A Measurement of the Angular Power Spectrum of the Cosmic Microwave Background with a Long Duration Balloon borne Receiver

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Cosmic Microwave Background with a Long Duration

Balloon-borne Receiver

Thesisby

Brendan P. Crill

In Partial Fulllmentof theRequirements

fortheDegreeof

Doctor ofPhilosophy

CaliforniaInstituteofTechnology

Pasadena,California

2001

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c

2001

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Abstract

This thesis describes Boomerang; a balloon-borne telescope and receiver designed to

map the Cosmic Microwave Background (CMB) at a resolution of 10 0

from the Long

Duration Balloon (LDB) platform. The millimeter-wave receiver employs new technology

in bolometers, readout electronics, cold re-imaging optics, millimeter-wave lters, and

cryogenics to obtain high sensitivity to CMB anisotropy. Sixteen detectors observe in 4

spectral bands centered at 90, 150, 240 and 400 GHz. The wide frequency coverage, the

longightduration,theopticaldesignandtheobservingstrategyallprovidestrongrejection

of systematiceects. We reportthein-ightperformanceof theinstrumentduringashort

test ight from Palestine, Texas, that mapped 230 square degrees and during a 10.5 day

stratospheric balloon ight launched from McMurdo Station, Antarctica, that mapped

2000 square degreesof the sky. The Antarctic datayielded a measurement of theangular

powerspectrumof theCMB between 50<`< 600 which shows apeakat `

peak

=1976

(1 error). A maximum likelihood estimation of cosmological parameters within the cold

darkmatter(CDM)paradigmofstructureformationindicatesthattheuniverseisatwith

a precisionof 6%and thatthedensityofbaryonsin theuniversemaybeslightlyhigher

than previously thought. The combination of observations of large scale structure (LSS)

and the Boomerang power spectrum impliesthepresence of bothdark matter and dark

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Acknowledgments

...let me ask you how the scholar who cultivates science to pass his life

agreeably diers from the drunkard who also seeks in life no more than

immediate enjoyment and nds it in wine? It is true that the scholar makes

a better choice of the source of his pleasures, since they are more intense and

more durable,butthat isall. Both ofthem,the drunkardand thescholarhave

thesame egotisticalaim, personal enjoyment.

... ifyouarereallythinkingofhelpinghumanity,ifthatiswhatyouaspireto

inyourstudies,youwillndyourselffacingaformidableobjection,for,insofar

asyou have anysenseof justice,you will immediatelyobserve that in

present-daysociety,scienceis onlya kindof luxurythatmakeslifemoreagreeable to a

few,and remainsabsolutelyinaccessibleto almost thewholeof humanity.

Peter Kropotkin,To the Young(1885)

Boomerang is an enormous project which has required huge amounts of labor from

quite a few people since it began in 1993. The author lists on each of the Boomerang

publications, no matter how long, can never properly credit all of the people who have

contributed to this project over the years. My thanks goes out to all of these people,

withoutwhomthisthesis wouldnot exist.

As of June 2000, here is the list in alphabetical order of everyone who has worked

on Boomerang: Peter Ade, Kashif Alvi, Joa Applegate, Elisabetta Aquilini, Ricardo

Artusa,AndyBeard,JeBeeman,RavinderBhatia,JamieBock,DickBond,JulianBorrill,

Andrea Boscaleri, KurtCampbell, John Cartwright, Sarah Church,Kim Coble, Matthieu

Contensou, Paolo deBernardis, Giancarlo de Gasperis, Marco dePetris, Grazia deTroia,

HectorDelCastillo,Mark Devlin,PhilFarese,Ken Ganga,Massimo Gervasi, Massimiliano

Giacometti,VicHaynes,CaraHenson,EricHivon,DaveHorseley,ViktorHristov,Armando

Iacoangli, Andrew Jae, Andrew Lange, Adrian Lee, Jon Leong, Sam Li, Tao Long,

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Tom Montroy, Barth Nettereld, Dan Osgood, Chris Paine, Ricardo Paniagua, Enzo

Pascale, ByronPhilhour,Francesco Piacentini, Francesco Pongetti, SimonPrunet, Andrea

Raccanelli, Mike Radford, Paul Richards, Gianni Romeo, John Ruhl, Marcus Runyan,

FrancescoScarramuzzi,KacieShelton,GeorgeSmoot,EricTorbet,IvyTurkington,Valerio

Venturi,Nicola Vittorio, BetsyVillalpando, JohnnyWu, andLunming Yuen.

ThankstoStephenPeterzen,DannyBall,thelaunchcrewatNSBFandtheNSFsupport

team at McMurdoStation.

Additional thanks to Ravinder Bhatia, Samantha Edgington, Bill Jones, Eric Hivon,

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Contents

Abstract iii

Acknowledgments iv

1 Introduction 1

1.1 Overviewof Boomerang . . . 4

2 Theory 6 2.1 Map Making . . . 6

2.2 AngularPowerSpectrum . . . 8

2.3 CosmologicalParameters . . . 10

3 Instrument Design 12 3.1 Telescope and Gondola. . . 12

3.2 Thermal Design. . . 13

3.3 Cryogenics. . . 14

3.4 Optics . . . 15

3.5 Bandpass Selection . . . 17

3.6 SingleMode Feed . . . 17

3.7 Multi-colorPhotometer . . . 20

3.8 Calibration Lamp. . . 21

3.9 Detectors . . . 21

3.10 Integrating Cavity . . . 24

3.11 Readout Electronics . . . 24

3.12 Rejection ofRFand MicrophonicPickup . . . 25

4 Instrument Characterization 27 4.1 OpticsTestbed . . . 27

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4.4 OpticsBox . . . 29

4.5 Feed Testbed . . . 30

4.6 OpticalEÆciency ofFeed Structures . . . 31

4.7 Characterization ofNeutral DensityFilters . . . 32

4.8 IntegratedFocal Plane . . . 35

4.9 SpectralBandpass . . . 35

4.10 BlueLeaks . . . 36

4.11 LoadCurves. . . 37

4.12 Time Constant . . . 38

4.13 NoisePerformance . . . 41

4.14 BeamMaps . . . 44

4.15 LabCalibration . . . 45

5 1997 Test Flight 48 5.1 TestReceiver . . . 48

5.2 Observations . . . 48

5.3 PowerSpectrumEstimation . . . 49

5.4 Systematics Tests . . . 50

5.5 Measuring Curvature . . . 51

5.6 Discussion . . . 51

6 1998 Flight Performance 53 6.1 Electronics . . . 54

6.2 In-ight Calibrationof theSunSensor . . . 55

6.3 Attitude Reconstruction . . . 55

6.4 Thermal Performance . . . 57

6.5 Cryogenics. . . 58

6.6 BeamMap . . . 59

6.7 Deglitching . . . 64

6.8 TransferFunction. . . 65

6.9 Detector Noise . . . 67

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7 Calibration 73

7.1 LabScaledto Flight . . . 73

7.2 Dipole . . . 74

7.3 Relative Calibration . . . 78

7.4 Sources . . . 79

7.5 Calibration Stability . . . 84

7.6 Sensitivity . . . 85

7.7 Discussion . . . 86

8 Power Spectrum and Cosmological Parameters 88 8.1 Maps. . . 88

8.2 PowerSpectrum . . . 91

8.3 CosmologicalParameterEstimation . . . 96

8.3.1 Choice of Parameters . . . 97

8.3.2 Results . . . 99

9 Other Science with Boomerang 103 9.1 Galactic Dust . . . 103

9.2 Sunyaev-Zel'dovichEect in Clusters. . . 103

9.3 SerendipitousCluster Searches . . . 104

9.4 High-redshiftGalaxies . . . 105

10Discussion 106 A Bolometer Data Summary 111 A.1 Time Constant . . . 111

A.2 Bolometer Impedence . . . 112

A.3 In-ight loadcurve . . . 113

A.4 LabLoadCurves . . . 114

A.5 Flight Noise . . . 115

A.6 Flight OpticalBackground. . . 116

A.7 In-Flight Responsivity . . . 117

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B Calculation of Beam Oset Parameters 119

B.1 Rotation oftheGondola Boresight . . . 119

B.2 Calculationof BeamPosition . . . 120

B.3 Calculationof BeamOset Parameters. . . 121

C Roll Correction to Azimuth and Elevation 123

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Chapter 1 Introduction

The2.7KCosmicMicrowaveBackground(CMB),discoveredin1964[55 ],isoneofthemost

powerfulobservational pillars supportingthe current picture of cosmology. The spectrum

of the CMB (measuredbyCOBE/FIRAS to bethe best t to a blackbodyspectrum ever

observedinnature[41 ])stronglyindicatesthattheuniverseevolvedfromahot,densestate.

