Quad: a Millimeter-Wave Polarimeter for Observation of the Cosmic Microwave Background Radiation

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

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Prof. Sarah E. Church Principal Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Prof. Giorgio Gratta

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Prof. Steven Kahn

Approved for the University Committee on Graduate Studies.

iii iv Abstract

This thesis describes the design and performance of the QUaD experiment and presents some of its earliest results. QUaD is a millimeter-wavelength polarimeter designed for observing the Cosmic Microwave Background (CMB). QUaD was commissioned at the MAPO observatory at the Amundsen-Scott South Pole Station in the Austral Summer of 2004/2005, achieved first light in Feb 2005, and began science observation in May. QUaD observes the CMB with an array of 31 polarization-sensitive Neutron Transmutation Doped (NTD) germanium bolometers split between two frequency bands centered at 100 and 150 GHz. The telescope is a 2.6 m on-axis Cassegrain design with beam sizes of 6.3 and 4.2 at the two respective observing frequencies. The resolution and scan strategy are optimized to probe the CMB 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 temperature anisotropy measurements already performed, confirming our basic understanding 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. vi 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

vii 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.

viii Contents

Acknowledgements vii

1 Introduction 1 1.1CosmologyandtheCosmicMicrowaveBackground...... 2 1.1.1 OriginandHistoryoftheCMB...... 2 1.1.2 TheModernCosmologicalPicture...... 3 1.1.3 CMBTemperatureAnisotropies...... 7 1.2ThePolarizationoftheCMB...... 12 1.2.1 StokesParameters...... 12 1.2.2 OriginsandCharacterizationofCMBPolarization...... 14 1.2.3 ExistingMeasurements...... 22 1.3TheQUaDExperiment...... 24 1.3.1 Overview...... 24 1.3.2 ScienceGoals...... 26 1.4ThesisOutline...... 28

2 Experiment Description 31 2.1TheSouthPoleObservingSite...... 31 2.2TheDASIMount...... 32 2.3Optics...... 33 2.3.1 Overview...... 33 2.3.2 LensesandColdStop...... 34

ix 2.3.3 Filtering...... 36 2.3.4 CorrugatedFeeds...... 39 2.3.5 PolarizationSensitiveBolometers...... 40 2.3.6 TheFocalPlane...... 42 2.4Cryogenics...... 46 2.4.1 Cryostat...... 46 2.4.2 Sub-Kelvin Refrigerator ...... 48 2.4.3 TheScienceCore...... 52 2.4.4 Thermometry...... 54

3 Readout Electronics 57 3.1Description...... 57 3.1.1 BiasGenerator...... 59 3.1.2 LoadResistorBoxes...... 61 3.1.3 FocalPlaneWiring...... 63 3.1.4 JFETBoxes...... 65 3.1.5 LockinAmpliﬁers...... 67 3.1.6 TheDataAcquisitionSystem...... 70 3.2Performance...... 71 3.2.1 FunctionalityTests...... 71 3.2.2 NoisePerformance...... 77 3.2.3 ChannelCapacitance...... 85 3.2.4 Microphonics...... 89 3.2.5 RadioFrequencyInterference...... 91

4 Receiver Characterization 93 4.1BolometerCharacterization...... 93 4.1.1 BolometerModel...... 93 4.1.2 LoadCurves...... 95 4.2OpticalCharacterization...... 100

x 4.2.1 OpticalTestbed...... 100 4.2.2 SpectralBands...... 102 4.2.3 OpticalEﬃciency...... 106 4.2.4 ResponsivityandTimeConstants...... 110 4.2.5 CosmicRaysandImpulseResponse...... 113 4.3PolarizationProperties...... 116 4.3.1 Formalism...... 117 4.3.2 DerivationoftheExpectedSignal...... 120 4.3.3 TheMeasurementSetup...... 123 4.3.4 ResultsandDiscussion...... 124

5 Instrument Performance 131 5.1OpticalPerformance...... 131 5.1.1 RasterMaps...... 131 5.1.2 FeedOﬀsets...... 137 5.1.3 Beams...... 139 5.1.4 TimeConstants...... 142 5.2Calibration...... 144 5.2.1 AtmosphericTransmission...... 144 5.2.2 RoutineGainCalibration...... 149 5.2.3 AbsoluteCalibration...... 155 5.3SensitivityandNoise...... 159 5.3.1 OpticalLoading...... 159 5.3.2 NoiseEquivalentPower...... 163 5.3.3 NETandNEQ...... 174

6 First Observations 177 6.1SurveyDescription...... 177 6.1.1 FieldSelection...... 177 6.1.2 ObservingStrategy...... 179

xi 6.2FirstMaps...... 182 6.2.1 TemperatureMaps...... 182 6.2.2 PolarizationMaps...... 190 6.2.3 Discussion...... 193

A Focal Plane Temperature Control 197

B Commissioning QUaD 201 B.1 Receiver Testing ...... 202 B.2FoamConeInstallation...... 202 B.3SecondaryInstallationandAlignment...... 204 B.4GroundShieldExtension...... 205 B.5 Receiver Installation ...... 206

C Calibration Source Hardware 209

xii List of Tables

1.1QUaDkeynumbers...... 26 1.2QUaDtimeline...... 27 1.3TheQUaDcollaboration...... 30

3.1QUaDchanneltable...... 58 3.2 Warm electronics testing noise budget ...... 82 3.3 Electronics noise budget ...... 85

4.1Bolometerparameters...... 101 4.2Averagespectralbandproperties...... 104 4.3Averageopticaleﬃciencies...... 108

5.1Measuredbeamparameters...... 140 5.2EstimatedQUaDopticalloading...... 160

6.1Temperaturemapnoise...... 187 6.2Single-feedpolarizationmapnoise...... 190 6.3Polarizationmapnoise...... 192

xiii xiv List of Figures

1.1WMAPCMBtemperaturemap...... 4 1.2AnnotatedCMBtemperaturepowerspectrum...... 8 1.3WMAPCMBtemperaturepowerspectrum...... 9 1.4 Detector orientations for measuring Q and U ...... 12 1.5 CMB polarization originates from anisotropic Thompson scattering . 14 1.6Localquadrupolepatterns...... 15 1.7EandBFouriermodes...... 17 1.8EandBhotspots...... 18 1.9RandomEandBpatterns...... 19 1.10PredictedCMBpowerspectra...... 20 1.11WMAPTEcorrelation...... 22 1.12ExistingE-modepolarizationmeasurements...... 23 1.13PanoramicviewoftheQUaDtelescope...... 25 1.14QUaDpredictedE-modespectrum...... 28 1.15QUaDpredictedtemperaturespectrum...... 29

2.1QUaDgeneralassembly...... 32 2.2QUaDopticalpath...... 34 2.3QUaDpixelschematic...... 35 2.4Coldopticsschematic...... 36 2.5Averagespectralbands...... 37 2.6Feedhorns...... 38

xv 2.7Feedhornbeampattern...... 39 2.8PSBmoduleandabsorber...... 41 2.9Pixelpositionandorientation...... 43 2.10HornandPSBmounting...... 44 2.11 The receiver core ...... 45 2.12TheQUaDcryostat...... 46 2.13Three-stagefridge...... 48 2.14Examplefridgeoperation...... 49 2.15Afridgecycle...... 51 2.16FocalplaneCADrendering...... 52 2.17Focalplanetemperature...... 55 2.18 Installing the focal plane in the receiver ...... 56

3.1Electronicsoverviewschematic...... 57 3.2Biasgeneratorschematic...... 59 3.3Coldelectronicsoverview...... 61 3.4Loadresistorboard...... 62 3.5Thefocalplanebowl...... 64 3.6JFETmembrane...... 65 3.7JFETboxCADmodel...... 66 3.8Lockincardschematic...... 67 3.9Lockinamplifierboxphoto...... 68 3.10Measuredspectrumofbiasgenerator...... 71 3.11Lockincardfilteringdetail...... 72 3.12Lockin475HzLPfiltermeasuredresponse...... 73 3.13Lockin20HzLPfiltermeasuredresponse...... 74 3.14Lockin20HzLPfiltermeasuredresponse(impulsemethod)..... 75 3.15Electronicsnoisetestingsetup...... 77 3.16Lockinboxnoisespectra...... 78 3.17Amplifiernoisevs.sourceresistance...... 80

xvi 3.18Biasnoise...... 82 3.19 Electronics stability ...... 83 3.20Bolometerreadoutincludingstraycapacitance...... 86 3.21MeasuredQUaDchannelcapacitance...... 87 3.22Attenuationresultingfromstraycapacitance...... 88 3.23Microphonicresponse...... 89 3.24Microphonicresponse...... 90 3.25WarmRFﬁltering...... 91

4.1Bolometerthermalandelectricalmodels...... 94 4.2Loadcurvesexample...... 96 4.3Bolometerresistancevs.temperature...... 97 4.4MeasuringQfromloadcurves...... 98 4.5TheQUaDopticaltestbed...... 102 4.6LaboratoryopticaltestingwithQUaD...... 103 4.7QUaDspectralbands...... 105 4.8Opticaleﬃciencywithloadcurves...... 106 4.9Opticaleﬃciencyhistograms...... 109 4.10Responsivitycurve...... 110 4.11Labtimeconstantmeasurements...... 112 4.12Cosmicrayimpulseresponse...... 114 4.13ModelQUaDimpulseresponse...... 115 4.14Aligningthepolarizinggridfortesting...... 116 4.15 Polarizing grid mounted on receiver window ...... 117 4.16Polarizationresponsefromtwohorns...... 118 4.17MeasuredPSBorientations...... 119 4.18 Measured PSB angle and orthogonality ...... 120 4.19Measuredcross-polarleakage...... 121 4.20Cross-polarleakageinQUaDvs.thetestbed...... 126

xvii 5.1Azimuthencoderwhilemapping...... 132 5.2TelescopeRA/DECwhilerastermapping...... 133 5.3Elevationjitter...... 134 5.4RCW38maps...... 135 5.5Measuredfeedpositions...... 137 5.6RCW38fromeveryfeed...... 138 5.7Predictedbeampattern...... 139 5.8Timeconstants...... 143 5.9Skydipdata...... 144 5.10QUaDtauvs.350microntipper...... 145 5.11Tauvs.time...... 146 5.12Calibrationsource...... 150 5.13Calibrationsourcedata...... 151 5.14Elevationnodexample...... 153 5.15A/Bratiosfromthreecalibrationtechniques...... 154 5.16 dB/dT evaluatedforQUaDbands...... 155 5.17 Receiver loading vs. time ...... 161 5.18 Receiver loading ...... 162 5.19NEPbreakdown...... 163 5.20TotalNEPversusbias...... 167 5.21Responsivitycurves...... 169 5.22Averageresponsivity...... 169 5.23Atmosphericnoisetime-ordereddata...... 170 5.24PowerspectrumofQUaDnoiseinNEPunits...... 172 5.25NEPdistribution...... 173 5.26NETdistribution...... 174

6.1 QUaD 2005 ﬁeld ...... 178 6.2Hitmaps...... 181 6.3Mapﬁltering...... 183

xviii 6.4QUaDCMBtemperaturemaps...... 184 6.5QUaDtemperaturemapscomparedwithB2KandWMAP...... 185 6.6Deckrotationjackknives...... 189 6.7Single-feedpolarizationmaps...... 191 6.8 Stokes Q maps...... 194 6.9 Simulated Stokes Q maps...... 195

A.1Focalplanetemperaturecontrolschematic...... 198 A.2Theeﬀectoffocalplanetemperaturecontrol...... 199

B.1 Installing the foam cone ...... 203 B.2 Installing the receiver ...... 205 B.3 The receiver room ...... 207

xix xx 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 observations 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 pioneering 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) instrument 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 applies 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 4 CHAPTER 1. INTRODUCTION

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

light would eventually diverge. The strongest evidence for a ﬂat universe comes directly from measurements of the CMB temperature anisotropies [Spergel et al., 2003].

Dark Matter Only a small fraction (∼ 10%) of the matter in the universe is normal, 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 observations 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 1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND 5

general relativity predicts that the expansion of the universe should accelerate with time, rather than decelerate. The most direct evidence for dark energy comes from observations of high-redshift supernovae [Perlmutter et al., 1999, Riess et al., 2001, Knop et al., 2003].

Inflation The theory of Inflation posits that the universe expanded by a factor of ∼ 1050 in the first ∼ 10−35 seconds after the Big Bang [Guth, 1981]. This rapid initial expansion naturally resolves the following weaknesses with the standard BigBangmodel.

