antarctic winter (average winter temperature ∼ −60 C). Additionally, it allows

nearly all maintenance and troubleshooting of the receiver and drive components,

including the daily cryogen refills, to be performed without donning the “extreme

cold weather gear” needed for outdoor activity.

The mount is an altitude-azimuth design, with absolute pointing and tracking

errors under 1′ RMS. An optical pointing camera combined with a frame grabber

are integrated with the data acquisition system (DAS). Daily observations of bright

stars keep the pointing model up to date. The entire face plate of the mount (which

supports the receiver and telescope optics) can rotate about the optical symmetry

axis. Termed “deck” rotation, this feature is critically necessary as it allows the

feeds to scan across the same patch of sky at different orientation angles. This

would otherwise be impossible at the South Pole site, since there is no natural sky

rotation. Figure 2.1 shows the QUaD receiver installed on the DASI mount.

2.3 Optics

2.3.1 Overview

The QUaD telescope uses an on-axis Cassegrain design that was partially based

on the COMPASS experiment [Farese et al., 2004, Piccirillo et al., 2002], including

an identically-designed primary mirror. QUaD also adopted COMPASS’s strat-

egy of supporting the secondary mirror with a transparent foam cone to avoid the

potentially-polarized scattering that would result from metal feed legs.

Figure 2.2 shows the QUaD optical path. The telescope collects incident radiation

and brings it to a focus inside the receiver where a pair of cryogenic reimaging lenses

couples the radiation onto the focal plane array of 31 polarization-sensitive pixels.

Optical elements inside the receiver reject unwanted radiation both spectrally (filters)

and spatially (feed horns and cold stop). Figure 2.4 shows the major optical elements

in the receiver.


Figure 2.2: (left) The QUaD optical path. (right) The foam cone encloses theprimary mirror and supports the secondary. The lenses and focal plane are containedin the cryogenically cooled receiver that mounts below the primary (see Figure 2.1).

Each of the 31 pixels is comprised of optical filters to determine the spectral

bandpass, a corrugated microwave feed horn and a pair of orthogonal polarization

sensitive bolometers (Figure 2.3). The PSBs absorb radiation polarized along their

axis of sensitivity and a thermistor detects the associated minute increase in tem-

perature.

To achieve the sensitivity necessary for detecting the faint CMB signal, the

bolometers must be cooled to sub-Kelvin temperatures. To this end, the QUaD

receiver is housed in a two-stage liquid nitrogen/liquid helium cryostat. Section 2.4

describes the cryogenic design of the receiver including the cryostat and the sub-

Kelvin refrigerator used to cool the bolometers to their operating temperature of

∼ 250 mK. The following sections detail the cryogenic optical components.

2.3.2 Lenses and Cold Stop

The two re-imaging lenses were made from high density polyethylene (HDPE) on

a CNC lathe in the Stanford Physics Machine shop. A proprietary anti-reflection

2.3. OPTICS 35

+

-

PSB Pair ReadoutIncident Radiation LP Filter

Feed

Throat(HP Filter)

V ~ Ix - Iy

x

y

2 2

Figure 2.3: Schematic of a QUaD pixel. A filter determines the high frequency edgeof the spectral bandpass, and the corrugated feed determines the beam pattern. Thenarrow waveguide throat section of the feed horn sets the low frequency band edge.The two orthogonal bolometers in the PSB pair each measure the intensity of theincident radiation along their axes of sensitivity (x and y). The readout differencesthe intensities, resulting in a signal proportional to the Stokes parameter Q = Ix−Iy.Note: the intensity signal from each detector is actually read out and stored. Thedifferencing happens in software during analysis.

coating was applied to both surfaces of the lenses by collaborators at the Univer-

sity of Cardiff. Both lenses are cooled with liquid helium to reduce their thermal

emission. Radiative loading combined with the long thermal path separating them

from the helium can results in an operating temperature of ∼ 10 K (thermodynamic

temperature).

The lenses serve two purposes. First, they decrease the F-number of the slow

beam off the secondary mirror. This reduces the physical size of the focal plane and

feed horns. Additionally, they form an image of the primary mirror between the

second lens and the focal plane, at the location labelled “4 K cold stop” in Figure

2.4.1 Two lenses were necessary to achieve a good focus at both the focal plane and

the cold stop.

A knife-edged aluminum aperture surrounds the image of the primary at the cold

stop. The underside of the knife-edge is blackened with carbon-loaded Stycast so as

to be absorbing [Bock, 1994]. To understand the operation of the cold stop, it is

1The original design also called for a rotating, cryogenic, half waveplate at the location ofthe cold stop to modulate the polarization signal at the detectors. Due to difficulties with themanufacture of the waveplate, it will not be used during the 2005 observing season.


Window (AR-coated UHMW PE)IR blocker

IR blocker

IR blocker

8 cm edge

12 cm edge

9 cm edge

7 cm edge

Band defining filters (see text)

Feed

PSB module

Camera lens (AR-coated HDPE)

Field lens (AR-coated HDPE)

4K cold stop

4K

77K

300K

500mK

250mK

Figure 2.4: The optical components in the receiver. The black lines to the leftillustrate the nested structure of thermal shielding.

useful to think of the system in reverse with the feed horns transmitting radiation.

The system is designed so that the main beam (down to -20 dB) of the feed horns

passes through the stop aperture while the sidelobes are absorbed by the blackened

knife edge. This results in a well-defined beam on the primary and prevents the pos-

sibly large and time-varying signal that could result if the sidelobes passed through

the rest of the optics and landed on a warm object such as the ground or the moon.

2.3.3 Filtering

Bolometers are inherently sensitive to a broad range of frequencies, so filtering is

needed to limit the response to the desired band. Figure 2.4 shows the filter chain

required to provide an accurate bandpass with very low out-of-band leaks. Filtering

is also required to reduce the radiation loading on the various cold stages.

The spectral bandpass for each feed is set using two different techniques. The

low frequency edge of the band is set by the waveguide throat section of the feedhorn

2.3. OPTICS 37

Figure 2.5: QUaD average spectral bands (red, blue), the South Pole atmospherictransmission (solid black), and the CMB spectrum (dashed black). The QUaD bandsare normalized in terms of absolute transmission per polarization; however, they havebeen scaled upwards by a factor of two for clarity on this plot.

(Section 2.3.4). The high-frequency band edge is set via low-pass filters mounted on

the front of each feed.

The two frequency bands were chosen to correspond with windows in the atmo-

spheric transmission function (see Figure 2.5). The upper edge of the 100 GHz band

is set around 110 GHz to avoid the 119 GHz Oxygen line. The 150 GHz band begins

above this line and cuts off around 170 GHz to avoid the 183 GHz water line. Table

4.2 lists the average band center frequency and bandwidth.

The low-pass filters are made from multiple layers of copper mesh sandwiched

between dielectric [Lee et al., 1996, Ade et al., 2002]. These resonant, metal mesh

filters leak power at the harmonics of their cutoff frequency; consequently, a stack


150 GHz

100 GHz

Figure 2.6: QUaD corrugated feeds, band-defining filters, and filter caps. The lengthof the 100 GHz (150 GHz) feed is 100 mm (102 mm), not including the filters andfilter cap.

of several filters with staggered cutoff frequencies is needed to completely block out-

of-band radiation. In QUaD, this is accomplished with three filters at 100 GHz

and with two at 150 GHz. The optimal filter stack for each frequency band was

determined through testing many different combinations (Section 4.2.1 and Kirby

[2004]).

Figure 2.6 shows the filters mounted in front of the feed horns. They are retained

by a thin-walled brass cap that slips over the feed and is held in place with aluminum

tape. A thin ring of indium is used to make a light seal between the filter cap and

the first filter. A beryllium-copper wavy washer provides thermal contact between

the filter stack and the feed horn, and compensates for any differential contraction

during cool down. The filters are symmetric and so are expected to have very low

cross-polar leakage (Section 4.3).2

2.3. OPTICS 39

Figure 2.7: QUaD 100 GHz feed horn beam pattern, predicted and measured. Thebeam measurement was made at NUI Maynooth and published in Cahill et al. [2004].

2.3.4 Corrugated Feeds

Feed horns are needed to efficiently couple radiation onto the bolometers. The beam

pattern of the feed determines the illumination pattern on the cold stop (and thus

primary mirror). Figure 2.7 shows the modelled and measured beam pattern of a

100 GHz feed. The beam width is chosen to give a -20dB edge taper roughly 12.5

from the beam center, corresponding to the edge of the cold stop and the primary

mirror. Since the far-field beam pattern is given by the Fourier transform of the

primary illumination, the edge taper is necessary to reduce the sidelobes of the

telescope beam on the sky.

QUaD uses corrugated feeds which are substantially more expensive than smoothed

walled feeds, but offer a number of advantages that outweigh their greater cost. The

λ/4 depth corrugations in the interior of the feeds change the boundary condition to

E = 0 along the walls (instead of the usual E‖ = 0). This produces an aperture field

2The effect of the filters on cross-polar leakage was roughly characterized during laboratoryoptical testing – no measurable change in cross-polar leakage was seen when filters were added orremoved from the chain.


distribution that closely approximates a Gaussian which results in low side lobes,

and a symmetric beam that preserves linear polarization through the feed structure.

The profiled shape of the feed allows for reduced physical length compared with a

conical feed with the same sidelobe levels.

The internal diameter of the feed reaches a minimum in a section known as

the throat. This forms a waveguide that acts as a high-pass filter allowing only

wavelengths below cutoff to propagate. The metal-mesh low-pass filters before the

feed ensure that only a single waveguide mode is transmitted. Higher-order modes

do not preserve linear polarization and are thus undesirable. The final section of the

horn flares out again to couple the radiation with the bolometer module.

The front end of the feeds was designed by collaborators at NUI Maynooth and

the back end, by collaborators at Caltech. Thomas Keating Ltd3 manufactured the

horns by electroforming copper onto aluminum mandrels that are later dissolved.

The horns are then gold-plated to prevent oxidation. The design and performance

of the QUaD feeds is described in Cahill et al. [2004].

2.3.5 Polarization Sensitive Bolometers

A polarization sensitive bolometer (PSB) is a specialized form of bolometric detector

that is only sensitive to radiation of a given linear polarization. This subsection

briefly describes the operation of a standard bolometer. Then, the specialized design

of the QUaD PSB is discussed.

The basic operation of a bolometric detector is extremely simple. Incident radi-

ation warms an absorber that is connected by a weak thermal link to a bath of fixed

temperature. A thermistor on the absorber changes electrical resistance in response

to the µK-level temperature fluctuations caused by varying incident optical power.

This operation is described quantitatively in Section 4.1.1.

A traditional bolometer has a solid absorber. Recent CMB temperature experi-

ments have employed “spider web” bolometers wherein most of the absorber is etched

3Station Mills, Billingshurst, West Sussex, RH14 9SH UK

2.3. OPTICS 41

(a) (b)

Figure 2.8: (a) A QUaD PSB module contains two PSBs in a protective housing. (b)Schematic representation of a single PSB absorber. The thermistor chip is shownred. A conducting ring surrounds the absorber (shown green) to provide betterthermal contact with the thermistor.

away leaving only a fine mesh [Bock et al., 1995, Mauskopf et al., 1997]. As long as

the spacing of the mesh is much less than a wavelength, absorption is unhindered.

The advantages of the mesh design are a reduced cross-section to cosmic rays and a

lower heat capacity which results in faster response times.

The polarization sensitive bolometer (PSB) takes this concept even further. In-

stead of a spider-web design, the absorber is a series of parallel wires. The resulting

structure absorbs radiation polarized along the grid axis while transmitting the or-

thogonal polarization. Figure 2.8 shows a schematic representation of a QUaD PSB.

The devices are fabricated from silicon-nitride (Si3N4) at the JPL Micro Devices

Laboratory using photolithography. The absorber is metalized by depositing a layer

of gold (∼ 120 A) over a thin layer of titanium (∼ 20 A). The thickness of the

metalization layer, the width of the conductors, and their spacing was optimized

for maximum coupling using numerical simulation and experimentation with trial

devices (at Caltech/JPL). Non-metalized legs run perpendicular to the conductors

for mechanical support. Tests with trial devices show that they have negligible

impact on the optical properties. [Jones et al., 2003]

A neutron transmutation doped (NTD) germanium thermistor, located on one


side of the absorber, measures temperature changes.4 A thermally conducting ring

surrounding the absorber helps couple the thermistor to the entire absorber area.

The absorber and thermistor are thermally isolated from the bath temperature with

the dominant conducting path being through three leads near the thermistor (shown

in green in Figure 2.8). The central lead also carries the electrical signal from the

thermistor. The two additional leads were designed to be laser ablated if decreased

thermal conductivity was desired. For QUaD, this operation was not performed.

For safe handling and mounting, the delicate PSBs are housed in brass modules.

In order to measure both linear polarizations, two PSBs in orthogonal orientations

are mounted in each module. They are spaced 60 µm apart to ensure that they sam-

ple the same electric field. The interior of the module forms a cylindrical integrating

cavity with the detectors located λ/4 from the back wall. The module design is

optimized to maximize absorption of incident radiation. Details of the absorber and

cavity design for the very similar PSBs used on the BOOMERANG 2K experiment

can be found in Jones et al. [2003].

2.3.6 The Focal Plane

The focal plane holds the feed horns and PSBs at the correct position inside the

cryostat and also thermally connects them to the sub-Kelvin refrigerator. The optical

design required that the feed horns lie on a curved surface in order to maintain a

sharp focus over the entire 1.5 field of view. The focal “plane” thus had to be a

curved surface which presented a substantial design and manufacturing challenge.

The entire assembly was modelled using the IDEAS CAD package and machined on

a 3-axis CNC mill in the Stanford Physics Department machine shop out of a solid

block of 6061 aluminum.5 The focal surface is a section of a sphere with radius of

4J. Beeman, www.haller-beeman.com5We chose to make the focal plane from aluminum rather than copper for several reasons. First,

aluminum is much less expensive, both for the raw material and machining costs. Since it requiredmore than a full-week of machine time, this was not a small matter. Secondly, aluminum resulted ina substantial savings in weight which is important both for mechanical and thermal considerations.We felt that these reasons outweighed the increased thermal conductivity of copper.

2.3. OPTICS 43

Figure 2.9: The position and orientation of the 31 pixels on the focal plane. Thelayout is composed of three regions: a central grouping of seven 150 GHz pixels(red), a middle ring of twelve 100 GHz pixels (blue), and an outer ring of twelve 150GHz pixels (red). Each feed is oriented along one of two possible angles (differingby 45) corresponding to Stokes Q and U . Although not shown in this figure, thefeeds for the two frequencies differ in diameter (Figure 2.6). Figure courtesy of B.Rusholme.

curvature 175 mm.6 The diameter (as would be measured with a ruler across the

top of the “bowl”) is 305 mm.

The PSBs reference and heatsink to the mounting flange on the rear of the

feedhorns but are attached to the focal plane bowl for mechanical stability. An

alignment pin sets their angular position. Mounting holes were drilled to allow

two different angular positions for each PSB, differing by 45 (allowing each pixel

to be changed between Stokes Q or U). Figure 2.9 shows the final positions and

orientations of the PSBs for the 2005 season.

6For ease of manufacture, the “bowl” is not a smooth surface, but rather is a staircase approx-imation made from a series of discrete steps. After the shape was roughed out, flats and mountingholes for the feed horns and PSBs were added. This machining was done on the same CNC machine,but this time the bowl was mounted on a rotary table which in turn was mounted on a sine table.For each feed position, the rotary table and sine table were set to the correct angles by hand.


Figure 2.10: The mounting arrangement for QUaD horns and PSB modules. Theprotruding bracket below the PSBs is to support the readout wiring.

The focal plane bowl provides the top surface of a cylindrical enclosure that

houses the PSB modules and the load resistor boards. This enclosure is necessary

to block stray infrared radiation from the PSB modules which are themselves not

light-tight. The load resistor boards (Section 3.1.2) mount vertically inside the

enclosure as shown in Figure 2.16. The inner surface of the enclosure, not including

the underside of the bowl, is blackened with carbon-loaded Stycast to reduce stray

light.

2.3. OPTICS 45

Figure 2.11: QUaD receiver core including the focal plane, JFET boxes, hexapod,and cold wiring. The feed horns and cylindrical light-tight bolometer enclosureare at 250 mK. Vespel legs stand this off from the intermediate temperature (∼400 mK) stage below. A Vespel hexapod isolates the intermediate stage from the4 K baseplate. Low thermal conductivity ribbon cable, wrapped around the Vespellegs, connects the focal plane to the JFET boxes on the bottom right and reads outthermometers located on both temperature stages. The cutout in the 4 K baseplateis for access to attach the focal plane to the fridge during installation (see Section2.4.3).


2.4 Cryogenics

The cryogenic systems, including the cryostat and the refrigerator, cool the focal

plane for optimum bolometer performance. The cryostat is designed so that the key

receiver components – the focal plane array and associated electronics – live in an

easily removable inner section known as the “science core” (Figure 2.11). A two-

tiered structure made from thin-walled Vespel tubing supports the roughly 10 kg

focal plane assembly and thermally isolates it from the 4 K baseplate. A compact

helium adsorption refrigerator, also attached to the baseplate, further cools the focal

plane to the operating temperature of ∼ 250 mK.

2.4.1 Cryostat

Figure 2.12: The QUaD cryostat. The liquid nitrogen tank and thermal shield isshown in blue. The liquid helium tank and shield is shown in red. The intermediatetemperature stage (orange) and thermal shield surround the focal plane. The twopurple rectangles underneath the focal plane are the JFET boxes.

The QUaD cyrostat was designed by collaborators at the University of Cardiff

and manufactured by AS Scientific.7 Figure 2.12 shows an exterior photograph of

7www.asscientific.co.uk

2.4. CRYOGENICS 47

the cryostat along with an annotated schematic highlighting the key components.

The upwards-looking cryostat attaches to the faceplate of the DASI mount. When

installed, the main body lies below the primary mirror in a small enclosure known as

the receiver room. A narrow snout, containing the two reimaging lenses protrudes

through the primary hole into the volume enclosed by the foam cone. Both of these

spaces are heated to nearly room temperature throughout the season meaning that

the cryostat did not have to be specially designed to deal with the extreme cold

of the South Pole winter. Figure B.3 shows the cryostat and associated readout

electronics mounted in the receiver room.

Within the cryostat, thin-walled aluminum shields surround each thermal stage.

For added insulation, each shield is wrapped with multi-layer super insulation (MLSI).

The focal plane itself is surrounded by a similar shield that is tied to the interme-

diate head of the sub-kelvin refrigerator, maintaining a temperature near 400 mK.

Filtered apertures on the top of each shield allow the optical signal to reach the focal

plane, while blocking out-of-band IR radiation.

The liquid cryogens are contained in concentric, toroidal tanks that surround

the science core. A G-10 truss structure supports the tanks, providing rigidity with

minimal thermal conductivity. Sections of thin-walled stainless steel bellows limit

the conductivity through the refill tubes. The volume of the two tanks is 35 L and

21 L for nitrogen and helium respectively. This results in maximum hold times of

roughly 2.5 and 1.5 days for the two stages. In practice, both tanks are refilled once

per day.

The refill tubes on the cryostat are inaccessible when it is installed in the DASI

mount. Fills are thus performed via two short extensions of flexible transfer line

that are attached to one of the fill tubes on each tank. These extension sections are

installed before mounting the cryostat. The additional fill tube in each tank serves

as a vent and also contains an electronic level gauge that monitors the cryogen

consumption.


2.4.2 Sub-Kelvin Refrigerator

Figure 2.13: The QUaD 3-stage fridge, mounted in the cryostat.

QUaD uses a three-stage adsorption refrigerator to cool the focal plane.8 Com-

pared with other sub-Kelvin coolers, adsorption refrigerators offer high cooling power

and simplicity of operation. The QUaD fridge provides two cold heads at different

temperatures. The first, known as the ultra cold head, provides the coldest tem-

perature in the system (approximately 250 mK). This cools the focal plane, feed

horns, load resistors and bolometers. The second fridge cold head, known as the in-

termediate head, operates at approximately 400 mK. Sinking all of the sub-K wiring

and the focal plane radiation shield to this stage reduces the thermal loading on the

ultra-cold stage, allowing colder temperatures to be reached.

8Chase Research Cryogenics, 35 Wostenholm Road, Sheffield S7 1LB, United Kingdom

2.4. CRYOGENICS 49

C

baseplate

pump

condensation point

still

LHe

Cold Head

Figure 2.14: A single-stage helium adsorption fridge. The upper chamber, known asthe pump, contains charcoal that adsorbs helium gas, lowering the vapor pressureabove the liquid helium contained in the still below. The two chambers operateat different temperatures and are only joined by a delicate section of thin-walledstainless steel tubing. When all of the liquid in the still has been adsorbed, thefridge needs to be cycled in order to continue cooling. The charcoal is warmed usingthe embedded heater resistor, driving off the adsorbed gas which liquifies at thecondensation point and collects in the still. The entire system is sealed and has nomoving parts.

Figure 2.14 illustrates the concept of operation for a simpler, single-stage fridge.

The basic physical principal is that the boiling point of a liquid can be reduced by

lowering the pressure of the vapor above it.9 Fridges of this design use charcoal to

pump a helium bath located in the still. When the liquid is entirely boiled away, the

fridge can no longer cool and it needs to be cycled. This is accomplished by passing

an electric current through heater resistors embedded in the charcoal. The charcoal

is warmed to approximately 50 K, driving off the helium vapor which liquifies and

collects in the still below.

A three-stage fridge, as is used in QUaD, combines one helium-4 stage with two

helium-3 stages. The helium-4 stage operates off of a 4 K baseplate and provides

the colder temperature necessary to condense helium-3 in the other two stages. The

two helium-3 stages provide the intermediate and ultra-cold temperatures used to

cool the focal plane to the sub-Kelvin temperature necessary for optimum bolometer

9This principle is familiar to anyone who has boiled water at a high altitude.


sensitivity. The intermediate stage is used to buffer the ultra-cold stage, reducing the

thermal loading on the latter. Bhatia et al. [2000] details the design and operation

of this type of fridge.

For minimum thermal resistance, the fridge is mounted directly on the underside

of the LHe tank. This allows for greater condensation efficiency during cycling and

a lower final temperature. The fridge is located on the opposite side of the cryostat

from the refilling tubes. The fill tubes must remain near the top of the cryostat

when the telescope is tipped down in elevation. Placing the fridge on the opposite

side ensures that the fridge base remains in contact with the liquid at all elevations.

The three stages combined with the large mass of the focal plane complicate the

fridge cycle. Optimizing the QUaD cycle for maximum hold time with minimum

cycle time required a considerable effort. The procedure that was developed allows

the QUaD fridge to be cycled in approximately four hours and results in hold times

for the ultra-cold and intermediate stages of 30 and 24 hours respectively. Figure

2.15 shows an example fridge cycle. The fridge cycling procedure is implemented

by a special-purpose computer that communicates with the main control system via

ethernet.10

10The fridge control system was designed by collaborators at the University of Cardiff.

2.4. CRYOGENICS 51

Pump Temperatures

0 1 2 3 4 5hours

0

10

20

30

40

50

60T

emp

(K)

He-4 pumpInter pumpUltra pump

Cold Heads

0 1 2 3 4 5hours

0

2

4

6

8

10

Tem

p (K

)

Intermediate headUltracold head

Figure 2.15: Fridge component temperatures during a typical cycle. The start timeof this graph is 30 MAY 2005 12:00 UTC.


Figure 2.16: Model of the focal plane and supporting structure. The 250 mK lightshield beneath the focal plane is not shown, allowing the load resistor boards to beseen. The support legs connecting the intermediate stage (400 mK ring) to the focalplane are also not shown in this rendering. Compare this model with the completedassembly in Figure 2.11.

2.4.3 The Science Core

The receiver “science core” is comprised of the focal plane and associated mechanical

and electrical support hardware. The entire structure is mounted to a removable

baseplate for easy installation into the cryostat. A two-tiered structure made from

thin-walled Vespel tubing (0.031” wall thickness) supports the 250 mK focal plane

and thermally isolates it from the 4 K baseplate. Cryogenic JFET amplifiers are

mounted to the baseplate beneath the focal plane. Figure 2.16 shows the main

components and Figure 2.11 shows the completed assembly.

The two-tiered focal plane support structure was designed for maximum rigidity

with minimal thermal conductivity. The supports in the first tier are arranged into

a hexapod structure that provides exceptional rigidity with a minimum of material.

The legs are 6” long and are made from type SP-1 Vespel. The second tier legs

2.4. CRYOGENICS 53

are shorter (1.75”) so that a simple vertical “table leg” arrangement of supports

provides adequate rigidity. The shorter legs are made from graphite-loaded Vespel

(SP-22) which provides a factor of two lower thermal conductivity than SP-1 over

the 400 mK to 250 mK temperature range. An aluminum ring, heat sunk to the

intermediate fridge temperature (∼ 400 mK), joins the two tiers. This two-tiered

design is necessary to reduce the thermal load on the fridge ultra-cold stage.

Both stages are attached to their respective cold heads on the fridge via flexible,

copper heat straps. The straps are made from braided OFHC shielding found in

high-quality speaker cable. Up to nine pieces of this braid are twisted together to

obtain a substantial cross sectional area (of order 1 cm2). For improved conductivity,

the straps were annealed prior to installation. Good coupling between the stages and

the cold heads improves the efficiency of the fridge cycle and decreases the operating

temperature of the focal plane.