The radiation originates from thetime when the matter in theuniverse transitioned from

an opaque plasma to transparent gas(the timeof recombination), at a redshiftof 1000,

about300,000 years afterthe BigBang.

Mapping the background radiation provides a snapshot of the universe in its infancy.

Thetiny(a partin10 5

ofthebackground)uctuationsseeninthetemperaturecorrespond

to uctuations in matter density at the time of recombination. A measurement of the

angular power spectrum of the uctuations of the CMB can test inationary models of

structure formation. Furthermore, within the context of the class of cold dark matter

models, constraintscan beplacedon cosmological parameters.

Thestandardinationary,colddarkmatterclassofmodelspredictsstructureformation

asfollows. Theseedsofstructureareprovidedbyrandomquantumuctuationsstretchedto

cosmologicalsizeduringtheperiodofrapidinationaryexpansion. Theamplitudeofthese

\primordial"uctuationsisgenerallyexpectedtobenearlyscaleinvariant. Duetothesmall

amplitude ofthe uctuations, they evolve linearlyinthe plasma. Gravitational collapseis

resisted by photon pressure and the perturbations oscillate acoustically. Recombination

occursrelativelyrapidly,sothephaseoftheoscillationsisfrozenintotheCMBatthetime

of lastscattering.

Because of the oscillation, the amplitude of uctuations at particular scales will be

enhancedrelativetotheprimordialscale-invariantamplitude. Thiseectappearsasaseries

of \acoustic peaks" inthe angular power spectrum. The rst peak in order of decreasing

angular scale corresponds to the sound horizon at the surface of last scattering; in other

words,the distancethat soundcould travel betweentheBig Bang andlastscattering.

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geometryoftheuniverse. Forexample,aatuniverseisexpectedtohave anacousticpeak

at a multipoleof `=200,or1 Æ

scales.

There aredegeneracies inthisrelation;twodierent sets of parameterscan give nearly

identical angular power spectra. For example, a large fractional density of baryons in

the early universe can decrease thesound speed of the plasma,making thesound horizon

smaller. This eect mimics a change in curvature. By further constraining the shape of

theangularpowerspectrum,these degeneraciescan belargelyovercome. Forexample,the

ratioof power intherst and second peaks constrainsthe baryon density of theuniverse.

Another means of overcoming degeneracies is by including data from other branches of

cosmology which constrain parameters inorthogonal ways; for example, measurements of

lightelementabundances,mapsoflargescalestructure,measurementsofHubble'sconstant,

and Supernovae (SN1A) measurementsofthe expansionofthe universeto high redshift.

Because of the tiny amplitude of the anisotropy in the CMB, it has taken decades of

technological development of receivers, telescopes, and observation strategies forprecision

mapping to be successful. The past decade has seen a rapid series of advances in

mea-surement of the angular power spectrum and thecosmology that itimplies. Temperature

anisotropy was rst discovered on large scales (>7 Æ

) by the DMR instrument aboard the

COBE satellitein 1990. Moreover, at largescales it wasfoundthat thespectrumis

scale-invariant,lending furthersupportto theidea of ination.

Subsequently, a host of ground-based and balloon-borne experiments detected

aniso-tropy at a variety of angular scales (see Figure 1.1 for a summary). Starting with the

Saskatoon experiment [50 ], the eld beganto move from the realm of making a detection

to making spectroscopic measurements of power over a range of angular scales.

Ground-based experiments have been limited by atmospheric noise, prompting moves to dry and

high altitudesites, such as the Atacama desert in Chile[48 ] and theSouth Pole [16 ] with

interferometers thathave successfullydefeated atmosphericnoise[64]. Balloon-based

mea-surements have been limited by detector technology and integration time. Flights above

North Americaare normally5-6hours long and allowonlya smallregionof the skyto be

measured.

In1999resultswerereleasedrstbytheTOCOexperiment[48 ]and thenfromthe1997

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Figure 1.1:

Measurementsof theangularpowerspectrum oftheCosmicMicrowave Backgroundinthe

vicinityoftherstpeakpublishedbetween1995andNovember1999. Thesolidcurveshows

thebestt modelfrom thetest ight of Boomerang (see Chapter5 of thisthesis).

1999,whichexploitedadvancesinreceiveranddetectortechnologyandthelongintegration

time available from the Long Duration Balloon (LDB) platform to make a highly precise

measurement of the angular scale of the rst acoustic peak [4 ]. A parabolic t to the

data nds that the peak is located at a multipole of ` = 203 6 (1 error). Standard

cosmological analysisimpliesthat thedensityparameter =1.01 0.06. The universe is

atto 6%.

Combined withother cosmologicaldata, an even more interestingpicture emerges. For

the total density of the universe to be so close to the critical density, a huge fraction of

it must be made up of dark matter. Furthermore, results from SN1A measurements of

theexpansionof the universeindicatethat Einstein'scosmological constant isnon-zero,

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cosmological measurementindetail.

1.1 Overview of Boomerang

Boomerang incorporatesfour unique designfeatures which allow a precise measurement

of theangularpowerspectrumof theCMB.

First, Boomerang is a quasitotal-powerradiometer. The temperature of one part of

theskyismeasuredrelativeto itssurroundingsbyslowlyscanning(scanperiod 1minute)

theentiretelescopeinazimuth. TheoutputfromeachdetectorisACcoupledtoanamplier

at low frequency(f = 0.016 Hz). The stable, virtually transparent atmosphere at balloon

oat altitude and the intrinsic stability of the bolometric detectors and readout amplier

chainmake itpossibleto maplargeareas of theskywithhigh sensitivity.

Second,Boomerang isdesignedtotakeadvantageofthelongintegrationtimepossible

from a balloon borne platform own over the Antarctic. During the austral summer, the

polar vortex winds provide a stable orbit for balloons at the top of the stratosphere at

an altitude of roughly 38 km. This observation platform launched 1200 km from thepole

providesight durationsof 7to 20 days,thusallowingmeasurementsto berepeatedmany

times in order to check for systematic eects. The relatively small fraction (<10%) of

the sky that is accessible from a balloon platform duringthe austral summerfortuitously

includesthepart ofthesky thatislowest inforegroundcontamination.

Third, the Boomerang receiver has a high instantaneous sensitivity, due to its

opti-mized low-background bolometers and high-bandwidth feeds operating at cryogenic

tem-peratures. The channelsat 90 GHz and 150 GHz are positionedin frequencyto optimally

avoidgalactic foregroundcontamination. Inaddition,combiningthese channelswiththose

at 240 GHz and 400 GHz allowspowerfuldetection andremovalof foregroundsignals.