• 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 expansion, 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 6 CHAPTER 1. INTRODUCTION

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 polarization 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 polarization 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 certainly be only one of many experiments needed to fully realize it. 1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND 7

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 characteristic 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 rarefaction/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)= amYm(θ, φ) (1.1) =2 m=− 8 CHAPTER 1. INTRODUCTION

Figure 1.2: Example CMB Temperature power spectrum with the key features labelled. (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 1 C ≡ |a |2 |a |2 . m = m (1.2) 2 +1m=− It is a property of the spherical harmonics that the zeros are spaced at the approximate 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 1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND 9

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

to modes that reached maximum rarefaction and compression. Above ∼ 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. 10 CHAPTER 1. INTRODUCTION

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 interferometer 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 constraints 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 1.1. COSMOLOGY AND THE COSMIC MICROWAVE BACKGROUND 11

to photon pressure. This enhances the compressional (odd-numbered) peaks in the power spectrum relative to the rarefactional (even-numbered) peaks. Inﬂationary theories make predictions about the spatial power spectrum of the primordial potential ﬂuctuations that eventually give rise to the observed CMB anisotropies. There are three possible types of metric perturbations that each evolve separately:

Scalar 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 gravitational 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 perturbations 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 12 CHAPTER 1. INTRODUCTION

Q Detector U Detector y xy- xy+

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)componentsas

I = Iup + Ip. (1.3)

The degree of polarization, p, is deﬁned as the ratio of the polarized intensity to the total I p p . = I (1.4) For linear polarization, as is expected for the CMB, the two intensity quantities Q and 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 measured by two orthogonal detectors aligned with the local x and y axes as

2 2 Q = Ex−Ey ≡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 E2 −E2 ≡I − I . = x+y x−y x+y x−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 I2 Q2 U 2 χ U/Q. p = + and tan 2 = (1.9)

Measurements of the Stokes parameters I, Q,andU 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. 14 CHAPTER 1. INTRODUCTION

Incident Warm radiation

Incident e- Cool radiation

Partially polarized scattered radiation

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

1.2.2 Origins and Characterization of 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 polarized 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 2 polarization directions (Eˆ and Eˆ respectively) as dσT /dΩ ∝|Eˆ · Eˆ | . In particular, 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 1.2. THE POLARIZATION OF THE CMB 15

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

plasma) leads to a net polarization. In terms of the spherical harmonics 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 perturbation. 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 toward 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 resulting 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 16 CHAPTER 1. INTRODUCTION the perturbation (up/down in Figure 1.6), the scalar mode results in a pattern that is purely Stokes Q (since the polarization direction is always parallel or perpendicular to the wave vector). The tensor mode results in a mixture of Q and U [Hu and White, 1997]. The observed polarization pattern on the sky results from the superposition of the signals from many diﬀerent scalar and tensor modes with randomly oriented wave vectors. Because of this superposition, the resulting pattern will contain both Stokes Q and U components (even if only scalar modes were present). Because of this mixing, a Stokes parameter description of the all-sky CMB polarization pattern does not allow an easy separation of the contributions from scalar and tensor modes. The following subsection introduces a mathematical tool, the E-B decomposition, designed to accomplish just this.

E and B decomposition

Polarization direction is a spin-2 quantity since it is invariant under rotation by 180◦. The full CMB polarization pattern on the sky can be expanded in terms of spin-2 spherical harmonics in an analogous manner as the temperature anisotropies are expanded in scalar spherical harmonics. Like the scalar spherical harmonics, the spin-2 harmonics form a complete and orthogonal basis. Linear combinations of the spin-2 harmonics can be formed that transform as scalars. These are named “E-modes” after the closely related curl-free pattern of a static electric ﬁeld. Simi- larly, linear combinations that transform as pseudo-scalars are named “B-modes” in analogy with a divergence-free magnetic ﬁeld. Any full-sky polarization map can be expanded in terms of these E and B modes. The E/B decomposition was introduced in Zaldarriaga and Seljak [1997] and Kamionkowski et al. [1997].1 Physically, this decomposition is useful because scalar perturbations produce only E modes whereas tensor perturbations produce both E and B modes.

1The latter use the notation of G (grad) and C (curl) modes rather than the now more common E and B introduced by the former. 1.2. THE POLARIZATION OF THE CMB 17

E Pattern B Pattern

Figure 1.7: Example E (left) and B (right) Fourier modes. In both cases, the wave vector lies along the x axis running horizontally. 18 CHAPTER 1. INTRODUCTION

E Pattern B Pattern

Figure 1.8: E and B “hot spots” formed from the superposition of eight (properly phased) plane waves of the form shown in Figure 1.7 evenly distributed in angle Note that the E mode patterns are invariant under reﬂection whereas the B patterns are not. 1.2. THE POLARIZATION OF THE CMB 19

E Pattern B Pattern

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

Over a small region of sky, the flat sky approximation can be used and the spin-2 harmonics reduce to the mathematically simpler Fourier modes [Bunn, 2002]. Figure 1.7 shows representative E and B Fourier modes. For the E modes, the polarization aligns parallel or perpendicular to the wave vector, like the polarization pattern resulting from a scalar density perturbation. For B modes, the polarization aligns at a45◦ 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 characteristic 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 superposition of random Fourier modes. Inspection of the two maps reveals the characteristic “hotspot” patterns shown in Figure 1.8. 20 CHAPTER 1. INTRODUCTION

Figure 1.10: The four CMB power spectra for the standard cosmological model (solid lines). Annotations indicate physical processes responsible for key features. See text for explanation. The dashed lines show the gravitational wave (tensor mode) contribution to the E and B spectra (note the roughly equal magnitude of the two) assuming a value of r =0.1. The dashed-dotted line shows the gravitational lensing contribution to the B mode spectrum which dominates at small angular scales. Dot- ted lines show the expected change in the spectra resulting from reionization (using the WMAP measured value of τ ∼ 0.17). Figure from Carlstrom et al. [2003] and derived using the CMBFAST computer code of Seljak and Zaldarriaga [1996]. 1.2. THE POLARIZATION OF THE CMB 21

The power spectra

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

of the polarization field, Em and Bm, analogous to the am of eq. 1.1 for the TT temperature field. In analogy with eq. 1.2, six power spectra can be formed: C , TE EE BB TB EB C , C , C , C , C . 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 22 CHAPTER 1. INTRODUCTION

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

of last scattering, mix a small fraction of the polarized power between E and B modes. This mixing occurs at small angular scales where it dominates the expected B-mode signal. This sets a limit on the values of the tensor scalar ratio that could be measured even with a perfect instrument of ∼ 10−4 [Knox and Song, 2002]. If the relict tensor modes lie below this level, they cannot be measured from the CMB.

1.2.3 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 measurements; 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. 1.2. THE POLARIZATION OF THE CMB 23

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

• DASI - The Degree Angular Scale Interferometer was a 13-element interferometer 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 polarization sensitive. Figure 1.11 shows the measured TE correlation resulting 24 CHAPTER 1. INTRODUCTION

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 bolometers (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 spectrum come from temperature experiments that were retrofit for polarization sensitivity. 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 26 CHAPTER 1. INTRODUCTION

Table 1.1: QUaD key numbers.

Primary diameter (mm) 2640 Secondary diameter (mm) 450 Frequencies (GHz) 100 150 Bandwidths (%) 28 27 Nominal beam sizes (arcmin) 4.2 6.3 Pixels 12 19 Available pixels 2005 season1 10 16 Sensitivity2 (µKsec1/2) 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 detected 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 Proposal Initial optical design

2001-2002 Optical design ﬁnalized Primary mirror manufactured Electronics, focal plane, and cryostat design

2003 Laboratory testing of receiver components Installation of primary mirror on DASI mount

Mar. 2004 Integration and laboratory testing of receiver

Nov. 2004 Commissioning at the South Pole

Feb. 2005 Engineering observations

May 2005 Science observations begin 28 CHAPTER 1. INTRODUCTION

Figure 1.14: QUaD predicted ﬁrst-year EE power spectrum. The red points are from the ﬁrst season of observation and the blue points from a three-year survey. Points without error bars represent upper limits. Figure courtesy M. Bowden.

1.4 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 coveredineachchapter.

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-year result (blue). Note that atmospheric 1/f noise limits temperature observation to smaller angular scales than for polarization.

Chapter 5: Instrument performance based primarily on data from South Pole commissioning observations

Chapter 6: First-year survey description and preliminary data 30 CHAPTER 1. INTRODUCTION

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

The QUaD Collaboration

Caltech / JPL A.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. Zemcov Cryostat design, cryogenics, ﬁlters design, optical component design and manufacture

Coll`ege de France K. M. Ganga Simulations, software, and science support

National University of Ireland, Maynooth J. A. Murphy, C. O’Sullivan, G. Cahill Optical design and modelling

Stanford University S. E. Church, M. Bowden, J. R. Hinderks, E. Kirby, B. A. Rusholme, K. Thompson Receiver integration and characterization, focal plane design and manufacture, readout electronics, optical testing

University of Chicago J. E. Carlstrom, C. Pryke, E. M. Leitch Telescope and mount, data acquisition system, receiver installation, optical alignment, and control system software

University of Edinburgh A.N.Taylor,M.L.Brown,P.Castro Software development and science support

The South Pole R.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 45◦54’14.8”W, 89◦59’36.3”S at an elevation of 2785 m. The observatory is part of the Amundsen-Scott South Pole Station, which is overseen by the National Science Foundation’s Oﬃce of Polar Programs. This site is unsurpassed for ground-based, millimeter-wave observations, [Lane, 1998, Lay and Halverson, 2000, Peterson et al., 2003, Bussmann et al., 2005]. The winter precipitable water vapor averages only 0.26 mm due to the inland location, the high altitude, and the extreme cold temperatures. The atmospheric conditions are stable over long periods of time with minimal diurnal variation. The six month “night” during the winter season allows for virtually uninterrupted observation. The location near Earth’s axis permits deep integrations on small areas since the entire

31 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 laboratory. 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 strategy 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. 34 CHAPTER 2. EXPERIMENT DESCRIPTION

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

Each of the 31 pixels is comprised of optical ﬁlters to determine the spectral bandpass, a corrugated microwave feed horn and a pair of orthogonal polarization sensitive bolometers (Figure 2.3). The PSBs absorb radiation polarized along their axis of sensitivity and a thermistor detects the associated minute increase in temperature. 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

Incident Radiation LP Filter Throat PSB Pair Readout (HP Filter) x + V ~ Ix2 - Iy 2 Feed - y

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

coating was applied to both surfaces of the lenses by collaborators at the Univer- sity of Cardiﬀ. Both lenses are cooled with liquid helium to reduce their thermal emission. Radiative loading combined with the long thermal path separating them from the helium can results in an operating temperature of ∼ 10 K (thermodynamic temperature). The lenses serve two purposes. First, they decrease the F-number of the slow beam oﬀ the secondary mirror. This reduces the physical size of the focal plane and feed horns. Additionally, they form an image of the primary mirror between the second lens and the focal plane, at the location labelled “4 K cold stop” in Figure 2.4.1 Two lenses were necessary to achieve a good focus at both the focal plane and the cold stop. A knife-edged aluminum aperture surrounds the image of the primary at the cold stop. The underside of the knife-edge is blackened with carbon-loaded 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 of the cold stop to modulate the polarization signal at the detectors. Due to diﬃculties with the manufacture of the waveplate, it will not be used during the 2005 observing season. 36 CHAPTER 2. EXPERIMENT DESCRIPTION

300K Window (AR-coated UHMW PE) IR blocker IR blocker 77K 12 cm edge IR blocker

9 cm edge 4K 8 cm edge Camera lens (AR-coated HDPE) Field lens (AR-coated HDPE) 4K cold stop

7 cm edge 500mK Band defining filters (see text)

250mK Feed PSB module Figure 2.4: The optical components in the receiver. The black lines to the left illustrate the nested structure of thermal shielding. useful to think of the system in reverse with the feed horns transmitting radiation. The system is designed so that the main beam (down to -20 dB) of the feed horns passes through the stop aperture while the sidelobes are absorbed by the blackened knife edge. This results in a well-deﬁned beam on the primary and prevents the possibly 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 atmospheric transmission (solid black), and the CMB spectrum (dashed black). The QUaD bands are normalized in terms of absolute transmission per polarization; however, they have been scaled upwards by a factor of two for clarity on this plot.

(Section 2.3.4). The high-frequency band edge is set via low-pass ﬁlters mounted on the front of each feed.

The two frequency bands were chosen to correspond with windows in the atmospheric 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 38 CHAPTER 2. EXPERIMENT DESCRIPTION

150 GHz

100 GHz

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

of several filters with staggered cutoff frequencies is needed to completely block 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. The beam measurement was made at NUI Maynooth and published in Cahill et al. [2004].

2.3.4 Corrugated Feeds

Feed horns are needed to efficiently couple radiation onto the bolometers. The beam pattern of the feed determines the illumination pattern on the cold stop (and thus primary mirror). Figure 2.7 shows the modelled and measured beam pattern of a 100 GHz feed. The beam width is chosen to give a -20dB edge taper roughly 12.5◦ from the beam center, corresponding to the edge of the cold stop and the primary mirror. Since the far-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 laboratory optical testing – no measurable change in cross-polar leakage was seen when filters were added or removed from the chain. 40 CHAPTER 2. EXPERIMENT DESCRIPTION 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 radiation 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 experiments 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 shown red. A conducting ring surrounds the absorber (shown green) to provide better thermal contact with the thermistor.

away leaving only a ﬁne mesh [Bock et al., 1995, Mauskopf et al., 1997]. As long as the spacing of the mesh is much less than a wavelength, absorption is unhindered. The advantages of the mesh design are a reduced cross-section to cosmic rays and a lower heat capacity which results in faster response times. The polarization sensitive bolometer (PSB) takes this concept even further. In- stead of a spider-web design, the absorber is a series of parallel wires. The resulting structure absorbs radiation polarized along the grid axis while transmitting the orthogonal polarization. Figure 2.8 shows a schematic representation of a QUaD PSB.