The Vespel legs that support the focal plane provide natural attachment points

for the signal wiring that runs between the stages (Figure 2.11). All the non-

isothermal wiring in the cryostat is 44 SWG manganin (0.0032”) for low thermal

conductivity. These thin manganin wires are woven into a robust ribbon cable along

with nylon thread for strain relief.11 These cables are then routed along the Vespel

legs, wrapping them in a helical pattern to lengthen the thermal path.

Two additional Vespel legs were added running between the 400 mK ring and

the JFET modules in order to simplify the wiring along this critical signal path.

Rigidly fixing down these wires is extremely important for reducing susceptibility

to microphonic pickup. High-impedance bolometers are particularly vulnerable to

this form of pickup wherein mechanical vibration generates an electrical signal by

modulating the capacitance between the wiring and ground. In addition to being

tightly wrapped around the Vespel supports, the QUaD wiring was fixed down at

regular intervals using a combination of teflon tape and waxed lacing tape.

The structure was designed so that the predicted contributions to the fridge heat

11www.tekdata.co.uk


load were nearly equally divided between the Vespel mechanical supports and the

manganin signal wiring. The estimated load from these two sources is 50 µW and

0.4 µW on the fridge intermediate and ultra cold heads respectively. The total

loading on the two fridge stages is estimated from fridge load curves as roughly

400 µW and 3 µW .

The large focal plane mass (∼ 10 kg) combined with the thermally isolating

support structure results in a very long cool down period. Starting at room temper-

ature, both tanks are initially filled with liquid nitrogen. Approximately seven days

later, the focal plane reaches 100 K at which point the inner tank is filled with liquid

helium. Two more days of cooling are then required before the fridge can be cycled.

Actively-heated gas-gap heat switches speed up the cool down. These switches are

turned off once the focal plane temperature approaches 4 K.

2.4.4 Thermometry

Temperature sensors monitor all the major cryogenic components including the focal

plane, the fridge (pumps and cold heads), the baseplate, the snout (which holds the

two lenses), and the liquid nitrogen can. Silicon diode sensors (Lake Shore DT-470

series) are used for components that operate at or above liquid helium tempera-

tures.12 Germanium resistance temperature sensors, known as GRTs, monitor the

sub-Kelvin components (Lake Shore GR-200 series). Diodes mounted on the focal

plane are used to monitor the cool down from room temperature; however, their

large power dissipation (∼ 15 µW) necessitates that they be switched off during

sub-Kelvin operation. Both types of sensors are read out by the same custom hard-

ware that interfaces with the fridge. A separate system consisting of an AC-biased

thermistor, a heater resistor, and commercial controller maintains the focal plane

at a constant temperature during operation (Appendix A). Figure 2.17 shows the

temperature readout from the focal plane and intermediate stage GRT sensors over

the course of a routine CMB observation.

12Lake Shore Cryotronics, Inc. www.lakeshore.com

2.4. CRYOGENICS 55

Focal Plane

0 5 10 15 20hours

0.252

0.253

0.254

0.255

0.256

0.257

Tem

p (K

)

Intermediate Stage

0 5 10 15 20hours

0.420

0.425

0.430

0.435

Tem

p (K

)

Figure 2.17: Focal plane (top) and intermediate stage (bottom) temperature asmeasured by their respective GRT sensors during CMB observation on May 31,2005. The temperature control system maintains the focal plane at an extremelystable temperature. The four small positive spikes seen on the focal plane temper-ature occur during load curves (Sections 4.1 and 6.1.2) – at maximum bias, powerdissipation in the load resistors is sufficient to warm the focal plane above the setpoint. The intermediate stage temperature is not controlled. The two large stepchanges in temperature correspond to changes in the “deck” rotation angle whereinthe cryostat is rotated 60 about the optical axis (Section 6.1.2). The telescope wasat an elevation angle of roughly 45 while this data was taken.


Figure 2.18: (top) Inserting the science core into the cryostat. The cryostat is in-verted so that it is looking downwards. The entire 4 K baseplate plus focal planeassembly is lowered in. Extreme care is necessary during this operation to avoiddisturbing the fridge. (bottom) Once the 4 K baseplate is bolted in place, braidedOFHC copper heat straps are used to attach the ultra and intermediate fridge headsto the two thermal stages of the hexapod. Access is through a cutout in the 4 Kbaseplate which is then sealed with a thin aluminium plate. Kapton-coated rib-bon cables (shown unplugged here) connect the 55-pin hermetic connectors on thecryostat bottom (covered with red caps) to the JFET boxes.

Chapter 3

Readout Electronics

3.1 Description

+

-

ACBiasGen.

Amplification /Demodulation(gain = 100,000)

JFETBuffers

RL

RL

Reference freq.

Cold Electronics

to ADC

V+

V-

Figure 3.1: QUaD readout electronics overview. The variable resistor symbol denotesthe thermistor on the bolometer’s absorber.

The thermistor chip on each PSB registers the temperature change of the ab-

sorber arising from fluctuations in the incident optical power. The readout elec-

tronics measure the thermistor resistances while contributing minimal noise in the

frequency range of interest. The block diagram in Figure 3.1 overviews the compo-

nents involved.

The QUaD readout chain begins with the bias generator. This circuit makes two

57

58 CHAPTER 3. READOUT ELECTRONICS

Table 3.1: Breakdown, by function, of the 96 channels of readout.

62 Light detectors1

8 Dark detectors2

4 Resistors3

8 Shorts4

3 Thermistors5

11 Unused

1These channels readout the 31 PSB modules attached to feed horns. This is the sciencedata.

2These readout the four “dark” PSB modules. Rather than being attached to horns,these modules are blanked off. They serve as monitors of the focal plane temperature.

3These channels are attached to 10 MΩ metal film resistors mounted on the focal plane.They were intended as monitors of the electronics noise; however, failure to adequatelyrestrain their wiring has resulted in excess microphonic noise in these channels makingestimation of the electronics noise difficult.

4These channels are attached to low-impedance shorts. They serve as monitors of theJFET and warm amplifier noise (but not any noise from the bias). See Section 3.2.2.

5The thermistors are used to monitor the focal plane temperature (Appendix A).

sine waves, 180 degrees out of phase that are used to bias the bolometers. Each

bolometer is wired in series with two cold load resistors, forming a balanced bridge

circuit. The bridge is followed by two stages of amplification. First, cold JFET

followers located just below the focal plane buffer the high-impedance bolometer

signals, reducing their susceptibility to pickup and interference. The buffered signals

then exit the cryostat where they are further amplified and demodulated by warm

lockin amplifiers. In the final step of the chain, the data acquisition system digitizes

and stores the amplified and filtered signals. The following subsections describe the

detailed operation of each module.

The QUaD electronics, including the load resistors, JFETs, and warm lockin

amplifiers, provides 96 channels of readout. Most (62) of these are used for reading

out our science data from the 31 PSB modules attached to feed horns. An addi-

tional eight channels readout four “dark” PSB modules which are blanked off rather

3.1. DESCRIPTION 59

than being attached to feed horns. These serve as sensitive monitors of the focal

plane temperature. The remaining channels are divided between housekeeping and

monitoring tasks and spares. Table 3.1 lists the channel-by-channel breakdown and

Figure 3.3 outlines how the 96 channels are divided between the four load resistor

boards and two JFET boxes.

The basic AC bias readout scheme employed in QUaD has a long heritage

of successful use in CMB experiments including SuZIE [Holzapfel et al., 1997],

BOOMERANG [Crill et al., 2003], and BOLOCAM [Glenn et al., 1998]. The QUaD

design is based on these predecessors with improvements such as DC offset removal

and per-channel phase optimization that will be described in the following sections.

3.1.1 Bias Generator

TunableBP Filter

Multiplying

DAC

Multiplying

DAC

VoltageRef.

+10V

4 MHzcrystal

Digital amplitude control

Divideby N

Switch

+1 +1

+1

V+

V+

-1 -1

-1

V-

V-

Balanceoutput

q=10

to 100 GHz bolos

to 150 GHz bolos

Figure 3.2: QUaD bias generator.

This circuit generates two sine waves V+(t) = V0 sin(ω0t) and V−(t) = −V0 sin(ω0t).

Both the amplitude, V0, and the frequency, ω0 are adjustable under computer con-

trol. The sine wave output must be exceedingly stable in amplitude1 and reasonably

stable in frequency.2 A variety of different sine-wave generation circuits were tried

1Bias amplitude variations look like optical signals in the data and thus must be kept to anabsolute minimum.

2A standard 50 PPM / C quarts clock oscillator provides adequate stability.


and the architecture in Figure 3.2 was found to give the best results.

The frequency reference for this circuit is derived from a 4.0 MHz crystal os-

cillator. A programmable divide-by-N circuit slows the clock down to the desired

frequency range of approximately 40 - 250 Hz. The exact value of N is computer

controllable and the output frequency has a resolution of better than 0.1 Hz. This

digital square wave drives an analog switch that selects between two amplifiers of

precise gain equal to plus and minus one. A low-noise 10 V reference (AD587) pro-

vides the input to the switches. The switches and amplifiers are contained in an

AD630 modulator / demodulator chip.

The resulting 20 V peak-to-peak square wave is filtered by a second-order, state-

variable bandpass filter. The center frequency is adjustable under computer control

(12-bit resolution) and the quality factor is fixed at ten. During operation, the square

wave generator is set to the desired frequency and the bandpass filter center frequency

is tuned to maximize the output amplitude. The tuning procedure is controlled by

an on-board microcontroller and is fully autonomous. Tuning ensures that the peak

of the bandpass filter is aligned with the fundamental frequency of the square wave

minimizing sensitivity to any component drifts. By three times the fundamental

frequency, the response of the bandpass filter has fallen to approximately 0.0375

relative to the peak making the third harmonic power in the output sine wave at

nearly -40 dB (see Figure 3.10). This level of spectral purity is more than sufficient.

Finally, the sine wave is scaled by multiplying DACs to provide two outputs that

lie in the range 0 - 1.5 V and are adjustable with 12-bit resolution. After scaling, low-

noise buffers generate balanced outputs for driving the bolometer bridge circuit. One

output drives the 100 GHz bolometers and the other drives the 150 GHz channels.

The bias board provides several features not shown in Figure 3.2.

• A DC bias output mode is available. DC bias is essential for testing (especially

load curves). Since the bias is at 0 Hz, there is no reduction in bias current

or phase shift (Section 3.2.3). Switching between the AC and DC modes is

performed via the control system.

3.1. DESCRIPTION 61

Vdd

Vss

Focal Plane(300 mK)

JFET box(4K)

(300 K)

(77K)

V+

RL RL

S+ S- V-

FETS 150 FETS 100

LRB LRBLRB LRB

FP1 FP2 FP3 FP4

150 GHzsignals

100 GHzsignals

Bias /pwr

300K

4K

250mK

Figure 3.3: (left) A single channel from the QUaD bolometer readout chain. Thethermistor (on the bolometer) is shown as the variable resistor in the top center.(right) The subsystems in the cold readout chain. Each load resistor box handles24 channels of readout and each JFET box, 48.

• Bias amplitude monitors are provided for both channels. These consist of

lockin amplifiers on the board that demodulate the scaled AC bias signal. The

resulting DC signals (proportional to the bias amplitudes) are archived with

the rest of the bolometer data.

• Additional circuitry on the bias board provides the power supply voltages for

the JFET amplifiers.

3.1.2 Load Resistor Boxes

Figures 3.1 and 3.3 show the bridge circuit used for biasing the bolometers. For

maximum stability and rejection of electrical interference, the circuit is balanced

and fully differential. All the cold wiring is formed in twisted pairs. Due to thermal

considerations, no shielding is present.

The load resistors, labelled RL in the figures, have a value of 20 MΩ. They are

substantially larger than the nominal 5-10 MΩ bolometers and thus convert the con-

stant voltage bias into a quasi-constant current. Physically, they are on four circuit


Figure 3.4: QUaD load resistor board inside a protective box. Due to space con-straints, the boxes were not used in the final design.

boards mounted beneath the focal plane inside the light-tight box. To reduce John-

son noise, they are cooled to the same sub-Kelvin temperature as the bolometers.

The resistor dies are nichrome metal film on a silicon substrate manufactured by

Mini Systems, Inc.3 The dies were housed in surface mount packages by the Sun-

belt Microelectronics Division of Mini Systems. Each package contains 14 dies, 12

of which are used. Jumpers are provided so that the two spare dies can be easily

swapped in to replace defective dies. This, however, has not proved to be necessary.

Each load resistor board handles 24 readout channels. The boards themselves are

standard FR-4 and were manufactured by a local company, Sierra Proto Express.4

Despite the presence of fine traces (8 mil) and small vias (12 mil drill diameter) we

did not experience a single failure even after months of sub-Kelvin operation and

numerous thermal cycles.

Input and output from the board is via surface mount 51-way micro D connectors

manufactured by Cristek Interconnects Inc.5 Christek custom designed this connec-

tor for NASA JPL, and with the proper authorization allowed QUaD to use it. The

3www.mini-systems.biz4www.sierraprotoexpress.com5www.cristek.com

3.1. DESCRIPTION 63

long surface mount leads provide some springiness that takes up the differential con-

traction between the fiberglass board and its aluminum mounting structure. Due

to the three rows of fine-pitch leads, soldering these connectors with a conventional

iron is difficult if not impossible. We attached them using solder paste applied with

a custom made stencil from PCBexpress.6 The connectors and board were mounted

in a specially made jig while the solder paste was reflowed in an oven. This method

produced excellent results – after attaching over one dozen connectors there was not

a single faulty joint.

3.1.3 Focal Plane Wiring

Wiring within the focal plane assembly connects the load resistor boards to the

individual PSB modules. This high-impedance section of wiring is particularly vul-

nerable to microphonic pickup. To reduce the susceptibility to this pickup, relatively

stiff, large diameter wire was chosen for the focal plane.7 Furthermore, the wiring is

rigidly mounted to the backside of the focal plane using a combination of aluminum

tape and copper mesh. The mesh is screwed to the focal plane, clamping the wires

beneath. It is used in areas where the wiring is too bulky to be effectively fixed with

tape (see Figure 3.5). For neatness, and to reduce susceptibility to magnetic pickup,

the wiring is grouped into twisted quad bundles (one quad per PSB module).

6http://www.pcbexpress.com/essentials/index.php7Belden 28 AWG stranded copper with PTFE insulation


Figure 3.5: Two views of the focal plane bowl. (top) Top view showing the curvedbowl, feeds, and filters. (bottom) Bottom view showing the PSB modules andwiring.

3.1. DESCRIPTION 65

3.1.4 JFET Boxes

Figure 3.6: QUaD JFET box membrane (photo courtesy James Bock, JPL).

The high-impedence bolometer signals are carried from the focal plane to the

cold JFET amplifiers located on the 4 K baseplate beneath. This short section of

low thermal conductivity manganin wiring is routed along the Vespel support legs

of the science core (Section 2.4.3). The JFETs buffer these signals, lowering their

impedance which makes them far less susceptible to interference. The roughly 2 m

of low-impedance wiring downstream of the JFETS (leading to the warm lockin

amplifiers) does not need to be routed or tied down as carefully.

In order to keep the JFETs as physically close as possible to the detectors, they

are mounted to the 4 K plate just below the focal plane. The transistors themselves,

however, cannot operate below about 50 K and have a minimum of noise around

120 K. This disparity in temperature between the mounting plate and the desired

operating temperature presents a design challenge.

The JFET boxes used in QUaD (designed and manufactured at NASA JPL)

elegantly solve this problem.8 Bare JFET dies9 are mounted on a silicon nitride

8These boxes were designed at NASA JPL for the Spire satellite mission.9Siliconix U401


Figure 3.7: QUaD JFET box CAD model (image courtesy James Bock, JPL).Fromfront to back, the box is roughly 10 cm long.

membrane that is supported by the wires carrying the input and output signals

(Figure 3.6). These wires are formed by lithography and have low thermal conduc-

tivity (∼ 0.5 µW/K) due to their small cross section. The power dissipation in the

transistors themselves is sufficient to warm the membrane to the desired temper-

ature. Each membrane contains 24 dual-matched JFET pairs (48 transistors) and

dissipates approximately 6.5 mW of power. Heater resistors are provided to warm

the membrane at startup, but are not used during normal operation. In addition to

being thermally efficient, this design results in JFET boxes that are very compact

(see the model in Figure 3.7).

Internally, the JFETS are wired as source followers as shown in Figure 3.1 with

a gain of around 0.99. Each bolometer is buffered by a matched transistor pair

contained on the same die. Any drifts in source voltage due to changes in baseplate

temperature result in a common-mode change in the output signal that is rejected

by the downstream electronics.10

10This is extremely important for DC-biased testing with QUaD. In the AC-biased mode, slowdrifts are always rejected by the demodulation process. However, the balanced bridge design with

3.1. DESCRIPTION 67

3.1.5 Lockin Amplifiers

++

--

SquareWaveDemod.

BP Filterx5

LP FilterLP Filter

SwitchSwitch

Preampx100

Offsetremovalx100

DACPhaseDelayReference freq. in

IN+

OUT+

OUT-

IN-

+1

-1

Preampx100

“Preamp” out

“Low-gain” out

“High-gain” out

Figure 3.8: QUaD lockin card schematic.

After the JFETs, the signals exit the cryostat through hermetic connectors on the

base. Warm lockin amplifier boxes attached beneath the cryostat perform further

amplification and filtering. Each lockin box contains 12 cards each of which processes

the signal from the pair of detectors in a PSB module.

Figure 3.8 is a block diagram of the lockin cards. Each differential signal pair

(from a single detector) first enters a low-noise instrumentation amplifier with a gain

of 100 (AD624). The signals then go through a wide bandpass filter to suppress noise

far from the bias frequency. This bandpass filter is composed of a 4-pole butterworth

low-pass filter with a cutoff of 475 HZ followed by a 2-pole butterworth high-pass

filter with 2.8 Hz cutoff. The filter is designed to have a broad region of flat response

over the possible bias frequency range of 40 - 250 Hz.

The square-wave demodulator (AD630) multiplies the signal by +1 when the

reference signal is positive and -1 when it is negative. This results in a near DC signal

for inputs near the reference frequency. Additionally, there is the usual component at

dual JFETs per channel is still very desirable because it helps ensure that all pickup (regardless offrequency) is common mode.


Figure 3.9: A QUaD amplifier box containing ten out of twelve possible lockin cards.

twice the reference frequency familiar from sine-wave lockin amplification as well as

higher order harmonics associated with the square wave reference. The butterworth

low-pass filter (6-pole, f3dB = 20 Hz) following the demodulator suppresses the high-

frequency terms, leaving only the desired low-frequency components.

The demodulator reference signal comes from the bias board and is the same

frequency and phase as the bias itself (but of constant amplitude). A phase delay

on the lockin cards is computer controllable and compensates each channel for the

phase delay caused by stray capacitance inside the cryostat (Section 3.2.3). The

output signal from the 20 Hz low-pass filter is proportional to cos(φ) where φ is the

phase difference between the input signal and the reference frequency from the bias

board. An automatic, computer-controlled tuning procedure sets the phase delay to

maximize the output signal.

3.1. DESCRIPTION 69

After amplification, demodulation and low-pass filtering the bolometer signals

are in theory ready to be digitized. In practice, however, this proved not to be

feasible. The signals are typically around 3 Volts with an RMS noise of 0.1 microvolt.

Direct digitization at this point would require an ADC card with greater resolution

than standard 16-bit cards provide. Adequate resolution ADC chips do exist, but

commercial systems using these chips were limited and expensive. A custom solution

with eight channels was successfully designed, but scaling up to the required 96

channels proved difficult.

Instead, we chose a simpler route: DC offset removal. This is possible because

the signals from the sky are a small (10 mV) modulation on top of a large (3 V) DC

voltage from the rectified bias. An instrumentation amplifier driven by a stable DAC

is used to remove the large DC offset and provide further gain of 100 to the signals.

This additional gain of 100 is equivalent to increasing the effective number of bits

of the ADC by 6.6 which makes a 16-bit card more than adequate. An automatic,

computer-controlled procedure performs the tedious task of setting the correct offset

voltage for each channel. This is done as often as necessary to keep the signals from

drifting off scale due to changes in the atmospheric conditions. A final low-pass filter

(30 Hz 2-pole butterworth) further suppresses any high-frequency noise. The DC

offset level (DAC value) is archived allowing the full DC-coupled bolometer voltage

to be reconstructed.

Finally, analog switches on the card determine which of three possible outputs

is routed to the ADC card. The first possibility is the signal after the preamplifier

with gain equal to 100 (referred to as preamp). This output is used for DC-biased

load curves as well as other testing. The second option is the post-demodulation

output with a gain of 500 (referred to as low-gain). The control system uses this

output to determine the required setting for the DC offset removal. It is also useful

for general testing and debugging. The final output option (referred to as high-

gain) is after the DC offset removal and final amplification. It has a gain of 50,000.

This is the standard output for observation. Whichever output is chosen, buffers


create a balanced differential output for driving the cable to the ADC, resulting in

an additional factor of two gain.

Each lockin card contains two complete amplifiers, providing the readout for a

PSB pair. Twelve cards are located in each of the four lockin boxes that mount

on the bottom of the cryostat (see Figure 3.9). In addition to the twelve lockin

cards, each box contains a motherboard and an interface card. The interface card

contains voltage regulators that provide ±15 V and +5 V to all the cards, the voltage

reference for the DC offset removal DACS, and isolators for all the digital control

lines. The motherboard contains only connectors and bypass capacitors. All active

components are on cards for easy replacement.

3.1.6 The Data Acquisition System

The data acquisition system (DAS) is based on the DASI system with substantial

updates for QUaD. All realtime operations including telescope control and digitiza-

tion of the bolometer data is handled by a VME controller in a crate mounted next

to the cryostat. The controller runs the VXWorks realtime operating system. Two

64-channel, 16-bit ADC cards in the crate digitize the bolometer data (VMIVME-

3122 from VMIC). A Linux-based PC system provides the user interface and data

archiving for the realtime controller.

Software commands are provided for adjusting nearly all aspects of the readout

electronics including the bias amplitudes and frequency, the lockin phases, dc offsets

and the output mode. Additionally, higher-level commands for automatically setting

the optimum offsets and phases are also implemented. These commands can be

placed in files along with telescope control commands to form complete observing

scripts. A client program allows users anywhere in the world to connect with the

control computer, run scripts, and monitor the signal voltages in realtime.11

11This is limited to the roughly twelve hours per day during which the South Pole has internetaccess.

3.2. PERFORMANCE 71

Measured Bias Spectrum, f0 = 100 Hz

0 500 1000 1500Hz

-80

-60

-40

-20

0

dB

Measured spectrum

BP

(f0 / f) × BP

Figure 3.10: The bias spectrum.

3.2 Performance

3.2.1 Functionality Tests

Bias Generator

The design for the QUaD bias generator evolved from several prototypes that were

used in various bolometer test beds. The final board was populated in stages, testing

each subsystem before stuffing the next. The performance and reliability of the board

was verified with extensive laboratory tests, both by itself and integrated with the

full electronics chain including the cryostat, JFETs, and detectors.

As described in Section 3.1.1, the primary goal of the bias generator is stability

not spectral purity. Nevertheless, a measurement of the spectrum confirms that the

operation is as expected. The circuit creates an approximation to a sine wave by


+

-

SquareWaveDemod.

LP Filter475 Hz

HP Filter2.1 Hz

LP Filter20 HzPreamp

Preamp output

lockinoutputIN+

IN-

Reference Freq.

Figure 3.11: Filtering on the amplifier cards. This shows the location and nominalcutoff frequencies of the filters that are measured in this section. See Figure 3.8 fora more complete block diagram.

filtering a square wave with a bandpass filter centered on the fundamental frequency.

We thus expect the spectrum of the output waveform to contain prominent lines

at the odd harmonics. The amplitude of the peaks is determined by the intrinsic

spectrum of a square wave multiplied by the response of the bandpass filter. The

amplitude of the Fourier components of a square wave fall off as f0/f where f0 is

the fundamental frequency (i.e. the third harmonic is a factor of three down in

amplitude).

The filter in the bias generator is a second order, Q = 10 bandpass filter. The

response of such a filter is given by

BP (ω, Q) =ω0ω√

Q2(ω20 − ω2)2 + (ω0ω)2

, (3.1)

which has been normalized so that f(ω0) = 1. The measured spectrum, seen in

Figure 3.10, shows the expected pattern of peaks. The function (f0/f)×BP (f) fits

the peak amplitudes, indicating that the circuit is working as expected.

3.2. PERFORMANCE 73

0 200 400 600 800 1000Hz

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Sca

led

Res

pons

e

Figure 3.12: Measured response of the 475 Hz low-pass portion of the bandpass filter.The filter is a 4-pole Butterworth. The solid, black line shows the nominal response.Device-to-device variation is small near the bolometer bias frequency of 110 Hz.

Amplifier Cards

The QUaD amplifier card was developed in parallel with the bias generator, during

which time extensive testing was performed on prototype and intermediate versions.