Finally, the Boomerang receiver uses re-imaging optics which provide good image

qualityoveralargefocalplane. Thereceiversimultaneouslymeasures16bolometerchannels

in8pixelswithbeamsseparatedbyupto4 Æ

onthesky. Thewideformatofthefocalplane

andlargenumberofdetectorsallowedbythere-imagingopticsprovidestheabilitytosearch

forandremove sourcesofcorrelated noise,sinceobservationsofa specicregionofthesky

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2), the design and testing of the Boomerang instrument (Chapters 3 and 4) and its

performance during its 10.5 day ight above Antarctica during 1998-1999 (Chapter 6).

Chapter 5 contains a short section on the performance of the instrument during the test

ight of 1997. The calibration of the instrument with observations of the CMB dipole

is described in Chapter 7. A descriptionof the cosmological analysis and implications is

included in Chapter 8. Finally, the prospects for further research with the Boomerang

data are discussed in Chapter 9. The thesis emphasizes my contributions to the

Boom-erangexperiment,whichrequiredalargeinternationalcollaborationtodevelop,eld,and

produce results. My contributions were the development and testing of the receiver, the

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Chapter 2 Theory

ThetheoryofhowuctuationsintheCosmicMicrowaveBackgroundareproducedandhow

they depend on various cosmological parameters has been well developed [61] [29 ]. This

thesisfocusesonthemeasurementofthesecosmologicalparametersasaninstrumentaland

an analyticalchallenge.

ExtractingcosmologicalinformationfromobservationsoftheCMBinvolvesthreesteps.

The rst step is the construction of the maximum likelihood map from the time stream

data. Second,apowerspectrum iscomputed fromthe map. Third,the power spectrumis

comparedto theoreticalpowerspectrafromvariousmodeluniversesto determinethemost

likelycosmological parameters.

2.1 Map Making

Following[68 ], thebolometertimestream dataare modeled asfollows:

d

t =P

tp

p +n

t

(2.1)

where d is the timestream data array,P is the pointing array which maps the data onto

thesky,is thetemperature of thesky,nis thedetector noise, t is thetimeindex and p

is the pixel index. Because Boomerang is a quasi total-power experiment, the pointing

array P contains onlyone non-zero element per row; at any given time, only one pixel is

beingobserved.

An estimator for theminimumvariance mapcan be foundbyminimizingthequantity

2

=(d P) y

N 1

(d P),whereN 1

istheinversetime-timecorrelationmatrixwhich

isdened ashnn y

i 1

:

~

=

P y

N 1

P

1

P y

N 1

d (2.2)

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~ = P y P 1 P y d (2.3)

The term P y

d is a pixel array containing the sum of all measurements of a pixel and

P y

P

isthenumberofhitsperpixel. Thisversionoftheequationisequivalentto anaive

binning of the data in pixels. In the case of non-white noise, the map is still made by

binningthedata inpixels,except witha\whitening"lter, N 1

applied to thedata.

Thepracticalchallengesinvolvedinsolvingequation2.2areasfollows. First,thematrix

to be inverted is huge (n

pix n

pix

, typically 100,000 100,000 for Boomerang) and

involves considerable computational resources. Second, the noise correlation matrix must

be estimated fromthe timestream datad

t

itself because n

t

isnot a separately measurable

quantity. Third,there aregapsinthedata(duetocosmic rayhitsorother glitches) which

complicate estimationof thenoiseand lteringofthedata.

An iterative scheme was developed [58 ] to address these problems. For each iteration,

a noise time stream estimate is made by subtracting the signal estimate from the data

time stream. Next, a noise correlation matrix and a correction to the previous map is

constructed:

n (j)

= d P

~ (j) (2.4) N (j) 1 = hn (j) n (j)y i 1 (2.5) ~ (j+1) ~ (j) = P y WP 1 PN (j) 1 n (j) (2.6)

The initialmapused istheunlteredbinnedmap:

~ (0) = P y P 1 P y d (2.7)

Forcomputational speed,thelter W istaken to be thenumberofobservations perpixel.

Gapsinthedataareofparticularconcernwhenanylterisappliedtothedatabecause

each unagged sample is aected by the value of nearby agged data. To deal with this

issue, at each step in the iteration scheme, a new constrained realizationof the measured

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A pixel-pixel noise correlation matrix is necessary for calculating the power spectrum

fromthemap. Thiscan beobtainedfrom thenoisetimestream thatisestimatedwiththis

iterative process: N pp 0 = P y N 1 tt 0 P 1 (2.8)

A map and a noisecorrelation matrixobtained inthisway can be used inthe subsequent

powerspectrumanalysis.

2.2 Angular Power Spectrum

The temperatureon theskyat each pixelp can beexpandedin sphericalharmonics:

p = X `m a `m B ` Y `m ( p ;' p ) (2.9) whereY `m

arethesphericalharmonicsandB

`

isthe\windowfunction"ofthebeam,orthe

patternof theexperimentalbeamin`space. The correlation betweensignalsis therefore:

S pp 0 = X `m X ` 0 m 0 ha `m a ` 0 m 0iB ` B ` 0Y `m ( p ;' p )Y ` 0 m 0( p 0;'

p

0) (2.10)

The uctuations are assumed to be isotropic, meaning that ha

`m a

` 0

m 0i =C

` Æ`` 0 Æmm 0 ,

sothesignal correlationsreduce to:

S pp 0 = X `

2`+1

4 C ` P ` ( pp 0 )B 2 ` (2.11) where P `

are the Legendre polynomials and

pp

0 is the angle between pixels p and p'.

The coeÆcientsC

`

completelycharacterizethe temperatureeldon the skyand providea

model-independentway to comparemeasurementswithmodels.

Because of incomplete sky coverage, C

`

cannot be determined independently for each

`. Therefore, the power spectrum is computed for `-space bins. The sky coverage also

determinesthesmallest`(the largest angularscale)at whichpowercan bemeasured.

The angularresolution oftheexperimentwhichmakestheobservations determinesthe

maximum `for which a power spectrum can becomputed. The beam shape of the

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shape generally determines thecut-o insensitivity dueto the beamsize. For example, a

Gaussianbeamprole withFWHM

C

(inradians) yieldsa windowfunction:

B 2

` exp

`(`+1)

( p

8ln2 1 C ) 2 ! (2.12)

The value of `at which thesensitivityfallsto halfthemaximumsensitivityistherefore:

` c p 8 C (2.13)

For example, the Boomerang experiment had an angular resolution of 10 0

,therefore the

half-powervalueof `is 972.

The MADCAP software package [10 ] computes the power spectrum C

`

by using a

Newton-Raphsonmethod todetermine themaximumlikelihoodpowerspectrum. A

Gaus-sian probabilitydistribution forthemapgiven a particularpowerspectrumC isassumed:

P(mjC)=(2) Np=2 exp 1 2 (m T M 1

m+Tr[lnM])

(2.14)

where N

p

is the number of pixels, m is the experimental map, and M is the matrix of

average pixel-pixel correlations expected for thetheoretical power spectrum C. This leads

to the following expression for the log likelihood which must be maximized to determine

thebest-tpowerspectrum:

L(C)= 1 2 (m T M 1

m+Tr[lnM]) (2.15)

If this function were quadratic, the correction ÆC

0

to an initial guess C

0

that would

yield thepeak likelihoodwouldbe:

ÆC 0 = 0 @ " @ 2 L @C 2 # 1 @L @C 1 A C=C 0 (2.16)

L(C)isnotaperfectquadraticfunction,sothiscorrectionisnotstrictlycorrect.