The devices are fabricated from silicon-nitride (Si3N4)attheJPLMicroDevices 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 42 CHAPTER 2. EXPERIMENT DESCRIPTION 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 sample 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.com 5We chose to make the focal plane from aluminum rather than copper for several reasons. First, aluminum is much less expensive, both for the raw material and machining costs. Since it required more than a full-week of machine time, this was not a small matter. Secondly, aluminum resulted in a substantial savings in weight which is important both for mechanical and thermal considerations. We felt that these reasons outweighed the increased thermal conductivity of copper. 2.3. OPTICS 43

Figure 2.9: The position and orientation of the 31 pixels on the focal plane. The layout is composed of three regions: a central grouping of seven 150 GHz pixels (red), a middle ring of twelve 100 GHz pixels (blue), and an outer ring of twelve 150 GHz pixels (red). Each feed is oriented along one of two possible angles (differing by 45◦) corresponding to Stokes Q and U. Although not shown in this figure, the feeds for the two frequencies differ in diameter (Figure 2.6). Figure courtesy of B. Rusholme.

curvature 175 mm.6 Thediameter(aswouldbemeasuredwitharuleracrossthe 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 approximation made from a series of discrete steps. After the shape was roughed out, ﬂats and mounting holes for the feed horns and PSBs were added. This machining was done on the same CNC machine, but this time the bowl was mounted on a rotary table which in turn was mounted on a sine table. For each feed position, the rotary table and sine table were set to the correct angles by hand. 44 CHAPTER 2. EXPERIMENT DESCRIPTION

Figure 2.10: The mounting arrangement for QUaD horns and PSB modules. The protruding bracket below the PSBs is to support the readout wiring.

The focal plane bowl provides the top surface of a cylindrical enclosure that houses the PSB modules and the load resistor boards. This enclosure is necessary to block stray infrared radiation from the PSB modules which are themselves not light-tight. The load resistor boards (Section 3.1.2) mount vertically inside the enclosure as shown in Figure 2.16. The inner surface of the enclosure, not including the underside of the bowl, is blackened with carbon-loaded Stycast to reduce stray light. 2.3. OPTICS 45

Figure 2.11: QUaD receiver core including the focal plane, JFET boxes, hexapod, and cold wiring. The feed horns and cylindrical light-tight bolometer enclosure are at 250 mK. Vespel legs stand this oﬀ from the intermediate temperature (∼ 400 mK) stage below. A Vespel hexapod isolates the intermediate stage from the 4 K baseplate. Low thermal conductivity ribbon cable, wrapped around the Vespel legs, connects the focal plane to the JFET boxes on the bottom right and reads out thermometers located on both temperature stages. The cutout in the 4 K baseplate is for access to attach the focal plane to the fridge during installation (see Section 2.4.3). 46 CHAPTER 2. EXPERIMENT DESCRIPTION

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 is shown in blue. The liquid helium tank and shield is shown in red. The intermediate temperature stage (orange) and thermal shield surround the focal plane. The two purple rectangles underneath the focal plane are the JFET boxes.

The QUaD cyrostat was designed by collaborators at the University of Cardiﬀ and manufactured by AS Scientiﬁc.7 Figure 2.12 shows an exterior photograph of

7www.asscientiﬁc.co.uk 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 intermediate 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. 48 CHAPTER 2. EXPERIMENT DESCRIPTION

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 temperature 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 intermediate 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

baseplate

C pump

condensation point

still

LHe Cold Head Figure 2.14: A single-stage helium adsorption fridge. The upper chamber, known as the pump, contains charcoal that adsorbs helium gas, lowering the vapor pressure above the liquid helium contained in the still below. The two chambers operate at different temperatures and are only joined by a delicate section of thin-walled stainless steel tubing. When all of the liquid in the still has been adsorbed, the fridge needs to be cycled in order to continue cooling. The charcoal is warmed using the embedded heater resistor, driving off the adsorbed gas which liquifies at the condensation point and collects in the still. The entire system is sealed and has no moving parts.

Figure 2.14 illustrates the concept of operation for a simpler, single-stage fridge. The basic physical principal is that the boiling point of a liquid can be reduced by lowering the pressure of the vapor above it.9 Fridges of this design use charcoal to pump a helium bath located in the still. When the liquid is entirely boiled away, the fridge can no longer cool and it needs to be cycled. This is accomplished by passing an electric current through heater resistors embedded in the charcoal. The charcoal is warmed to approximately 50 K, driving off the helium vapor which liquifies and collects in the still below. A three-stage fridge, as is used in QUaD, combines one helium-4 stage with two helium-3 stages. The helium-4 stage operates off of a 4 K baseplate and provides the colder temperature necessary to condense helium-3 in the other two stages. The two helium-3 stages provide the intermediate and ultra-cold temperatures used to cool the focal plane to the sub-Kelvin temperature necessary for optimum bolometer

9This principle is familiar to anyone who has boiled water at a high altitude. 50 CHAPTER 2. EXPERIMENT DESCRIPTION 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 60 He-4 pump Inter pump 50 Ultra pump

30 Temp (K) 20

0 0 1 2 3 4 5 hours Cold Heads 10 Intermediate head Ultracold head 8

Temp (K) 4

0 0 1 2 3 4 5 hours

Figure 2.15: Fridge component temperatures during a typical cycle. The start time of this graph is 30 MAY 2005 12:00 UTC. 52 CHAPTER 2. EXPERIMENT DESCRIPTION

Figure 2.16: Model of the focal plane and supporting structure. The 250 mK light shield beneath the focal plane is not shown, allowing the load resistor boards to be seen. The support legs connecting the intermediate stage (400 mK ring) to the focal plane are also not shown in this rendering. Compare this model with the completed assembly in Figure 2.11.

2.4.3 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 54 CHAPTER 2. EXPERIMENT DESCRIPTION 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 temperature, 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 temperatures.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 hardware 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 0.257

0.256

0.255

0.254 Temp (K)

0.253

0.252 0 5 10 15 20 hours Intermediate Stage 0.435

0.430

Temp (K) 0.425

0.420 0 5 10 15 20 hours

Figure 2.17: Focal plane (top) and intermediate stage (bottom) temperature as measured by their respective GRT sensors during CMB observation on May 31, 2005. The temperature control system maintains the focal plane at an extremely stable temperature. The four small positive spikes seen on the focal plane temperature occur during load curves (Sections 4.1 and 6.1.2) – at maximum bias, power dissipation in the load resistors is suﬃcient to warm the focal plane above the set point. The intermediate stage temperature is not controlled. The two large step changes in temperature correspond to changes in the “deck” rotation angle wherein the cryostat is rotated 60◦ about the optical axis (Section 6.1.2). The telescope was at an elevation angle of roughly 45◦ while this data was taken. 56 CHAPTER 2. EXPERIMENT DESCRIPTION

Figure 2.18: (top) Inserting the science core into the cryostat. The cryostat is in- verted so that it is looking downwards. The entire 4 K baseplate plus focal plane assembly is lowered in. Extreme care is necessary during this operation to avoid disturbing the fridge. (bottom) Once the 4 K baseplate is bolted in place, braided OFHC copper heat straps are used to attach the ultra and intermediate fridge heads to the two thermal stages of the hexapod. Access is through a cutout in the 4 K baseplate which is then sealed with a thin aluminium plate. Kapton-coated ribbon cables (shown unplugged here) connect the 55-pin hermetic connectors on the cryostat bottom (covered with red caps) to the JFET boxes. Chapter 3

Readout Electronics

3.1 Description

Cold Electronics Amplification / V+ Demodulation (gain = 100,000) RL

AC + Bias to ADC Gen. -

RL JFET V- Buffers

Reference freq.

Figure 3.1: QUaD readout electronics overview. The variable resistor symbol denotes the thermistor on the bolometer’s absorber.

The thermistor chip on each PSB registers the temperature change of the absorber arising from ﬂuctuations in the incident optical power. The readout electronics measure the thermistor resistances while contributing minimal noise in the frequency range of interest. The block diagram in Figure 3.1 overviews the components 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 science data. 2These readout the four “dark” PSB modules. Rather than being attached to horns, these modules are blanked off. They serve as monitors of the focal plane temperature. 3These channels are attached to 10 MΩ metal film resistors mounted on the focal plane. They were intended as monitors of the electronics noise; however, failure to adequately restrain their wiring has resulted in excess microphonic noise in these channels making estimation of the electronics noise difficult. 4These channels are attached to low-impedance shorts. They serve as monitors of the JFET and warm amplifier noise (but not any noise from the bias). See Section 3.2.2. 5The thermistors are used to monitor the focal plane temperature (Appendix A).

sine waves, 180 degrees out of phase that are used to bias the bolometers. Each bolometer is wired in series with two cold load resistors, forming a balanced bridge circuit. The bridge is followed by two stages of amplification. First, cold JFET followers located just below the focal plane buffer the high-impedance bolometer signals, reducing their susceptibility to pickup and interference. The buffered signals then exit the cryostat where they 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 additional 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

Voltage Tunable Balance Ref. Switch BP Filter output V+ +1 q=10 +1 Multiplying +10V DAC V- -1 -1 to 100 GHz bolos

V+ +1 4 MHz Divide Multiplying DAC V- crystal by N -1

to 150 GHz bolos Digital amplitude control

Figure 3.2: QUaD bias generator.

This circuit generates two sine waves V+(t)=V0 sin(ω0t)andV−(t)=−V0 sin(ω0t).

Both the amplitude, V0, and the frequency, ω0 are adjustable under computer control. The sine wave output must be exceedingly stable in amplitude1 and reasonably stable in frequency.2 A variety of diﬀerent sine-wave generation circuits were tried

1Bias amplitude variations look like optical signals in the data and thus must be kept to an absolute minimum. 2A standard 50 PPM / ◦C quarts clock oscillator provides adequate stability. 60 CHAPTER 3. READOUT ELECTRONICS and the architecture in Figure 3.2 was found to give the best results. The frequency reference for this circuit is derived from a 4.0 MHz crystal oscillator. 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) provides 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

Focal Plane FP1 FP2 FP3 FP4 (300 mK) RL RL

Vdd 250mK LRB LRB LRB LRB

JFET box (4K) FETS 150 FETS 100 4K Vss (77K) 300K (300 K) 150 GHz Bias / 100 GHz V+ S+ S- V- signals pwr signals

Figure 3.3: (left) A single channel from the QUaD bolometer readout chain. The thermistor (on the bolometer) is shown as the variable resistor in the top center. (right) The subsystems in the cold readout chain. Each load resistor box handles 24 channels of readout and each JFET box, 48.

• Bias amplitude monitors are provided for both channels. These consist of lockin ampliﬁers on the board that demodulate the scaled AC bias signal. The resulting DC signals (proportional to the bias amplitudes) are archived with the rest of the bolometer data.

• Additional circuitry on the bias board provides the power supply voltages for the JFET ampliﬁers.

3.1.2 Load Resistor Boxes

Figures 3.1 and 3.3 show the bridge circuit used for biasing the bolometers. For maximum stability and rejection of electrical interference, the circuit is balanced and fully diﬀerential. All the cold wiring is formed in twisted pairs. Due to thermal considerations, no shielding is present.

The load resistors, labelled 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 constant voltage bias into a quasi-constant current. Physically, they are on four circuit 62 CHAPTER 3. READOUT ELECTRONICS

Figure 3.4: QUaD load resistor board inside a protective box. Due to space constraints, 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 connector for NASA JPL, and with the proper authorization allowed QUaD to use it. The

3www.mini-systems.biz 4www.sierraprotoexpress.com 5www.cristek.com 3.1. DESCRIPTION 63 long surface mount leads provide some springiness that takes up the differential contraction 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 vulnerable to microphonic pickup. To reduce the susceptibility to this pickup, relatively stiff, large diameter wire was chosen for the focal plane.7 Furthermore, the wiring is rigidly mounted to the backside of the focal plane using a combination of aluminum tape and copper mesh. The mesh is screwed to the focal plane, clamping the wires beneath. It is used in areas where the wiring is too bulky to be effectively fixed with tape (see Figure 3.5). For neatness, and to reduce susceptibility to magnetic pickup, the wiring is grouped into twisted quad bundles (one quad per PSB module).

6http://www.pcbexpress.com/essentials/index.php 7Belden 28 AWG stranded copper with PTFE insulation 64 CHAPTER 3. READOUT ELECTRONICS

Figure 3.5: Two views of the focal plane bowl. (top) Top view showing the curved bowl, feeds, and ﬁlters. (bottom) Bottom view showing the PSB modules and wiring. 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 66 CHAPTER 3. READOUT ELECTRONICS

Figure 3.7: QUaD JFET box CAD model (image courtesy James Bock, JPL).From front to back, the box is roughly 10 cm long.

membrane that is supported by the wires carrying the input and output signals (Figure 3.6). These wires are formed by lithography and have low thermal conductivity (∼ 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 temperature. Each membrane contains 24 dual-matched JFET pairs (48 transistors) and dissipates approximately 6.5 mW of power. Heater resistors are provided to warm the membrane at startup, but are not used during normal operation. In addition to being thermally efficient, this design results in JFET boxes that are very compact (see the model in Figure 3.7). Internally, the JFETS are wired as source followers as shown in Figure 3.1 with a gain of around 0.99. Each bolometer is buffered by a matched transistor pair contained on the same die. Any drifts in source voltage due to changes in baseplate temperature result in a common-mode change in the output signal that is rejected by the downstream electronics.10

10This is extremely important for DC-biased testing with QUaD. In the AC-biased mode, slow drifts are always rejected by the demodulation process. However, the balanced bridge design with 3.1. DESCRIPTION 67

3.1.5 Lockin Ampliﬁers

“Preamp” out +1 OUT+ “Low-gain” out

-1 OUT- Switch Switch “High-gain” out

IN+ + Square IN- Wave + - Demod. - BP Filter LP Filter Preamp x5 Offset LP Filter x100 removal x100 Phase DAC Reference freq. in Delay

Figure 3.8: QUaD lockin card schematic.