Once the final design was reached, a contract manufacturer assembled the full com-

plement of approximately 50 cards in several runs. Each card has a large number

of components (approximately 170 passives and 20 integrated circuits) and eight

jumpers allow different modes of operation to be selected. Given all these possibili-

ties for errors, it seemed sensible to test every card for basic functionality. The large

number of cards made individual testing impractical, so different automated testing

procedures were developed. The reader is referred to Figure 3.8 for a block diagram

of the lockin card. Figure 3.11 gives a simplified view concentrating on the main

filters.

The first setup used an SRS 340 synthesized function generator to create test


0 10 20 30 40Hz

0.0

0.2

0.4

0.6

0.8

1.0

1.2S

cale

d R

espo

nse

Figure 3.13: Measured response of the 20 Hz low-pass, post-demodulator filter. Thefilter is a 6-pole Butterworth. The solid black line shows the nominal response.

signals and a Keithely 2700 benchtop DVM to measure the response. Both instru-

ments were controlled via serial ports on a PC running a custom testing program.

A multiplexer on the DVM allowed up to ten cards to be sequentially tested with

no human intervention. This setup allowed an extremely thorough diagnostic to be

performed.

• Bandpass filter - The low-pass portion of the bandpass filter (f3dB = 475 Hz)

was mapped out by measuring the “preamp” output using the AC voltage

setting on the DVM with different frequency input sine waves. The results are

shown in Figure 3.12.

• Low pass filter - The 20 Hz low-pass filter following the demodulator defines

the system bandwidth. It is the most complicated part of the card in terms

of number of components. To measure its response, the arbitrary waveform

capability of the SRS was used to generate an amplitude modulated signal

3.2. PERFORMANCE 75

0 10 20 30 40 50Hz

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Sca

led

Res

pons

e

Figure 3.14: Filter bands as measured by impulse response testing (see text fordetails). This measures the product of the bandpass filter and the 20 Hz lowpassfilter response. Only the 2.1 Hz high-pass edge of the bandpass filter is visible sincethe post-demodulator filter cuts off long before the 475 Hz high-pass edge. The solid,black line shows the nominal response.

consisting of a carrier with a sinusoidal envelope at one tenth the frequency.

After demodulation, an oscillation at the envelope frequency remains. This

signal was played at various frequencies and the output recorded with the AC

voltage setting of the DVM.12 The results are shown in Figure 3.13.

• Phase adjustment - The reference phase adjustment circuit adds a delay to the

demodulator reference to compensate for phase shifts on the signal lines inside

the cryostat. In order to test its operation, a fixed sine wave was applied to

the input and the DC level at the “low-gain” output was recorded for various

phase delays.

12Because the carrier also changed frequencies, the measured response of the 475 Hz low-passfilter should also be taken into account. For envelope frequencies below 20 Hz (carrier frequenciesbelow 200 Hz), the correction would be negligible. For higher frequencies, it would be at most 5%.


• DC offset removal - The DC removal circuit was tested by applying a fixed

sine wave input and monitoring the DC level on the “high-gain” output (see

Figure 3.8) while adjusting the DAC voltage. This confirmed operation of the

DAC and measured the gain of the final amplifier (nominally 100).

Approximately 30 cards were tested using this procedure and several problems

were discovered and repaired. Unfortunately, we did not receive the last batch of

cards until after the bulk of the experiment had shipped to the Pole. Some of the

test equipment had to remain at Stanford, so a new procedure was developed for

testing at the Pole.

The second setup used the bias generator to create test signals and the DAS to

record the response. This setup was able to test a complete box (12 cards) at a time,

but the options were more limited.

• Gain - DC and sine wave inputs were used to measure the DC and AC gains

of the card at the “preamp” and “low-gain” outputs respectively.

• Filters - The 20 Hz post-demodulator filter response was measured in a com-

pletely different way. First, the reference input to the demodulator was set

at a positive voltage. This disables the demodulator, setting it to a constant

gain of one. Next, the bias board was programmed to generate impulse func-

tions one millisecond wide spaced a few seconds apart. The data was recorded

and Fourier transformed in software to give the filter responses seen in Figure

3.14. This also measures the response of the 2.1 Hz high-pass filter which was

not measured in the other setup. However, no information is obtained on the

475 Hz low-pass filter.13

• Phase adjustment - The same procedure as for the previous setup was used.

• DC offset removal - No specific tests were performed; however, basic function-

ality was verified in the course of noise testing (Section 3.2.2).

13The low sampling frequency of the ADC (100 Hz) prevented the impulse method from beingused. The limited frequency range of the bias board (40-250 Hz) prevented direct measurement).

3.2. PERFORMANCE 77

+

-

ACBiasGen.

Amplifier Card2K

1K

2K

Reference freq.

V+

V-

Figure 3.15: The setup for electronics noise testing.

This procedure found problems in several cards. A final round of testing was

performed once all the cards were installed. This gave us confidence that all the

cards were stuffed correctly and allowed us to confidently interpret the results of the

noise tests described in the next section.

3.2.2 Noise Performance

Warm Electronics – Amplifiers and Bias Generator

The noise performance of the QUaD warm readout electronics was extensively tested

using the setup shown in Figure 3.15. The bias generator drives a “fake” bolometer

/ load resistor stack composed of precision metal film resistors.14 The value of 1 k

for the resistors used in place of the bolometers was chosen to contribute minimal

Johnson noise while at the same time having similar output impedance to the JFETs

that would be driving the amplifier cards in the complete system. The 2 x 2 k load

resistors give a similar division factor as the real bolometer / load resistor stack.

Figure 3.16 shows the results of testing Lockin Box 1 with its final contingent

of 12 amplifier cards. The bias frequency was set to 90 Hz and the amplitude to

7.5 mV RMS across the 1 k resistor which is roughly the same as that used with the

real bolometers. The DAS was used to collect time-ordered data that was Fourier

14Vishay-Dale PTF-56 series with 10 ppm / C temperature coefficient of resistance, distributedby Newark Electronics.


Card 54

0.01 0.10 1.00 10.00 100.00Hz

1

10nV

/Hz1/

2Card 2

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 24

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 4

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 5

0.01 0.10 1.00 10.00 100.00Hz

1

10nV

/Hz1/

2

Card 6

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 7

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 8

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 9

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 10

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 11

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Card 12

0.01 0.10 1.00 10.00 100.00Hz

1

10

nV/H

z1/2

Figure 3.16: Noise spectra for the 12 amplifier cards in QUaD lockin box 1 for thetest setup seen in Figure 3.15. These spectra include contributions from the biasand 1 k fake bolometer. Each card has two independent amplifiers which are shownin black and red. The large spike at 30 Hz results from beating of the AC biasfrequency (90 Hz for this data set) with the power line mains frequency of 60 Hz.The spikes at 10 Hz visible in some channels result from beating with the ADCsampling frequency of 100 Hz.

3.2. PERFORMANCE 79

transformed in software to produce the spectra seen in Figure 3.16.

The PSDs show a broad flat region at low frequencies and a sharp cutoff corre-

sponding to the 20 Hz bandwidth-defining low pass filter. The white noise level is

computed for each channel as the median of the PSD between frequencies of 1 Hz

and 10 Hz. The average white noise for the 24 channels of box 1 for this setup is

found to be 6.8 nV Hz−1/2. This includes contributions from the amplifier, the bias,

and the test setup itself.

In order to break down the various contributions into a noise budget, each of

these sources is considered in turn:

Test setup: The expected noise from the test setup itself can be calculated as

the quadrature sum of the Johnson noise from the fake bolometer and load

resistors:

e2setup =

[eJ (1k ‖ 4k)

]2= 3.6nV Hz−1/2

where eJ =√

4kBTR is the Johnson noise of a resistor, R. Since the test setup

operates at room temperature, T ∼ 295 K. The value 1 k ‖ 4 k = 0.8 k is the

effective resistance of the fake bolometer in parallel with the load resistors.

Amplifier: In order to quantify the amplifier noise contribution, noise measure-

ments were made for a variety of source impedances. Different valued resistors

were connected in turn to the inputs of the amplifier (with the minus input also

connected to ground) and power spectra were measured. Figure 3.17) shows

the results for a dozen different resistances between 0 and 20 k.

A simple model including only amplifier noise and Johnson noise of the source

(blue line) does not fit the data. Inclusion of an amplifier current noise term

(green line) results in a much better fit:

e2 = e2amp +

[eJ(R)

]2+[inR

]2(3.2)

where in, the current noise density of the input amplifier, is found to be ∼


+

-

ACBiasGen. Amplifier

Card

R

Reference freq.

Amplifier Noise Test Setup

Amplifier Noise Spectra

1 10 100Freq (Hz)

0.1

1.0

10.0

100.0

nV H

z-1/2

20k3.9k1kGnd

Amplifier Noise vs. Source Resistance

0 5 10 15 20 25Res (K)

0

10

20

30

nV H

z-1/2

MeasuredAmp + JohnsonAmp + Johnson + current

Figure 3.17: Amplifier noise as a function of source resistance. (top) The testingsetup. Although the bias voltage itself is not used for this test, the bias board stillprovides the reference frequency for the lockin amplifier. (middle) Noise spectrafor several of the tested source resistances. (bottom) The data are well fit by thequadrature sum of a constant amplifier voltage noise term, an amplifier current noiseterm, and the Johnson noise term from the source resistance (eq. 3.2).

3.2. PERFORMANCE 81

800 fA Hz−1/2. The voltage noise of the amplifier is measured to be eamp =

5.0 nV Hz−1/2 and current noise is seen to be negligible for source impedances

below a few kΩ.

Bias: Tests were performed to determine the noise contribution of the bias gener-

ator. Spectra were taken with the warm testing setup of Figure 3.15 with the

bias again set at ∼ 7.5 mV RMS. Other spectra were taken with a similar setup

except the 2 k load resistors were grounded instead of being connected to the

bias board. Figure 3.18 shows the results. Subtracting the white noise levels

measured with these two different setups gives a value for the bias generator

ebias = 2.8 nV Hz−1/2.

Combining these results yields the noise budget shown in Table 3.2. The warm

readout noise is dominated by the amplifier cards. The next subsection examines

the total electronics noise, including the contribution from the JFETs.

In addition to a low white noise level, the readout electronics are required to

have good low-frequency stability. To allow scans of approximately a minute, it was

desired that the 1/f knee from the electronics be of order 10 mHz. Figure 3.19 shows

the average power spectrum from Lockin Box 1, computed by averaging the PSDs

from all 24 amplifiers. A fit to a 1/f noise model results in a knee frequency which

satisfies the design requirement. It should be emphasized that these results represent

the stability of the entire warm electronics chain. The fake “bolometer” was biased

at approximately the same level that would be used with a real bolometer and the

DC offset removal was similarly set to a reasonable value.


Table 3.2: Noise budget for the results of warm noise testing shown in Figure 3.16.The first line refers to the contribution from the bias generator. The second linerefers to the noise from 1 k ‖ 4 k warm fake bolometer testing setup. The third linerefers to the noise from the amplifier card (dominated by the voltage noise of thepreamplifier chip).

Source nV Hz−1/2 Percent contribution

Bias 2.8 17%Setup 3.6 28%

Amplifier 5.0 55%Total 6.8 100%

Noise Spectra with / without Bias

1 10 100Freq (Hz)

0.1

1.0

10.0

nV H

z-1/2

Fake bolometer biased

Fake bolometer grounded

Card grounded

Figure 3.18: Spectra used to determine the noise contribution from the bias gener-ator. The black trace shows the grounded amplifier input noise for reference. Thegreen trace shows the result for the test setup of Figure 3.15 with the fake bolometerbiased at 7.5 mVRMS. The blue trace results from grounding the load resistors ratherthan connecting them to the bias board.

3.2. PERFORMANCE 83

Figure 3.19: Average noise spectrum for all 24 amplifiers in Lockin Box 1. Thedashed blue lines show the white noise level and a fit to a 1/f noise model. The1/f knee frequency is 7.5 mHz, satisfying the stability requirement. Since the fake“bolometer” was biased during testing, these results represent the stability of theentire warm electronics chain including the bias generator and the DC offset removalcircuit.


Readout Chain

The previous subsection measured the noise from the warm readout electonics. This

subsection describes similar measurements for the entire readout chain, including

the cold JFET buffers. This noise level is extremely important for quantifying the

performance of the receiver. Three different methods were used estimate the end to

end electronics noise over a frequency range of 1 - 10 Hz:

1. In the previous sub-section, the amplifier cards were measured to contribute 5.0

nV Hz−1/2 and the bias to contribute 2.8 nV Hz−1/2. Tests with a prototype

JFETs box at NASA JPL under similar operating conditions as in QUaD

resulted in a median noise of 7.6 nV Hz−1/2. Combining these in quadrature

yields ∼ 9.5 nV Hz−1/2.

2. A preliminary run was made with the QUaD receiver where the bolometers

were replaced with 10 MΩ fixed resistors. At the operating temperature of

265 mK, the Johnson noise of the resistor and load resistor network is 11.9 nV

Hz−1/2. The median white noise from 24 channels was 14.5 nV Hz−1/2. The

resistors were biased so that noise contribution from the bias board factors in

at approximately the right level. Subtracting the average measured noise level

from the calculated Johnson noise of the 10 MΩ fixed resistor results in a total

electronics noise level of 8.3 nV Hz−1/2.

3. In the final receiver configuration, eight of the 96 total channels are configured

as shorts wherein the inputs to the JFET buffers are short circuited together.

These are designed to be used as in situ monitors of the readout noise. Mea-

surements of these eight channels showed a mean noise of ∼ 8.25 nV Hz−1/2.

Adding in the expected noise from the bias generator, the total noise is ∼ 8.75

nV Hz−1/2.

The second two tests indicate that the electronics have slightly lower noise than

expected. This is likely due to the actual JFETs performing better than the tests

3.2. PERFORMANCE 85

Table 3.3: QUaD readout electronics noise budget. Note this breakdown is approx-imate with uncertainty and channel-to-channel variations at the 10% level.

Source nV Hz−1/2 Percent contribution

Bias 3 10%JFETs 7 60%

Amplifiers 5 30%Total 9 100%

on the prototype box indicated. For estimates of the electronics contribution to the

total system noise, a conservative average value of Vn ∼ 9 nV Hz−1/2 will be used.

This satisfies the original design requirement that the electronics noise be at or below

10 nV Hz−1/2. A rough breakdown of the various contributions to the electronics

noise are given by the noise budget in Table 3.3. Section 5.3 places the electronics

noise in context by comparing it with other sources of noise in the system (i.e. see

Figure 5.19).

3.2.3 Channel Capacitance

As described in 3.1.4, stray capacitance on the high-impedance signal lines between

the bolometers and the JFET buffers leads to several problems. In order to under-

stand their severity, the capacitance for each channel needs to be measured. This

section describes such a measurement for QUaD.

Measurement Setup

We measured the capacitance, by replacing the bolometers with fixed metal-film

resistors. The “fake bolometer” resistors are the same composition, and are from

the same vendor, as the load resistors. Figure 3.20 shows the bolometer readout

circuit including the stray capacitance on the line between the bolometer and the

JFETs. In this setup, R = 10 MΩ and as usual, the load resistance, RL, is 20


RL

RL

R CVbias Ibolo

Ibias

IC Vsig

Figure 3.20: Bolometer readout bridge, including stray capacitance.

MΩ. The capacitance is really distributed along the signal cable, but for purposes

of analysis, it is shown here as a lumped element. The main effect is to shunt some

of the (AC) bias current through the capacitor instead of the bolometer.

Basic circuit analysis applied to Figure 3.20 yields the following set of equations:

Vbias = 2IbiasRL + IboloR

Vsig = IboloR = IC1

iωC

Ibias = Ibolo + IC

that can be solved for the output signal voltage as

Vsig =R

R + 2RL + 2RRLiωCVbias. (3.3)

A little algebra puts this in a more suggestive form

Vsig =R

R + 2RL

(1

1 + iωReffC

)Vbias (3.4)

where Reff = 2RLR/(2RL + R) is the effective resistance of the bridge network.

The output voltage (Vsig) and the bolometer bias current (Ibolo) are exactly what

would result if there were no capacitance times a single pole filter response with

time constant τC = ReffC.

The single-pole filter response results in a bias current attenuation factor and

3.2. PERFORMANCE 87

output signal phase delay that is given by:

AC =1√

1 + ω2τ 2C

φC = tan−1 ωτC .

The next subsection applies these equations to measured QUaD data to determine

the channel capacitance.

QUaD Parameters

Single Channel Fit

0 50 100 150 200Bias freq (Hz)

0.75

0.80

0.85

0.90

0.95

1.00

Nor

mal

ized

Sig

nal

C = 86 pFReff = 8MΩ

QUaD Channel Capacitance

0 20 40 60 80Channel

70

75

80

85

90

95

100

Cap

(pF

)

Figure 3.21: Measured QUaD capacitance. (left) A fit to data for a single channel.(right) The measured capacitance for all available channels.

Figure 3.21 (left) shows the result for a typical QUaD channel. The data was

taken using the standard readout electronics and data acquisition system. Data

points were taken with the bias generator set to 12 different frequencies between 40

and 150 Hz and the lockin amplifier cards set in “low-gain” mode. After changing

frequency, the phase delay for each lockin channel was set to maximize the signal

and the value of the lockin output voltage was recorded. At each frequency, the

bias monitor (a lockin channel on the bias board) recorded the amplitude of the bias

voltage. This was used to scale the results in order to take account of the small


Attenuation and Phase for Typical QUaD Parameters

0 50 100 150 200Bias freq (Hz)

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

Atte

nuat

ion

-25

-20

-15

-10

-5

0

Pha

se d

elay

(de

g)

AttenuationPhase

C = 100 pF

R = 5MΩ

Figure 3.22: The reduction in bias current (attenuation) and phase delay versus biasfrequency for typical QUaD channel parameters. The 2005 bias frequency of 110 Hzis indicated by the vertical line.

frequency dependence (∼ 1%) of the bias generators output sine wave amplitude. A

measurement at DC was used to establish the DC gain of the readout electronics. A

one-parameter fit was then applied to the data to find the capacitance.

Figure 3.21 (right) shows the results for each channel. The values range from

approximately 75 - 95 pF with a mean of 85 pF and a standard deviation of 4 pF.

Note that these measurements do not include the focal plane wiring, but do include

the correct number of connectors (since the fake bolometer boards have the same

connectors as the focal plane). A measurement of a sample of the focal plane wiring

(using a capacitance meter) yielded approximately 10 pF. So a conservative estimate

of the total channel capacitance for QUaD is ∼ 100 pF. Figure 3.22 shows the bias

current attenuation and signal phase shift that would result for this capacitance

assuming a typical bolometer resistance. At the 110 Hz bias frequency, the average

channel sees a roughly ∼ 4% attenuation in bias current and a ∼ 20 phase shift.

3.2. PERFORMANCE 89

Microphonic Noise Spectrum

0 200 400 600 800Freq. (Hz)

1

10

100

1000

nV H

z-1/2

baselinebanging

Figure 3.23: Microphonic response for a single QUaD channel comparing two cases:“baseline” (receiver undisturbed) and “banging” (receiver tapped lightly with a rub-ber mallet). The attenuation above 400 Hz is from the electronics bandpass filter(Figure 3.8).

3.2.4 Microphonics

The microphonic response of the receiver was measured by tapping the cryostat

lightly with a rubber tipped mallet while recording the bolometer signals with a

spectral analyzer. The bolometers were DC biased and the “preamp” readout mode

of the warm amplifiers was used. This allowed the full bandwidth to be monitored

rather than the narrow, 20 Hz bandwidth available with either of the demodulated

outputs. Figure 3.23 shows the microphonic response for a single channel from 0 Hz

through 800 Hz. Figure 3.24 plots several channels over the more limited range

of possible bias frequencies. Correlation among the channels can be attributed to

vibrations of the entire focal plane structure rather than the individual channel wires.

In particular, the 100 and 150 GHz channels travel through independent cabling and

JFET boxes. Results for the same test with the telescope scanning in azimuth were

indistinguishable from the baseline (stationary) case – a testament to the smooth

operation of the DASI mount.


Baseline

0 50 100 150 200 250Freq. (Hz)

10

100

1000nV

Hz-1

/2

150-44C100-14C150-01H

Banging

0 50 100 150 200 250Freq. (Hz)

10

100

1000

nV H

z-1/2

150-44C100-14C150-01H

Figure 3.24: Microphonic response for three channels over the possible bias frequencyrange.

The cleanest region of the spectrum is around 200 Hz. Indeed bolometer noise

tests with the bias frequency set here showed a complete absence of microphonic

features. It was, however, felt that this frequency range was too high given the

3.2. PERFORMANCE 91

Hermetic connector

Filtered “D” connector

Electronics boxes

RF-tight interface box

Cabling to DAS

QUaDReceiver

Figure 3.25: Warm RF filtering. All lines entering or leaving the cryostat passthrough filtered connectors (shaded gray) at the entrance to the RF-tight interfacebox. Figures 4.6 and B.3 show photographs of the electronics boxes attached to thecryostat.

capacitance effects measured in the previous section (Figure 3.22). Instead, a bias

frequency of 110 Hz was chosen. Operating in AC bias mode with this bias frequency,

all channels are free of microphonic resonances over the frequency range of interest

(Figure 5.24).

3.2.5 Radio Frequency Interference

A signal wire connecting the bolometers to the data acquisition can act as antenna,

picking up radio-frequency (RF) power. Some of the RF power dissipates in the

bolometer’s thermistor chip which heats the detector and produces a spurious signal.

Because of the negative temperature coefficient of resistance for NTD germanium

thermistors (eq. 4.7), radio frequency interference (RFI) always results in a negative

voltage signal. Frequencies of order 1 GHz are most problematic since they couple


well to typical wire lengths. Unfortunately, this frequency range is heavily used by

modern wireless communication equipment.

To reduce susceptibility to RFI, QUaD filters all lines entering or leaving the

cryostat using filtered D connectors15 as shown in Figure 3.25. A second stage of

filtering occurs as the signals pass through the 4 K baseplate inside the cryostat

using filtered micro-D connectors.16 Despite this filtering, the short section of wiring

connecting the JFETS to the focal plane is still vulnerable to pickup from RF en-

tering the cryostat through the optical window. In order to minimize capacitance

on this high-impedance wiring, no filtering is provided at the entrance to the focal

plane enclosure (see Section 3.2.3).

With the cryostat window blanked off, testing with an RF sweep generator

showed no response, indicating that the filtering is working. On the contrary, with

the window open considerable interference was seen at frequencies in the range

∼ 1 − 10 GHz. In both cases, negligible response was seen to low frequency RF

(∼ 10 MHz), presumably due to the attenuation resulting when such long-wavelength

radiation passes through the 6” cryostat window combined with its poor coupling to

the short internal wiring.

Fortunately for QUaD, the South Pole in winter provides an extremely clean RF

environment. Due to the sensitive nature of many of the experiments operating at

the site, sources of RFI are strictly monitored. During the winter, the use of wireless

communication devices is prohibited in the area surrounding QUaD (known as the

Dark Sector) except in emergencies. Since installing the receiver in the telescope in

February 2005, no trace of RFI has been detected.

15Spectrum Control Series 700 connectors with pi filters (www.spectrumcontrol.com).16Cristek Inc., (www.cristek.com).

Chapter 4

Receiver Characterization

4.1 Bolometer Characterization

The QUaD receiver was integrated and characterized at Stanford from April through

October of 2004 prior to shipping it to the South Pole. This chapter presents the

results of that testing.

4.1.1 Bolometer Model

A simple model, shown schematically in Figure 4.1, describes the thermal and elec-

trical operation of a bolometer. A model for the thermal operation of a semicon-

ductor bolometer and its noise properties is developed in the pioneering papers by

Mather [Mather, 1982, 1984]. Sudiwala et al. [2002] describes the process by which

model parameters are determined through laboratory measurements on actual de-

vices. Runyan [2002] provides a good review of the subject. The treatment presented

in this section is based on these references.

The model assumes that the absorber, warmed by optical power from incident

radiation and electrical power dissipation in the thermistor operates at a temper-

ature, Tbolo, greater than the baseplate temperature, Tbase. The optical power is

typically referred to as Q while the electrical power is called P . Power flows from

93

94 CHAPTER 4. RECEIVER CHARACTERIZATION

Absorber ( )Tbolo

Thermistor (R0, )

Baseplate (Tbase

)

Thermal link (G0, )

Q

P=IV

RL

RL

RV

bias

Ibias

Vbolo

Figure 4.1: (left) Bolometer thermal model. (right) Bolometer electrical readoutcircuit.

the bolometer to the baseplate through a thermal link with temperature-dependent

conductivity. In thermal equilibrium, the power flowing into the absorber equals

the power leaving. This is expressed quantitatively by the power-balance equation

which is written as follows

P + Q =∫ Tbolo

Tbase

G(T ) dT (4.1)

where G(T ) is called the differential thermal conductivity. For semiconductor bolome-

ters, G(T ) can be modelled with a power law:

G(T ) = G0

(T

T0

)β

(4.2)

where T0 is an arbitrary reference temperature. For QUaD, typical values are G0 ∼100 pW/K and β ∼ 1.3 for T0 = 300 mK. Using this model for G(T ), the power-

balance equation becomes

P + Q =G0

T β0 (β + 1)

(T β+1

bolo − T β+1base

). (4.3)

The electrical power dissipated in the thermistor can be manipulated into three

4.1. BOLOMETER CHARACTERIZATION 95

standard forms using Ohm’s law:

P = Ibias Vbolo = I2bias R(T ) =

V 2bolo

R(T ). (4.4)

The voltage across the thermistor, Vbolo, can be related to the bias voltage and

current using the schematic of the readout circuit shown in Figure 4.1:

Ibias =Vbias − Vbolo

2RL(4.5)

Vbolo =R(T )

R(T ) + 2RLVbias. (4.6)

The final step is to relate the thermistor resistance to temperature. For NTD Ger-

manium thermistors, a simple functional form gives excellent results:

R(T ) = R0e√

∆/T . (4.7)

The parameter R0 depends on exact size and shape of the thermistor chip and varies

considerably from device to device. On the other hand, ∆ is a property of the

material and tends to be more stable.