There-fore, thecorrectionto C

`

is iterated untilÆC

n

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2.3 Cosmological Parameters

Inthecontext ofcolddark matter (CDM)models, itispossibleto usethemeasured C

` to

accurately determine cosmological parameters such as the baryon content of the universe

(

b

), thetotalenergy densityoftheuniverse (),and thespectralshapeoftheprimordial

density uctuations(n

s ) [7 ].

Here, a maximum likelihood method is used to measure cosmological parameters. A

database of model power spectra are created assuming a particular range of parameters.

Thesearecompared to theexperimentalmeasurementsbyevaluatinga likelihoodfunction

for each model power spectrum which estimates the probability of this power spectrum

given themeasuredpower spectrum.

Given a set of parameters x with a prior probability distribution P(xjprior) and a

likelihood function of theparameters given theexperiment L(x), theBayes theorem gives

thetotal probabilitydistributionof theparameters:

P(x)/L(x)P(xjprior) (2.17)

If errorsinthecosmologicalparametersÆx=x x

0

aboutthemeanx

0

aresmall,then

L can be quadraticallyexpandedaboutthemaximum:

LL

m exp 0 @ 1 2 X ij F ij Æx i Æx j 1 A (2.18) where F ij

is theFisher informationmatrix, which is given by the derivatives of the CMB

powerspectrumwith respect to theparametersx:

F ij = X ` 1 (C ` ) 2 @C ` @x i @C ` @x j (2.19)

Oset-lognormalapproximationsto theFisherinformationmatrix[9 ]are usedto compute

thelikelihoodL(x)=P(C

B

jx) foreach combinationof parameters inthedatabase.

Some parametersarenotofinterestand can be marginalized. Marginalizedparameters

can includecosmological parameters whichare notof interest, orexperimental parameters

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like-priors andintegrating over themarginalizedparameters x

m :

L=P(xjC

B )=

Z

P

prior

(x)L(x)dx

m

(2.20)

AglobalsearchformaximaofLisperformedfortheentiredatabase. Theaverageand1

points are determined by ndingthe location in the database at which the integral of L

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Chapter 3 Instrument Design

ThischapterdescribesthedesignoftheBoomerang experiment. Theexperimenthasthe

following requirements: a high sensitivity to Cosmic Microwave Background uctuations

and the rejection of spurioussignals from the atmosphere, the ambient environment, and

astrophysicalsources.

In addition,all systemsintheBoomerang payloadmustoperateat balloon altitudes,

which include very low ambient pressure and extreme temperature swings (varying from

-50 Æ

C in the shade to +50 Æ

C in the Sun). The controlsystems in the payload must be

autonomous forthe7-14 days of along durationballoon ight.

The characterization ofthe instrument isdescribed inChapter4.

3.1 Telescope and Gondola

Thetelescopeisdesignedtosmoothlyscaninazimuthatxedelevation,andhasanattitude

control system similar to those described in [11 ], [12 ], and [13 ]. The azimuth pointing of

thetelescopeiscontrolledbytwotorquemotors(InlandQT6205d);thersttorquesalarge

ywheel, the other torques against the steelcables connecting the payloadto theballoon.

The two motors provideenough torqueto move thegondola inazimuthand to correct for

randomrotationoftheballoon. Theelevationofthetelescopecan becontrolledbytipping

the inner frame with a DC gear motor. An overview of the gondola frame is shown in

Figure3.1. Thecontrolhardwareconsistsoftworedundant386CPU's. Awatchdogcircuit

switchescontrolof thepointing fromone CPU ina fewmillisecondsincase of areboot.

Pointing informationisprovided bya dierentialGPSarray,a two-axis Sunsensor, an

encoderontheelevationaxis,andthreeorthogonalaxislaserrategyroscopes. Theazimuth

gyroscopeprovidesvelocityfeedbackforcontrollingthescanofthetelescope. Theabsolute

pointingdatafromtheSunsensorisusedtoresetthedriftinthegyroscopesandtoprovide

dataforpost-ight attitudereconstruction.

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of Boomerang will include a star tracking camera with the proper lter to operate in

daytime.

Sun Shields

Ground Shield

Primary Mirror

Solar Panels

Flywheel

Cryostat

To Balloon

Figure 3.1:

An overview of theBoomerang gondola.

3.2 Thermal Design

Theextremeconditions oftheballoon-borneobservation platformrequiresome careinthe

thermaldesign of thepayload. Electronicsmust notbe allowed to get too hot ortoo cold

tofunction. Moreimportantly,thecryostat mustnotreachatemperatureatwhichO-rings

freeze, which could lead to a leak. The cryostat O-rings are made from Buna-N rubber,

which freeze at temperatures below-50 Æ

C.

The outside of the gondola is covered with 1 00

thick open-cell styrofoam panels (Dow

extrudedpolystyrene\bluefoam")with50mmylarbondedto25mthickaluminumfoil.

Withthemylarsidefacingoutwards,thecombination oflayersprovideshighreectivityin

theopticalbandandhighemissivityintheinfraredband,thusprotectingthepayloadfrom

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structedforthepayload. Twocaseswereconsideredfortheinputpower{\cold"and\hot."

The cold case assumed that the payload is over water and receives 1044 W/m 2

radiation

fromtheSunanda9%albedoforthesurfaceoftheEarthfor177W/m 2

ofpower. Thehot

caseassumed thatthepayloadisabovefresh snowand receives1397 W/m 2

radiationfrom

the Sunand 213 W/m 2

from the Earth with an albedo of 95%. Table 3.2 shows the

pre-dictedrangeoftemperatures fora fewofthekeyexperimentalcomponents. Allelectronics

were expected to maintain reasonabletemperaturesduringthe ight,aswasthecryostat.

Item PredictedTemperature

Æ

C

Attitude ControlSystem -8 Æ

to 12 Æ

Data Storage System 17

Æ

to 27 Æ

Data AcquisitionSystem -7 Æ to 6 Æ Cryostat -29 Æ to 27 Æ

BolometerReadout Electronics -31 Æ

to 2 Æ

SolarArray 55

Æ

to 92 Æ

Table3.1:

Predictedequilibriumtemperaturesforelectronic componentsof thepayload.

3.3 Cryogenics

Thecryogenic systemforBoomerang keeps thedetectorsat an operatingtemperatureof

0.28KfortheentiretwoweeksofanLDBballoonight. Ithas60litersofvolumeat2Kto

contain the photometers, re-imagingoptics, baes, and cold preampliers. The system is

composedof a self-containedsorption-pumped 3

He refrigerator[37 ] and ahelium/nitrogen

main cryostat [38 ]. The 3

He fridge contains 40 liters STP of 3

He and runs at 0.280 K

with a load of 27 W. The main cryostat holds 65 liters of liquid nitrogen and 60 liters

of liquid helium. The tanks, toroidal in shape, are suspended by means of Kevlar cords.

Radiation from the 300 K ambient environment to the77 K tank is shieldedbya blanket

of superinsulation aluminizedmylar (30 layers). The 77 K tank contains copper braidto

maintain cryogenic thermal contact in the event of the nitrogen freezing. Radiation from

the77 Ktankto theheliumtankis shieldedbyan intermediate temperature shieldcooled

to <20 Kbythe 4

(24)

plagued with thermo-acoustic oscillations, making it necessary to pump the bath down

in a controlled manner over the course of 12 hours. Therefore, Boomerang is launched

withtheheliumbathalreadyatlowpressure. Externalplumbingwithelectricallyactuated

valves is used to pressurize the nitrogen bath during the ight and to maintain the low

pressureof theheliumbathduringascent. At oat altitudetheheliumvalve isopenedfor

theremainderof theight.