After the JFETs, the signals exit the cryostat through hermetic connectors on the base. Warm lockin amplifier boxes attached beneath the cryostat perform further amplification and filtering. Each lockin box contains 12 cards each of which processes the signal from the pair of detectors in a PSB module. Figure 3.8 is a block diagram of the lockin cards. Each differential signal pair (from a single detector) first enters a low-noise instrumentation amplifier with a gain of 100 (AD624). The signals then go through a wide bandpass filter to suppress noise far from the bias frequency. This bandpass filter is composed of a 4-pole butterworth low-pass filter with a cutoff of 475 HZ followed by a 2-pole butterworth high-pass filter with 2.8 Hz cutoff. The filter is designed to have a broad region of flat response over the possible bias frequency range of 40 - 250 Hz. The square-wave demodulator (AD630) multiplies the signal by +1 when the reference signal is positive and -1 when it is negative. This results in a near DC signal for inputs near the reference frequency. Additionally, there is the usual component at dual JFETs per channel is still very desirable because it helps ensure that all pickup (regardless of frequency) is common mode. 68 CHAPTER 3. READOUT ELECTRONICS

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)whereφ 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 70 CHAPTER 3. READOUT ELECTRONICS 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 digitization 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 internet access. 3.2. PERFORMANCE 71

Measured Bias Spectrum, f0 = 100 Hz 0

Measured spectrum BP × (f0 / f) BP -20

-40 dB

-60

-80 0 500 1000 1500 Hz

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 72 CHAPTER 3. READOUT ELECTRONICS

Preamp output

lockin IN+ + Square output IN- Wave - Demod. LP Filter HP Filter LP Filter Preamp 475 Hz 2.1 Hz 20 Hz

Reference Freq.

Figure 3.11: Filtering on the amplifier cards. This shows the location and nominal cutoff frequencies of the filters that are measured in this section. See Figure 3.8 for a more complete block diagram.

filtering a square wave with a bandpass filter centered on the fundamental frequency. We thus expect the spectrum of the output waveform to contain prominent lines at the odd harmonics. The amplitude of the peaks is determined by the intrinsic spectrum of a square wave multiplied by the response of the bandpass filter. The amplitude of the Fourier components of a square wave fall off as 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

ω ω BP(ω,Q)= 0 , (3.1) Q2 ω2 − ω2 2 ω ω 2 ( 0 ) +( 0 ) 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

1.2

1.0

0.8

0.6

0.4 Scaled Response

0.2

0.0 0 200 400 600 800 1000 Hz

Figure 3.12: Measured response of the 475 Hz low-pass portion of the bandpass ﬁlter. The ﬁlter is a 4-pole Butterworth. The solid, black line shows the nominal response. Device-to-device variation is small near the bolometer bias frequency of 110 Hz.

Ampliﬁer Cards

The QUaD amplifier card was developed in parallel with the bias generator, during which time extensive testing was performed on prototype and intermediate versions. Once the final design was reached, a contract manufacturer assembled the full com- plement of approximately 50 cards in several runs. Each card has a large number of components (approximately 170 passives and 20 integrated circuits) and eight jumpers allow different modes of operation to be selected. Given all these possibili- ties for errors, it seemed sensible to test every card for basic functionality. The large number of cards made individual testing impractical, so different automated testing procedures were developed. The reader is referred to Figure 3.8 for a block diagram of the lockin card. Figure 3.11 gives a simplified view concentrating on the main filters. The first setup used an SRS 340 synthesized function generator to create test 74 CHAPTER 3. READOUT ELECTRONICS

1.2

1.0

0.8

0.6

0.4 Scaled Response

0.2

0.0 0 10 20 30 40 Hz

Figure 3.13: Measured response of the 20 Hz low-pass, post-demodulator ﬁlter. The ﬁlter is a 6-pole Butterworth. The solid black line shows the nominal response.

signals and a Keithely 2700 benchtop DVM to measure the response. Both instruments 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

1.2

1.0

0.8

0.6

0.4 Scaled Response

0.2

0.0 0 10 20 30 40 50 Hz

Figure 3.14: Filter bands as measured by impulse response testing (see text for details). This measures the product of the bandpass filter and the 20 Hz lowpass filter response. Only the 2.1 Hz high-pass edge of the bandpass filter is visible since the post-demodulator filter cuts off long before the 475 Hz high-pass edge. The solid, black line shows the nominal response.

consisting of a carrier with a sinusoidal envelope at one tenth the frequency. After demodulation, an oscillation at the envelope frequency remains. This signal was played at various frequencies and the output recorded with the AC voltage setting of the DVM.12 The results are shown in Figure 3.13.

• Phase adjustment - The reference phase adjustment circuit adds a delay to the demodulator reference to compensate for phase shifts on the signal lines inside the cryostat. In order to test its operation, a ﬁxed sine wave was applied to the input and the DC level at the “low-gain” output was recorded for various phase delays.

12Because the carrier also changed frequencies, the measured response of the 475 Hz low-pass ﬁlter should also be taken into account. For envelope frequencies below 20 Hz (carrier frequencies below 200 Hz), the correction would be negligible. For higher frequencies, it would be at most 5%. 76 CHAPTER 3. READOUT ELECTRONICS

• DC offset removal - The DC removal circuit was tested by applying a fixed sine wave input and monitoring the DC level on the “high-gain” output (see Figure 3.8) while adjusting the DAC voltage. This confirmed operation of the DAC and measured the gain of the final amplifier (nominally 100).

Approximately 30 cards were tested using this procedure and several problems were discovered and repaired. Unfortunately, we did not receive the last batch of cards until after the bulk of the experiment had shipped to the Pole. Some of the test equipment had to remain at Stanford, so a new procedure was developed for testing at the Pole. The second setup used the bias generator to create test signals and the DAS to record the response. This setup was able to test a complete box (12 cards) at a time, but the options were more limited.

• Gain - DC and sine wave inputs were used to measure the DC and AC gains of the card at the “preamp” and “low-gain” outputs respectively.

• Filters - The 20 Hz post-demodulator filter response was measured in a completely 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 functions 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 functionality was verified in the course of noise testing (Section 3.2.2).

13The low sampling frequency of the ADC (100 Hz) prevented the impulse method from being used. The limited frequency range of the bias board (40-250 Hz) prevented direct measurement). 3.2. PERFORMANCE 77

V+

2K Amplifier Card AC + Bias 1K Gen. - 2K

V- Reference freq.

Figure 3.15: The setup for electronics noise testing.

This procedure found problems in several cards. A final round of testing was performed once all the cards were installed. This gave us confidence that all the cards were stuffed correctly and allowed us to confidently interpret the results of the noise tests described in the next section.

3.2.2 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, distributed by Newark Electronics. 78 CHAPTER 3. READOUT ELECTRONICS

Card 54 Card 2 Card 24 10 10 10 1/2 1/2 1/2 nV/Hz nV/Hz nV/Hz

1 1 1 0.01 0.10 1.00 10.00 100.00 0.01 0.10 1.00 10.00 100.00 0.01 0.10 1.00 10.00 100.00 Hz Hz Hz Card 4 Card 5 Card 6 10 10 10 1/2 1/2 1/2 nV/Hz nV/Hz nV/Hz

1 1 1 0.01 0.10 1.00 10.00 100.00 0.01 0.10 1.00 10.00 100.00 0.01 0.10 1.00 10.00 100.00 Hz Hz Hz Card 7 Card 8 Card 9 10 10 10 1/2 1/2 1/2 nV/Hz nV/Hz nV/Hz

1 1 1 0.01 0.10 1.00 10.00 100.00 0.01 0.10 1.00 10.00 100.00 0.01 0.10 1.00 10.00 100.00 Hz Hz Hz Card 10 Card 11 Card 12 10 10 10 1/2 1/2 1/2 nV/Hz nV/Hz nV/Hz

1 1 1 0.01 0.10 1.00 10.00 100.00 0.01 0.10 1.00 10.00 100.00 0.01 0.10 1.00 10.00 100.00 Hz Hz Hz

Figure 3.16: Noise spectra for the 12 amplifier cards in QUaD lockin box 1 for the test setup seen in Figure 3.15. These spectra include contributions from the bias and 1 k fake bolometer. Each card has two independent amplifiers which are shown in black and red. The large spike at 30 Hz results from beating of the AC bias frequency (90 Hz for this data set) with the power line mains frequency of 60 Hz. The spikes at 10 Hz visible in some channels result from beating with the ADC sampling frequency of 100 Hz. 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 corresponding 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: 2 e2 e . −1/2 setup = J (1k 4k) =36nV Hz √ 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 4k=0.8kisthe eﬀective resistance of the fake bolometer in parallel with the load resistors.

Amplifier: In order to quantify the amplifier noise contribution, noise measurements 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 e2 e R 2 i R 2 = amp + J ( ) + n (3.2)

where in, the current noise density of the input ampliﬁer, is found to be ∼ 80 CHAPTER 3. READOUT ELECTRONICS

Amplifier Noise Test Setup

AC + Bias R - Gen. Amplifier Card Reference freq.

Amplifier Noise Spectra 100.0

10.0 -1/2 nV Hz 1.0 Gnd 1k 3.9k 20k 0.1 1 10 100 Freq (Hz)

Amplifier Noise vs. Source Resistance 30 Measured Amp + Johnson Amp + Johnson + current

20 -1/2 nV Hz

0 0 5 10 15 20 25 Res (K)

Figure 3.17: Amplifier noise as a function of source resistance. (top)Thetesting setup. Although the bias voltage itself is not used for this test, the bias board still provides the reference frequency for the lockin amplifier. (middle) Noise spectra for several of the tested source resistances. (bottom) The data are well fit by the quadrature sum of a constant amplifier voltage noise term, an amplifier current noise term, and the Johnson noise term from the source resistance (eq. 3.2). 3.2. PERFORMANCE 81

−1/2 800 fA Hz . The voltage noise of the ampliﬁer is measured to be eamp = 5.0nVHz−1/2 and current noise is seen to be negligible for source impedances belowafewkΩ.

Bias: Tests were performed to determine the noise contribution of the bias generator. 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 −1/2 ebias =2.8nVHz . 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. 82 CHAPTER 3. READOUT ELECTRONICS

Table 3.2: Noise budget for the results of warm noise testing shown in Figure 3.16. The first line refers to the contribution from the bias generator. The second line refers to the noise from 1 k 4 k warm fake bolometer testing setup. The third line refers to the noise from the amplifier card (dominated by the voltage noise of the preamplifier chip).

Source 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 10.0 -1/2 1.0 nV Hz

Card grounded Fake bolometer grounded Fake bolometer biased

0.1 1 10 100 Freq (Hz)

Figure 3.18: Spectra used to determine the noise contribution from the bias generator. The black trace shows the grounded ampliﬁer input noise for reference. The green trace shows the result for the test setup of Figure 3.15 with the fake bolometer biased at 7.5 mVRMS. The blue trace results from grounding the load resistors rather than connecting them to the bias board. 3.2. PERFORMANCE 83

Figure 3.19: Average noise spectrum for all 24 amplifiers in Lockin Box 1. The dashed blue lines show the white noise level and a fit to a 1/f noise model. The 1/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 the entire warm electronics chain including the bias generator and the DC offset removal circuit. 84 CHAPTER 3. READOUT ELECTRONICS

Readout Chain

The previous subsection measured the noise from the warm readout electonics. This subsection describes similar measurements for the entire readout chain, including the cold JFET buﬀers. This noise level is extremely important for quantifying the performance of the receiver. Three diﬀerent methods were used estimate the end to end electronics noise over a frequency range of 1 - 10 Hz:

1. In the previous sub-section, the ampliﬁer cards were measured to contribute 5.0 nV Hz−1/2 and the bias to contribute 2.8 nV Hz−1/2. Tests with a prototype JFETs box at NASA JPL under similar operating conditions as in QUaD resulted in a median noise of 7.6nVHz−1/2. Combining these in quadrature yields ∼ 9.5nVHz−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 11.9nV 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 approximate 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 −1/2 total system noise, a conservative average value of Vn ∼ 9nVHz 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 understand 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 86 CHAPTER 3. READOUT ELECTRONICS

Ibias RL

Vbias Ibolo R IC C 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 V I R I 1 sig = bolo = C iωC

Ibias = Ibolo + IC that can be solved for the output signal voltage as

R Vsig = Vbias. (3.3) R +2RL +2RRLiωC

A little algebra puts this in a more suggestive form

R 1 Vsig = Vbias (3.4) R +2RL 1+iωReffC where Reff =2RLR/(2RL + R) is the effective resistance of the bridge network.

The output voltage (Vsig)andthebolometer 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:

1 AC = 2 2 1+ω τC −1 φC =tan ωτC .

The next subsection applies these equations to measured QUaD data to determine the channel capacitance.

QUaD Parameters

Single Channel Fit QUaD Channel Capacitance 1.00 100

95 0.95

90 0.90 85

0.85 Cap (pF) 80 Normalized Signal

0.80 75 C = 86 pF R = 8MΩ 0.75 eff 70 0 50 100 150 200 0 20 40 60 80 Bias freq (Hz) Channel 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 88 CHAPTER 3. READOUT ELECTRONICS

Attenuation and Phase for Typical QUaD Parameters 1.00 0 Attenuation Phase 0.98 -5

0.96 -10 0.94 -15 0.92 Attenuation

-20 Phase delay (deg) 0.90

0.88 -25 C = 100 pF R = 5MΩ 0.86 0 50 100 150 200 Bias freq (Hz)

Figure 3.22: The reduction in bias current (attenuation) and phase delay versus bias frequency for typical QUaD channel parameters. The 2005 bias frequency of 110 Hz is indicated by the vertical line.

frequency dependence (∼ 1%) of the bias generators output sine wave amplitude. A measurement at DC was used to establish the DC gain of the readout electronics. A one-parameter ﬁt was then applied to the data to ﬁnd the capacitance.