Equations 4.3 through 4.7 determine the incident optical power, Q, given mea-

surements of Vbolo, Vbias and Tbase. First, however, the bolometer must be character-

ized by determining the device-dependent parameters R0, ∆, G0, and β. This is the

subject of the next section.

4.1.2 Load Curves

The load curve is the fundamental tool for determining the parameters of a particular

bolometer. The test involves recording the bolometer voltage while ramping the bias

voltage from zero to some maximum value. Using equation 4.5, the results can be

plotted as bolometer voltage versus bias current. Equation 4.6 allows the bolometer

resistance to be determined. Load curves can be taken under a variety of optical


Figure 4.2: Three load curves for a single PSB looking at different temperature loads.

loading conditions (various values of Q).

Figure 4.2 shows sample load curves for the same device looking at three different

temperature blackbody loads – room temperature, liquid nitrogen and liquid helium.

For low bias current values, bolometers behave like ordinary resistors. But increased

bias current results in self-heating which causes a deviation from Ohmic behavior.

For small amounts of optical power and large bias currents the load curves “turn

over” entering a regime where increased bias results in less signal. For heavily loaded

bolometers, it is difficult to apply enough bias current to see this effect.

The load curves shown in Fig 4.2 were taken using three different temperature

blackbody loads. The room-temperature load was a sheet of unpainted Eccosorb

CV-3 (egg-carton shaped absorbing foam) placed over the cryostat window. The

liquid nitrogen load was a styrofoam cooler filled with LN2 with a piece of the same

Eccosorb foam placed inside. Dry styrofoam was found to be extremely transparent

at the frequencies of interest (Transmission > 0.99). A small fan was placed to

blow a steady stream of warm air through the gap between the load and window to

ensure that condensation did not form on the cold load. The liquid helium load was

a similar, but smaller styrofoam box (owing to the greater cost and much smaller


Figure 4.3: Resistance vs. temperature for the six dark detectors in QUaD.

heat capacity of liquid helium). The load was covered with a styrofoam lid with a

small (1 cm) hole used for transferring the helium. The load held liquid for just over

the minute necessary for the load curve.

The standard procedure for determining the parameters R0 and ∆, is with a

series of ‘dark’ (Q = 0) load curves at different baseplate temperatures, obtained

by blanking off the bolometer inside the cryostat. The low-bias points of each load

curve are used to determine the bolometer’s resistance. The power-balance equation

(eq. 4.3) shows that with Q = 0 and P very small, Tbolo ≈ Tbase. A sequence of load

curves at different values of Tbase maps out R(Tbolo) allowing the parameters R0 and

∆ to be determined. A coordinate transformation

x = 1/√

T (4.8)

y = ln R (4.9)

linearizes eq. 4.7 which is useful for plotting the results as in Fig 4.3. Deviation


Figure 4.4: The optical loading, Q, for the three load curves in Figure 4.2. For eachload temperature, the power is independent of bias, indicating a successful fit forG0 and β. As noted in the text, it is difficult to make an absolute measurementof the loading due to sensitivity to the bolometer parameters and the baseplatetemperature. Also, these results are not corrected for the approximately 2 pW ofloading due to emission from inside the cryostat (Section 5.3.1).

from a straight-line, especially for the coldest points, is common. This indicates

stray power warming the detector, or a temperature offset between the bolometer

and the baseplate thermometer. Reliable measurements of R0 and ∆ are difficult

and require careful experimental technique to ensure that no stray light warms the

detector under test.

With R0 and ∆ known, any load curve can be used to fit for G0 and β. Equation

4.7 is used to convert Vbolo into Tbolo and eq. 4.4, to find P (the electrical power).

The derivative of the power balance equation gives:

dP

dTbolo

∣∣∣∣∣Tb

=d

dTbolo

∫ Tbolo

Tbase

G0

(T

T0

)β

dT = G0

(Tbolo

T0

)β

(4.10)

which can be manipulated so that a linear fit gives the two unknown parameters

G0 and β. In practice, the results from the linear fit should be used as the starting


values for a non-linear fit to the difference equation

P2 − P1 =G0

T β0 (β + 1)

(T β+1

bolo2− T β+1

bolo1

). (4.11)

where the subscripts 1 and 2 refer to two successive points of the load curve.

With these parameters known, the power-balance equation can be used to solve

for the optical power, Q, at every point of any load curve:

Q =G0

T β0 (β + 1)

(T β+1

bolo − T β+1base

)− P. (4.12)

Figure 4.4 shows the results of this procedure for the three load curves presented at

the beginning of this section. As expected, Q is constant for all bias values indicating

a successful fit.

The values of Q obtained in this way can be used to estimate the loading caused

by emission from filters and other optical elements in the system (Section 5.3.1).

They can also be used to estimate the loading from the atmosphere (Section 5.2.1).

However, it should be emphasized that an absolute measurement of the loading at

any given time is extremely difficult because it requires an accurate knowledge of the

bolometer parameters and the baseplate temperature. Aside from the difficulties of

calibrating a sub-Kelvin thermometer, the true baseplate temperature seen by the

bolometer is itself difficult to measure due to the finite conductivity of the focal

plane and Kapitza resistance at interfaces.1

We intended to dark test all of the QUaD detectors in a separate test bed be-

fore installation; however, time constraints made this impossible. Detector failures

prevented many of the devices we did test from being used in the final instrument.

Common PSB failure modes included the following:

• Popcorn noise - Random discrete jumps in the bolometer voltage resulted in an

1Assuming the parameter ∆ is known, a dark load curve can be fit for R0 and a temperatureoffset from the assumed baseplate temperature. These are found to be as high as 10 mK for thedark load curves in Figure 4.3 with substantial device to device variation. Uncertainties in thebaseplate temperature at this level lead to uncertainties in Q of order GδT ∼ 1 pW.


RMS noise level several orders of magnitude higher than normal. The problem

was eventually traced to a bad batch of NTD thermistors affecting an entire

run of PSBs.

• Open circuit - The electrical connection would open, often during thermal

cycling. This was usually due to a bad wire bond between the connector and

the PSB membrane.

• Electrical short - An electrical connection between the two halves of the PSB

pair. This usually also implied an undesirable thermal short between the de-

vices, resulting in high measured cross polar leakage. This usually resulted

from machining tolerances placing the two membranes too close (nominal sep-

aration ∼ 60 µm).

In the end, only seven out of the 62 total light detectors have known values of R0

and ∆. Table 4.1 summarizes the parameters for these devices. The six functioning

dark detectors also listed in the table were characterized in situ (see Figure 4.3).

4.2 Optical Characterization

4.2.1 Optical Testbed

Prior to integration, optical testing was performed on individual pixels using the

optical testbed shown in Figure 4.5. The testbed design and the testing results are

detailed in [Kirby, 2004]. The optical testbed is a simplified version of the QUaD

receiver with minimal fore optics and a single feed. It is based on a downward-

looking LN2 / LHe cryostat and uses a single-stage helium-3 adsorption refrigerator

to achieve bolometer temperatures of order 265 mK. The single-stage fridge requires

a baseplate temperature below ∼ 2.5 K in order to condense helium-3, so pumping

on the LHe bath is required. As in QUaD, the focal plane is thermally isolated from

the baseplate via Vespel legs. The electronics are a scaled down version of the full

4.2. OPTICAL CHARACTERIZATION 101

Table 4.1: The bolometer parameters for the subset of QUaD detectors that havedark characterization. The top section of the table lists the detectors that are nowopen to light. The R0 and ∆ parameters for these detectors were determined ina separate test bed prior to installation in QUaD. The G0 and β parameter werefit from a load curve under typical observing conditions. The bottom section listsdetectors that are currently dark. They were characterized in QUaD (R(T ) datashown in Figure 4.3).

PSB R0 ∆ G0 β(Ω) (K) (pW/K)

150-12H 93.4 41.0 120.7 1.47150-12C 82.6 40.8 152.0 1.45150-21H 80.5 41.2 129.7 1.44150-21C 78.9 41.4 155.9 1.46150-04H 133.5 39.8 159.3 1.42150-04C 94.3 40.0 123.4 1.36150-15C 113.8 39.3 107.0 1.35150-01H 156.8 40.3 117.6 1.41150-01C 96.0 41.2 116.1 1.43150-32H 99.2 45.5 92.3 1.82150-53C 81.0 42.5 98.3 1.70100-43C 135.6 38.7 48.5 1.52100-22C 156.5 37.1 51.2 1.55

QUaD readout including a duplicate bias board, single amplifier card, and a custom

two-channel JFET box.

Tests performed with the testbed include:

• Spectroscopy - Various combinations of band-defining filters were tested at 100

and 150 GHz to find a combination that yielded the desired cutoff with no out-

of-band leaks. Measurements of the final filter stack in QUaD are described in

Section 4.2.2.

• Beam pattern - The FWHM for each frequency feed was measured and found

to agree with the predicted value.


Figure 4.5: The QUaD optical testbed. (left) Photo with all thermal shields re-moved. The JFET box is visible in the foreground and the load resistor box islocated to the left of the feed. (right) Assembly drawing.

• Optical efficiency - The optical efficiency was measured for several devices at

each frequency. These early tests showed the low efficiency of the 100 GHz

channels that is seen in QUaD (Section 4.2.3).

• Cross polar leakage - The cross polar leakage was measured for multiple devices

at both frequencies. Again, these early tests showed the poorer performance

of the 100 GHz channels relative to the 150s. Comparison of the testbed and

QUaD results is presented in Section 4.3.

4.2.2 Spectral Bands

The QUaD spectral bands are fixed at the low-frequency end by the feed horn throat

and on the high end by metal-mesh low-pass filters as described in Section 2.3.3. Dur-

ing development, the filter bands were tested with a Fourier transform spectrometer

(FTS) at Stanford. Once the filter stack was finalized and installed, every pixel was

tested with an FTS at the South Pole.


Figure 4.6: The QUaD receiver setup for laboratory testing with the Stanford FTS.

An FTS is a Michelson interferometer with one fixed and one movable mirror. The

bolometer voltage is recorded as the moving mirror varies the path length resulting

in an interference pattern known as an interferogram. The Fourier transform of

the interferogram gives the transmission function of the pixel being tested. The

transmission function (or spectral response function) is denoted f(ν).

Figure 4.7 shows the transmission spectra for all 31 feed horns. For plotting, the

transmission spectra are normalized so that the peak is equal to one. Normalization

is discussed more in the next section. Feeds that will not be used in final CMB

analysis due to problems with one PSB are shown dashed.

The measured bandpass is typically characterized by several parameters including

a center frequency (ν0) and a bandwidth (∆ν). These parameters are useful for

estimates and general discussions of the band properties; however, in practice noisy


Table 4.2: Average spectral band properties.

Num ν0 (GHz) ∆ν (GHz) ∆ν (%)12 94.5 ± 0.6 26.5 ± 2 2819 149.5 ± 0.6 40.5 ± 2 27

data and complicated bandpass shapes make them difficult to quantify. Multiple

definitions are commonly used, and each leads to slightly different values on real-

world data.

For QUaD, we defined the band center to be

ν0 =

∫∞0 ν f(ν) dν∫∞0 f(ν) dν

(4.13)

which is a band-weighted average frequency. For the bandwidth, we used the half-

power points of the transmission spectra (FWHM). Table 4.2 gives average values

of these parameters for the spectra in Figure 4.7.


Figure 4.7: The QUaD spectral bands as measured at the South Pole. The bandsshown dashed correspond to feeds with at least one non-functional channel.


Figure 4.8: Power difference computed from the load curves in Figure 4.2.

4.2.3 Optical Efficiency

Definition

The optical efficiency is defined as the fraction of in-band power incident on the

receiver that is actually detected by the bolometer. It is always less than one because

of reflection and absorption losses from each element in the optical chain. Values of

40% are typical of state-of-the-art millimeter-wave receivers.

The optical power (Q) incident on a PSB for observations of a beam-filling,

blackbody source is given by an integral over frequency:

Q =1

2

∫AΩfn(ν) B(T, ν) dν (4.14)

where AΩ is the throughput of the optical system and fn is the normalized spec-

tral response. The factor of 1/2 arises because the PSB detects only one linear


polarization.2 In the Raleigh-Jeans limit, eq. 4.14 can be simplified to

Q = kT∫

fn(ν) dν (4.15)

where the equality AΩ = λ2 (valid for single-moded optical systems such as QUaD)

has been used. The efficiency can then be defined as the band-average of the nor-

malized transmission:

η =1

ν2 − ν1

∫ ν2

ν1

fn(ν) dν (4.16)

If the power contained outside the band interval (ν1, ν2) is small, we can approximate

eq. 4.15 as Q ≈ kT η ∆ν which is frequently used for estimates. Note this defines η

as the efficiency of the detector to radiation polarized along its axis of sensitivity.

Measurement with Load Curves

Load curve measurements can be used to normalize the raw spectra as measured

from the FTS (sec 4.2.2). In principal, eq. 4.3 allows η to be determined for any

characterized bolometer from a single load curve observing a blackbody of known

temperature; however, as noted in Section 4.1, sensitivity to the parameters and

internal emission from the receiver make this difficult. Another method, involving

two load curves, avoids this problem and does not require knowledge of any of the

bolometer parameters.

Two load curves are taken while looking at beam-filling blackbody loads at two

different temperatures, T1 and T2. The curves are plotted in units of bolometer resis-

tance versus electrical bias power. Figure 4.8 shows the results for a single detector

looking at room temperature and liquid nitrogen loads. Lines of constant resistance

(horizontal) on the plot correspond to lines of constant bolometer temperature (eq.

4.7) and thus constant P + Q (eq. 4.3 assuming constant baseplate temperature);

the curve corresponding to the colder load requires more electrical power to warm

2The factor of 1/2 could be absorbed into fn(ν); however, the definition here makes comparisonof efficiencies with total power experiments simpler.


Table 4.3: Average optical efficiencies. “Inner” refers to the central group of seven150 GHz pixels and “outer” refers to the outer ring of 12 pixels (Figure 2.9).

100 GHz all 26 ± 6%150 GHz inner 35 ± 5%150 GHz outer 29 ± 5%150 GHz all 32 ± 6%

the bolometer to the same temperature. So the difference in optical power is equal

to the difference in electrical power:

Q2 − Q1 = P1 − P2. (4.17)

This difference should be constant along the load curve and the multiple measure-

ments can be averaged. Equation 4.14 relates the power difference to the load tem-

peratures

∆Q2 − ∆Q1 = α∫

AΩ f(ν)[B(T2, ν) − B(T1, ν)

]dν (4.18)

allowing the normalization constant, α, to be determined. The transmission spec-

trum for this detector can then be normalized as:

fn(ν) = αf(ν) (4.19)

allowing the optical efficiency to be determined via eq. 4.16. It should be noted that

in general α = η.

Results for QUaD

This procedure was applied to QUaD using the spectra described in 4.2.2. The loads

were room temperature and liquid nitrogen Eccosorb as described in Section 4.1.

For the optical efficiency measurements, it is important that the liquid nitrogen load


Figure 4.9: QUaD optical efficiencies. The shaded region of the 150 GHz histogramshows the distribution for the central ring of seven feed horns.

is dry, since thermal emission from condensation will make it appear warmer – an

effect that is indistinguishable from reduced optical efficiency. For the same reason,

the cryostat window must be clean and dry.

The results are summarized in Figure 4.9 and Table 4.3. The optical efficiencies

for the central group of seven feed horns are significantly better than the outer

ring of 150 GHz feeds. This is largely attributable to a selection effect; the best

performing detectors from previous runs were grouped in the center because this

region of the focal plane has the best optical properties. The cause of the generally

poorer performance of the 100 GHz detectors is unknown, but believed to be caused

by the horn bolometer interface (see Section 4.3).


Figure 4.10: Responsivity of a quad detector.

4.2.4 Responsivity and Time Constants

DC Responsivity

The DC Responsivity (SDC) of a bolometer is defined as the change in bolometer

voltage for a small change in incident optical power assuming the bolometer is in

thermal equilibrium during the process:

SDC =dVbolo

dQ.

Using the equations in Section 4.1.1 one can derive the following expression

SDC =RL

2Vbolo

z − R

z + 2RL

(4.20)

where z, the dynamical impedance, given by

z =dVbolo

dIbias

, (4.21)


is the the slope of the load curve. The responsivity as defined in eq. 4.20 is always

negative for QUaD since our detectors have a negative temperature coefficient of

resistance (eq. 4.7). However, it is common in practice to refer to the absolute value

when speaking of responsivity. Figure 4.10 shows responsivity curves corresponding

to the load curves in Fig 4.2. Increased optical loading warms the detector resulting

in decreased responsivity. In practice, bolometers are not biased to be at the peak of

the responsivity curve because here the sensitivity to changes in background loading

is maximized, making the system difficult to calibrate (see Section 5.3.2).

Bolometer Time Constants

The absorber and thermistor in real bolometers have a finite heat capacity meaning

that it takes some time for them to change temperature. This results in a frequency-

dependent attenuation to the DC responsivity given in the previous section. This

frequency-dependence must be understood in order to use the bolometer voltages to

accurately reconstruct time-varying signals.

The responsivity can be written as a product of three factors:

S(ω) =dVbolo

dR

dR

dT

dT

dQ. (4.22)

The first two factors are frequency independent; however, the last is not. Its fre-

quency dependence can be determined from a simple model. If we apply a small

perturbation ∆Q(t) = ∆Qeiωt and assume that the electrical power, P remains

constant, the power-balance equation gives ∆Q − G ∆T = C ∆T where C is the

bolometer’s heat capacity (J/K). Assuming ∆T = ∆T (ω)eiωt results in

∆T

∆Q∝ 1

1 + iωτ(4.23)

where τ = C/G is known as the time-constant of the bolometer. This is the same

form as the response of a single-pole low-pass filter.

The assumption that the electrical power remains constant for changing optical


150-13-B

0 5 10 15 20 25 30Freq (Hz)

0.0

0.2

0.4

0.6

0.8

1.0

1.2Tau lab: 10.1

150-14-A

0 5 10 15 20 25 30Freq (Hz)

0.0

0.2

0.4

0.6

0.8

1.0

1.2Tau lab: 32.7

Figure 4.11: Lab time constant measurements for two example detectors Time con-stants are in ms in the upper right corner of each plot.

loading is incorrect. In fact, the bias current remains (nearly) constant, but in-

creased optical loading results in decreased bolometer resistance and thus decreased

electrical power (P ). The decreased P compensates for the increased Q resulting in

the bolometer coming to equilibrium faster than it would have without this electro-

thermal feedback. Including this feedback, the form of eq. 4.23 remains valid with

τ replaced by an effective time constant τe = C/(G − αP ) where α = R−1 dR/dT

which is of order −16 K−1 for typical QUaD bolometer parameters. Higher bias

current is seen to result in faster detectors (decreased τe). Putting this together, the

frequency-dependent responsivity is given by

S(ω) =SDC

1 + iωτe. (4.24)

Laboratory Measurement

The QUaD time constants were measured in the lab with a rotating chopper wheel

mounted between the cryostat window and a liquid nitrogen cold load. The chopper


wheel had alternate transparent and opaque (Eccosorb foam) sections. The resulting

square-wave signal was digitized and demodulated in software. The amplitude was

recorded for a variety of chopper rotation frequencies. The data was taken using the

DC-biased mode of the readout electronics since chopper rotations faster than the

20 Hz cut off frequency were needed. Figure 4.11 shows data and model fits for two

detectors.

Unfortunately, during the test, the bolometer bias current was set a factor of

4.5 higher than the standard observing value (see Section 5.3.2) and the chopped

load presented roughly six times more optical loading than is seen in the field (see

Section 5.3.1). These different operating conditions make the results of these tests

less useful. Section 5.1.4 presents an alternate method of measuring time constants

under typical observing conditions.

4.2.5 Cosmic Rays and Impulse Response

Being thermal detectors, bolometers respond to many forms of incident energy. The

substantial filtering in the QUaD receiver (see Figure 2.4) prevents out-of-band op-

tical power from reaching the detectors; however, cosmic rays easily penetrate. Even

though PSBs present a substantially reduced cross section relative to a solid ab-

sorber, QUaD still sees a background of cosmic ray events at a rate of ∼ 0.5 /

channel / hour.3 Since cosmic ray impacts are essentially instantaneous (relative

to all relevant thermal and electronic time constants), they approximate a delta

function disturbance and thus provide a means of measuring the receiver impulse

response.

Figure 4.12 shows a typical cosmic ray event as well as a best-fit model (blue) of

the receiver impulse response. The model has four free parameters, the bolometer

time constant (τb), the time constant (τf ) of the post-demodulation low pass filter

(f3dB ∼ 20 Hz), and an overall scale factor and temporal shift. The filter time

3Note that this rate is low enough that scans containing a cosmic ray impact can simply beignored from the main CMB analysis with negligible loss of data.


Cosmic Ray Impulse Response

0.0 0.2 0.4 0.6 0.8 1.0sec

-6

-4

-2

0

2V

olts

Impulse model

Spline

Data

Impulse model

Spline

Data

Figure 4.12: A cosmic ray impact shows the receiver’s impulse response.

constant, τf has been measured for every channel (Figure 3.14), but temperature

variations in the receiver room may slightly change its value which is why it is left as

a free parameter. The good fit of the impulse model to the cosmic ray data indicates

that these four parameters are the most important factors.

The following outlines the derivation of the impulse response model beginning

with the transfer functions for the bolometer and the post-demodulation low-pass

filter. The bolometer transfer function is a simple first-order response:

Hbolo(s) =1

τbs + 1(4.25)

where s = −iω. The post-demodulation filter is a 6-pole Butterworth with a nominal

3 dB point of 20 Hz. The transfer function for a 6-pole filter is

H(s) =1

(τ 2f s2 + Aτfs + 1)(τ 2

f s2 + Bτfs + 1)(τ 2f s2 + Cτfs + 1)

(4.26)


Impulse Response Model

0.00 0.05 0.10 0.15 0.20 0.25sec

-0.10

0.00

0.10

0.20

0.30

0.40

Vol

ts

0 ms

10 ms

20 ms

30 ms

0 ms

10 ms

20 ms

30 ms

Figure 4.13: Model QUaD impulse response for several different bolometer timeconstants.

which is a product of three general, second-order responses. For a Butterworth, the

coefficients are A = 0.5176387, B =√

2, and C = 1/A. The overall transfer function

is given by the product of these two as

H(s) = Hfilter(s)Hbolo(s). (4.27)

The impulse function is determined by inverse Laplace transforming the transfer

function. Since the transfer function is quotient of two polynomials, this can be done

analytically using a partial-fraction decomposition which leads to a series of damped

sine and cosine terms. Figure 4.13 shows plots of simulated impulse responses gener-

ated from this model. The left hand plot shows that for a constant impulse, a longer

bolometer time constant leads to a lower peak voltage and a longer decay; however,


Figure 4.14: Aligning the polarizing grid.

the bolometer time constants obtained with this procedure are known to disagree

with those obtained optically [Woodcraft et al., 2003]. For PSBs, the agreement is

worse due to the absorber geometry. Cosmic ray hits thus provide a useful monitor

of the electronics transfer function but not an effective way to measure bolometer

time constants.

4.3 Polarization Properties

In order to characterize the polarization performance of the receiver, we measured

the orientation angle of each PSB and its cross-polar leakage. Cross polar leakage

refers to the response of a PSB to linearly polarized radiation oriented orthogonally

to the designed axis of sensitivity. Both of these measurements were performed

with the same setup which involved placing a rotating wire-grid polarizer above the

cryostat window while observing a chopped thermal load read out with a lockin

4.3. POLARIZATION PROPERTIES 117

Figure 4.15: The polarizing grid mounted on the cryostat.

amplifier synched to a chopper-synchronous reference. In this section, I derive the

expected signal, describe the setup in more detail, present the results, and finally

consider the effects of the measured cross-polar leakage.

4.3.1 Formalism

This section provides a brief introduction to the Jones and Meuller formalisms which

the following sections use to analyze the polarization properties of the receiver. Both

formalisms represent electromagnetic waves of arbitrary polarization as column vec-

tors and optical elements as square matrices. They allow a complicated optical

system, composed of many elements, to be reduced to a single matrix by combining

the matrices corresponding to the individual elements using matrix multiplication.

The Jones formalism represents electromagnetic waves as complex, two-component


Figure 4.16: Measuring the polarization angles.

column vectors which give the amplitude and phase of the electric field as

E =

⎛⎜⎝ E0xe

iφx

E0yeiφy

⎞⎟⎠ (4.28)

where the E0 and φ are real. An overall time dependence of eiωt is assumed and only

the real part of E has physical significance. The Jones vectors are usually normalized

to unity irradiance so that, for example, a wave linearly polarized at a 45 direction

to the x axis would be represented by the simple expression:

E45 =1√2

⎛⎜⎝ 1

1

⎞⎟⎠ . (4.29)

Passing this beam through a horizontally-oriented polarizing grid results in the new

beam, Ef , given by Ef = Jh E45. The Jones matrix of a horizontal polarizer, Jh, is


Figure 4.17: Measured PSB orientations.

given by

Jh =

⎛⎜⎝ 1 0

0 0

⎞⎟⎠ (4.30)

so that Ef = 1/√

2(1 0

)T. The output is polarized in the horizontal direction as

expected.