3.4 Optics

The Boomerang telescope consists of an ambient temperature (-20 Æ

C in the shade at

oat altitude) o-axis paraboloidalprimary mirror which feeds a pair of cold re-imaging

mirrorsinsidethecryostat. Theprimarymirroris1.3mindiameterand hasa45 Æ

o-axis

angle for a projected size of 1.3 1.2 m. The mirror can be tipped in elevation by +10 Æ

and 12 Æ

to cover elevation angles from 33 Æ

to 55 Æ

. Radiation from the sky is reected

bytheprimary mirrorand passes into thecryostat througha thin (50 m)polypropylene

window near the prime focus. The window is dividedin two circles sideby side, each 6.6

cm indiameter. Filters to reject high frequencyradiation and to reduce the thermalload

on the 2 K and 0.3 K stages of the cryostat are mounted on the 77 K and 2 K shieldsin

front of the cold mirrors. These are capacitive multilayer metal mesh low pass lters [72 ]

withcutosat540GHzand480GHzrespectively. Neutraldensitylterswithtransmission

of 1.5% used to reduce the loading on the detectors for ground testing are mounted on a

mechanism which can move the lters in and out of the beam near the prime focus. See

Figure 3.2foran overview of theoptics.

The o-axis ellipsoidalsecondary and tertiary mirrors are surroundedby blackbaes

and re-image the prime focus onto a detector focal plane with diraction-limited

perfor-mance at 1 mmovera 2 Æ

5 Æ

eldof view.

The re-imaging optics form an image of the primary mirror at the 10 cm diameter

tertiarymirror. Thesizeofthetertiarymirrorlimitstheilluminationoftheprimarymirror

to thecentral50% inareato reduce sidelobe response.

The secondaryand tertiarymirrors areellipsoidalreectorswitheective focallengths

(25)

Figure 3.2:

An overview of theBoomerang optics.

mirror is 10 cm in diameter, corresponding to an 85 cm diameter aperture on the 1.2 m

diameterprimary.

The Boomerang focal plane containsa combination of four single-frequency

channel-s fed by smooth-walled conical horns and four multicolor photometers fed by parabolic

concentrators (Winston horns). Although the image quality from the optics is diraction

limitedat 150GHzovera2 Æ

5 Æ

eld,allofthefeedopticsareplacedinsidetwocircles2 Æ

indiameter,separatedcenterto centerby3:5 Æ

. The focalplaneareaoutsidethesecirclesis

vignetted by blockinglters at the entrance to theoptics boxand on the77 K shield and

is unusable. Dueto thecurvature ofthe focalplane, thehorns are placedat the positions

of thebeam centroidsdetermined fromgeometric raytracing. Allofthe feedsareoriented

towards thecenter of thetertiarymirror.

A schematic of the relative positions and sizes of the beams on the sky is shown in

Figure3.3. Thefocalplane layoutwaschosensoasto repeatobservationsofthesame part

of the sky on many dierent time scales. The telescope scans in azimuth, and at 1 Æ

/sat

45 Æ

elevation,channelsonoppositesidesof thefocal planewillobservethesame sky2 s

apart. TherotationoftheskyaboveAntarcticaallowseach rowofdetectorsto observethe

(26)

admixture ofcarbonlampblackto assistintherejection ofstrayhigh-frequency light.

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20’

12’

30’

2.4

90 GHz

150 GHz

150/240/400 GHz

2.7

3.5

4.0

A1

A2

A

A

B

B

B1

B2

Figure 3.3:

The Boomerang focal plane projected onto the sky. The labels \A," \B," \A1," \A2,"

\B1," and \B2" aredesignationsforeach ofthechannels.

3.5 Bandpass Selection

The Boomerang bands were chosen to provide a wide enough frequency coverage that

CMB uctuations can be unambiguously measured and foreground sources of signal can

be separated from contaminants. SeeFigure 3.4 for a comparison of the four bandpasses

selected withthe spectra of theforegroundcontaminants: synchrotronradiation[65 ],

free-free emission [46 ], and thermal emission from dust [21]. Despite the small atmospheric

optical depth at balloon oat altitude, strong atmosphericabsorption lines were avoided.

Bandscenteredat90GHz,150GHz,and240GHzwereselectedtomeasureprimarilyCMB

anisotropy, and a fourth band at 400 GHz was chosen to monitor thermal dust emission,

which wasexpected to be themostimportantcontaminant.

3.6 Single Mode Feed

Thefocalplanecontainsfoursinglefrequencychannels;twoat90GHzandtwoat150 GHz

(see Figure 3.3). The feeds follow the Planck HFI prototype design [15 ]. The

(27)

Figure 3.4:

The Boomerang bands compared with spectra of sources on the sky. The upper

panel shows a model of the atmosphere at balloon oat atmosphere (HITRAN model,

http://www.hitran.com). Thethicklineshows thespectrumof theCMB. Thelowerpanel

compares the spectrum of CMB anisotropy with various galactic foregrounds. The heavy

solid line shows the spectrum of a CMB anisotropy. The small-dashed line shows the

spectrum of free-free radiation, the large-dashed line shows the spectrum of synchrotron

radiation,andthedottedlineshowsthespectrumofthermaldustemission. Thelightsolid

line shows the sum of the three galactic components. In each panel, the hatched columns

show theselected Boomerang bands.

(28)

beam waist at the phase center of the horn, which in turn denes a relation between the

hornaperturediameterand thehorn lengthasfollows.

Fora smoothwalledconicalfeed,thebeamwaistattheapertureisw

a

=0:768a,where

aistheapertureradius. ForahornpropagatingasingleGaussianmode,thewaistdiameter

at thephase centeris

w 0 =w a s 1+ w 2 a L 2 (3.1)

whereListhelengthofthehorn. Thewaistsizeasafunctionofdistancezfromthephase

center isgiven by:

w(z)=w

0 s 1+ z w 2 0 2 (3.2)

The hornaperturesizeisthendeterminedbyrequiringadesirededgetaperat theLyot

stop. Let the Lyot stop have radius r

L

and distance z

L

from the phase center. The edge

taperis:

T =10log

10 exp 2r 2 L w 2 (z L ) ! (3.3)

Specifyingtheedge taperTyieldsa beam waistat theLyot stop:

w(z

L )=r

L s

8:686

T(dB)

(3.4)

Solvingforw

0

,arange ofaperture sizes(a) and hornlengths(L)are specied:

L= w 2 a s w a w 0 2 1 (3.5)

The solution with minimum length is selected, which gives diameters of 19.66 mm and

11.8 mmand are anglesof19.7 Æ

and 10.5 Æ

forthe 90GHz and 150 GHz structures.

At the throat of the entrance feed, a 3 length of waveguide with a radius r =0:35

denesthelowfrequencyedgeofthepassbandandsetsthethroughputofthefeedstructure

suchthatonlythelowestorderGaussianmodeispropagatedthroughtherestofthesystem.

(29)

Capacitivemetalmeshlters denetheupperedgeof theband[72][34 ]. Eachofthese

has high-frequency leaks at twice and three times the cuto frequency and must be used

in combination with another lter which blocks the leaks. In the 150 GHz feeds, lters

with cutos at 168 GHz and 198 GHz are used, and in the 90 GHz feeds, 99 GHz and

177 GHz lters are used. An f/4 re-expanding feed re-emits the light through the lters

and anidenticalre-concentrating feedconcentrates thelightinto thebolometercavity. An

alkali-halide/carbon layered polyethylene lter [74 ] blocks infrared and optical light ( >

1650 GHz)and is tunedinthicknessto maximizetransmissionat the centerof theband.

Identicallowdensitypolyethelylenehyperboliclensesareplacedat theapertureofeach

of thetwo face-to-face horns. The focallengthof thelenses is setto maximally match the

lowest order Gaussian mode propagating from each of the horns through the intervening

lters inthethinlensapproximation.