Figure 3.21 (right) shows the results for each channel. The values range from approximately 75 - 95 pF with a mean of 85 pF and a standard deviation of 4 pF. Note that these measurements do not include the focal plane wiring, but do include the correct number of connectors (since the fake bolometer boards have the same connectors as the focal plane). A measurement of a sample of the focal plane wiring (using a capacitance meter) yielded approximately 10 pF. So a conservative estimate of the total channel capacitance for QUaD is ∼ 100 pF. Figure 3.22 shows the bias current attenuation and signal phase shift that would result for this capacitance assuming a typical bolometer resistance. At the 110 Hz bias frequency, the average channel sees a roughly ∼ 4% attenuation in bias current and a ∼ 20◦ phase shift. 3.2. PERFORMANCE 89

Microphonic Noise Spectrum 1000 baseline banging

100 -1/2 nV Hz 10

1 0 200 400 600 800 Freq. (Hz)

Figure 3.23: Microphonic response for a single QUaD channel comparing two cases: “baseline” (receiver undisturbed) and “banging” (receiver tapped lightly with a rubber 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. 90 CHAPTER 3. READOUT ELECTRONICS

Baseline 1000 150-44C 100-14C 150-01H -1/2 100 nV Hz

10 0 50 100 150 200 250 Freq. (Hz)

Banging 1000 150-44C 100-14C 150-01H -1/2 100 nV Hz

10 0 50 100 150 200 250 Freq. (Hz)

Figure 3.24: Microphonic response for three channels over the possible bias frequency range.

The cleanest region of the spectrum is around 200 Hz. Indeed bolometer noise tests with the bias frequency set here showed a complete absence of microphonic features. It was, however, felt that this frequency range was too high given the 3.2. PERFORMANCE 91

QUaD Receiver

Hermetic connector RF-tight interface box Filtered “D” connector

Electronics boxes

Cabling to DAS

Figure 3.25: Warm RF filtering. All lines entering or leaving the cryostat pass through filtered connectors (shaded gray) at the entrance to the RF-tight interface box. Figures 4.6 and B.3 show photographs of the electronics boxes attached to the cryostat. capacitance effects measured in the previous section (Figure 3.22). Instead, a bias frequency of 110 Hz was chosen. Operating in AC bias mode with this bias frequency, all channels are free of microphonic resonances over the frequency range of interest (Figure 5.24).

3.2.5 Radio Frequency Interference

A signal wire connecting the bolometers to the data acquisition can act as antenna, picking up radio-frequency (RF) power. Some of the RF power dissipates in the bolometer’s thermistor chip which heats the detector and produces a spurious signal. Because of the negative temperature coefficient of resistance for NTD germanium thermistors (eq. 4.7), radio frequency interference (RFI) always results in a negative voltage signal. Frequencies of order 1 GHz are most problematic since they couple 92 CHAPTER 3. READOUT ELECTRONICS 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 entering 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 electrical operation of a bolometer. A model for the thermal operation of a semiconductor 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 devices. 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 temperature, Tbolo, greater than the baseplate temperature, Tbase. The optical power is typically referred to as Q while the electrical power is called P .Powerﬂowsfrom

93 94 CHAPTER 4. RECEIVER CHARACTERIZATION

Q Ibias RL

Absorber (Tbolo ) R ,)D R V Thermistor ( 0 P=IV Vbias bolo

Thermal link (G0 ,)b

RL Baseplate (Tbase)

Figure 4.1: (left) Bolometer thermal model. (right) Bolometer electrical readout circuit.

the bolometer to the baseplate through a thermal link with temperature-dependent conductivity. In thermal equilibrium, the power ﬂowing into the absorber equals the power leaving. This is expressed quantitatively by the power-balance equation which is written as follows

T bolo P + Q = G(T ) dT (4.1) T base where G(T ) is called the diﬀerential thermal conductivity. For semiconductor bolometers, G(T ) can be modelled with a power law:

T β G(T )=G0 (4.2) T0 where T0 is an arbitrary reference temperature. For QUaD, typical values are G0 ∼

100 pW/K and β ∼ 1.3forT0 = 300 mK. Using this model for G(T ), the power- balance equation becomes

G β β P + Q = 0 T +1 − T +1 . (4.3) T β β bolo base 0 ( +1)

The electrical power dissipated in the thermistor can be manipulated into three 4.1. BOLOMETER CHARACTERIZATION 95

standard forms using Ohm’s law:

V 2 P = I V = I2 R(T )= bolo . (4.4) bias bolo bias R(T )

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:

Vbias − Vbolo Ibias = (4.5) 2RL

R(T ) Vbolo = Vbias. (4.6) R(T )+2RL

The ﬁnal step is to relate the thermistor resistance to temperature. For NTD Ger- manium thermistors, a simple functional form gives excellent results: √ ∆/T R(T )=R0e . (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,givenmea- surements of Vbolo, Vbias and Tbase. First, however, the bolometer must be characterized by determining the device-dependent parameters R0,∆,G0,andβ.Thisisthe 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 96 CHAPTER 4. RECEIVER CHARACTERIZATION

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 4.1. BOLOMETER CHARACTERIZATION 97

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 =0andP 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 =lnR (4.9) linearizes eq. 4.7 which is useful for plotting the results as in Fig 4.3. Deviation 98 CHAPTER 4. RECEIVER CHARACTERIZATION

Figure 4.4: The optical loading, Q, for the three load curves in Figure 4.2. For each load temperature, the power is independent of bias, indicating a successful fit for G0 and β. As noted in the text, it is difficult to make an absolute measurement of the loading due to sensitivity to the bolometer parameters and the baseplate temperature. Also, these results are not corrected for the approximately 2 pW of loading due to emission from inside the cryostat (Section 5.3.1). from a straight-line, especially for the coldest points, is common. This indicates stray power warming the detector, or a temperature offset between the bolometer and the baseplate thermometer. Reliable measurements of 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

4.7isusedtoconvertVbolo into Tbolo and eq. 4.4, to ﬁnd P (the electrical power). The derivative of the power balance equation gives: T β β dP d bolo T Tbolo = G0 dT = G0 (4.10) dT dTbolo T T T bolo Tb base 0 0 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 4.1. BOLOMETER CHARACTERIZATION 99

values for a non-linear ﬁt to the diﬀerence equation

G β β P − P = 0 T +1 − T +1 . (4.11) 2 1 T β β bolo2 bolo1 0 ( +1)

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,ateverypointofanyloadcurve:

G β β Q = 0 T +1 − T +1 − P. (4.12) T β β bolo base 0 ( +1)

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 before 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

1 Assuming the parameter ∆ is known, a dark load curve can be ﬁt for R0 and a temperature oﬀset from the assumed baseplate temperature. These are found to be as high as 10 mK for the dark load curves in Figure 4.3 with substantial device to device variation. Uncertainties in the baseplate temperature at this level lead to uncertainties in Q of order GδT ∼ 1pW. 100 CHAPTER 4. RECEIVER CHARACTERIZATION

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 devices, resulting in high measured cross polar leakage. This usually resulted from machining tolerances placing the two membranes too close (nominal separation ∼ 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 have dark characterization. The top section of the table lists the detectors that are now open to light. The R0 and ∆ parameters for these detectors were determined in a separate test bed prior to installation in QUaD. The G0 and β parameter were ﬁt from a load curve under typical observing conditions. The bottom section lists detectors that are currently dark. They were characterized in QUaD (R(T )data shown in Figure 4.3).

PSB R0 ∆ G0 β (Ω) (K) (pW/K) 150-12H 93.4 41.0 120.7 1.47 150-12C 82.6 40.8 152.0 1.45 150-21H 80.5 41.2 129.7 1.44 150-21C 78.9 41.4 155.9 1.46 150-04H 133.5 39.8 159.3 1.42 150-04C 94.3 40.0 123.4 1.36 150-15C 113.8 39.3 107.0 1.35 150-01H 156.8 40.3 117.6 1.41 150-01C 96.0 41.2 116.1 1.43 150-32H 99.2 45.5 92.3 1.82 150-53C 81.0 42.5 98.3 1.70 100-43C 135.6 38.7 48.5 1.52 100-22C 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. 102 CHAPTER 4. RECEIVER CHARACTERIZATION

Figure 4.5: The QUaD optical testbed. (left) Photo with all thermal shields removed. The JFET box is visible in the foreground and the load resistor box is located to the left of the feed. (right) Assembly drawing.

• Optical efficiency - The optical efficiency was measured for several devices at each frequency. These early tests showed the low efficiency of the 100 GHz channels that is seen in QUaD (Section 4.2.3).

• Cross polar leakage - The cross polar leakage was measured for multiple devices at both frequencies. Again, these early tests showed the poorer performance of the 100 GHz channels relative to the 150s. Comparison of the testbed and QUaD results is presented in Section 4.3.

4.2.2 Spectral Bands

The QUaD spectral bands are fixed at the low-frequency end by the feed horn throat and on the high end by metal-mesh low-pass filters as described in Section 2.3.3. Dur- ing development, the filter bands were tested with a Fourier transform spectrometer (FTS) at Stanford. Once the filter stack was finalized and installed, every pixel was tested with an FTS at the South Pole. 4.2. OPTICAL CHARACTERIZATION 103

Figure 4.6: The QUaD receiver setup for laboratory testing with the Stanford FTS.

An FTS is a Michelson interferometer with one ﬁxed and one movable mirror. The bolometer voltage is recorded as the moving mirror varies the path length resulting in an interference pattern known as an interferogram. The Fourier transform of the interferogram gives the transmission function of the pixel being tested. The transmission function (or spectral response function) is denoted f(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 104 CHAPTER 4. RECEIVER CHARACTERIZATION

Table 4.2: Average spectral band properties.

Num ν0 (GHz) ∆ν (GHz) ∆ν (%) 12 94.5 ± 0.6 26.5 ± 228 19 149.5 ± 0.6 40.5 ± 227

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 ∞ νf(ν) dν ν 0 0 = ∞ f ν dν (4.13) 0 ( ) 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. 4.2. OPTICAL CHARACTERIZATION 105

Figure 4.7: The QUaD spectral bands as measured at the South Pole. The bands shown dashed correspond to feeds with at least one non-functional channel. 106 CHAPTER 4. RECEIVER CHARACTERIZATION

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:

1 Q = AΩfn(ν) B(T,ν) dν (4.14) 2 where AΩ is the throughput of the optical system and fn is the normalized spectral response. The factor of 1/2 arises because the PSB detects only one linear 4.2. OPTICAL CHARACTERIZATION 107

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 normalized transmission: 1 ν2 η = fn(ν) dν (4.16) ν2 − ν1 ν1

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 resistance 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

2 The factor of 1/2 could be absorbed into fn(ν); however, the deﬁnition here makes comparison of eﬃciencies with total power experiments simpler. 108 CHAPTER 4. RECEIVER CHARACTERIZATION

Table 4.3: Average optical eﬃciencies. “Inner” refers to the central group of seven 150 GHz pixels and “outer” refers to the outer ring of 12 pixels (Figure 2.9) .

100 GHz 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 measurements can be averaged. Equation 4.14 relates the power diﬀerence to the load temperatures ∆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 spectrum 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 4.2. OPTICAL CHARACTERIZATION 109

Figure 4.9: QUaD optical eﬃciencies. The shaded region of the 150 GHz histogram shows the distribution for the central ring of seven feed horns.

is dry, since thermal emission from condensation will make it appear warmer – an eﬀect that is indistinguishable from reduced optical eﬃciency. For the same reason, the cryostat window must be clean and dry.

The results are summarized in Figure 4.9 and Table 4.3. The optical efficiencies for the central group of seven feed horns are significantly better than the outer ring of 150 GHz feeds. This is largely attributable to a selection effect; the best performing detectors from previous runs were grouped in the center because 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). 110 CHAPTER 4. RECEIVER CHARACTERIZATION

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:

dV S bolo . DC = dQ

Using the equations in Section 4.1.1 one can derive the following expression

RL z − R SDC = (4.20) 2Vbolo z +2RL where z, the dynamical impedance, given by

dVbolo z = , (4.21) dIbias 4.2. OPTICAL CHARACTERIZATION 111

is the the slope of the load curve. The responsivity as defined in eq. 4.20 is always negative for QUaD since our detectors have a negative temperature coefficient of resistance (eq. 4.7). However, it is common in practice to refer to the 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:

dV dR dT S ω bolo . ( )= dR dT dQ (4.22)

The ﬁrst two factors are frequency independent; however, the last is not. Its frequency 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 1 ∝ (4.23) ∆Q 1+iωτ 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 112 CHAPTER 4. RECEIVER CHARACTERIZATION

150-13-B 150-14-A 1.2 1.2 Tau lab: 10.1 Tau lab: 32.7 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0.0 0.0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Freq (Hz) Freq (Hz) Figure 4.11: Lab time constant measurements for two example detectors Time constants are in ms in the upper right corner of each plot.

loading is incorrect. In fact, the bias current remains (nearly) constant, but increased 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 −1 τ replaced by an eﬀective time constant τe = C/(G − αP )whereα = R 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

SDC S(ω)= . (4.24) 1+iωτe

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 4.2. OPTICAL CHARACTERIZATION 113

wheel had alternate transparent and opaque (Eccosorb foam) sections. The resulting square-wave signal was digitized and demodulated in software. The amplitude was recorded for a variety of chopper rotation frequencies. The data was taken using the DC-biased mode of the readout electronics since chopper rotations faster than the 20 Hz cut off frequency were needed. Figure 4.11 shows data and model fits for two detectors. Unfortunately, during the test, the bolometer bias current was set a factor of 4.5 higher than the standard observing value (see Section 5.3.2) and the chopped load presented roughly six times more optical loading than is seen in the field (see Section 5.3.1). These different operating conditions make the results of these tests less useful. Section 5.1.4 presents an alternate method of measuring time constants under typical observing conditions.