Jones matrices are best-suited to the analysis of completely polarized radiation.

For the case of partial polarization, the Meuller formalism, based on Stokes pa-

rameters, is more appropriate. In this formalism, the radiation is represented by a

real, four-component Stokes vector S =(I,Q,U ,V

)T. Optical elements acting on

the radiation are represented by 4x4 real matrices. Given a Jones matrix, J, for a

component or system, the corresponding Meuller matrix is given by

Mij =1

2tr(σiJσjJ

†) (4.31)

where the σ are Pauli matrices [Born and Wolf, 1980].

A more detailed description of these formalisms, including a table of Jones and

Meuller matrices for common elements, can be found in standard optics texts such


Figure 4.18: Measured PSB orientation angle error and PSB pair orthogonality.

as Hecht [1998]. Examples of the use of Jones matrices to analyze more complex

systems can be found in Lesurf [1990] and O’Dell [2001]. The former analyzes a

polarized Fourier transform spectrometer and the latter, a correlation polarimeter.

Application of this formalism to PSBs is presented in Jones [2005] and reviewed in

the next subsection which applies these methods to the QUaD receiver testing setup.

4.3.2 Derivation of the Expected Signal

As described earlier, the receiver was tested by rotating a linear polarizing grid

in front of the window while observing a chopped thermal load. From elementary

optics, we expect a sinusoidal response from the PSB as we rotate the polarizing

grid. However, deriving the full result including the effect of cross polar leakage

provides a useful application of the Jones matrix formalism. We imagine orienting

the PSB axis of sensitivity along the x axis and place a linear polarizer oriented at

an angle θ above it. Written in terms of Jones matrices, the electric field that is

detected by the PSB is given by

E = JPSB Jpθ Ei (4.32)


Figure 4.19: Measured cross-polar leakage.

where JPSB and Jpθ are the Jones matrices of the PSB and the polarizing grid

respectively and Ei is the unpolarized input radiation.

A PSB acts as an imperfect linear polarizer followed by a total power detector

Jones [2005]. The optical power incident on the PSB will be proportional to the

intensity of E:

Popt ∝⟨E† E

⟩=⟨|E2

x|⟩

+⟨|E2

y |⟩

(4.33)

where <> denotes time averaging.4

The Jones matrix for the PSB is given by

JPSB =

⎛⎜⎝ η 0

0 δ

⎞⎟⎠ (4.34)

where η ∼ 1 and δ 1 parameterize the cross polar leakage [Jones, 2005]. The

4The symbol Popt is used instead of Q to denote the optical power absorbed by a PSB to avoidconfusion with the Stokes parameter Q.


Jones matrix for a linear polarizer oriented at an angle, θ, to the x axis is given by

Jpθ = R

⎛⎜⎝ 1 0

0 0

⎞⎟⎠RT (4.35)

where R is a standard rotation matrix given by

R =

⎛⎜⎝ cos θ − sin θ

sin θ cos θ

⎞⎟⎠ . (4.36)

Simplifying, this gives

Jpθ =1

2

⎛⎜⎝ 1 + cos 2θ sin 2θ

sin 2θ 1 − cos 2θ

⎞⎟⎠ . (4.37)

The initially unpolarized radiation field can be represented with the Jones vector

Ei =1√2

⎛⎜⎝ 1

eiφ(t)

⎞⎟⎠ (4.38)

where φ(t) is random phase that varies on timescales much faster than the detection

period (∼ 10 ms) but much slower than the frequency of oscillation of the electric

field (∼ 10 ps) such that⟨eiφ(t)

⟩= 0.

Plugging these expressions into eqs. 4.32 and 4.33 yields Popt(θ). The change

in voltage output of the bolometer is proportional to the change in incident optical

power over a small range: ∆v ∝ ∆Popt. Synchronous demodulation of the chopped

source ensures that v = 0 when Popt = 0 which gives the output voltage of the lockin

amplifier as:

v(θ) ∝ 1

2

(η2 + δ2

)+

1

2

(η2 − δ2

)cos 2θ. (4.39)

As expected, this is a sinusoid where the period reflects the fact that the polarizing

grid appears identical after a 180 rotation. The maximum value of the sine wave


is η2 and the minimum is δ2. Cross polar leakage is thus immediately obvious in a

plot of V (θ) as an offset between the x axis and the minimum signal.

4.3.3 The Measurement Setup

The polarizing grid is a thin sheet of polypropylene with parallel traces of copper

deposited on one surface with a 10 micron spacing. The grid spacing was verified

using the diffraction pattern created with a standard red laser pointer. The grid was

manufactured by our collaborators in Cardiff using the same lithographic technique

used for filter construction. The polarizing efficiency of the grid (at 150 GHz) is

greater than 99.9%.5

The grid was mounted onto a ball-bearing rotating stage to allow positioning at

any angle. The stage was driven by a high-resolution stepper motor (400 steps per

revolution) through a zero-backlash belt,6 with a gear reduction of 12:1. A micro

switch provided a reference mark once per revolution. The grid was aligned with

respect to the reference mark to better than 0.5 using the diffraction pattern from

a laser pointer (Figure 4.14). Figure 4.15 shows the complete system mounted on

the cryostat window.

During testing, the cryostat observed a chopped 77 K / 300 K load. The chop

frequency was set at ∼ 2 Hz. An opto-interrupter provided a chopper-synchronous

reference that was digitized on one of the spare channels of the main data acquisition

system. A software lockin amplifier, synchronized to the digitized reference, was

applied to the signals during the analysis.

Testing was performed with a “step and integrate” sequence whereby the grid

was rotated an amount ∼1 then held stationary for several chopper periods. The

DAS recorded data continuously during this process. In order to divide the data into

5The efficiency was determined by measuring the transmission through a stack of two identically-manufactured grids first with the grids oriented orthogonally and then aligned parallel. The mea-surement was made with the single-pixel optical testbed (Section 4.2.1) looking through the stackedgrids at a chopped load.

6W.M. Berg, Inc. www.wmberg.com


steps, the polarizing grid motor driver set a digital “data good” flag high whenever

the grid wasn’t rotating.

During testing, a stationary Eccosorb mask was placed between the polarizing

grid and the cryostat window. The mask had 0.5” holes drilled through it at the

locations of the beams corresponding to each horn. The 31 beam centers were derived

from the optics model (using Zemax, an optics package) and output to a file. The file

was used to program a CNC mill for precise placement of the holes. The perimeter

of the mask was also machined on the CNC mill to fit snugly in the window holder.

Once the mask was installed, its optimum rotational orientation was determined by

maximizing the signal from the chopped load (before installing the polarizing grid).

In Figure 4.15, the mask is visible through the polarizing grid.

The purpose of the mask is twofold. First, it limits the change in loading on

the detectors during the rotational cycle of the polarizing grid to keep the detector

response linear. As the grid rotates, it alternately appears reflective (minimal load-

ing) or transparent (maximal loading as the detectors see the 300K-77K chopped

signal). Secondly, the reduced aperture limits highly off-axis rays which are known

from optical models to produce higher cross-polar response.

4.3.4 Results and Discussion

The PSBs in QUaD are nominally oriented at one of four possible angles (0, 45,

90, 135 degrees) as seen in Figure 2.9. The two halves of a PSB pair are always

nominally orthogonal. Figure 4.16 shows test data for two PSB pairs representing

the four different orientations. The signals appear out of phase as expected and

approximately 3% cross polar leakage is seen. Sinusoids are fit to the results for all

the working PSBs and Figures 4.17, 4.18, and 4.19 display the resulting distribution

of orientations and cross polarization.

Most of the PSBs are oriented within ±2 of their nominal position and are

orthogonal to the same tolerance. Several mechanisms contribute to the errors in

PSB orientation including machining tolerances of the focal plane plate and PSB


modules, transmission through the cryostat optical chain, and placement of the

absorber within the PSB module. In particular the specified tolerance of ±1 on the

absorber position can account for much of the distribution.

The cross polar leakage results are more puzzling. The lower limit of the contri-

bution of the PSBs themselves is believed to be between 2 and 3% based on extensive

numerical modelling and testing of a previous generation of devices [Jones, 2005].

This figure is not in agreement with the QUaD results seen in Figure 4.19 which give

a mean value of 5% at 150 GHz and 8% at 100 GHz. The 150 GHz pixels perform

overwhelmingly better than the 100s and the best approach the 3% specification.

This substantial difference in performance is surprising given that the PSB modules,

feed horns, filtering, and fractional bandwidth in the two cases are extremely similar

and the optical chain is identical.

Prior to integration into QUaD, an optical testbed was used to test individual

pixels with a simplified optical chain that contains no lenses (Section 4.2.1). The

testbed contains a single feed and PSB located on axis. The band-defining and IR

blocking filters are very similar to those used in QUaD.

Testing began with a 150 GHz detector and extremely high levels of cross polar

leakage were measured (∼ 10%). Substantial effort was spent trying to determine

the source of the leakage. The interior surface of the cryostat was blackened to pre-

vent stray reflections and great care was taken to ensure that no chopped signal was

leaking around the polarizing grid without passing through it. Tests with different

blocking filters, a narrower bandpass, and a different feed horn showed no improve-

ment. The problem was eventually traced to a thermal connection between the two

orthogonal absorbers in the PSB pair. This particular thermal short was visible at

room temperature as a high-impedance connection between the electrical leads of

the two devices.

Our shipping deadline left us less time for testing the 100 GHz pixels in the

testbed; however, the higher cross polarization result was verified for one pixel. No

definitive explanation was found for the generally poor performance of the 100 GHz


Figure 4.20: Comparison of the measured cross polar leakage for the same detectorsin QUaD (solid) and the optical testbed (dashed). The data points from the testbedare shown as filled circles. Both data sets were taken through a 0.5” Eccosorbaperture located at the cryostat window. The testbed data points for each detectorare phased to best align with the QUaD data. These are the only PSBs that weremeasured in the testbed and installed in the final instrument.


pixels but the problem likely involves the horn bolometer interface or the horn it-

self since this is the only major difference between the optical chains for the two

frequencies.

This theory is supported by measurements of the horns return loss that were

performed using a vector network analyzer at NASA JPL. Return loss quantifies the

power that is lost to reflection when using the horn to transmit. The horns were

coupled to the analyzer using a modified PSB housing (containing no bolometers).

The return loss for the 100 GHz horns showed a feature around 90 GHz that depended

strongly on the interface between the horn and analyzer. Increased mating force was

able to reduce, but not eliminate this feature. An analogous feature was not seen

for the 150 GHz horns.

There were two PSB pairs that were tested in the testbed and are present in

the final receiver configuration. For both pairs, the results from the testbed were

comparable to, but slightly better than, that achieved in QUaD (see Figure 4.20).

This indicates that the lenses are not a significant source of cross polar leakage. The

large variation seen in Figure 4.19 is attributed to variations in the PSBs, horns,

and their interface.

All PSBs were screened based on warm resistance measurements and close visual

inspection under a microscope. Nevertheless, testing of large numbers of pixels in the

QUaD cryostat revealed PSB modules with intrinsically high cross polarization and

no obvious explanation. Every effort was made to relegate the poorly performing

devices to dark channels or omit them entirely; however, a severe shortage of PSBs

prevented us from being overly discriminating.

Fortunately, the orientation errors and the sources of cross polar leakage are built

into the instrument and are stable with time. They are small enough that they can

be ignored for rough calculations, but they must be included in the final analysis.

The next subsection explores some of the effects of these non-optimalities.


Response of a PSB to an Input of Arbitrary Polarization

Jones [2005] derives the voltage signal resulting from a PSB in response to input

radiation in an arbitrary polarization state. This subsection outlines that calculation

which results in eq. 4.42.

Since the incident radiation is incoherent and partially polarized, it is more nat-

urally described using Stokes parameters and the Meuller formalism. Recall that

a PSB is equivalent to an imperfect polarizer followed by a total power detector

(Section 4.3.2). The partially polarized incident radiation is represented by a Stokes

vector Si = (I,Q,U ,V)T . The PSB first acts as an imperfect polarizer, transforming

the incident Stokes vector, Si to Sf with Sf = MSi where M is the Meuller matrix

for the polarizer. The PSB then acts as a total power detector, giving a voltage

response proportional to the I component of Sf .

The Meuller matrix for the polarizer, M, can be found from its Jones matrix

using 4.31 with J given by

J = R

⎛⎜⎝ η 0

0 δ

⎞⎟⎠RT (4.40)

where R is the rotation matrix defined in eq. 4.36. Since the PSB only detects

the total intensity component (I) of Sf , we only need to calculate the top row of

Sf = MSi to determine the output voltage, v, as

v ∝ If =(

MII MIQ MIU MIV

)Si (4.41)

where If is the intensity component of Sf . Evaluation of the four components of M

listed in eq. 4.41 results in:

v = s[(1 + ε)I + (1 − ε) (Q cos 2θ + U sin 2θ)

](4.42)

where ε = δ2/η2 and θ is the orientation angle of the PSB and s is a calibration

constant that depends on detector responsivity, optical throughput (AΩ), optical


efficiency, bandwidth, and readout electronics gain. In practice, s is determined

using astronomical calibration (Section 5.2.3).

Implications

From eq. 4.42, the signal from a single PSB at a given angle is a linear combination

of the I,Q, and U components of the incident radiation. The three terms have

different angular dependencies allowing them to be separately determined, from

multiple measurements at different orientations.

The detector cross polar leakage, parameterized by ε, results in a loss of sensitivity

to the polarized portion of the radiation, but not in a mixing of I,Q, and U (i.e.

their angular dependence remains unchanged). For a map made with a single PSB,

uncertainty in ε translates into uncertainty in the overall calibration of the polarized

map to the total power map but not in a mixing of the individual maps – the

faint polarization signal will not be swamped by leakage from the much brighter

temperature signal.

In principal, a field can be characterized with a single PSB by measuring the

same patch of sky at multiple orientations. However, for a ground-based experiment,

where the large unpolarized atmospheric emission dominates, it is advantageous to

consider the difference signal from the two, nominally orthogonal PSBs in a pair. We

can take into account the small non-orthogonality of the two PSBs by considering

them to be oriented at angles (θ, θ + π/2 + ∆) where ∆ 1. The difference signal

is given by

va − vb = s(1 − ε)[(

Q +∆

2U)

cos 2θ +(U +

∆

2Q)

sin 2θ]. (4.43)

The difference signal is completely insensitive to unpolarized emission. The non-

orthogonality is seen to result in mixing between Q and U ; however, provided ∆ is

known, Q and U can still be uniquely determined with measurements at two angles.


In order for the contribution of the unpolarized radiation, I, to cancel upon dif-

ferencing two PSBs, eq. 4.43 assumed that the calibration constant, s, was the same

for the two channels. However, differing detector optical efficiencies, responsivities,

and amplifier gains mean that this will almost never be the case. Since QUaD reads

out both detectors individually, we can correct for this by applying a “software gain”

to the channels during post-processing.

The voltage signal from a QUaD PSB is dominated by unpolarized atmospheric

emission and noise:

va = saI + na

vb = sbI + nb

where sa and sb reflect differing gains of the two channels and na and nb are uncor-

related random noise (Section 5.3.2).

Consider the difference signal, with a gain correction factor, k, applied to vb:

va − kvb = (sa − ksb)I + na − knb (4.44)

An obvious method of determining k is to chose the value that minimizes the expec-

tation value of the square of the corrected difference signal for a segment of data:

0 =d

dk

⟨(va − kvb)

2⟩

→ k =〈va vb〉〈v2

b 〉=

sa

sb

〈I 2〉〈I 2〉 + 〈n2

b〉/s2b

(4.45)

where 〈〉 denotes the expectation value.

Equation 4.45 shows that in the limit where the unpolarized signal dominates the

polarized signal and the noise, the correct gain ratio sa/sb will be obtained. If the

unpolarized signal does not dominate the noise, k will underestimate the true gain

ratio. A technique for generating a large, unpolarized signal using the atmosphere

for the purpose of gain matching is discussed in Section 5.2.2.

Chapter 5

Instrument Performance

QUaD was commissioned at the South Pole during the 2004/2005 summer season

and began CMB observations in May 2005. Appendix B describes the main com-

missioning tasks involved with integrating the receiver and telescope. This chapter

describes tests done to characterize and monitor the performance of the completed

instrument.

5.1 Optical Performance

The performance of the optical system was verified by observing compact galactic

HII regions, which are the brightest sources visible above the ground shield (0 <

ZA < 55). Of these, the source known as RCW38 is the brightest.

5.1.1 Raster Maps

Raster maps of RCW38 were among the first observations with QUaD. While track-

ing the source, the telescope was scanned in azimuth as shown in Figure 5.1. The

scans begin with a short period of acceleration, then move at constant velocity, de-

celerate, and finally repeat the motion in reverse to return to the initial position

relative to the source. After a few scans, there is a short pause to change elevation

131

132 CHAPTER 5. INSTRUMENT PERFORMANCE

0 200 400 600 800 1000time (sec)

-148

-146

-144

-142

-140

-138A

zim

uth

Enc

oder

(de

g)

Figure 5.1: The azimuth encoder reading while raster mapping RCW38. The overallnegative slope results from tracking the source with sky rotation. The pause afterevery fourth constant velocity section (half-scan) allows time for the telescope tochange elevation and the DC offsets to be reset.

by a fraction of a beam width and to reset the DC offsets for the changed air mass.

A simple procedure converts the resulting time-ordered data into a pixelized map:

1. Convert the telescope axis encoder data into a right ascension (RA) and dec-

lination (DEC) value for every data point (sample).

2. Generate an empty, two dimensional array for the map data and a second one

to record the number of hits per pixel.

3. For each ADC data sample, determine which pixel it falls into from the RA

and DEC arrays. Add the data value to the appropriate pixel in the map, and

increment the corresponding entry in the hits per pixel array.

4. Divide the map by the hits array so that each pixel is appropriately weighted.

5.1. OPTICAL PERFORMANCE 133

Telescope Position

134.0 134.5 135.0 135.5 136.0RA (deg)

-49.0

-48.5

-48.0

-47.5

-47.0

-46.5

-46.0

DE

C (

deg)

Figure 5.2: The telescope RA/DEC position from an early QUaD raster map ofRCW38 shows sections of large elevation jitter. For clarity, only one out of everyfour half-scans is plotted and only every fourth elevation step is used. The elevationjitter problem was resolved shortly after this data was taken (see text).


RCW38 Raw Scan APR 10 HRN150-02

0 10 20 30 40 50sec

-0.3

-0.2

-0.1

0.0

0.1

1.4 × El (deg)

Signal (Volts)

Elevation Jitter Corrected

0 10 20 30 40 50sec

-0.3

-0.2

-0.1

0.0

0.1

Vol

ts

Signal - 1.4 × El

Figure 5.3: (top) Scan across the source RCW38 showing the effect of elevationjitter, which was present in early observations with QUaD. The elevation encoder,overplotted in red, is highly correlated with the bolometer signal. (bottom) Re-moving the best-fit scaled encoder signal reduces the effects of elevation jitter exceptwhen scanning across the source. This is purely illustrative as this technique is notused for any further analysis.


Figure 5.4: Maps of the galactic HII region, RCW38 at 100 (left) and 150(right) GHz. The top two plots are minimally processed – only the mean has beensubtracted from each scan line. The middle plots show the results of subtracting afifth-order polynomial from each row. The bottom plots use a neighboring feed tosubtract out the common mode signal. The object faintly visible below and to theright is a companion source.


Because QUaD is very near the Geographic South Pole, the relationship between

AZ/EL and RA/DEC is roughly given by:

RA ≈ AZ + 15 × LST

DEC ≈ −EL

where LST is the local sidereal time in hours. Figure 5.2 shows the telescope

RA/DEC during a raster map of RCW38. The declination axis shows the effects of

“elevation jitter,” a problem that plagued early observations with QUaD. The jitter

introduced an elevation-correlated signal into the time-ordered data that was par-

ticularly noticeable at 150 GHz. Figure 5.3 shows the effect on a single scan across

RCW38.

This problem was determined to result from the change in the telescope balance

point that occurred with the installation of the QUaD receiver. For angles near the

balance point, the servo system tended to oscillate around this unstable equilibrium.

The problem was corrected by shifting the balance point to an elevation below the

ground shield with the addition of several hundred pounds of counter weight.

The raw raster maps can benefit from several simple filters. Removing a best-

fit polynomial from every azimuth row acts as a high-pass filter, reducing the slow

drifts that result in the visible “striping” seen in the raw maps. Of course, any

known source must be masked out during the polynomial fit. For observations of

a compact source such as RCW38, feed differencing provides an extremely effective

filter since much of the atmospheric signal is common to all feeds. This technique

also removes astronomical signals on scales larger than the separation between the

two feeds and would therefore not be appropriate for CMB observations. Figure 5.4

shows example maps of RCW38 at both frequencies and the results of these filters.


5.1.2 Feed Offsets

Accurate knowledge of the feed offsets from the array center is needed in order to

combine maps of the same region made from different feeds in the focal plane. These

offsets can be determined from a large enough raster over a compact source such as

RCW38. If the dimensions of the raster are larger than the telescope field of view,

then each feed independently maps the source. The position of the source in the

map corresponds to the feed offset from the array center. Figure 5.6 shows maps for

all 31 feeds from the April 10th RCW38 raster.

Figure 5.5 compares the measured feed offsets to their nominal positions. The

agreement for the central pixels is good, with some distortion visible in the outer

rings.

QUAD Feed Postions

-1.0 -0.5 0.0 0.5 1.0deg

-1.0

-0.5

0.0

0.5

1.0

deg

Measured

Nominal

Figure 5.5: QUaD feed positions measured from RCW38.


Figure 5.6: QUaD raster maps of RCW38 from every feed in the focal plane.


Figure 5.7: Predicted beam pattern on the sky for the on-axis pixel. Figure courtesyof the QUaD optics team, NUI Maynooth.

5.1.3 Beams

Collaborators at NUI Maynooth (see Table 1.3) performed extensive modelling of

the QUaD optical system using Gaussian beam analysis and commercial software

packages (Zemax physical optics module, GLAD, and GRASP8). These calculations

resulted in the predicted beam patterns shown in Figure 5.7. The full width at

half maximum (FWHM) for the two frequencies are expected to be 4.2′ at 150 GHz

and 6.3′ at 100 GHz. For both frequencies, the peak of the cross-polar response is

below -30 dB relative to the co-polar beam. The modelling process and results are

described in more detail in Cahill et al. [2004] and Cahill [2005].

Measurements of the primary mirror surface indicate an RMS deviation of 0.12 mm

from the ideal parabolic figure. Most of this deviation is due to a “potato-chip” warp

which is well-modelled by a Zernike polynomial fit. This warp results in astigmatism

wherein the mirror has two different focal lengths along orthogonal axes aligned with

the warp. If the system is out of focus, then this effect results in an elliptical beam

pattern. Proper focusing results in circular beams; however, this is found not to


Table 5.1: Beam parameters as measured from RCW38 raster maps for the threegroups of detectors: The inner group of 150 GHz pixels, the outer ring of 150 GHzpixels, and the ring of 100 GHz pixels. The initial focus data is an average of fourdata sets taken between April and June 2005. The post refocus data results fromtwo data sets taken during July 2005. The full width at half maximum (FWHM) isdefined as the average of the FWHMs along the beam’s major and minor axes. Theellipticity is given by the ratio of the major to minor widths. A/B matching refersto the RMS deviation of these parameters between the beams of the two orthogonaldetectors in a PSB pair. Coefficients from 2D-Gaussian fits to each channel for eachRCW38 raster run were provided by C. Pryke and were used to generate the averageresults in this table.

Beam parameters A/B Matching

Group FWHM Ellipticity FWHM Ellipticity

Nominal 150 4.2 1.0 0% 0%100 6.3 1.0 0% 0%

Initial Inner 150 6.2 1.8 1% 2%focus Outer 150 5.2 1.5 1% 3%

100 6.0 1.3 1% 2%July 9 Inner 150 4.7 1.3 1% 2%refocus Outer 150 4.4 1.1 2% 2%

100 5.6 1.1 2% 3%

be possible over the entire field of view. In particular, the inner and outer rings of

150 GHz detectors cannot be simultaneously focused to be circular. Modelling in-

dicates that this effect does not substantially degrade the polarization performance

of the telescope – even for the most off-axis pixels, the maximal co-polar response is

predicted to remain 25 dB down. The distance between the primary and secondary

was found to be the critical parameter for setting the focus due to the fast (F/# =

0.5) beam off the primary. The system is much less sensitive to the receiver position

due to the slower beam off the secondary (F/# = 2).

Raster maps of RCW38, like those displayed in Figure 5.4, were used to charac-

terize the QUaD beams. Initial focusing and alignment was performed during the


summer season (see Appendix B.3). Table 5.1 summarizes the measured beam pa-

rameters. The 150 GHz beams, especially for the inner group, were larger than the

nominal value and showed high ellipticities. The results agreed with the predictions

from the optics modelling and indicated that the secondary was several mm out of

position. Note that despite the defocus, matching of beam parameters between the

two halves of a PSB pair is within a few percent.