A re-entrant black bae heat sunk to the1.8 Kstage surrounds the gap between the

twohorns,preventingstraylightfromenteringtheopticalsystem. Theinnersurfaceofthe

bae ispaintedwithBockblack[6].

Integrating Cavity

Bolometer

Thin Lenses

0.3 K

Waveguide

168 GHz LP

Alkali-Halide Filter

198 GHz LP

1.8 K

Baffles

Figure 3.5:

Schematic ofa 150 GHz singlefrequency feedstructure.

3.7 Multi-color Photometer

The focal plane for the Antarctic LDB ight of Boomerang contains 4 three-color

(30)

regionof skythroughthesame columnof atmosphereinthree frequencybands.

Thephotometersarefedbyback-to-backparabolicconcentrators(Winstonhorns)

mount-ed on the2 Kstage. The inputhornis set at f/3.4 to maximallycoupleto the re-imaging

optics. The horn has an entrance aperture diameter of 1 cm producing a 12 0

beam on

the sky, corresponding to the diraction limit at 150 GHz. The horn has a short are in

the shape of a 45 Æ

section of a circle witha diameter of 1.3 cm to reduce sidelobes at low

frequency.

The throughput of the photometer is dened by the 1.45 mm diameter exit aperture

of the Winston horn to be 0.05 cm 2

sr. The re-expanding Winston horn has an aperture

which matcheslight pipe locatedon the0.3 Kstageacross a 0.5mmgap. At the entrance

to the lightpipe,there is a metalmeshlowpasslter witha cuto of 480 GHz to improve

theout-of-band rejection.

In the light pipe, two dichroic lters tipped 22.5 Æ

o-axis direct light at frequencies

greater than 270 GHz and 180 GHz through inductive multi-layer metal mesh bandpass

lters which pass 400 GHz and 240 GHz, respectively. Radiation at frequency less than

180 GHz is transmittedthroughthetwo dichroicsand througha 150 GHz bandpasslter.

Parabolichornsconcentratethelightintointegratingbolometercavitieswhereitisdetected.

3.8 Calibration Lamp

A 1 cm diameter hole located in the center of the tertiary mirror contains a handmade

micromesh bolometer with copper leads for use as a calibration lamp. An NTD-4 chip

provides highimpedanceat 2K. The electronicssendaxed current ontheorder ofa few

microampsthroughthebolometerfor1second every 13 minuteswhich providesan optical

sourceto beused asatransfer calibrator.

Thecalibrationlampwasusedtodeterminethedetectorbiasatwhichmaximumoptical

responsivityoccursand to trackdrifts inresponsivityduringtheight.

3.9 Detectors

(31)

Figure 3.6:

Schematic ofthe Boomerang multi-colorphotometer.

suchasabovetheEarth'spolarregions. Thebolometerabsorberconsistsofasiliconnitride

meshratherthana solid. A NeutronTransmutationDoped (NTD) germaniumthermistor

isused to measure thetemperatureriseof theabsorber.

(32)

Figure 3.7:

A bolometer used by Boomerang. The web absorber shown here is 4 mm in diameter.

The entireringis 3/4 00

indiameter.

0

n d s G

(GHz) (mm) (m) (pW/K) (ms)

90 2 5.6 400 60 24

150 6 3.4 425 60 15

240 4 4.0 150 180 10

400 4 4.0 150 360 6

Table3.2:

Boomerang bolometerdesignparameters,includingtheweb diameterd,thegridspacing

s, thetarget thermalconductance,G andtarget timeconstant,.

use semiconductor thermistors,so Johnsonnoise isalso a contributorto theoverall noise.

In this case the Noise Equivalent Power NEP = p

4k

B T

2

G , where G is the thermal

conductance,T isthebathtemperature, and 1:2forourchoice ofthermistormaterial.

Foragivenbackgroundload,Q,maximumsensitivityisachievedforGQ=T. Thedesired

time constant of a bolometer C=G for a given modulation scheme sets a limit on the

minimum thermal conductance that can be selected. The bolometers are optimized for a

10 K RJ spectrum background using the optimization scheme of [26 ], and the resulting

(33)

3.10 Integrating Cavity

Since an electriceldgoesto zero at thesurfaceof a conductor, anaive guess would place

the bolometer absorber at a distance =4 from the exit aperture of the reconcentrating

horn and at a distance =4 from a backshort inorder to maximize theelectric eld inthe

cavityattheabsorber. SimulationsofabolometercavityusingtheHFSSsoftware package

(Hewlett-Packard) showthat the=4distance isindeedcorrect [24 ].

3.11 Readout Electronics

The slow scan observation scheme requires stabilityof the detector and the readout

elec-tronics from the bolometerthermalcuto frequency( 10 Hz) down to the characteristic

scanfrequencyattensofmHz. Thedetectorreadoutschemeimplementsanelectronic

mod-ulation/demodulationtechniqueto providestabilityatlowfrequency,bymovingthesignal

bandwidthwellabove the 1/f knee of theJFET and the warm electronics. Modulation is

achieved by biasing the bolometerwith AC current, hence modulating its responsivity by

a known periodicfunction.

ThedetectorsareACvoltagebiasedwitha318Hzsinewave. Dual10Mloadresistors

provideanapproximatecurrentbias. ThesignalfromeachdetectorpassesthroughaJFET

source follower circuit on the 2 K stage. It provides gain of the bolometer signal power,

thus reducing the susceptibility to microphonics. The JFETs were selected forlow power

dissipationand arepackagedbyIRLabs (IR LabsTIA).

ThesignalfromthecoldJFETspassesthroughapreamplierstageandaBandPass

Fil-terstagepriorreachingthesynchronousdetector. Thesynchronousdemodulator(Lock-In)

multipliesthesignalsynchronouslyby+1/-1timesthebiasreference. A4-poleButterworth

low pass lter with cuto at 20 Hz removes the high-frequency terms of the product and

actsasananti-aliasinglterfortheDataAcquisitionSystem (DAS). AnAC-couplinghigh

pass lter with a cuto at 0.016 Hz and extra gain is applied to the signal to match the

signaldynamics to theDAS dynamicrange.

Including thecoldJFETs, theentirereadoutelectronicscontribute lessthan

10nV

rms =

p

Hz to the signal noise in thefrequency range of 0.016 Hz to 20 Hz. The

(34)

Cold JFET Pair

Load Resistor

Bolometer

Load Resistor

Cryostat

4 K Faraday Cage

0.3 K Faraday Cage

Bias

JFET Power

Room Temparture

Faraday Cage

Lock-in

4 pole LPF

AC HPF

Signal Out

RF filters: Spectrum Pi filters

RF filters: Eccosorb feedthrough

RF filters: 20 pF feedthrough

Figure 3.8:

A schematic ofthe Boomerang readoutelectronics.

3.12 Rejection of RF and Microphonic Pickup

BolometricdetectorsaresusceptibletospuriousheatingfromRFdissipatedinthe

(35)

JFET source followers. There are several microwave transmitters for satellite

communi-cations on board theBoomerang payloadwhich arepotentially sources of RF pickupin

thebolometers. The frequencies ofconcern arean ARGOStransmitter at 400 MHz and a

TDRSS2.3GHz transmitter.