4.2.5 Cosmic Rays and 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 optical power from reaching the detectors; however, cosmic rays easily penetrate. Even though PSBs present a substantially reduced cross section relative to a solid absorber, 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 be ignored from the main CMB analysis with negligible loss of data. 114 CHAPTER 4. RECEIVER CHARACTERIZATION

Cosmic Ray Impulse Response 2

-2 Volts

-4 Data Spline Impulse model

-6 0.0 0.2 0.4 0.6 0.8 1.0 sec

Figure 4.12: A cosmic ray impact shows the receiver’s impulse response.

constant, 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:

1 Hbolo(s)= (4.25) τbs +1 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

1 H(s)= (4.26) 2 2 2 2 2 2 (τf s + Aτf s +1)(τf s + Bτf s +1)(τf s + Cτf s +1) 4.2. OPTICAL CHARACTERIZATION 115

Impulse Response Model 0.40

0 ms 10 ms 0.30 20 ms 30 ms

0.20 Volts 0.10

0.00

-0.10 0.00 0.05 0.10 0.15 0.20 0.25 sec

Figure 4.13: Model QUaD impulse response for several diﬀerent bolometer time constants.

which is a product of three general, second-order responses. For a Butterworth, the √ coeﬃcients are A =0.5176387, 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 generated 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, 116 CHAPTER 4. RECEIVER CHARACTERIZATION

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 vectors 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 118 CHAPTER 4. RECEIVER CHARACTERIZATION

Figure 4.16: Measuring the polarization angles. column vectors which give the amplitude and phase of the electric ﬁeld as ⎛ ⎞ iφx ⎜ E0xe ⎟ E = ⎝ ⎠ (4.28) iφy E0ye

iωt where the E0 and φ are real. An overall time dependence of e 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: ⎛ ⎞ √1 ⎜ 1 ⎟ E45 = ⎝ ⎠ . (4.29) 2 1

Passing this beam through a horizontally-oriented polarizing grid results in the new beam, Ef ,givenbyEf = Jh E45. The Jones matrix of a horizontal polarizer, Jh,is 4.3. POLARIZATION PROPERTIES 119

Figure 4.17: Measured PSB orientations.

given by ⎛ ⎞ ⎜ 10⎟ Jh = ⎝ ⎠ (4.30) 00

√ T so that Ef =1/ 2 10 . 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 parameters, is more appropriate. In this formalism, the radiation is represented by a T real, four-component Stokes vector S = I, Q, U, V . Optical elements acting on the radiation are represented by 4x4 real matrices. Given a Jones matrix, J,fora component or system, the corresponding Meuller matrix is given by

1 † Mij = tr σiJσjJ (4.31) 2 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 120 CHAPTER 4. RECEIVER CHARACTERIZATION

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) 4.3. POLARIZATION PROPERTIES 121

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: † 2 2 Popt ∝ E E = |Ex| + |Ey | (4.33) where <> denotes time averaging.4

The Jones matrix for the PSB is given by ⎛ ⎞ ⎜ η 0 ⎟ JPSB = ⎝ ⎠ (4.34) 0 δ where η ∼ 1andδ 1 parameterize the cross polar leakage [Jones, 2005]. The

4 The symbol Popt is used instead of Q to denote the optical power absorbed by a PSB to avoid confusion with the Stokes parameter Q. 122 CHAPTER 4. RECEIVER CHARACTERIZATION

Jones matrix for a linear polarizer oriented at an angle, θ,tothex axis is given by ⎛ ⎞

⎜ 10⎟ T Jpθ = R ⎝ ⎠ R (4.35) 00 where R is a standard rotation matrix given by ⎛ ⎞ ⎜ cos θ − sin θ ⎟ R = ⎝ ⎠ . (4.36) sin θ cos θ

Simplifying, this gives ⎛ ⎞ 1 ⎜ 1+cos2θ sin 2θ ⎟ Jpθ = ⎝ ⎠ . (4.37) 2 sin 2θ 1 − cos 2θ

The initially unpolarized radiation ﬁeld can be represented with the Jones vector ⎛ ⎞ 1 ⎜ 1 ⎟ Ei = √ ⎝ ⎠ (4.38) 2 eiφ(t) 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 =0whenPopt = 0 which gives the output voltage of the lockin ampliﬁer as: 1 1 v(θ) ∝ η2 + δ2 + η2 − δ2 cos 2θ. (4.39) 2 2 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 4.3. POLARIZATION PROPERTIES 123

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 measurement was made with the single-pixel optical testbed (Section 4.2.1) looking through the stacked grids at a chopped load. 6W.M. Berg, Inc. www.wmberg.com 124 CHAPTER 4. RECEIVER CHARACTERIZATION 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 loading) 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 4.3. POLARIZATION PROPERTIES 125

modules, transmission through the cryostat optical chain, and placement of the absorber within the PSB module. In particular the speciﬁed tolerance of ±1◦ on the absorber position can account for much of the distribution.

The cross polar leakage results are more puzzling. The lower limit of the contribution 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 prevent 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 improvement. 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 126 CHAPTER 4. RECEIVER CHARACTERIZATION

Figure 4.20: Comparison of the measured cross polar leakage for the same detectors in QUaD (solid) and the optical testbed (dashed). The data points from the testbed are shown as filled circles. Both data sets were taken through a 0.5” Eccosorb aperture located at the cryostat window. The testbed data points for each detector are phased to best align with the QUaD data. These are the only PSBs that were measured in the testbed and installed in the final instrument. 4.3. POLARIZATION PROPERTIES 127 pixels but the problem likely involves the horn bolometer interface or the horn itself 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. 128 CHAPTER 4. RECEIVER CHARACTERIZATION

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 naturally 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 T vector Si =(I, Q, U, V) . 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 ⎛ ⎞ ⎜ η 0 ⎟ J = R ⎝ ⎠ RT (4.40) 0 δ where R is the rotation matrix deﬁned in eq. 4.36. Since the PSB only detects the total intensity component (I)ofSf , 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 + )I +(1− )(Q cos 2θ + U sin 2θ) (4.42) where = 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 4.3. POLARIZATION PROPERTIES 129

eﬃciency, bandwidth, and readout electronics gain. In practice, s is determined using astronomical calibration (Section 5.2.3).

Implications

From eq. 4.42, the signal from a single PSB at a given angle is a linear combination of the I, Q,andU 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 , results in a loss of sensitivity to the polarized portion of the radiation, but not in a mixing of I, Q,andU (i.e. their angular dependence remains unchanged). For a map made with a single PSB, uncertainty in 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 − ) Q + U cos 2θ + U + Q sin 2θ . (4.43) 2 2

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. 130 CHAPTER 4. RECEIVER CHARACTERIZATION

In order for the contribution of the unpolarized radiation, I, to cancel upon differencing 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 uncorrelated 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 expectation value of the square of the corrected diﬀerence signal for a segment of data:

d v v s I 2 2 a b a 0= (va − kvb) → k = = (4.45) 2 2 2 2 dk vb sb I + nb /sb 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 commissioning 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 tracking 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, decelerate, 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

-138

-140

-142

-144 Azimuth Encoder (deg) -146

-148 0 200 400 600 800 1000 time (sec)

Figure 5.1: The azimuth encoder reading while raster mapping RCW38. The overall negative slope results from tracking the source with sky rotation. The pause after every fourth constant velocity section (half-scan) allows time for the telescope to change elevation and the DC oﬀsets to be reset.

by a fraction of a beam width and to reset the DC oﬀsets for the changed air mass. A simple procedure converts the resulting time-ordered data into a pixelized map:

1. Convert the telescope axis encoder data into a right ascension (RA) and declination (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 -46.0

-46.5

-47.0

-47.5 DEC (deg)

-48.0

-48.5

-49.0 134.0 134.5 135.0 135.5 136.0 RA (deg)

Figure 5.2: The telescope RA/DEC position from an early QUaD raster map of RCW38 shows sections of large elevation jitter. For clarity, only one out of every four half-scans is plotted and only every fourth elevation step is used. The elevation jitter problem was resolved shortly after this data was taken (see text). 134 CHAPTER 5. INSTRUMENT PERFORMANCE

RCW38 Raw Scan APR 10 HRN150-02 0.1

0.0

-0.1

Signal (Volts) -0.2 1.4 × El (deg)

-0.3 0 10 20 30 40 50 sec Elevation Jitter Corrected 0.1

0.0

-0.1 Volts

-0.2 Signal - 1.4 × El -0.3 0 10 20 30 40 50 sec

Figure 5.3: (top) Scan across the source RCW38 showing the effect of elevation jitter, which was present in early observations with QUaD. The elevation encoder, overplotted in red, is highly correlated with the bolometer signal. (bottom)Re- moving the best-fit scaled encoder signal reduces the effects of elevation jitter except when scanning across the source. This is purely illustrative as this technique is not used for any further analysis. 5.1. OPTICAL PERFORMANCE 135

Figure 5.4: Maps of the galactic HII region, RCW38 at 100 (left) and 150 (right) GHz. The top two plots are minimally processed – only the mean has been subtracted from each scan line. The middle plots show the results of subtracting a ﬁfth-order polynomial from each row. The bottom plots use a neighboring feed to subtract out the common mode signal. The object faintly visible below and to the right is a companion source. 136 CHAPTER 5. INSTRUMENT PERFORMANCE

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 particularly 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. OPTICAL PERFORMANCE 137

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 enoughrasteroveracompactsourcesuchas 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

Measured Nominal

0.5

0.0 deg

-0.5

-1.0 -1.0 -0.5 0.0 0.5 1.0 deg

Figure 5.5: QUaD feed positions measured from RCW38. 138 CHAPTER 5. INSTRUMENT PERFORMANCE

Figure 5.6: QUaD raster maps of RCW38 from every feed in the focal plane. 5.1. OPTICAL PERFORMANCE 139

Figure 5.7: Predicted beam pattern on the sky for the on-axis pixel. Figure courtesy of the QUaD optics team, NUI Maynooth.

5.1.3 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 140 CHAPTER 5. INSTRUMENT PERFORMANCE

Table 5.1: Beam parameters as measured from RCW38 raster maps for the three groups of detectors: The inner group of 150 GHz pixels, the outer ring of 150 GHz pixels, and the ring of 100 GHz pixels. The initial focus data is an average of four data sets taken between April and June 2005. The post refocus data results from two data sets taken during July 2005. The full width at half maximum (FWHM) is defined as the average of the FWHMs along the beam’s major and minor axes. The ellipticity is given by the ratio of the major to minor widths. A/B matching refers to the RMS deviation of these parameters between the beams of the two orthogonal detectors in a PSB pair. Coefficients from 2D-Gaussian fits to each channel for each RCW38 raster run were provided by C. Pryke and were used to generate the average resultsinthistable.

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 indicates 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 characterize the QUaD beams. Initial focusing and alignment was performed during the 5.1. OPTICAL PERFORMANCE 141 summer season (see Appendix B.3). Table 5.1 summarizes the measured beam parameters. 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 investigation into this effect has not yet been made, but it likely results from these pixels 142 CHAPTER 5. INSTRUMENT PERFORMANCE 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. 5.1. OPTICAL PERFORMANCE 143

150 RCW38 Lab

100 Tau (mS)

0 0 10 20 30 40 50 Detector

Figure 5.8: (top) Measuring time constants with RCW38. Forward and backward scans across the source are plotted versus the azimuth oﬀset. The source appears in a slightly diﬀerent position depending on the scan direction due to the delay associated with the receiver transfer function including the bolometer time constant. Figure courtesy of C. Pryke. (bottom) Time constants as measured from scanning across RCW38 compared with those measured in the lab. The lab values are smaller due to the higher loading and bias during these measurements (Section 4.2.4). RCW38 time constant values provided by C. Pryke. 144 CHAPTER 5. INSTRUMENT PERFORMANCE

Figure 5.9: QUaD skydip data from April 4, 2005. The symbols are data points and the line is a fit to the model described in the text (eq. 5.5). For this data, the median of the fits to the seven bolometers yields τTatm =10.4±0.5 K and the tipper gives Tatm as 222 K making τ =0.047. The different y-intercepts correspond to the difference 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 function 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 the relation derived in Runyan [2002] for ACBAR 2001 skydip data with their 150 GHz band.