The defocus was discovered during initial engineering observations at the start of

the 2005 winter season; however, attempting to refocus at this point was deemed too

risky. The secondary mirror had been designed to have a motorized focusing system

but for several reasons, including mechanical and electrical failures, the system was

not installed. Instead, the secondary mirror is mounted using an improvised system

that was developed on site at the South Pole. Three 1/2” threaded rods hold the

mirror in place on the top cap of the foam cone. Nuts are used to set the secondary

position, which determines the focus. Adjusting these nuts requires reaching in

through the top of the foam cone while standing outside on top of a ladder. The

nuts were custom made from large, rectangular blocks of aluminum which were

designed for gloved hands; nevertheless adjustment is not a simple task.

By early July, QUaD had completed a first pass over the CMB field (Chapter 6).

At this point it was felt that refocusing was necessary to confirm the optics model

in order to aid with planning upgrades for the next observing season. On July 9th,

the winter-over crew adjusted the secondary mirror position with excellent results.

Based on modelling from the optics team, a position was chosen that optimized the

focus for the outer ring of 150 GHz detectors due to the large number of pixels in

this group.

The bottom three rows in Table 5.1 summarizes the results of the refocus. The

beams are smaller and the ellipticity is reduced for all groups of detectors with the

outer group of 150s performing nearly within the initial specification. The 100 GHz

beams are seen to be ∼ 10% smaller than the nominal value. Extensive investiga-

tion into this effect has not yet been made, but it likely results from these pixels


illuminating the primary more than was expected (edge taper > −20 dB) which will

result in slightly more spillover and higher sidelobes.

Provided the beam shape is known, the ellipticity does not present a problem for

the data analysis. The larger beam size at 150 GHz for the initial focus does degrade

our sensitivity to small angular scales for the first pass over the field, limiting us to

the range < 2000. The reduced beam sizes after refocusing should enable future

passes over the field to reach our target of ∼ 2500.

Plans are in progress for an improved focusing system that will be installed during

the 2005/2006 summer season. The motorized system will allow the secondary mirror

position to be adjusted under computer control so that more frequent refocusing will

be practical. Commercial ultrasonic measuring systems are being investigated that

will allow real-time monitoring of the critical primary/secondary distance for any

changes that result from the large (50 C) changes in ambient temperature that

occur during the Polar winter.

5.1.4 Time Constants

Section 4.2.4 introduced bolometer time constants and described how they were

measured in the laboratory. As noted in that section, the laboratory loading and

bias setting were substantially different than during CMB observations. This section

describes how the time constants were remeasured under more typical observing

conditions.

The method involved scanning the telescope forward and backward (increasing

/ decreasing azimuth) across RCW38 and looking at the delay introduced by the

receiver transfer function (eq. 4.27). Figure 5.8 (top) plots the resulting data against

the azimuth offset, showing the separation in the apparent source azimuth position as

measured from the forward and backward going half-scans. A fit then determines the

value of the bolometer time constant necessary to produce the observed separation.

The bottom plot compares the results with the laboratory measurements.


0 10 20 30 40 50Detector

0

50

100

150

Tau

(m

S)

RCW38Lab

Figure 5.8: (top) Measuring time constants with RCW38. Forward and backwardscans across the source are plotted versus the azimuth offset. The source appears in aslightly different position depending on the scan direction due to the delay associatedwith the receiver transfer function including the bolometer time constant. Figurecourtesy of C. Pryke. (bottom) Time constants as measured from scanning acrossRCW38 compared with those measured in the lab. The lab values are smaller dueto the higher loading and bias during these measurements (Section 4.2.4). RCW38time constant values provided by C. Pryke.


Figure 5.9: QUaD skydip data from April 4, 2005. The symbols are data pointsand the line is a fit to the model described in the text (eq. 5.5). For this data, themedian of the fits to the seven bolometers yields τ Tatm = 10.4±0.5 K and the tippergives Tatm as 222 K making τ = 0.047. The different y-intercepts correspond to thedifference in absolute loading reported by the detectors.

5.2 Calibration

5.2.1 Atmospheric Transmission

The optical efficiency of the telescope system is reduced by atmospheric absorption.

Similarly, atmospheric emission causes excess loading that warms the bolometers

and leads to excess noise. Both of these affect the instrument sensitivity and thus

must be quantified. For QUaD this is done with a procedure known as a skydip,

wherein the atmospheric emission is measured at multiple zenith angles. Changing

weather conditions, necessitate frequent monitoring.

The quantity of interest is the band-averaged atmospheric transmission as a func-

tion of zenith angle. Using a simple model, we can parameterize the zenith angle

5.2. CALIBRATION 145

Figure 5.10: QUaD skydip data plotted against data from the 350 micron tipper.The line gives the best-fit linear relation between the two. The red line gives therelation derived in Runyan [2002] for ACBAR 2001 skydip data with their 150 GHzband.

dependence as Tatm = e−τ/ cos θ where τ , known as the optical depth, depends on the

frequency band of observation. The atmospheric emissivity, ε, is given by

ε = 1 − Tatm

= 1 − e−τ/ cos θ. (5.1)

As the telescope tips toward the horizon, atmospheric loading increases. Conversely,

loading from the CMB (assumed to be the dominant astrophysical source) decreases


Figure 5.11: Atmospheric opacity data from the 350 micron tipper, scaled using thelinear relation in Figure 5.10. QUaD data is overplotted as crosses.

due to the decreased atmospheric transmission. This can be summarized as:

Tload(θ) = Tfixed + ε T RJatm + (1 − ε)T RJ

CMB (5.2)

= Tfixed +(1 − e−τ/ cos θ

)T RJ

atm + e−τ/ cos θT RJCMB (5.3)

where T RJatm and T RJ

CMB are the Raleigh-Jeans temperatures of the atmosphere and the

CMB.1 The constant, Tfixed, includes all sources of loading that do not vary with

1Tatm is a weighted, line-of-sight averaged atmospheric temperature and is not in general thesame as the surface air temperature.


zenith angle such as emission from the filters and the telescope. Simplification yields

Tload(θ) = Tfixed + Tatm − e−τ/ cos θ(T RJ

atm − T RJCMB

). (5.4)

The Raleigh-Jeans (RJ) temperature of a black body of thermodynamic temperature

T is defined as

∫dν f(ν) 2

ν2

c2kT RJ AΩ =

∫dν f(ν) B(ν, T ) AΩ

where B(ν, T ) is the Planck function and f(ν) is the frequency band of the instru-

ment. Simplification yields

T RJ =c2

2k

∫dν f(ν)B(ν, T )ν−2∫

dν f(ν)

which is dependent on the shape of the receiver’s spectral band but not its overall

normalization. The RJ temperature is always less than the thermodynamic temper-

ature, but the difference becomes insignificant for kT hν. At the QUaD bands,

the CMB is not in the RJ region. For the QUaD average spectral bands (shown in

Figure 2.5), the RJ temperatures of the CMB are 1.07 K and 0.562 K at 100 and

150 GHz.

Simplifications to eq. 5.4 can be used in practice. First, the atmospheric tem-

perature is sufficiently large (> 200 K) that its physical temperature is the same

as its RJ temperature. Second, the signal from the CMB can be neglected since

it is much smaller than that from the receiver, the telescope, and the atmosphere.

Finally, τ/ cos θ 1 so eq. 5.1 may be approximated2 as ε ≈ τ/ cos θ. Making these

approximations in eq. 5.2, the loading becomes

Tload(θ) ≈ Tfixed +τ Tatm

cos θ. (5.5)

2At the South Pole, τ150 is always less than ∼ 0.1 and QUaD is restricted to zenith angles lessthan 45.


Thus with QUaD skydip data alone, it is not possible to separately fit for τ and Tatm.

Fortunately, we have access to data from the AST/RO 350 micron tipper (located

on an adjacent building) which measures Tatm (and τ at 350 microns) several times

per hour.3

During routine observing, QUaD performs one skydip per day. Approximately

30 seconds of integration is performed at each of nine zenith angle steps. For sim-

plicity, the data are taken in DC biased mode. The raw bolometer voltages are

converted to power and then to loading temperature using the procedure outlined

in Section 4.1.2. A load curve, taken immediately following the skydip, is used to fit

for G0 and β. Figure 5.9 shows the results of a typical run for the bolometers with

dark characterization listed in Table 4.1.

The offset present on all the bolometers in Fig 5.9 corresponds to the constant

term in eq. 5.5 and includes contributions from the cryostat internal loading, emis-

sion from the telescope, and the atmospheric loading at zenith. The value is very

sensitive to the focal plane temperature and the parameters R0 and ∆, resulting in

the large scatter seen in the plot.

In order to have more frequent updates on the atmospheric transmission, without

spending valuable observing time on skydips, a correlation is performed between the

150 GHz τ obtained by QUaD and the 350 micron τ from the tipper. Figure 5.10

shows the correlation between the two data sets. The best fit line gives the relation

τ150 = 0.0134 + 0.0148τ350µm. (5.6)

Figure 5.11 shows the tipper data, scaled to 150 GHz using the linear relation, with

the QUaD skydip data overplotted.

3The key to measuring τ and Tatm with a skydip is to operate at a shorter wavelength or go toextremely low elevations such that τ Tatm/ cos θ ∼ 1 and fitting with eq. 5.4.


5.2.2 Routine Gain Calibration

Bolometric receivers need to be frequently recalibrated since small changes in base-

plate temperature and optical loading (due to changing weather or elevation angle)

cause drifts in the overall gain (via changing bolometer responsivity). The following

describes three methods QUaD uses to monitor the relative system gain.

RCW38 Row Cals

As discussed in Section 5.1, the Galactic HII region RCW38 is the brightest and

best characterized source available to QUaD. Raster mapping RCW38 with every

feed requires the better part of a day, so frequent recalibration with this technique

would be impractical.

An alternative technique, known as a “row cal” was developed in which each of

the seven rows of the focal plane array are scanned in turn across the source. The

height of the blips from the source provide a gain calibration for each feed. We

currently perform four row cals per day. Each of these is preceded by an observation

known as a “pointing cross” in which the central pixel is scanned in azimuth and in

elevation over the source. This allows any pointing offset between the instrument

and telescope axes to be quantified.

Calibration Source

Design Overview

The QUaD calibration source sits inside the foam cone, just above the secondary

mirror. Figure 5.12 shows a photo of the mechanism and a schematic of its location

and key parts. When the cal source is not in use, the central part of the beam from

each feed passes through the hole in the secondary onto the sky. During a run of the

cal source, a flip mirror behind the secondary hole rotates 45, directing this part of

the beam through a polarizing grid onto a blackbody source at ambient temperature.


Blackbodysource

Rotating grid

IR datalink

Flip mirror

Secondary

Cryostatsnout

(NOT TO SCALE)

Figure 5.12: The QUaD calibration source. (top) Photograph showing the majorcomponents. (bottom) Cartoon placing the calibration source in context. Note, inorder to see the cal source clearly, the primary mirror is shown much smaller andcloser to the secondary than it really is. See Figure 2.1 for an accurate drawing ofthe optics.


Figure 5.13: (top left) The reduced cal source flip mirror. (top right) A single runof the cal source as recorded by the central pixel. (bottom left) Data (black) andsine wave fit (red) measured in low gain mode.(bottom right) Another run, this timerecorded in high-gain mode.


Rotating the polarizing grid produces a modulated signal.4

When the cal source was first operated, the modulated signal was much larger

than expected, and it caused the ADC to saturate when the electronics were operated

in the usual observing mode (the high-gain setting). Additionally, substantial excess

loading resulted when the mirror was flipped down, changing the operating point

of the bolometers and making any calibration results less meaningful. Our solution

was to mill away most of the flip mirror, leaving only a small reflecting disk suspend

in the center with nylon string. Figure 5.13 (top) shows the second version of the

flip mirror and the resulting signal from a cal source run.

The top part of the flip mirror frame still covers the secondary hole resulting in

a small change in the loading level when the mirror is down; however, the problem

is greatly reduced with the new design. At this point, it was felt the amplitude of

the modulated signal could be increased so we doubled the size of the reflecting disk.

Figure 5.13 (bottom) shows the high signal-to-noise data that resulted from the final

configuration.

Origin of the Modulated Signal

Consideration of how the cal source modulated signal arises reveals a weakness in

the optical design. Minima in the cal signal result when the polarizing grid is anti-

aligned with the PSB axis of sensitivity – the grid appears transparent and the PSB

is loaded by the black body source resulting in a lower voltage. The optical path

here is well-understood and the temperature of the black body source is monitored

with a built in thermometer. Maxima occur when the grid is aligned with the PSB

axis and thus reflective. Here the optical path is not well understood – some of the

reflected power will again pass through the primary hole and fall on the cryostat

window or the primary mirror, the rest will be scattered or absorbed inside the cal

source itself. This is far from ideal.

4The calibration source was designed and manufactured by the QUaD collaborators at theUniversity of Cardiff. The controlling electronics were rebuilt at the Pole when the original systemwas destroyed by static electricity.


El Nod - 150-03

0 10 20 30 40 50 60sec

0.0

0.5

1.0

1.5

2.0

Sig

nal

150-03A (Volts)150-03B (Volts)

Elevation offset (deg)

A/B Correlation

0.0 0.2 0.4 0.6 0.8 1.0Signal B (Volts)

0.0

0.2

0.4

0.6

0.8

1.0

Sig

nal A

(V

olts

)

Gain A/B = 0.74

Figure 5.14: (left) The signals from an elevation nod for a single feed. (right) Thesignals are highly correlated. The slope of the best-fit line gives the ratio of the gainsfrom the two detectors.

Elevation Nods

We developed a third method of relative calibration known as an elevation (or el)

nod. Here, the telescope performs a miniature sky dip, offsetting in elevation by

1.5 from the initial position. The resulting change in air mass generates a signal of

order a Volt in a typical detector. Figure 5.14 (left) shows the signal from a sample

el nod for the two halves of a PSB pair. The right half of the figure shows a simple,

but very useful, way to analyze the data. The two signals are plotted against each

other and the slope of the best-fit line gives the ratio of the gains. This quantity is

known as the A/B ratio, where A and B refer to the two detectors in the pair. This

method is very reliable since the two detectors are looking through the same feed at

the same column of (unpolarized) atmosphere. El nods can also be used to find the

relative gain from feed to feed, although a correction must be applied to account for

the different air mass seen from different rows.


QUAD Relative Calibration

0 5 10 15 20Hours

0.4

0.6

0.8

1.0

1.2

1.4

1.6

A/B

gai

n ra

tio

150-04

150-03

150-02

row cal

el nod

cal src

row cal

el nod

cal src

16 MAY 2005 17:45:40 Row cals: 4 El Nods: 132 Cal srcs: 132

Figure 5.15: The A/B gain ratio for three feeds measured using the three differenttechniques discussed in this section: RCW38 row calibrations, elevation nods, thecalibration source.

Summary

A comparison and summary of the three calibration methods discussed so far is in

order. Figure 5.15 shows the A/B gain ratio derived from the three methods over

the course of a single observing day.

RCW38 row cals These provide an absolute calibration for each detector, but the

measurement is slow.

Cal source The cal source gives extremely stable results which provides great reas-

surance in the gain stability of QUaD; however, the relative gain measurements

it gives do not agree with those derived from the other two methods. This is

not surprising given its poorly understood optical path.


dB/dT at T = TCMB

0 100 200 300 400Freq (GHz)

0.0

0.2

0.4

0.6

0.8

1.0

150 GHz band100 GHz band

dB/dT

Figure 5.16: The factor dB/dT evaluated at T = TCMB enters into the calibrationvia eq. 5.9. It is approximately twice as large for the 150 GHz channels as itis for the 100 GHz channels. This combined with larger bandwidth and higheroptical efficiency makes the 150 GHz channels more responsive to CMB temperaturefluctuations in terms of V/µK despite having only ∼ 1/2 the throughput.

Elevation nods The el nod procedure is simple, quick, and the resulting signals

are well understood. Thus, el nods provide the best method of matching the

gains between detectors on a regular basis.

In summary, the provisional strategy is to use the row cals to normalize the respon-

sivity several times per day and el nods to provide a relative calibration between

detectors on shorter time scales.

5.2.3 Absolute Calibration

In order to compare our CMB maps with theoretical predictions and results from

other experiments, we need to convert the signals we measure from Volts into a

standard flux unit. The preferred unit for CMB experiments is ∆TCMB in µK.


This gives the temperature fluctuation about T0 = 2.728K necessary to produce the

observed flux. Performing this conversion (from Volts to µK) is called calibration.

The absolute calibration of millimeter-wave experiments is never easy, but the sit-

uation is made more difficult for QUaD. The high ground shield and Polar location

prevent us from observing planets, which are the best-characterized astronomical

calibration sources at these wavelengths. This section presents calibrations obtained

from three different methods. The first estimates the calibration factor from the

laboratory measurements made in Chapter 4. The second method compares QUaD

measurements of RCW38’s flux with published results for this source. Finally, cali-

bration results obtained by comparing preliminary QUaD CMB maps with those of

previous experiments are presented.

Estimates from Laboratory Characterization

Raw bolometer signals, in units of Voltage as recorded by the ADC, can be converted

into CMB temperature units (Kelvin) as

T (t) =

⎛⎝SDC G

dPB

dT

∣∣∣∣∣TCMB

⎞⎠

−1

V (t) ≡ sK/V × V (t) (5.7)

where the second equality defines the conversion constant, sK/V, from Volts to Kelvin.

The function PB gives the optical power from a beam-filling astronomical blackbody

source such as the CMB:

PB(T ) =1

2TatmηT

∫AΩ fn(ν) B(T, ν) dν (5.8)

where Tatm is the atmospheric transmission (Section 5.2.1), ηT is the optical efficiency

of the telescope optics, fn(ν) is the absolute spectral bandpass of the receiver defined

in eq. 4.19, AΩ = λ2 is the throughput, and B(T, ν) is the Planck spectrum.

For the QUaD bands, the derivative dPB/dT evaluated at TCMB is given with good

accuracy (a few percent) by evaluating dB/dT at the band center and approximating


the integral asdPB

dT≈ 1

2Tatmηλ2

0 ∆νdB

dT

∣∣∣∣∣T=TCMB, ν=ν0

. (5.9)

where η is the total optical efficiency of the system given by the product of the

receiver efficiency and the telescope efficiency:

η ≡ ηR × ηT . (5.10)

The telescope efficiency is estimated to be ∼ 0.82 including loss from the foam cone,

the primary mirror, and most significantly the blockage caused by the secondary

mirror (Table 5.2). This results in an average total efficiency of ∼ 0.26 for the

150 GHz detectors, using the average receiver efficiency listed in Table 4.3.

For the QUaD bands, using the average value of the properties at each frequency,

this results in the calibration estimates of

100 GHz: 5.1 · 105 µK

volt×(

0.94

Tatm

)(0.82 · 0.26

ηT ηR

)(26.5 GHz

∆ν

)(3.6 × 108 V/W

SDC

),

150 GHz: 4.3 · 105 µK

volt×(

0.94

Tatm

)(0.82 · 0.32

ηT ηR

)(40.5 GHz

∆ν

)(3.1 × 108 V/W

SDC

).

Estimates from RCW38

The estimates in the previous section rely on using system parameters that are

measured in the laboratory. These parameters are difficult to measure and subject to

error. This section uses the previously measured flux of RCW38 in order to estimate

the calibration factor for QUaD with minimal reliance on laboratory quantities.

ACBAR measured the flux density from RCW38 within an 8’ radius with their

150 GHz band [Runyan, 2002]. Averaging their 2000 and 2001 values, J150RCW38 =

145 Jy with a 10% uncertainty. The uncertainty is dominated by systematics includ-

ing the errors from their planetary calibration, voltage integration, and responsivity

scaling. Coble et al. [2003] found the flux at 90 GHz from RCW38 to be ∼ 10%

larger than at 150 GHz, allowing a calibration of the QUaD 100 GHz channels as


well.

The integrated flux in an 8’ radius was computed for QUaD raw RCW38 maps

yielding a value in Volts arcmin2 (VRCW38) for each channel. This allows a conversion

into units of temperature fluctuations about the mean CMB temperature as:

sK/V =

(JRCW38 × 10−26

VRCW38

)⎛⎝ dB

dT

∣∣∣∣∣TCMB, ν0

⎞⎠

−1 (sr

arcmin2

)(5.11)

where B(ν, T ) is the Planck spectrum and the derivative is evaluated at the measured

band center frequency (Figure 5.16).

In terms of average QUaD values, this yields calibrations of:

100 GHz: 6.0 × 105 µK

volt×(

14.3 Volts arcmin2

VRCW38

)(0.94

Tatm

)(5.12)

150 GHz: 4.6 × 105 µK

volt×(

9.4 Volts arcmin2

VRCW38

)(0.94

Tatm

). (5.13)

Cross Calibration with B2K

The final QUaD calibration will come from cross correlating our CMB temperature

measurements with those of B2K for the same region of sky. Chapter 6 discusses

our field selection and overlap with the B2K experiment in more detail, and Figure

6.5 shows our respective maps. A preliminary cross-correlation of the initial maps

yields calibration values that are consistent with the two methods presented above5:

100 GHz: 5.0 × 105 µK

volt(5.14)

150 GHz: 4.3 × 105 µK

volt(5.15)

5Thanks to J. Kovac for providing these calibration results.

5.3. SENSITIVITY AND NOISE 159

These values are used to calibrate all of the maps shown in Chapter 6.

5.3 Sensitivity and Noise

5.3.1 Optical Loading

QUaD performs several load curves each day and these can be used to investigate

the total loading as a function of time. From each load curve, eq. 4.12 provides an

estimate of the total optical power falling on the bolometer, just as in the sky dip

analysis. Again, this can only be performed for the seven detectors with known R0

and ∆ parameters listed in Table 4.1. Figure 5.18 shows the results for load curves

spanning several months.

The dashed blue line in the top plot is the loading predicted by eq. 5.5 based on

atmospheric data from the AST/RO 350 micron tipper and the telescope elevation

angle. The agreement between the black and blue lines over time indicates that the

atmosphere is causing the variations in the loading. This confirms that there is not,

for example, a steady increase of loading that would indicate an accumulation of ice

on the cryostat window or some similar problem.6 Figure 5.17 (bottom, red curve)

shows the nearly-constant difference between total and atmospheric loading.

This analysis can also be used to determine the loading caused by the telescope.

This includes contributions from the foam cone, the primary mirror, and the sec-

ondary mirror. This is possible because in an early test run in December 2004 we

took several load curves and sky dips without the telescope optics. Figure 5.17 shows

the loading from the receiver measured in this configuration (green). This is the total

loading minus the approximately 13.5 K of loading from the atmosphere on that day

at zenith. Comparison with the mean receiver loading from data with the full opti-

cal system (red) indicates approximately 10 K of excess loading from the cone, the

primary, and the secondary. Table 5.2 gives an estimated component-by-component

breakdown accounting for the observed total loading.

6The receiver window cannot be accessed or viewed once the receiver is installed in the telescope.


Table 5.2: QUaD estimated loading component by component breakdown. For thereceiver section of the table, the optical component drawing in Figure 2.4 may beuseful.

Component Physical Loading Incident Total Power atComponent Trans. temp. temp. power trans. detector

(K) (K) (pW) (pW)Atmosphere 0.943 220.00 12.44 7.31 0.290 2.12

TelescopeFoam cone 0.975 220.00 5.50 3.23 0.297 0.96Primary Mirror 0.990 220.00 2.20 1.29 0.300 0.39Secondary loss 0.150 32.44 4.87 2.86 0.353 1.01Telescope total 2.36

ReceiverWindow 0.995 220.00 1.10 0.65 0.355 0.23Reflection loss 0.010 160.00 0.08 0.05 0.359 0.02IR filter 0.995 160.00 0.80 0.47 0.361 0.17

IR filter 0.995 160.00 0.80 0.47 0.362 0.1712 cm edge 0.995 160.00 0.80 0.47 0.364 0.17IR filter 0.995 160.00 0.80 0.47 0.366 0.17

9cm edge 0.995 20.00 0.10 0.06 0.368 0.028cm edge 0.995 20.00 0.10 0.06 0.370 0.02Lens 1 0.990 10.00 0.07 0.04 0.377 0.02Reflection loss 0.010 10.00 0.07 0.04 0.377 0.02Lens 2 0.990 10.00 0.07 0.04 0.385 0.02Reflection loss 0.010 10.00 0.07 0.04 0.385 0.02Waveplate 1.000 7.00 0.00 0.00 0.385 0.00Spillover 0.030 7.00 0.12 0.07 0.385 0.03

7cm edge 0.995 0.50 0.00 0.00 0.387 0.00Bolo. assembly 0.387 0.25 0.15 0.09 1.000 0.09Receiver total 1.15

Total 5.63

It should again be emphasized that measurements of the absolute loading are

extremely difficult as discussed in Section 4.1.2. All the results in this section may

be in error by a constant loading term of order 0.5 pW reflecting the scatter in the

loading values reported by the seven characterized light detectors. However, loading


QUAD Loading Comparison

17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21

Apr May Jun

0

2

4

6

8

10Lo

adin

g (p

W)

0

10

20

30

40

TR

J (K

)

Total (load curves)Atmosphere (sky dips)Other (difference)Receiver only

Figure 5.17: Receiver loading (red) determined by subtracting the total loading(black, measured with QUaD load curves) from the atmospheric loading (blue, mea-sured by QUaD sky dips). The flatness of the red curve confirms that variableloading from snow or ice accumulation is not a large factor. The same procedurewas applied to data from Dec 19, 2004, which was taken without the foam cone,the primary, and the secondary (green line). The measured difference (∼ 10 K) isattributed to loading from the telescope optics.

differences, used to determine atmospheric loading from skydips, are robust to this

offset.