Toguardagainstdegradationofthedetectorperformance,thebolometercavitydenes

a Faraday cage into which the only entrance is through the feed horn. Interfering RF is

kept out of this entrance path by the waveguide cuto in each feed. The wires exit the

cavity through surface mount 20 pF feed-through capacitors to ground mounted on the

wires exiting the Faraday cage which provide protection from RFI close to the detector.

Allbolometerleadsfromthe JFETpreampstage to thewarm ampliersrunthroughcast

eccosorb lters. The cast eccosorblters consist of striplinecablespotted incast eccosorb

(EV Roberts CR-124) and have signicant attenuation above a few GHz. These provide

theonlyexitfrom a secondFaradaycage surroundingthe2 Kstage.

A third Faraday cage surrounds the bolometer, cryostat electronics and wiring. The

ampliedsignalsarefed throughSpectrum lters(Spectrum 1212-0502) to theDAS.

The low suspended mass of the micromesh bolometers naturally provides a reduction

in microphonicresponse (measured resonant frequency >1 kHz); however, care was taken

to securely tie down the high impedance wiring connecting the bolometers to the JFET

follower stage. The wiring on the 0.3 K stage consists of 27 AWG shielded twisted pair

which was strapped down with Teon tape and nylon cord. Between the 0.3 K and 2 K

stages, cablesmade withlow thermalconductivity50 mmanganinwire were strappedto

the vespel posts. Inside the JFET box, all high impedance wires were potted in silicone

(36)

Chapter 4 Instrument Characterization

Thischapter describesthetestingof thereceivercomponentsdescribed inChapter 3,both

asseparate components andasan integrated receiver. AppendixA containsasummary of

bolometerparameters,measuredbothpre-ight and in-ight.

4.1 Optics Testbed

Atestbedwassetuptotestvariousopticalcomponents,includingthein-bandtransmission

oftheblockinglters,thetransmissionof theopticsbox,and thebeampatternofthefeed

horns. The testbedconsisted of a dewar witha 300 mK bolometerfed bya Winstonhorn

and auniversalmount on theoutsideof thedewarwindowto whichanyhornto betested

could be mounted. Thebolometerwasrunintwo dierentltercongurations;90 GHzto

testthe90GHzsinglemodefeed,and150GHztotestthe150GHzsinglemodefeedandthe

multi-colorphotometerfeedat150 GHz. Inbothcases,theabove bandleakwasmeasured

witha thickgrilllterto beless than5%. The testbed achieveda NoiseEquivalent Power

(NEP) of 10 15

W/ p

Hzwith abolometerwitha thermalroll-oat 5 Hz.

4.2 Blocking Filters

The in-bandtransmission of the blockinglters was measured at two dierence angles of

incidence using the optics testbed and a chopped 77 K blackbody. The band-integrated

transmissionofthelters weremeasuredat f/2 bymountingthem intheirproperposition

in the optics box, and at f/3.3 by placing the lters directly between the feed and the

source. Inboththe150 GHz and90GHz cases,theltershadhigherin-bandtransmission

at higher f/ number. This is dueto the fact that there are more o-axis rays in a low f/

number beam and the eective thickness seen by these rays is dierent than that of the

on-axisrays. SeeTable4.2fora summary oftheresults.

The predictedin-bandtransmissionat 150 GHz of thecombination of ltersis

(37)

Filter Type 150 GHz 150 GHz 90 GHz 90 GHz

f/2 f/3.3 f/2 f/3.3

480 GHz LP metalmesh 0.95 0.96 0.94 0.96

540 GHZLP metalmesh 0.98 0.98 0.95 0.94

1650 GHZLP alkali-halide 0.94 0.95 0.81 0.85

total 0.88 0.69

Table4.1:

The in-bandtransmissionof thethree blockinglters measuredintheopticstestbed.

designed for maximum transmission at 150 GHz, which is near minimum transmissionat

90 GHz. As seen in Table 4.2 it is readily apparent that including the alkali-halidelter

takes away a large amount of optical eÆciency. Due to these tests, it was decided to use

smaller lters and place them within each feed structure, so that the thickness could be

optimizedforeach frequency.

4.3 Beam Maps of Horns

The main lobe response of the feed horns was mapped using two methods. First, a

two-dimensional map was made using a 200 Æ

C source viewed through a 19 mm aperture at

a distance of 15 cm from the feed mounted on the front of the optics testbed cryostat.

Second, a one-dimensional slice of the beam pattern was made using a 900 Æ

C blackbody

source viewed through a 25 mm aperture at a distance of 28 cm from the feed. The 2D

maps were made to a noise-limited sensitivity of around -15 dB from the peak, whilethe

1Dmaps achieved a sensitivityof -20dBof thepeaksignal.

Twocorrectionsweremadeto thedata. First,aview factorofthecosineoftheo-axis

angle wasremoved. A correction was then made forthe angular sizeof the source. Allof

the beams were well t by a Gaussian as expected for a horn which propagates a single

mode. These correctionsreducedthemeasured beamFWHM by7-8%. SeeTable4.3fora

summary of thecorrected beam sizeand the edge taperat the tertiary mirror. Figure 4.1

shows the beam maps of theentrance feed. Vertical linesindicatethe locationof theedge

ofthetertiary mirror. The measurededgetaperat thetertiaryagreeswellwiththedesign

(38)

Figure 4.1:

Beammaps ofthetwo 150 GHz entrance horns. Theverticallines indicatethe edgeofthe

tertiary mirror. The designedgetaperis -5dB.

Horn FWHM FWHM edgetaperon tertiary designedgetaper

(degrees) (cmon tertiary) (dBfrom peak) (dBfrom peak)

90 GHz 16.5 9.8 -4.5 -5

150GHz sm 11.0 6.4 -6.4 -5

150 GHz mm 11.2 6.5 -6.1 -5

Table4.2:

The measuredbeam sizeandtertiary edgetaper ofthree feedhorns.

4.4 Optics Box

(39)

oftheopticsbox. Thissignalwascomparedtothesignalfrom thesourceobserved without

theoptics boxintervening.

The transmissionof theopticsboxwasalsomeasuredwiththeblockingltersinplace.

SeeTable4.4fora summary.

Position 90 GHz 150 GHz 90 GHz +lters 150 GHz +lters

90A 0.68 0.65 0.47 0.57

150A 0.65 0.66 0.45 0.58

90B 0.68 0.66 0.47 0.59

150B 0.64 0.67 0.44 0.58

A1 0.77 0.68

A2 0.76 0.67

B1 0.76 0.67

B2 0.79 0.70

Table4.3:

Themeasuredtransmissionoftheopticsboxwithfeedsmountedintheeightpositions,with

and without the blocking lters installed. The rst four rows of the 150 GHz column are

usingdatafrom thesingle mode feedand the lastfourareusingdata fromthe multimode

feed.

The multimodefeedtransmitsbetterthroughtheopticsboxthanthesinglemodefeed,

despite the fact that their beam patterns are virtually identical. This is due to the fact

that thesingle mode feeds view thetertiary at a largero-axis angle and therefore view a

smaller eective mirrorareathanthe multimodefeeds.

4.5 Feed Testbed

The full feed structures were tested in a dewar with a 300 mK bolometer. The dewar

wascongured inthree dierent ways;withthemulti-colorphotometer, the90 GHz single

mode feedand the150 GHzsingle mode feed. The front-end blockinglters were identical

to those usedin thenalBoomerang receiver. Thebolometerused intheoptics testbed

was usedinthefeedtestbed.