−τ/cos θ dependence as Tatm = e where τ, known as the optical depth, depends on the frequency band of observation. The atmospheric emissivity, ,isgivenby

=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 146 CHAPTER 5. INSTRUMENT PERFORMANCE

Figure 5.11: Atmospheric opacity data from the 350 micron tipper, scaled using the linear relation in Figure 5.10. QUaD data is overplotted as crosses.

due to the decreased atmospheric transmission. This can be summarized as:

T θ T TRJ − T RJ load( )= ﬁxed + atm +(1 ) CMB (5.2) T − e−τ/cos θ T RJ e−τ/cos θT RJ = ﬁxed + 1 atm + CMB (5.3)

T RJ T RJ where atm and CMB are the Raleigh-Jeans temperatures of the atmosphere and the 1 CMB. The constant, Tﬁxed, includes all sources of loading that do not vary with

1 Tatm is a weighted, line-of-sight averaged atmospheric temperature and is not in general the same as the surface air temperature. 5.2. CALIBRATION 147

zenith angle such as emission from the ﬁlters and the telescope. Simpliﬁcation yields

T θ T T − e−τ/cos θ T RJ − T RJ . load( )= ﬁxed + atm atm CMB (5.4)

The Raleigh-Jeans (RJ) temperature of a black body of thermodynamic temperature T is deﬁned as

ν2 dν f(ν)2 kT RJ AΩ= dν f(ν) B(ν, T ) AΩ c2 where B(ν, T ) is the Planck function and f(ν) is the frequency band of the instrument. Simplification yields c2 dν f(ν)B(ν, T )ν−2 T RJ = 2k 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 temperature, 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 temperature 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 1soeq.5.1maybeapproximated2 as ≈ τ/cos θ.Makingthese approximations in eq. 5.2, the loading becomes

τT T (θ) ≈ T + atm . (5.5) load ﬁxed cos θ

2 At the South Pole, τ150 is always less than ∼ 0.1 and QUaD is restricted to zenith angles less than 45◦. 148 CHAPTER 5. INSTRUMENT PERFORMANCE

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 simplicity, 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, emission 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.

3 The key to measuring τ and Tatm with a skydip is to operate at a shorter wavelength or go to extremely low elevations such that τTatm/ cos θ ∼ 1 and ﬁtting with eq. 5.4. 5.2. CALIBRATION 149

5.2.2 Routine Gain Calibration

Bolometric receivers need to be frequently recalibrated since small changes in baseplate 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. 150 CHAPTER 5. INSTRUMENT PERFORMANCE

Rotating grid Flip mirror Blackbody source

Secondary IR data link

Cryostat snout (NOT TO SCALE)

Figure 5.12: The QUaD calibration source. (top) Photograph showing the major components. (bottom) Cartoon placing the calibration source in context. Note, in order to see the cal source clearly, the primary mirror is shown much smaller and closer to the secondary than it really is. See Figure 2.1 for an accurate drawing of the optics. 5.2. CALIBRATION 151

Figure 5.13: (top left) The reduced cal source ﬂip mirror. (top right) A single run of the cal source as recorded by the central pixel. (bottom left) Data (black) and sine wave ﬁt (red) measured in low gain mode.(bottom right) Another run, this time recorded in high-gain mode. 152 CHAPTER 5. INSTRUMENT PERFORMANCE

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 the University of Cardiﬀ. The controlling electronics were rebuilt at the Pole when the original system was destroyed by static electricity. 5.2. CALIBRATION 153

El Nod - 150-03 A/B Correlation 2.0 1.0 150-03A (Volts) 150-03B (Volts) 0.8 1.5 Elevation offset (deg)

0.6

1.0 Signal 0.4 Signal A (Volts)

0.5 0.2 Gain A/B = 0.74

0.0 0.0 0 10 20 30 40 50 60 0.0 0.2 0.4 0.6 0.8 1.0 sec Signal B (Volts)

Figure 5.14: (left) The signals from an elevation nod for a single feed. (right)The signals are highly correlated. The slope of the best-ﬁt line gives the ratio of the gains from the two detectors.

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. 154 CHAPTER 5. INSTRUMENT PERFORMANCE

QUAD Relative Calibration 1.6

150-04 row cal 1.4 150-03 el nod 150-02 cal src

1.2

1.0 A/B gain ratio 0.8

0.6

16 MAY 2005 17:45:40 Row cals: 4 El Nods: 132 Cal srcs: 132

0.4 0 5 10 15 20 Hours

Figure 5.15: The A/B gain ratio for three feeds measured using the three diﬀerent techniques discussed in this section: RCW38 row calibrations, elevation nods, the calibration source.

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. 5.2. CALIBRATION 155

dB/dT at T = TCMB 1.0

0.8

0.6

0.4

0.2 dB/dT 100 GHz band 150 GHz band 0.0 0 100 200 300 400 Freq (GHz)

Figure 5.16: The factor dB/dT evaluated at T = TCMB enters into the calibration via eq. 5.9. It is approximately twice as large for the 150 GHz channels as it is for the 100 GHz channels. This combined with larger bandwidth and higher optical eﬃciency makes the 150 GHz channels more responsive to CMB temperature ﬂuctuations in terms of V/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 responsivity 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. 156 CHAPTER 5. INSTRUMENT PERFORMANCE

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 situation 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, calibration 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

⎛ ⎞ −1 dPB T t ⎝S G ⎠ V t ≡ s × V t ( )= DC dT ( ) K/V ( ) (5.7) TCMB 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:

1 PB(T )= T ηT AΩ fn(ν) B(T,ν) dν (5.8) 2 atm 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 5.2. CALIBRATION 157

the integral as dPB 1 dB ≈ T ηλ2 ∆ν . (5.9) dT 2 atm 0 dT T =TCMB,ν=ν0 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

µK 0.94 0.82 · 0.26 26.5GHz 3.6 × 108 V/W 100 GHz: 5.1 · 105 × , volt Tatm ηT ηR ∆ν SDC

µK 0.94 0.82 · 0.32 40.5GHz 3.1 × 108 V/W 150 GHz: 4.3 · 105 × . volt Tatm ηT ηR ∆ν 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 J 150 150 GHz band [Runyan, 2002]. Averaging their 2000 and 2001 values, RCW38 = 145 Jy with a 10% uncertainty. The uncertainty is dominated by systematics including 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 158 CHAPTER 5. INSTRUMENT PERFORMANCE well. The integrated flux in an 8’ radius was computed for QUaD raw RCW38 maps 2 V yielding a value in Volts arcmin ( RCW38) for each channel. This allows a conversion into units of temperature fluctuations about the mean CMB temperature as:

⎛ ⎞− − 1 J × 10 26 dB sr s = RCW38 ⎝ ⎠ (5.11) K/V V dT 2 RCW38 TCMB,ν0 arcmin 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:

µK 14.3 Volts arcmin2 0.94 . × 5 × 100 GHz: 6 0 10 V T (5.12) volt RCW38 atm

µ . 2 . . × 5 K × 9 4 Volts arcmin 0 94 . 150 GHz: 4 6 10 V T (5.13) volt RCW38 atm

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:

µK 100 GHz: 5.0 × 105 (5.14) volt

µK 150 GHz: 4.3 × 105 (5.15) volt 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 secondary 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 optical 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. 160 CHAPTER 5. INSTRUMENT PERFORMANCE

Table 5.2: QUaD estimated loading component by component breakdown. For the receiver section of the table, the optical component drawing in Figure 2.4 may be useful.

Component Physical Loading Incident Total Power at Component Trans. temp. temp. power trans. detector (K) (K) (pW) (pW) Atmosphere 0.943 220.00 12.44 7.31 0.290 2.12

Telescop e Foam cone 0.975 220.00 5.50 3.23 0.297 0.96 Primary Mirror 0.990 220.00 2.20 1.29 0.300 0.39 Secondary loss 0.150 32.44 4.87 2.86 0.353 1.01 Telescope total 2.36

Receiver Window 0.995 220.00 1.10 0.65 0.355 0.23 Reﬂection loss 0.010 160.00 0.08 0.05 0.359 0.02 IR 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 0.17 12 cm edge 0.995 160.00 0.80 0.47 0.364 0.17 IR 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 0.02 8cm edge 0.995 20.00 0.10 0.06 0.370 0.02 Lens 1 0.990 10.00 0.07 0.04 0.377 0.02 Reﬂection loss 0.010 10.00 0.07 0.04 0.377 0.02 Lens 2 0.990 10.00 0.07 0.04 0.385 0.02 Reﬂection loss 0.010 10.00 0.07 0.04 0.385 0.02 Waveplate 1.000 7.00 0.00 0.00 0.385 0.00 Spillover 0.030 7.00 0.12 0.07 0.385 0.03

7cm edge 0.995 0.50 0.00 0.00 0.387 0.00 Bolo. assembly 0.387 0.25 0.15 0.09 1.000 0.09 Receiver 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 5.3. SENSITIVITY AND NOISE 161

QUAD Loading Comparison 10

Total (load curves) Atmosphere (sky dips) 40 Other (difference) 8 Receiver only

30 6 (K) RJ 20 T

Loading (pW) 4

2 10

0 0 17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21

Apr May Jun

Figure 5.17: Receiver loading (red) determined by subtracting the total loading (black, measured with QUaD load curves) from the atmospheric loading (blue, measured by QUaD sky dips). The flatness of the red curve confirms that variable loading from snow or ice accumulation is not a large factor. The same procedure was applied to data from Dec 19, 2004, which was taken without the foam cone, the primary, and the secondary (green line). The measured difference (∼ 10 K) is attributed to loading from the telescope optics.

diﬀerences, used to determine atmospheric loading from skydips, are robust to this oﬀset. 162 CHAPTER 5. INSTRUMENT PERFORMANCE

QUAD Loading 10 45 9 40 8

35 (K) RJ

7 T

Loading (pW) 30 6 25 5 17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21

5 0.08 4 0.07

3 0.06 0.05 Tau 150 GHz

Tau 350 micron 2 0.04

1 0.03 17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21

Elevation (deg) 20

0 17 21 25 29 02 06 10 14 18 22 26 30 04 08 12 16 20 24 28 01 05 09 13 17 21 Apr May Jun

Figure 5.18: (top) The measured loading from approximately 300 load curves, obtained from eq. 4.12 averaged for the seven detectors in Table 4.1. The dashed blue line shows the loading that would be predicted from the model in eq. 5.5 using the τ and elevation information shown below. The atmospheric temperature data (not shown) is also from the 350 micron tipper and it varies between approximately 200 and 250 K. (middle) Atmospheric opacity data from the AST/RO 350 micron tipper scaled to 150 GHz using eq. 5.6. (bottom) The telescope elevation during the load curve measurements. When CMB observations began in May, we started taking load curves at the elevation of our observing ﬁeld rather than returning to zenith. For the astute observer, the 350 micron tipper was not functioning for a few days around April 12. 5.3. SENSITIVITY AND NOISE 163

Figure 5.19: Components of the noise equivalent power (NEP) versus bias current for 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, 164 CHAPTER 5. INSTRUMENT PERFORMANCE 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

4kBTR NEP 2 ∼ Johnson 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

z + R 2 S 2 2 k TP . NEPJohnson =4 B (5.16) z − R SDC

Phonon Noise Heat ﬂowing out of the absorber through the thermal link is quantized in the form of phonons giving rise to another source of noise. An approximate form is given by 2 ∼ k T 2G. NEPphonon 4 B

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 5.3. SENSITIVITY AND NOISE 165 is given as an integral in Mather [1984]

T 2 2 T tG(t) / TG(T ) dt 2 k G T T 2 base NEPphonon =4 B ( ) T (5.17) T G(t)/G(T ) dt base

β where T = Tbolo. For our power law model, G(T )=G0(T/T0) with the reference temperate taken to be the baseplate temperature (T0 = Tbase), the integrals can be explicitly evaluated as (β +1) (T/T )2β+3 − 1 2 2 0 NEP =4KBT G0 . (5.18) phonon 0 β+1 (2β +3) (T/T0) − 1

Ampliﬁer Noise The readout electronics contribute to the total NEP as

V 2(ω) NEP 2 = n (5.19) amp S(ω)2 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 approximately white over the frequency range of interest (0.1 - 2.5 Hz) with a value of ∼ −1/2 9nVHz . 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 2 Qhν. NEPPoisson =2

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 166 CHAPTER 5. INSTRUMENT PERFORMANCE term. The NEP associated with the bunching is given by

Q2 NEP 2 = Bose ∆ν where ∆ν is the optical bandwidth of the receiver. The quadrature sum gives the total photon noise 2 2 2 . NEPphoton =NEPPoisson +NEPBose

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:

2 2 2 2 2 . NEPtotal =NEPJohnson +NEPphonon +NEPamp +NEPphoton (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 contribution. 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 5.3. SENSITIVITY AND NOISE 167

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)versusthe 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 WHz−1/2 and it occurs 168 CHAPTER 5. INSTRUMENT PERFORMANCE at a bias value of ∼ 0.75 nA. In practice, however, a larger bias current is used. A variety of factors argue in favor of biasing above the NEP minimum. The NEP rises quickly below the minimum point owing to the rapidly decreasing detector responsivity. 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,andβ. 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 sensitivity 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 advantages more than outweigh the ∼ 5% decrease in raw sensitivity. 5.3. SENSITIVITY AND NOISE 169

Figure 5.21: Responsivity for all channels under typical observing conditions. The range of bias currents is indicated by the vertical red band (variations in detector resistance lead to a range of bias currents for a ﬁxed bias voltage).

Figure 5.22: (left) Average responsivity versus bias at several zenith angles and thus at diﬀerent values of loading. (right) The change in responsivity with loading versus bias current. Higher bias currents lead to responsivities that are more stable to loading changes. 170 CHAPTER 5. INSTRUMENT PERFORMANCE

Figure 5.23: Typical 150 GHz time-ordered data for two bolometers in a PSB pair (black and red traces) while observing a source-free region of sky. The green signal is one half times the diﬀerence of the black and red. The individual channels clearly show the eﬀect of atmospheric noise. The mean has been removed from each signal before plotting.