QUAD Loading

17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 215

6

7

8

9

10

Load

ing

(pW

)

25

30

35

40

45

TR

J (K

)

17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 211

2

3

4

5

Tau

350

mic

ron

0.03

0.04

0.05

0.06

0.07

0.08

Tau

150

GH

z

17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21

Apr May Jun

0

20

40

60

80

Ele

vatio

n (d

eg)

Figure 5.18: (top) The measured loading from approximately 300 load curves, ob-tained from eq. 4.12 averaged for the seven detectors in Table 4.1. The dashedblue line shows the loading that would be predicted from the model in eq. 5.5 usingthe τ and elevation information shown below. The atmospheric temperature data(not shown) is also from the 350 micron tipper and it varies between approximately200 and 250 K. (middle) Atmospheric opacity data from the AST/RO 350 microntipper scaled to 150 GHz using eq. 5.6. (bottom) The telescope elevation duringthe load curve measurements. When CMB observations began in May, we startedtaking load curves at the elevation of our observing field rather than returning tozenith. For the astute observer, the 350 micron tipper was not functioning for a fewdays around April 12.


Figure 5.19: Components of the noise equivalent power (NEP) versus bias currentfor a typical QUaD detector.

5.3.2 Noise Equivalent Power

Noise Sources

The sensitivity of bolometric detectors is limited by several different sources of noise.

These include noise from the device itself (Johnson and phonon), from the readout

electronics, and from the quantum nature of the optical signal (photon noise). These

noise sources cause the output voltage of the detector to fluctuate about a mean

value. The fluctuations can be characterized by an RMS value over some bandwidth

or more commonly by the power spectral density given in units of V Hz−1/2.

For millimeter and sub-millimeter detectors this voltage noise is often converted

into a noise equivalent power (NEP) by dividing by the responsivity. Physically,


the NEP gives the incident optical power required to generate an output voltage

equal to the RMS noise voltage computed over some bandwidth. Note that a one

second integration is equivalent to 0.5 Hz of bandwidth so that the NEP expressed

in W Hz−1/2 is equal to the optical power that can be measured with a signal to

noise ratio of one in a two second integration.

Figure 5.19 shows the contributions to the NEP for a typical QUaD detector.

Like noise voltages, NEPs from uncorrelated sources add in quadrature resulting in

the total NEP curve shown in black. The various noise sources are reviewed below.

Johnson Noise The high-impedance thermistor in the bolometer produces John-

son noise just like any resistive device. An approximate form for this term, useful

for estimates, is given by the intuitive expression

NEP 2Johnson ∼ 4kBTR

S 2

where the responsivity is used to convert the voltage noise into an NEP. However,

the non-Ohmic behavior of the thermistor and the presence of the load resistors

complicates the situation. The full expression is given in Mather [1984] as

NEP 2Johnson = 4kBTP

(z + R

z − R

)2 ( S

SDC

)2

. (5.16)

Phonon Noise Heat flowing out of the absorber through the thermal link is quan-

tized in the form of phonons giving rise to another source of noise. An approximate

form is given by

NEP2phonon ∼ 4kBT 2G.

Note that division by the responsivity is unnecessary since fluctuations in the power

flowing out of the absorber (∼ G ∆t) are equivalent to fluctuations in the incident

optical power (∆Q). This simple equation, however, does not take into account the

variation in temperature from Tbolo to Tbase along the absorber. The full expression


is given as an integral in Mather [1984]

NEP 2phonon = 4kBG(T )T 2

∫ TTbase

[tG(t)

]2/[TG(T )

]2dt∫ T

Tbase

[G(t)/G(T )

]dt

(5.17)

where T = Tbolo. For our power law model, G(T ) = G0(T/T0)β with the reference

temperate taken to be the baseplate temperature (T0 = Tbase), the integrals can be

explicitly evaluated as

NEP 2phonon = 4KBT 2

0 G0

(β + 1)[(T/T0)

2β+3 − 1]

(2β + 3)[(T/T0)β+1 − 1

] . (5.18)

Amplifier Noise The readout electronics contribute to the total NEP as

NEP 2amp =

V 2n (ω)

S(ω)2(5.19)

where Vn is the quadrature sum of the voltage noise arising from the JFETs and

the warm electronics as discussed in Section 3.2.2. The voltage noise, Vn, is approx-

imately white over the frequency range of interest (0.1 - 2.5 Hz) with a value of ∼9 nV Hz−1/2. This mean value of Vn is used for the amplifier noise term in the NEP

curves shown throughout this section.

Photon Noise The incident optical radiation is quantized which leads to two

additional noise terms collectively known as photon noise. The first term is the

standard shot noise due to the random arrival times of the individual photons and

is given by

NEP 2Poisson = 2Qhν.

The second term, known as the Bose or “bunching” term, arises because photons

are Bosons. Appendix B of Runyan et al. [2003] gives a review of the origin of this


term. The NEP associated with the bunching is given by

NEP 2Bose =

Q2

∆ν

where ∆ν is the optical bandwidth of the receiver. The quadrature sum gives the

total photon noise

NEP 2photon = NEP 2

Poisson + NEP 2Bose.

An absolute measurement of the optical loading, Q, is needed to calculate the

photon noise contribution to the NEP which, as discussed in Section 4.1, is difficult.

For a given load curve, the scatter in the values of Q determined from eq. 4.12

(∼20%) for the seven optical detectors listed in Table 4.1 differ far more than can

be explained by the scatter in their optical efficiencies (∼5%). In order to compare

the detectors more fairly, the loading actually used to compute the photon noise in

the NEP curves in this thesis is the average from the seven estimates. Fortunately,

errors in the assumed loading do not change the shape of the NEP curve since the

photon noise term is independent of bolometer temperature (and thus bias value).

Total NEP The total NEP is the quadrature sum of the individual components:

NEP 2total = NEP 2

Johnson + NEP 2phonon + NEP 2

amp + NEP 2photon. (5.20)

The first two terms (Johnson and phonon) are collectively referred to as detector

noise. Advances in detector design and materials has greatly reduced their contri-

bution. Advances in technology can similarly reduce amplifier noise. The photon

noise term can be limited by choosing the best observing site available and reducing

emission from the filters, cryostat, and telescope. Of course, it can never be reduced

below the limit imposed by the photons from the source radiation itself.

The terms that depend on the detector responsivity (Johnson and amplifier)

increase drastically at low bias values as the responsivity drops to zero. For large

biases, the Johnson noise does not increase as fast as the amplifier noise since the


Figure 5.20: Total NEP for a subset of the QUaD detectors.

detector resistance drops. The phonon contribution rises slowly as the absorber

warms with increasing bias.

Figure 5.20 shows the predicted NEP curves for the seven optical detectors listed

in Table 4.1. The curves show the low-frequency limit of the NEP (ω = 0) versus the

applied bias current. The bias level changes the bolometer operating temperature

which effects all the noise sources except the photon term.

Bias Optimization

Determine the best setting of the bolometer bias current for observing provides a

useful application for the NEP curves derived in the previous subsection. For the

detectors in Figure 5.20, the minimum NEP is ∼ 6 × 10−17 W Hz−1/2 and it occurs


at a bias value of ∼ 0.75 nA. In practice, however, a larger bias current is used.

A variety of factors argue in favor of biasing above the NEP minimum. The NEP

rises quickly below the minimum point owing to the rapidly decreasing detector re-

sponsivity. Under biasing any detector, even by a small amount, is thus undesirable.

This is evident in the total NEP curve shown in Figure 5.19.

The minimum point occurs at a different bias for each detector due to variations in

the parameters R0, ∆, G0, and β. However, the internal wiring of QUaD requires all

detectors of a given frequency (100 or 150 GHz) to have the same bias. Additionally,

the minimum point moves for a given detector with variations in loading caused by

changing weather or zenith angle.

Increasing the bias is desirable from the point of view of detector stability. Figure

5.22 (left) shows the average responsivity for all QUaD detectors at three different

elevations (on the same day, April 20, 2005) and thus three different loading levels.

The right plot shows the fractional change in responsivity in going from an elevation

of 55 to 45 which roughly corresponds to the QUaD field. Increasing bias keeps

the bolometer responsivity more stable.

For these reasons, QUaD biases at approximately 1.2 nA. Over-biasing decreases

the detector impedance resulting in additional advantages including reduced sensi-

tivity to microphonic and RF pickup. Increased electrical power also results in faster

detector response due to smaller effective time constants (Section 4.2.4). These ad-

vantages more than outweigh the ∼ 5% decrease in raw sensitivity.


Figure 5.21: Responsivity for all channels under typical observing conditions. Therange of bias currents is indicated by the vertical red band (variations in detectorresistance lead to a range of bias currents for a fixed bias voltage).

Figure 5.22: (left) Average responsivity versus bias at several zenith angles andthus at different values of loading. (right) The change in responsivity with loadingversus bias current. Higher bias currents lead to responsivities that are more stableto loading changes.


Figure 5.23: Typical 150 GHz time-ordered data for two bolometers in a PSB pair(black and red traces) while observing a source-free region of sky. The green signalis one half times the difference of the black and red. The individual channels clearlyshow the effect of atmospheric noise. The mean has been removed from each signalbefore plotting.

NEP from Voltage Noise

This section compares the NEP predicted from the various theoretical noise sources

with an estimate based on the measured voltage noise of the receiver. Figure 5.23

shows a segment of data (four half-scans) from both halves of a PSB pair taken

while scanning the telescope over a source-free region of sky (the CMB field). This

data was taken on a day with good weather conditions (τ150 ∼ 0.035); nevertheless,

considerable atmospheric 1/f noise contaminates the individual channels (red and

black). This noise arises because the atmosphere is not completely homogeneous

– pockets of more and less emissive air drift through the telescope beam causing a

slowly drifting output signal. The effect is worse at 150 GHz because the atmospheric

emission here is dominated by water vapor, which is poorly mixed. Atmospheric

1/f noise, as opposed to photon noise, is not included in the NEP estimates of

the previous section. The low-frequency noise is highly correlated between the two

channels since atmospheric emission is unpolarized. Differencing, which is required


to measure Q or U , results in a much more stable signal (green).

For each detector, division of the raw voltage, V (t), by the product of the elec-

tronics gain (G) and the bolometer responsivity (SDC) converts to optical power

absorbed by the detector P (t)

P (t) =V (t)

GSDC. (5.21)

The responsivity of each detector is obtained from a load curve at the same elevation

and weather condition as the time stream data of interest. The DC responsivity is

used because the detectors are fast enough that S(ω) is flat over the frequency range

of interest.

Labelling the two halves of a PSB pair as “a” and “b” we can consider the sum

and difference optical power:

Psum = Pa + Pb and Pdiff = Pa − Pb. (5.22)

The sum signal, Psum, gives the total optical power detected by the feed. This is

the same power that would be measured if a total power bolometer had been used

instead of a PSB pair.

Figure 5.24 shows the resulting power spectral density7 for the sum and difference

signals, labelled NEPsum and NEPdiff. In the absence of correlated noise, we expect

NEP 2sum = NEP 2

diff = NEP 2a + NEP 2

b . (5.23)

This is seen in the power spectrum plot as the two curves reach the same noise

level above ∼ 5 Hz. The difference signal exhibits a lower 1/f knee than the sum

signal confirming that PSB differencing successfully removes atmospheric noise. The

average value of NEPdiff over our frequency range of interest (0.1 - 2.5 Hz) is ∼

7The PSDs were computed by averaging the Fourier transforms of the constant velocity section(∼ 30 seconds) of each of approximately 250 half-scans taken over three hours. Extracting only themiddle portion of each half-scan excludes the turn around period when the telescope is accelerating.


Figure 5.24: NEP for PSB 150-12 for roughly 3 hours worth of data from May31, 2005. The telescope was scanning at 0.17 deg/sec on the sky. The (arbitrarilynormalized) E-mode CMB power spectrum is overlaid assuming this scanning speed.The top x axis is in units of CMB multipole moment (). The PSB difference powerspectrum is white above ∼ 100 through the cut off at ∼ 2500 correspondingto the 150 GHz beam size of 4’. The spikes seen in the data around 10 Hz aremostly microphonic resonances. The dashed black line shows the degradation inNEP that would result from including the reduction in high-frequency gain from thebolometer’s time constant. This curve assumes a value of 15 ms. Note that NEPsum

and NEPdiff are√

2 greater than the NEP of a single channel.


NEP 100 GHz

3 4 5 6 7NEP (10-17 W Hz-1/2)

0

2

4

6

8NEP 150 GHz

3 4 5 6 7NEP (10-17 W Hz-1/2)

0

2

4

6

8

Figure 5.25: Distribution of NEPs for both frequency bands (solid) and median value(dashed).

9.2 × 10−17 W Hz−1/2. We interpret this level as the NEP of a feed or PSB pair

including detector noise, amplifier noise, and photon noise, but not atmospheric

1/f . From eq. 5.23, we divide NEPdiff by√

2 to obtain an estimate of the NEP for

each individual detector in the PSB pair (assuming NEPa ∼ NEPb), resulting in

NEPa ∼ NEPb ∼ NEPdiff√2

= 6.4 × 10−17 W Hz−1/2. (5.24)

Performing this exercise for all detectors results in a median NEP of ∼ 4.4 and

5.6×10−17 W Hz−1/2 at 100 and 150 GHz respectively. Figure 5.25 shows the distri-

bution of NEPs at the two frequencies. Note that the example detector from eq. 5.24

(plotted in Figure 5.24) happens to lie at the noisy end of the distribution. From the

histogram, the 100 GHz detectors are seen to have a lower average NEP which is due

to the decrease in loading resulting from their lower optical efficiency. This decrease

in loading both lowers the photon noise and increases the average responsivity (3.6

vs. 3.1 × 108 V/W for the 100 and 150 GHz channels).


NET 100 GHz

200 300 400 500 600NETpair (µK sec1/2)

0

2

4

6

8

10NET 150 GHz

200 300 400 500 600NETpair (µK sec1/2)

0

2

4

6

8

10

Figure 5.26: Distribution of NETpair for both frequency bands (solid) and averagevalue (dashed).

5.3.3 NET and NEQ

The NEP is defined in terms of power absorbed by the detector. For quantifying

overall system performance, it is necessary to put this in terms of the source radia-

tion. CMB observers use the Noise Equivalent Temperature (NET) for sensitivity to

temperature anisotropies and the NEQ for polarization anisotropies, both in units

of µK sec1/2. These metrics take into account parameters such as throughput, ef-

ficiency, and bandwidth, as well as detector noise level, in order to quantify the

sensitivity of the system to the signal of interest.

The NET can be found directly from the power spectrum of the bolometer voltage

in an analogous manner as the NEP was in the previous section. The detector

voltages are first converted into CMB temperature units (Section 5.2.3) and then

the power spectrum of the signal is found. The NET is usually quoted in units of

µK sec1/2, not µK Hz−1/2. Conversion to the former requires division by√

2.

The NET of a single PSB gives the size of a CMB temperature fluctuation that

could be measured with a signal-to-noise ratio of one in a one second observation

using only this detector. With a PSB pair, the temperature is estimated by averaging


the two detectors8 as Tp = (Ta + Tb)/2, which for uncorrelated noise and identical

detectors, leads to

NETpair =NETa√

2=

NETb√2

. (5.25)

This states the intuitive fact that a better temperature measurement can be obtained

with two detectors than with one. As an aside, it is worth noting that the NET

obtainable from a total-power bolometer will be lower than NETp since each half

of the PSB pair contributes Johnson and amplifier noise. Thus PSBs are not the

detectors of choice for total power measurements.

Applying this procedure to the working QUaD channels yields a median NETpair

of ∼ 380 and 350 µK sec1/2 at 100 and 150 GHz respectively. The average calibrations

in eqs. 5.14 and 5.15 were used with the individual channel gains corrected using

elevation nod data. This is the same procedure used to calibrate the maps presented

in the next chapter. Figure 5.26 shows the distribution of NET at the two frequencies.

The 150 GHz pixels are slightly more sensitive (lower NET) than the 100 GHz pixels

due to their higher responsivity in terms of V/µK.

The NET can be directly related to the NEP as

NETsingle =NEPsingle√

2 (dPB/dT )|TCMB

(5.26)

where the factor of√

2 in the denominator converts from units of Hz−1/2 to sec1/2.

The factor dPB/dT is given by eq. 5.9 and can be obtained from the calibration

factors listed in Section 5.2.3 as dPB/dT = (sK/V · SDC)−1. Assuming identical

detectors, the NET of a pair can be found as

NETpair =NETsingle√

2. (5.27)

These forms are frequently used for estimating the sensitivity of a system during

8The detector signals are averaged rather than summed because the calibration constants pre-sented in Section 5.2.3 are normalized to convert the voltage from a single PSB into properly-calibrated CMB temperature units. This convention is not universal.


a design phase, with the NEP estimated by adding the expected noise sources (eq.

5.20).

The final metric, the NEQ, is applicable only to polarimeters. It gives the sen-

sitivity of a PSB pair to the Stokes parameters Q or U . Since a pair of PSBs is

required to measure Q or U , the NEQ is only defined for a pair of detectors. It

is calculated in the same way as the NETp except the sensitivity is degraded by a

factor of 1/(1− ε) to account for the loss of efficiency caused by cross polar leakage.

Using the values in Figure 4.19, this results in a 5% (8%) degradation relative to the

NET at 150 (100) GHz.

Chapter 6

First Observations

QUaD began science observations in late May 2005 and completed a first pass over

the CMB field in early July. This chapter describes the observing strategy and

presents a first look at the initial data. The QUaD analysis pipeline is still in its

early stages. Nevertheless, the simple analysis presented in this chapter is sufficient

to confirm that QUaD is meeting its target sensitivity for polarization measurements.

6.1 Survey Description

6.1.1 Field Selection

Our field location was constrained by a number of requirements:

• Low foregrounds - The field must be located in a region of low galactic emis-

sion. Emission from dust is predicted to be the dominant foreground at both

observing frequencies [Bowden et al., 2004]. Figure 6.1 shows the dust emission

over the Southern Hemisphere. Away from the Galactic Plane, there are large

regions that are relatively clean.

• Overlap with another experiment - In order to have a cross check on our results

and to help with calibration it is desirable for our field to at least partially over-

lap with a region covered by another CMB experiment. ACBAR, DASI, and

177

178 CHAPTER 6. FIRST OBSERVATIONS

Figure 6.1: The QUaD fields (white) over a map of galactic dust emission (DIRBE /IRAS composite infrared map extrapolated to 150 GHz [Schlegel et al., 1997]). Thesmall and large nested black regions are the B2K deep and wide fields respectively.Figure courtesy of Ken Ganga.

B2K have all made high sensitivity maps of fields in the Southern Hemisphere,

the later two in both temperature and polarization.

• Point sources - As a check on the pointing and beams, it is desirable to have at

least one bright radio source in the field. WMAP has cataloged the brightest

point sources over the entire sky at our observing frequencies.

The field we chose (white boundary in Figure 6.1) satisfies these requirements. It

is in an extremely low foreground region, partially overlaps with the B2K deep field,

and contains three bright radio point sources. The field has an area of approximately

50 square degrees which is smaller than optimal size for an E-mode survey [Bowden

6.1. SURVEY DESCRIPTION 179

et al., 2004]. This reduction in size allows us to cover the field with a higher signal

to noise ratio, a prudent strategy for a new experiment with possibly unknown

systematic effects. The tradeoff, reduced sensitivity to the low region, is relatively

minor.

6.1.2 Observing Strategy

During commissioning observations, it was noticed that some channels were con-

taminated with a low-level, ground-synchronous signal caused by variations in warm

emission from the ground structure picked up in the instrument sidelobes as the

telescope rotates. The pickup is largest when observing over the MAPO building

(the laboratory space attached to the telescope tower). Similar effects were seen with

DASI leading us to adopt a similar observing strategy. This strategy is designed to

allow redundancy for characterizing and removing this contamination.

The observing region is divided into two adjacent, equal-area patches known as

the lead and trail fields. Each field is 30 minutes wide in RA (7.5 of RA or ∼ 5

real degrees on the sky). Observations are synched with the sky rotation so that

successive observations of the two fields occur over the exact same azimuth range.

This ensures that any stable ground contamination will show up equally in the two

fields. Observations are timed to start after the field has rotated passed the MAPO

building.

Because the fields are continuous, maximum flexibility for analysis is retained.

Early indications are that the low-frequency ground pickup can be adequately re-

moved by high-pass filtering the data. In this case, the two fields can be analyzed

as one large area. As a jackknife (consistency check), the difference field (formed

by subtracting the maps of the lead and trail fields) can be analyzed as well. The

downside to this strategy is significant additional complexity – observations must

begin approximately four minutes earlier each successive day. Failure to start at

precisely the appointed time ruins the day’s data.


The following list describes the daily observing program in detail. A short sum-

mary of the essential points follows.

• Each day begins with a skydip followed by a full calibration set consisting of a

pointing cross, a row cal, an el nod, a cal source observation, and a load curve.

• Observations begin when the sky has rotated so that the lead field just clears

the MAPO building.

• This field is observed for 30 minutes. After this time, the sky has rotated the

trail field into position and observation switches to this field for another 30

minutes. This process is repeated eight times (for eight hours).

– Each 30 minute field observation consists of 16 azimuth scans divided

among four different elevation steps separated by 0.02 (approximately

1/3 of a beam width at 150 GHz).

– After every elevation step, the DC offsets on the readout electronics are

reset and a partial cal set, consisting of an el nod and a cal source obser-

vation, is obtained.

• Observation is followed by a second full calibration set.

• Next, the telescope is rotated about the optical axis (termed the “deck” axis)

which changes the angles of the PSBs with respect to the sky.

• The entire observing process, including the beginning and ending cal sets, is

repeated at the new deck angle. This completes the day’s observations.

• The approximately six remaining hours are used for cryogen refills, cycling the

fridge, and any small maintenance tasks (for example, removing accumulated

snow from the foam cone and ground shield).

The azimuth scanning speed is 0.2/sec. Each day covers an elevation range of

0.64. Successive days work down the field, offsetting in elevation by 0.16. The

6.1. SURVEY DESCRIPTION 181

Figure 6.2: Hit maps giving integration time in seconds per 1.2 arcmin square pixel.Maps are shown for the lead field at each frequency and each deck rotation angle.Note the larger integration time at 150 GHz (due to more feeds) and the slightlydifferent coverage pattern at the two rotation angles (due to the asymmetric focalplane resulting from non-functioning feeds). These hit maps result from 37 day’sdata taken between May 17 and July 8, 2005. Trail field hit maps are identical tothose shown above.

75% overlap allows for days to be missed due to bad weather or telescope problems

without creating dead areas in the map. For the first season, the same two deck

rotation angles (-3 and 57) have been used for all observations. Observations at

additional angles will likely be made next season.

The following summarizes the key points of the observing strategy, highlighting

the notation necessary to understand the maps presented in the next section:

• The observing region is divided into two adjacent, equal-area fields, labelled

lead and trail. Each is approximately 5 wide on the sky.


• Each field is observed at two deck rotation angles, -3 and 57.

Figure 6.2 shows the integration time per pixel achieved after the first complete pass

over the observing region.

6.2 First Maps

6.2.1 Temperature Maps

Temperature maps of the observation region are formed by combining the smaller

maps that are produced each day (one per PSB, per field, per deck angle, per day).1

For this analysis, the daily individual-PSB maps were first combined into full-field

maps (one per PSB, per field, per deck angle). The relative gains of the PSBs were set

using data from the elevation nods. An overall calibration (Section 5.2.3) was then

applied to the field maps. The two field maps from each feed horn (corresponding

to orthogonal PSB detectors) were then combined into an equal number of sum and

difference maps.

The raw maps (especially the sum maps) show low frequency noise from atmo-

spheric emission and ground contamination (Figure 6.3). These effects cause correla-

tions in the time-ordered data which our azimuth-based scanning strategy translates

into horizontal stripping in the map domain. High-pass filtering the maps with poly-

nomial removal suppresses the large-scale contamination resulting from these effects

while preserving small-scale structure from the CMB.

Eight field temperature maps can then be formed by combining the data from

the individual feeds using the measured feed offsets (Section 5.1.2). The eight maps

(Figure 6.4) correspond to the two fields at the two frequencies and the two deck

rotation angles. The integration time per pixel for these maps is given by the hit

maps in the previous section.

1Thanks to B. Rusholme for providing the daily individual-PSB maps used in the analysis inthis chapter.

6.2. FIRST MAPS 183

Figure 6.3: Polynomial filtering (right) compared with lead/trail differencing (left)for removing large scale contamination. This data is from a single feed horn (100-01).The data on the left is completely raw, having had only a mean subtracted from eachrow. The data on the right is high-pass filtered by removing a third-order polynomialfrom each row. The field difference map (lead - trail) resulting from each data set isshown in the bottom row. Field differencing only removes structure due to groundcontamination whereas polynomial filtering effectively removes contamination dueto both ground and atmosphere. After polynomial filtering (right), field differencing(bottom right) offers no further improvement. The color scale is in units of µK.


Figure 6.4: QUaD CMB temperature maps made from the first pass over the field(37 day’s worth of data). The eight maps correspond to the two fields (lead / trail)at the two frequencies (100 / 150 GHz) and the two deck rotation angles (57 and-3). The integration time per pixel is given by the hit maps in Figure 6.2. The xand y axes are RA and DEC offsets in units of real degrees on the sky. Two quasarsare visible in the lead field and one, in the trail field. Each map has been filteredwith row-wise removal of a third-order polynomial. The horizontal stripes on eitherside of the quasars (most visible in the trail field) are an artifact of not masking outthe source when performing the polynomial fit.

6.2. FIRST MAPS 185

Figure 6.5: QUaD CMB temperature maps compared with B2K and WMAP forthe entire observing region (lead plus trail fields). The QUaD maps (top) are inVolts whereas the B2K and WMAP maps are in µK. Cross correlating these mapsis used to derive a calibration in µK/V for QUaD. This factor has been used tocalibrate all the other QUaD maps presented in this chapter. Unlike previous mapsin this chapter, these have been smoothed with a beam-sized Gaussian point spreadfunction (PSF). Figure courtesy of J. Kovac.


Several general conclusions can be made regarding these maps. The agreement

between the maps indicates that they are signal dominated. Despite the fewer num-

ber of pixels, the 100 GHz temperature maps are of better quality than the 150 GHz

maps due to less contamination from atmospheric emission. This emission causes

correlation between adjacent samples, resulting in the visible striping of the 150 GHz

maps. The polynomial filter removes this striping on large scales, but on small scales

it cannot be removed without also filtering out the desired CMB signal. The weather

deteriorated as the run progressed, resulting in the increased striping seen at the bot-

tom of the field.

Combining information from all the channels of a given frequency for both fields

and both deck rotations results in the maps seen in Figure 6.5. As a confirmation

that the structure we are seeing is the CMB, the figure also shows the same region

as observed by B2K and WMAP. Note the qualitative agreement among the maps.

The QUaD map shown here (as with all QUaD maps in this Chapter) is, however,

extremely crude – the data from the 37 days of observation have been combined with

no correction for daily drifts in atmospheric opacity (τ) or instrumental gain drifts.

Additionally, the QUaD map is only minimally processed (polynomial removal from

each row). Detailed comparison among the experiments should be reserved until

QUaD produces a final map.

A more quantitative indication of QUaD’s performance can be obtained by con-

sidering the two maps of each field from the different deck rotation angles (Figure

6.6). In the absence of noise, these maps should be identical. Thus an estimate of

the signal-to-noise ratio can be computed by comparing the RMS of the map formed

by summing the two deck rotations to the analogous difference map.

In order to find the signal-to-noise per beam-sized pixel, rather than per 1.2

arcmin map pixel, the pixelized map is first smoothed by convolving with a beam-

sized Gaussian point spread function (PSF). The RMS noise per pixel (∆T ) for the

map is computed as

∆T 2 =⟨M2

ij

⟩−⟨Mij

⟩2(6.1)

6.2. FIRST MAPS 187

Table 6.1: RMS noise in µK for deck angle difference maps (Example maps for thelead field are shown in Figure 6.6). The measured noise level is compared with theexpected noise based on the receiver sensitivity and the integration time. The noiselevel in the “beam-sized pixel” column is determined after convolving the maps witha 6.3′ (4.2′) Gaussian point spread function at 100 (150) GHz.

1.2′ pixels Beam-sized pixels

Field Band Measured Expected Measured Expected

lead 100 57 50 11 6.5150 75 35 25 7

trail 100 57 50 11 6.5150 76 35 24 7

where Mij denotes the pixelized map. The symbol <> denotes a hit map weighted

average as ⟨Mij

⟩=

∑i,j HijMij∑

i,j Hij

(6.2)

where Hij (the hit map) gives the integration time per pixel (Figure 6.2).

Returning to the maps of Figure 6.6, the sum map is assumed to contain sig-

nal (the CMB) plus noise (receiver and atmospheric) while the difference map, only

noise. Applying the above procedure to these maps estimates the signal-to-noise per

beam-sized pixel as ∼ 6 and ∼ 3 at 100 and 150 GHz respectively. These figures

were computed using the top half of the field because of the generally poorer weather

conditions during the second half of the run (bottom half of the field) and the bright

point sources in this region. These results show that after 37 days of observation,

QUaD has already made a high signal-to-noise detection of the CMB temperature

anisotropy (something it was not designed to do). The lower signal-to-noise of the

150 GHz map results from the higher atmospheric noise at this frequency. Atmo-

spheric noise is much less of a problem for polarization measurements since it is

unpolarized.


The noise level of the deck angle difference maps (Figure 6.6, right) can be com-

pared to the value expected based on the receiver sensitivity (Section 5.3) and the

integration time (Figure 6.2). Table 6.1 summarizes the results for both fields, both

frequencies, and for two different pixel sizes. For the finer 1.2′ pixels, the 100 GHz

is close to the expected value whereas the 150 GHz channels show considerable ex-

cess noise due to atmospheric contamination. The results for the beam-sized pixels

confirms the presence of residual correlated structure (atmosphere and ground), es-

pecially at 150 GHz, that keeps the noise from integrating down as expected. This

contamination limits QUaDs ability to measure the CMB temperature power spec-

trum on large angular scales.

Fluctuations in atmospheric emission is the dominant contribution to the residual

contamination in the temperature maps; however, several systematic effects exist

that also result in differences between the maps made at the two deck angles. The

following list describes these effects and how the the final pipeline will deal with

them.

• Gain mismatches - Rotating the receiver in deck angle changes the effective

elevation of each feed resulting in gain difference due to the change in atmo-

spheric loading. Various calibration data including the cal source observations

and elevation nods can be used to correct for this.

• Pointing offsets - There is a small pointing offset between the two deck angles

which causes a shift between the two maps. Pointing cross observations taken

before each observation can be used to quantify this effect.

• Elliptical beams - The elliptical beams cause each pixel in the two deck rota-

tions to probe slightly different areas of the sky. The shapes of the beams are

known from periodic RCW38 beam maps and daily row cal observations.

6.2. FIRST MAPS 189

Figure 6.6: Deck rotation jackknives. QUaD observes each field at two deck rotationangles, dk1 = 57 and dk2 = −3. In the absence of noise, these two maps shouldbe identical. This figure shows the maps formed by summing and differencing thesetwo data sets. Each map above includes all channels for the given frequency. At100 GHz, the difference map is dominated by receiver noise. At 150 GHz, residualatmospheric contamination remains in the difference map. The signal-to-noise ratioestimated from these maps is ∼ 6 and ∼ 3.0 at 100 and 150 GHz respectively. Notethe maps shown in this figure are all for the QUaD lead field.


Table 6.2: RMS noise in µK per beam-sized pixel for single-feed polarization maps(Examples shown in Figure 6.7). At each frequency, the median noise of the availablefeeds (9 at 100 GHz and 15 at 150 GHz) is given. The standard deviation, inparenthesis, indicates the channel-to-channel scatter. Before computing the noise, adifferent order polynomial filter is applied to the map. The rightmost column givesthe expected noise (also in µK) based on the receiver sensitivity. Note that despitetheir higher sensitivity, the expected noise per beam on the 150 GHz channels islarger due to their smaller beam size.

Frequency Polynomial Filter Order Expected

(GHz) 1st 2nd 3rd 4th 5th100 30 (3) 29 (3) 28 (3) 27 (3) 27 (3) 26150 64 (14) 47 (7) 43 (5) 41 (5) 40 (5) 37

6.2.2 Polarization Maps

Polarization maps are formed by PSB differencing which removes the common-mode

signal resulting from unpolarized atmospheric emission. This frees them from much

of the low frequency contamination that plagues the temperature measurements.

Figure 6.7 shows example PSB sum and difference maps for a single feed at each

frequency. Applying the noise analysis presented in the previous section to the

single-feed, PSB difference maps results in Table 6.2. With sufficient filtering, de-

tectors at both frequencies meet the expected sensitivity within the (of order 10%)

calibration uncertainty. At 100 GHz, first-order filtering is sufficient whereas at least

second-order filtering is needed at 150 GHz. This is again due to the higher level of

atmospheric contamination at the higher frequency. More sophisticated processing

in the final pipeline should result in better gain matching within PSB pairs, increas-

ing the common-mode rejection so that only first order filtering is required at both

frequencies. Note that the expected RMS from the CMB polarization signal is ∼ 5

µK per pixel so that these single-feed maps are receiver-noise dominated (per pixel).

The feeds on the QUaD focal plane are each in one of two angular orientation

6.2. FIRST MAPS 191

Figure 6.7: Single-feed temperature (left) and polarization (right) maps for the leadfield. A and B denote the maps formed from the two halves of a PSB pair. The summap (left) gives the total intensity (Stokes I) as measured at each map pixel. Thedifference map (right) gives Stokes Q as defined by each PSBs coordinate system.Note, the sum and difference maps are actually formed as (A+B)/2 and (A-B)/2respectively in order to retain the calibration of the individual maps. These mapsare for a single field (lead), a single deck rotation angle (dk=57), and a single feedat each frequency.


Table 6.3: RMS noise in µK for combined polarization maps (Figure 6.8). In contrastto the temperature data, QUaD is meeting the expected noise levels in polarizationfor both frequencies and pixelizations. The target noise levels are ∼ 2 higher thanfor the temperature maps because these results are for a single deck angle (ratherthan the average of both) and because each feed only measures either Q or U .

1.2′ pixels Beam-sized pixelsBand Deck Stokes Measured Expected Measured Expected100 57 Q 84 87 11 11

U 129 123 17 16-3 Q 83 87 11 11

U 125 123 17 16150 57 Q 79 73 16 14

U 78 69 16 14-3 Q 77 73 16 14

U 73 69 15 14

groups (Figure 2.9) differing by 45. Ignoring the small orientation angle errors

(Figure 4.18), the two groups can be assumed to measure either pure Stokes Q or

U respectively. Combining (as a hit map weighted average) the single-channel maps

(Figure 6.7) of the feeds from each group results in Q and U maps for each field

at each deck rotation angle. Figure 6.8 shows example Q maps at both frequency

bands. For comparison, Figure 6.9 shows the results of applying the same mapping

pipeline to simulated, uncorrelated Gaussian random noise (using the real hit maps

to determine the “integration” time per pixel).

Table 6.3 quantifies the measured and expected noise levels in the combined

polarization maps. Unlike in the temperature maps (Table 6.1), QUaD is meeting

the expected noise level at both frequencies for both pixelizations. No differences

are seen in the results for two fields or the two deck rotation angles. The agreement

between the measured and expected results shows that the sensitivity of the QUaD

receiver to CMB polarization is consistent with the estimates of Section 5.3.

6.2. FIRST MAPS 193

6.2.3 Discussion

This chapter has presented initial QUaD data with an eye towards verifying the op-

eration of the receiver, especially with regards to noise performance and systematic

effects. Atmospheric emission and ground pickup contaminate the raw temperature

maps, but row-wise polynomial filtering is shown to reduce the severity of these con-

taminants. This allows a high signal-to-noise measurement of the CMB temperature

anisotropy to be made at both frequency bands, although the noise limit set by the

receiver sensitivity is not met at either observing frequency.

In contrast, the filtered PSB difference (polarization) maps are shown to integrate

down spatially and with time as expected, reaching the expected per-pixel noise level

set by the receiver sensitivity. This indicates an absence of systematic effects, (atmo-

spheric emission, ground pickup, astrophysical foreground contamination, leakage of

the CMB temperature signal) that would prevent QUaD from reaching the science

goals outlined in Section 1.3.2. In particular, this lends confidence in the predicted

CMB power spectrum of Figure 1.14.


Figure 6.8: Combined Stokes Q maps for both frequency bands and both fields atdeck = 57. Unlike the CMB temperature maps, these polarization maps are largelyfree from residual contamination.

6.2. FIRST MAPS 195

Figure 6.9: Simulated combined Stokes Q maps for both frequency bands and bothfields. These maps were generated using the same analysis pipeline that producedFigure 6.8 except a Gaussian random number generator provide the input.

Appendix A

Focal Plane Temperature Control

The focal plane temperature control subsystem attempts to maintain the focal plane

at a constant temperature during observations. The temperature reference comes

from a sensitive thermistor located on the focal plane which is AC biased and read

out using a cryogenic bridge circuit and the same warm lockin amplifier cards as for

the bolometers. Figure A.1 shows a block diagram of the system and a detail of the

bridge circuit.

The bridge circuit operates by comparing the resistance of the thermistor, R ∼3 MΩ, to that of a fixed reference resistor, R0 = 3.3 MΩ. The thermistor is a “type

D” NTD germanium chip made by Haller-Beeman.1 The two load resistors have the

larger value RL = 10 MΩ. The temperature set point is determined by changing the

ratio of the bias voltage for the two halves of the bridge circuit. Labelled “bias+”

and “bias-” in Figure A.1, the two biases are sine waves with the same frequency

as the bolometer AC bias. They are in phase and have independently adjustable

amplitude.

A warm lockin amplifier differences and demodulates the voltages from the two

sides of the bridge providing the error voltage input to an SRS-SIM9602 PID (pro-

portional integral derivative) control unit. The PID unit adjusts the heater output

current to null the error signal. The heater current flows through three 10 kΩ metal

film resistors wired in parallel and arranged symmetrically on the underside of the

1www.haller-beeman.com/thermis.htm2Stanford Research Systems, Inc. www.thinkSRS.com

197

198 APPENDIX A. FOCAL PLANE TEMPERATURE CONTROL

+

-

PIDbias+

bias-

BiasGen.

QUaDReceiver

error

heatercurrent

demodulator reference

RL

R0

RL

R

+

-

error

bias-

bias+

Warmlockinamplifier

Figure A.1: (top) The focal plane temperature control system. (bottom) Detail ofthe thermistor readout bridge. The dashed line indicates the receiver.

focal plane bowl. Because the system cannot cool the focal plane, the set point is

required to be several mK above the natural fridge operating temperature. This al-

lows the PID to smooth over changes in temperature due to, for example, changes in

telescope elevation and the small natural drift upwards in temperature that occurs

with time as the fridge depletes the condensed He-3. Figure A.2 contrasts the tem-

perature stability of the focal plane with and without temperature control enabled.

199

Focal Plane Temperature Control

0 5 10 15Hours

0.248

0.250

0.252

0.254F

P T

empe

ratu

re (

K)

Disabled

Enabled

Figure A.2: Temperature control stabilizes the temperature of the focal plane. Thedata plotted here is the DC level of one of the dark bolometers (PSB 150-01C). Thecalibration from Volts to Kelvin was obtained by correlating the bolometer signalwith the focal plane GRT. The “disabled” data was taken on April 8, 2005 and the“enabled” data, on April 10, 2005. In both cases, the telescope was raster-mappinga source while this data was taken. The steps seen in the data are digitization noise.

200 APPENDIX A. FOCAL PLANE TEMPERATURE CONTROL

Appendix B

Commissioning QUaD

QUaD was commissioned at the South Pole during the 2004/2005 summer season by

ten intrepid team members who deployed for periods ranging from several weeks to

the entire season. Completing this enormous task under the severe time constraint

imposed by the onset of winter, required a Herculean effort from everyone. In ad-

dition to the dedicated QUaD team, we were also fortunate to have the help of the

South Pole Station’s superb science support and construction personnel.

Despite being one of the most remote locations on the planet, the station offers

an extensive infrastructure that make it very attractive as an observing site. In

addition to the basic necessities, the station operates a liquid nitrogen plant and

maintains a store of liquid helium with a cryogenic expert on-call for immediate

assistance when needed. A fully-equipped machine shop in the MAPO building is

staffed by professional machinists dedicated to supporting astronomical research.

Several electronics shops offer components and test equipment for troubleshooting

and repairs. Although packages take several weeks to be delivered, the vast quantity

of parts and scraps accumulated over the stations many years in operation ensures

that ample spares can usually be obtained or constructed when needed. Perhaps

the biggest drawback to the remote location is that communication with the out-

side world, including data transfers, is limited to approximately half the day when

connections can be made via satellite.

201

202 APPENDIX B. COMMISSIONING QUAD

The following list includes some of the major tasks that were accomplished during

the commissioning period:

B.1 Receiver Testing

Upon unpacking the receiver, we performed a cool down without the focal plane.

This run tested the cryostat and the fridge to ensure they had survived the long

journey from California. Successfully cycling the fridge was cause for celebration

since any damage to the cryogenic systems would likely have resulted in losing the

entire observing season.

Just prior to shipping, we had changed all the filtering on the 100 GHz feeds

(to broaden the band) and installed several freshly minted PSBs. In fact, the final

PSB modules were hand-carried to the Pole and installed on the focal plane during

the cryogenic test run. Both to ensure that nothing had broken during shipping,

and to characterize all of the new detectors, our next run was dedicated to receiver

testing. We measured the optical efficiency, cross-polar leakage, PSB orientation,

the spectral bandpass for each feed, and the noise level for each detector. Most of

the results described in Section 4.2 are from this period of intense testing.

B.2 Foam Cone Installation

The crate containing the foam cone was designed to just fit in the cargo hold of the

LC-130 cargo planes that service the Pole. Unfortunately, this made it too large

for any commercial cargo planes except a special version of the Boeing 747. This

complicated the shipping arrangements resulting in significant delays. We were all

greatly relieved when the enormous box finally arrived at the Pole.

The cone is made of two layers of Zotefoam in the form of overlapping sectors

which are bonded together with adhesive. Fiberglass collars at the top and bottom

clamp the layers securely together. The cone is not particularly heavy, but handling

B.2. FOAM CONE INSTALLATION 203

Figure B.1: Installing the QUaD foam cone. The crane arm is just visible in theupper right corner. The two workers visible inside the ground shield guided thecone onto the telescope primary mirror (not visible), which was pointed towards thezenith.


it is extremely awkward due to its large size. Installing it onto the primary mirror

required the assistance of one of the station’s skilled crane operators and his crew.

Figure B.1 shows the cone in mid-air, partway along its journey to its final resting

place atop the primary mirror. Once on the mirror, the cone was aligned relative

to the hole in the primary mirror. It was secured to the primary mirror guard ring

with fiberglass bolts through a flange on the cone’s bottom collar.

B.3 Secondary Installation and Alignment

Before installing the secondary mirror, extensive testing of the mechanical stability

of the foam cone was performed using a custom laser measuring system. A corner-

cube reflector and plane mirror mounted near the vertex of the cone combined with

three lasers allowed measurement of the x, y, and z position of the vertex as well

as tip and tilt. Tests were performed with the telescope at different elevation and

theta angles. The initial results were extremely puzzling. After a change in telescope

position, the cone would show a quick “step” change in its position followed by a very

slow drift. The drift was eventually traced to thermal expansion as the cone reached

a new equilibrium temperature distribution reflecting its new position relative to the

sun. This effect was compounded by the black tarp we had covered it with in order

to make the laser spots more visible.

The secondary mirror was intended to be attached to the foam cone via a motor-

ized hexapod mount that would allow convenient and accurate position and focus

corrections throughout the season. However, nagging mechanical problems made this

option less attractive. We were forced to completely abandon this option when static

electricity destroyed its control processor and the spare. In the end, we mounted the

secondary to the foam cone’s top cap using three 1/2”-13 threaded rods. Nuts were

used to set the focus and then locked in place for the season.

Once the secondary was mounted, we performed the final alignment relative to

B.4. GROUND SHIELD EXTENSION 205

Figure B.2: Lifting the cryostat into the receiver room as seen from above.

the primary using an articulated measuring arm (Romer 3000i)1. We rigidly mounted

the base of the arm to the telescope and then touched the probe at the end of arm

to the mirror surfaces. Extremely high resolution encoders at the joints allow the

position of the probe to be measured in three dimensions to better than 0.01 mm

with respect to the base. An array of data points were taken over the primary and

secondary surfaces which were then fit to their known functional forms. Adjustments

were then made to the mounting screws to bring the surfaces into alignment.

B.4 Ground Shield Extension

With the original DASI ground shield, the top of the primary mirror would have

been able to “see” the ground when the telescope was tipped to low elevation angles.

This was deemed unacceptable and a plan was developed to extend the ground

1ROMER CimCore, 51170 Grand River Avenue, Wixom, MI 48393


shield by approximately four feet. Raytheon engineers designed and manufactured

the extension panels.

The panels were intended to arrive mid-season for installation by a construction

crew; however, a string of bad weather combined with large shipments of high-

priority building materials for the new station meant they just barely arrived with

enough time left to install them before station closing.

B.5 Receiver Installation

We performed the difficult task of mounting the receiver onto the telescope a total

of three separate times during the commissioning period. The first time was im-

mediately after unpacking, before the first cool down. At this point, the cryostat

and fridge still had their protective shipping hardware installed, and were least sus-

ceptible to physical damage from rough handling. The goal of this first installation

was to perform mechanical fit checking, to determine the best routing of the cryogen

refill lines, and to develop a reliable installation procedure. During future installa-

tions, the cryostat would be under vacuum and filled with liquid cryogens – so a safe

and reliable procedure was essential. For the second installation, the receiver was

cooled and fully operational. This run was mainly for testing microphonic response

while driving the telescope. The final installation was a few days before the end of

the season, just after the foam cone and secondary mirror had been installed and

mounted.

The physical installation procedure went as follows. First, we hoisted the cryostat

from the laboratory floor through the narrow entrance port into the receiver room

(around 20 feet total) using a hand operated winch (Figure B.2). Once the cryostat

was safely inside the receiver room, the real work began. First, we lowered it onto

a wheeled lifting table and pushed it underneath the mounting ring. We then used

the lifting table to raise the cryostat to its full extension which was just over half

the necessary distance. Then, we suspended the cryostat from the mounting ring

B.5. RECEIVER INSTALLATION 207

Figure B.3: (top) The receiver mounted to the telescope before installation of thewarm readout electronics. (bottom) The final configuration of the readout elec-tronics. The real time control computer is mounted on the left. The 19” rack on theright holds (top to bottom) two power supplies, the focal plane temperature controlunit, and the cryogenic temperature readout. The aluminum boxes hanging from thecryostat (just beyond the top of the image) house the bias generator and amplifiers.


with cargo straps while the table was lowered and a spacer inserted. We raised the

table again, lifting the cryostat until the six 0.5” diameter mounting bolts passed

through the mating flange on the cryostat. At this point, we engaged the nuts and

raised the cryostat the rest of the way by tightening them. During this lifting, we

had to ensure that the stingers for the cryogen lines were properly aligned with the

cryostat refill tubes and not binding.

Appendix C

Calibration Source Hardware

The calibration source includes the following hardware items:

Flip mirror The flip mirror itself has already been described in the text (see Figure

5.12). A small DC servo motor, like the kind commonly found in the steering

mechanisms of remote-controlled cars, drives the up/down motion. Hardware

stops at the limits ensure a repeatable positioning.

Polarizing grid The polarizing grid is a smaller version of the one seen in Figure

4.14. A precision stepper motor and gear train rotates the grid.

Blackbody source The black body source is a copper disk covered in carbon-

loaded Stycast epoxy. Its absorption properties were verified using an FTS.

The disk has a heater resistor embedded in it in case temperature regulation

was desired. A National Semiconductor LM35 temperature sensor provides a

monitor good to ±0.5o C.

Hall effect switch A steel vane on the perimeter of the polarizing grid engages a

Hall effect switch once per revolution, providing an home mark. Before flipping

the mirror down, the control system automatically homes the grid, ensuring

that all cal runs begin in the same state.

Battery pack Wires running from the primary up to the cal source inside the

secondary were extremely undesirable since they would introduce scattering

209

210 APPENDIX C. CALIBRATION SOURCE HARDWARE

that could be polarized. Hence the source was designed from the beginning to

run off of a lithium ion battery pack. However, this gives our “winter-over”

the unpleasant task of venturing into the Antarctic winter and standing on a

ladder to reach inside the foam cone and replace the battery. Fortunately, the

duty cycle of the source is quite low, so a reasonable battery life was obtained

by keeping the system standby current as low as possible. This was achieved

by powering down all the subsystems when not in use.

Infrared link The cal source receives commands and transmits data over an In-

frared data link that is implemented using the same chips that power the IrDA

data links commonly found in laptop computers and hand-held organizers. The

real-time control computer issues commands to the cal source over a standard

RS-232 serial line which links to a custom translator box. The translator box

interfaces with an IR transmitter/receiver located on the bottom edge of the

foam cone which communicates with the corresponding transceiver located just

behind the secondary (see Figure 5.12 for the approximate location of the link).

The protocol for RS-232 side of the link is completely ASCII based allowing

easy stand-alone operation with a terminal emulator program for troubleshoot-

ing. The translator box packages the command strings with a simple header

including a start characters, a string length, and a checksum byte. This has

resulted in an extremely robust and reliable link.

Control computer The cal source was designed to be operated by the same control

computer as the hexapod which was destroyed by static electricity late in the

summer season. A replacement system was designed mostly from scratch using

the spare components we had brought with us or were available on station. The

replacement system is based on a PIC16F873 (Microchip Technology Inc.) 8-

bit microcontroller. The chip’s 4 kB of program memory and 192 bytes of

RAM were filled to capacity by the program needed to interface with all the

subsystems.

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