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 5.3. SENSITIVITY AND NOISE 171 to measure Q or U, results in a much more stable signal (green). For each detector, division of the raw voltage, V (t), by the product of the electronics gain (G) and the bolometer responsivity (SDC) converts to optical power absorbed by the detector P (t)

V (t) P (t)= . (5.21) GSDC

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,givesthetotal optical power detected by the feed.Thisis 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

2 2 2 2. NEPsum =NEPdiﬀ =NEPa +NEPb (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 the middle portion of each half-scan excludes the turn around period when the telescope is accelerating. 172 CHAPTER 5. INSTRUMENT PERFORMANCE

Figure 5.24: NEP for PSB 150-12 for roughly 3 hours worth of data from May 31, 2005. The telescope was scanning at 0.17 deg/sec on the sky. The (arbitrarily normalized) E-mode CMB power spectrum is overlaid assuming this scanning speed. The top x axis is in units of CMB multipole moment (). The PSB difference power spectrum is white above ∼ 100 through the cut off at ∼ 2500 corresponding to the 150 GHz beam size of 4’. The spikes seen in the data around 10 Hz are mostly microphonic resonances. The dashed black line shows the degradation in NEP that would result from including the reduction in high-frequency gain from the bolometer’s time√ constant. This curve assumes a value of 15 ms. Note that NEPsum and NEPdiff are 2 greater than the NEP of a single channel. 5.3. SENSITIVITY AND NOISE 173

NEP 100 GHz NEP 150 GHz 8 8

6 6

4 4

2 2

0 0 3 4 5 6 7 3 4 5 6 7 NEP (10-17 W Hz-1/2) NEP (10-17 W Hz-1/2)

Figure 5.25: Distribution of NEPs for both frequency bands (solid) and median value (dashed).

9.2 × 10−17 WHz−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

NEP√ diﬀ −17 −1/2 NEPa ∼ NEPb ∼ =6.4 × 10 WHz . (5.24) 2

Performing this exercise for all detectors results in a median NEP of ∼ 4.4 and 5.6 × 10−17 WHz−1/2 at 100 and 150 GHz respectively. Figure 5.25 shows the distribution 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). 174 CHAPTER 5. INSTRUMENT PERFORMANCE

NET 100 GHz NET 150 GHz 10 10

8 8

6 6

4 4

2 2

0 0 200 300 400 500 600 200 300 400 500 600 µ 1/2 µ 1/2 NETpair ( K sec ) NETpair ( K sec )

Figure 5.26: Distribution of NETpair for both frequency bands (solid) and average value (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 radiation. CMB observers use the Noise Equivalent Temperature (NET) for sensitivity to temperature anisotropies and the NEQ for polarization anisotropies, both in units of µKsec1/2. These metrics take into account parameters such as throughput, efficiency, 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 √ µKsec1/2,notµKHz−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 5.3. SENSITIVITY AND NOISE 175

8 the two detectors as Tp =(Ta + Tb)/2, which for uncorrelated noise and identical detectors, leads to NET√ a NET√ b NETpair = = . (5.25) 2 2 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 µKsec1/2 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

√ NEPsingle NETsingle = (5.26) dPB/dT | 2( ) TCMB √ 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 −1 factors listed in Section 5.2.3 as dPB/dT =(sK/V · SDC) . Assuming identical detectors, the NET of a pair can be found as

NET√single NETpair = . (5.27) 2

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 presented 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. 176 CHAPTER 5. INSTRUMENT PERFORMANCE a design phase, with the NEP estimated by adding the expected noise sources (eq. 5.20). The final metric, the NEQ, is applicable only to polarimeters. It gives the sensitivity of a PSB pair to the Stokes parameters Q or U.SinceapairofPSBsis 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 − ) 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 emission. 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 overlap 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]). The small and large nested black regions are the B2K deep and wide ﬁelds respectively. Figure courtesy of Ken Ganga.

B2K have all made high sensitivity maps of ﬁelds in the Southern Hemisphere, the later two in both temperature and polarization.

• Point sources - As a check on the pointing and beams, it is desirable to have at least one bright radio source in the ﬁeld. WMAP has cataloged the brightest point sources over the entire sky at our observing frequencies.

The field we chose (white boundary in Figure 6.1) satisfies these requirements. It is in an extremely low foreground region, partially overlaps with the B2K deep field, and contains three bright radio point sources. The field has an area of approximately 50 square degrees which is smaller than optimal size for an E-mode survey [Bowden 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 removed 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. 180 CHAPTER 6. FIRST OBSERVATIONS

The following list describes the daily observing program in detail. A short summary 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 observation, 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 slightly different coverage pattern at the two rotation angles (due to the asymmetric focal plane resulting from non-functioning feeds). These hit maps result from 37 day’s data taken between May 17 and July 8, 2005. Trail field hit maps are identical to those shown above.

75% overlap allows for days to be missed due to bad weather or telescope problems without creating dead areas in the map. For the ﬁrst season, the same two deck rotation angles (-3◦ and 57◦) have been used for all observations. Observations at additional angles will likely be made next season. The following summarizes the key points of the observing strategy, highlighting the notation necessary to understand the maps presented in the next section:

• The observing region is divided into two adjacent, equal-area ﬁelds, labelled lead and trail. Each is approximately 5◦ wide on the sky. 182 CHAPTER 6. FIRST OBSERVATIONS

• 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 atmospheric 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 polynomial removal suppresses the large-scale contamination resulting from these effects while preserving small-scale structure from the CMB. Eight field temperature maps can then be formed by combining the data from the individual feeds using the measured feed offsets (Section 5.1.2). The eight maps (Figure 6.4) correspond to the two fields at the two frequencies and the two deck rotation angles. The integration time per pixel for these maps is given by the hit maps in the previous section.

1Thanks to B. Rusholme for providing the daily individual-PSB maps used in the analysis in this chapter. 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 each row. The data on the right is high-pass filtered by removing a third-order polynomial from each row. The field difference map (lead - trail) resulting from each data set is shown in the bottom row. Field differencing only removes structure due to ground contamination whereas polynomial filtering effectively removes contamination due to both ground and atmosphere. After polynomial filtering (right), field differencing (bottom right) offers no further improvement. The color scale is in units of µK. 184 CHAPTER 6. FIRST OBSERVATIONS

Figure 6.4: QUaD CMB temperature maps made from the first pass over the field (37 day’s worth of data). The eight maps correspond to the two fields (lead / trail) at the two frequencies (100 / 150 GHz) and the two deck rotation angles (57◦ and -3◦). The integration time per pixel is given by the hit maps in Figure 6.2. The x and y axes are RA and DEC offsets in units of real degrees on the sky. Two quasars are visible in the lead field and one, in the trail field. Each map has been filtered with row-wise removal of a third-order polynomial. The horizontal stripes on either side of the quasars (most visible in the trail field) are an artifact of not masking out the source when performing the polynomial fit. 6.2. FIRST MAPS 185

Figure 6.5: QUaD CMB temperature maps compared with B2K and WMAP for the entire observing region (lead plus trail ﬁelds). The QUaD maps (top) are in Volts whereas the B2K and WMAP maps are in µK. Cross correlating these maps is used to derive a calibration in µK/V for QUaD. This factor has been used to calibrate all the other QUaD maps presented in this chapter. Unlike previous maps in this chapter, these have been smoothed with a beam-sized Gaussian point spread function (PSF). Figure courtesy of J. Kovac. 186 CHAPTER 6. FIRST OBSERVATIONS

Several general conclusions can be made regarding these maps. The agreement between the maps indicates that they are signal dominated. Despite the fewer number 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 bottom 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 considering 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 )forthe map is computed as 2 2 2 ∆T = Mij − Mij (6.1) 6.2. FIRST MAPS 187

Table 6.1: RMS noise in µK for deck angle diﬀerence maps (Example maps for the lead ﬁeld are shown in Figure 6.6). The measured noise level is compared with the expected noise based on the receiver sensitivity and the integration time. The noise level in the “beam-sized pixel” column is determined after convolving the maps with a6.3 (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 6.5 150 75 35 25 7 trail 100 57 50 11 6.5 150 76 35 24 7

where Mij denotes the pixelized map. The symbol <> denotes a hit map weighted average as i,j HijMij Mij = (6.2) i,j Hij 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 signal (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 ∼ 6and∼ 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. 188 CHAPTER 6. FIRST OBSERVATIONS

The noise level of the deck angle difference maps (Figure 6.6, right) can be compared 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 excess noise due to atmospheric contamination. The results for the beam-sized pixels confirms the presence of residual correlated structure (atmosphere and ground), especially at 150 GHz, that keeps the noise from integrating down as expected. This contamination limits QUaDs ability to measure the CMB temperature power spectrum 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 atmospheric loading. Various calibration data including the cal source observations andelevationnodscanbeusedtocorrectforthis.

• 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 rotations 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 rotation angles, dk1 = 57◦ and dk2 = −3◦. In the absence of noise, these two maps should be identical. This figure shows the maps formed by summing and differencing these two data sets. Each map above includes all channels for the given frequency. At 100 GHz, the difference map is dominated by receiver noise. At 150 GHz, residual atmospheric contamination remains in the difference map. The signal-to-noise ratio estimated from these maps is ∼ 6and∼ 3.0 at 100 and 150 GHz respectively. Note the maps shown in this figure are all for the QUaD lead field. 190 CHAPTER 6. FIRST OBSERVATIONS

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 available feeds (9 at 100 GHz and 15 at 150 GHz) is given. The standard deviation, in parenthesis, indicates the channel-to-channel scatter. Before computing the noise, a diﬀerent order polynomial ﬁlter is applied to the map. The rightmost column gives the expected noise (also in µK) based on the receiver sensitivity. Note that despite their higher sensitivity, the expected noise per beam on the 150 GHz channels is larger due to their smaller beam size.

Frequency Polynomial Filter Order Expected (GHz) 1st 2nd 3rd 4th 5th 100 30 (3) 29 (3) 28 (3) 27 (3) 27 (3) 26 150 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, detectors 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, increasing 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 lead field. A and B denote the maps formed from the two halves of a PSB pair. The sum map (left) gives the total intensity (Stokes I)asmeasuredateachmappixel.The difference map (right) gives Stokes Q as defined by each PSBs coordinate system. Note, the sum and difference maps are actually formed as (A+B)/2 and (A-B)/2 respectively in order to retain the calibration of the individual maps. These maps are for a single field (lead), a single deck rotation angle (dk=57◦), and a single feed at each frequency. 192 CHAPTER 6. FIRST OBSERVATIONS

Table 6.3: RMS noise in µK for combined polarization maps (Figure 6.8). In contrast to the temperature data, QUaD is meeting the expected noise levels in polarization for both frequencies and pixelizations. The target noise levels are ∼ 2 higher than for the temperature maps because these results are for a single deck angle (rather than the average of both) and because each feed only measures either Q or U.

1.2 pixels Beam-sized pixels Band Deck Stokes Measured Expected Measured Expected 100 57 Q 84 87 11 11 U 129 123 17 16 -3 Q 83 87 11 11 U 125 123 17 16 150 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 operation 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, (atmospheric 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. 194 CHAPTER 6. FIRST OBSERVATIONS

Figure 6.8: Combined Stokes Q maps for both frequency bands and both ﬁelds at deck = 57◦. Unlike the CMB temperature maps, these polarization maps are largely free from residual contamination. 6.2. FIRST MAPS 195

Figure 6.9: Simulated combined Stokes Q maps for both frequency bands and both ﬁelds. These maps were generated using the same analysis pipeline that produced Figure 6.8 except a Gaussian random number generator provide the input. 196 CHAPTER 6. FIRST OBSERVATIONS 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 (proportional 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.htm 2Stanford Research Systems, Inc. www.thinkSRS.com

197 198 APPENDIX A. FOCAL PLANE TEMPERATURE CONTROL

heater current PID bias+ QUaD Bias Receiver Gen. bias- + error -

demodulator reference

bias- bias+

R0 R

+ error -

RL RL Warm lockin amplifier

Figure A.1: (top) The focal plane temperature control system. (bottom)Detailof the thermistor readout bridge. The dashed line indicates the receiver. focal plane bowl. Because the system cannot cool the focal plane, the set point is required to be several mK above the natural fridge operating temperature. This allows 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 temperature stability of the focal plane with and without temperature control enabled. 199

Focal Plane Temperature Control 0.254

0.252

0.250 FP Temperature (K) Enabled Disabled

0.248 0 5 10 15 Hours

Figure A.2: Temperature control stabilizes the temperature of the focal plane. The data plotted here is the DC level of one of the dark bolometers (PSB 150-01C). The calibration from Volts to Kelvin was obtained by correlating the bolometer signal with the focal plane GRT. The “disabled” data was taken on April 8, 2005 and the “enabled” data, on April 10, 2005. In both cases, the telescope was raster-mapping a source while this data was taken. The steps seen in the data are digitization noise. 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 addition 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 outside 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 the upper right corner. The two workers visible inside the ground shield guided the cone onto the telescope primary mirror (not visible), which was pointed towards the zenith. 204 APPENDIX B. COMMISSIONING QUAD 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 motorized 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 206 APPENDIX B. COMMISSIONING QUAD 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 immediately after unpacking, before the first cool down. At this point, the cryostat and fridge still had their protective shipping hardware installed, and were least susceptible 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 the warm readout electronics. (bottom) The final configuration of the readout electronics. The real time control computer is mounted on the left. The 19” rack on the right holds (top to bottom) two power supplies, the focal plane temperature control unit, and the cryogenic temperature readout. The aluminum boxes hanging from the cryostat (just beyond the top of the image) house the bias generator and amplifiers. 208 APPENDIX B. COMMISSIONING QUAD with cargo straps while the table was lowered and a spacer inserted. We raised the table again, lifting the cryostat until the six 0.5” diameter mounting bolts passed through the mating flange on the cryostat. At this point, we engaged the nuts and raised the cryostat the rest of the way by tightening them. During this lifting, we had to ensure that the stingers for the cryogen lines were properly aligned with the cryostat refill tubes and not binding. 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 troubleshooting. 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. Bibliography

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