A77Kthermalsourcewasoftenusedasameasurementsource;thisconsistedofeccosorb

soaked in a bath of LN

2

. A styrofoam bucket containing a piece of eccosorb largeenough

(40)

4.6 Optical EÆciency of Feed Structures

Optical eÆciency of each of the feed structures was measured by comparison of two I-V

curvesviewingloadsattwodierenttemperatures(77Kand300K).SeeFigure4.2fortwo

load curvesmeasured withthe 150 GHz single mode feed. At equal bolometerresistances

(equivalent to equalbolometertemperatures), the total powerdissipated inthe bolometer

isequal: R 77 = R 300 (4.1) T 77 = T 300 (4.2) P 77 e +Q 77 opt G = P 300 e +Q 300 opt G (4.3)

wherethesuperscripts77and300refertothethermalloadtemperature,Risthebolometer

resistance, G is the thermal conductance, T is the bolometer temperature, Q

opt is the

incidentopticalpower,andP

e

istheelectricalpowerdissipatedinthebolometer. Sincethe

thermalconductivity is a functionof temperature, it is equalin thetwo cases. Therefore,

thedierence inelectricalpower(P

e

)between thetwo cases is equivalent to thedierence

inincidentoptical power(Q):

P 77 e +Q 77 opt = P 300 e +Q 300 opt (4.4) Q 77 opt Q 300 opt = P 300 e P 77 e (4.5)

The assumption that equal bolometer resistance impliesequal bolometer temperature

breaks down in the case where the \electric eld eect" contributes to the bolometer

re-sistance. In this regime,the bolometer resistance becomesa function of voltage as wellas

temperature:

R=R

0 exp 0 @ s T BV T m+1 1 A (4.6)

where , R

0

(41)

rsttermintheexponentialcontributes. Ifthesecondtermcontributes,however, anequal

resistance does not imply an equal temperature. A test for this eect is to measure the

dierenceinelectricalpoweratseveraldierentbiasvoltagesandtocheckthatthedierence

inpowerisequal.

Thepredicteddierenceinopticalpowercanbedeterminedbyintegrationofthe

black-bodycurve:

Q=A

Z

B

(300K)t

d

Z

B

(77K)t

d

(4.7)

where A is the throughput of the feed, B

is the blackbody function, and t

is the

bandpass function of the lters. The measured dierence in power is compared to this

predictedincidentpowerto determinean optical eÆciency.

With thismethod, the 150 GHz and 90 GHz feed structures are foundto have optical

eÆciencies of 42% and 36%, respectively, while the multi-color photometer channels are

found to have eÆciencies of 27% and 23% at 150 GHz and 240 GHz, respectively. The

opticaleÆciency at 400 GHz wasnotmeasureduntilthephotometers were integratedinto

theightreceiver.

Combiningthemeasurementsof thefeedstructureoptical eÆciency withthe

measure-mentsof thetransmissionoftheopticsboxprovidesapredictionoftheopticaleÆciencyof

eachBoomerang channel. Forthesinglemodechannels,24%isexpectedatboth90 GHz

and 150 GHz. In the multi-color photometer, 18% and 15% eÆciencies are expected at

150 GHz and 240 GHz,respectively.

4.7 Characterization of Neutral Density Filters

The neutraldensity lters(NDF) usedinBoomerang consist ofa lightlymetallizedthin

(25m)lmof polyethylene mountedinan aluminumring. Thering is\wedged"soasto

tip the lm at a small angle relative to the principal optical axis to avoid the creation of

reective cavitiesin theoptics.

Measurement of the transmission of theNDF usingthe Boomerang bolometric

pho-tometersisdiÆcultbecausetheopticalpowerdierencebetweenthelteredand unltered

(42)

Figure 4.2:

Comparisonof load curvesof the 150 GHz single mode feed withthe bolometerviewing a

77Kload(bluecurve)and a300Kload(redcurve)throughtheneutraldensitylter. The

upper panel shows current versus voltage. The lower panel shows electrical power versus

resistance. The dierence in electricalpower is foundto be 1.5 pW. The predicted power

dierence is 224 pW times the neutral density lter's transmission of 1.6%, yielding an

optical eÆciency measurement of 42%. The dierence inpoweris independent of the bias

voltage, showingthat theelectriceld eect isnot contributing.

opticalpowerincidentonthebolometerisafactorof50to100dierentbetweentheltered

and unlteredcases. To bypassthenon-linearityproblems,the bolometer wasbiasedwith

enoughelectricpowerthatthechangeinopticalpowerwastiny(1%oftheelectricpower)

incomparison,therebykeepingthebolometeratthe sameresponsivityinboththeltered

(43)

erang multi-color photometer. On the rst day, the bolometers viewed the chopped

300 K/77 Ksourcedirectly. Onthesecond day,thebolometers viewed thesource through

the NDF, which was mounted on the 2 K stage in the feed testbed. The signals were

measuredat a rangeof bolometer biaspowers andcompared betweendays.

The background optical load on the 150 GHz bolometer is estimated to be 150 pW

without the NDF in the beam and 2 pW with the NDF in the beam. The bias on the

detector was increasedso that the electrical power dissipated in the detector is at least a

factor of 100 greaterthantheoptical powerdierence.

Figure 4.3shows themeasuredtransmissionasafunctionofbolometerbiaspower. The

transmissionateachofthefrequencies150,240,and400GHzweremeasured. Atlargebias,

the resultsbecome independentof bias,showing that non-linearitiesinthe detectors were

overcome. Thisparticularltershowsatransmissionof1.5%. The scatterinthemeasured

transmission show that the results are good to 20%. Additionally, the transmission of

theNDF is seento beindependentof electromagneticfrequency.

Figure 4.3:

Measured transmissionof theneutral density lters asa functionof bolometer bias power

(44)

The transmission of the two NDF's that were measured in this manner was found to

increasefromtheir300 Ktransmissionwhen cooled to2K. Thetypicalincreasewasabout

10%,whichisconsistentwithanincreasedconductivityofthemetallmatlowtemperature.

4.8 Integrated Focal Plane

Thefocalplaneconsistsoftwoeachofthe90GHzand150 GHzsinglemodefeedsandfour

multi-color photometers, for a total of 16 optical bolometers. Two dark bolometers and

a 5 M resistor were installed on the focal plane as diagnostic channels. One bolometer

(Dark A)wasinthesame bolometermount astheother detectors to providea monitorof

thermaluctuationsinthecoldstage. Thesecond(DarkB)ismounteddirectlyonthefocal

plane. A groundedJFETwasalso readoutto monitorproblemswiththe JFETstage. As

a monitorforproblems withthebias generator and the warm electronics, thebias voltage

foreach readoutboxwasalso amplied(Bias1-4) and readoutbytheDAS.

The detectors wereread outby fourelectronicsboxes. TheACbias generatorsin each

electronicsboxwereslavedto a masterbias generator. Witha slaved bias,signal crosstalk

between boxes occurs at zero frequency. The rst box read out the single mode channels

(90A, 90B, 150A, and 150B) and the grounded JFET channel (GNDFET). The second

box read out themulti-moded150 GHz channels (150A1, 150A2, 150B1, and 150B2) and

one dark channel(Dark A). Thethirdbox readoutthe240 GHz channels(240A1, 240A2,

240B1, and240B2)andtheotherdarkchannel(DarkB).Thenalelectronicsboxreadout

the400 GHz channels(400A1, 400A2, 400B1, 400B2) and theresistor(Load Res).

See Figure3.3for aschematic of whereeach beamappears onthe sky.

4.9 Spectral Bandpass

The spectralbandpass oftheinstrument wasmeasuredbeforeight usingaFourier

trans-formspectrometer(FTS).Interferogramsaremeasuredforeachchanneland Fourier

trans-formed to measure the spectral response. The nal spectra are corrected for the 250 m

thickpolypropylenebeamsplitterandthespectrumofthe77Kthermalsource. Abandpass

(45)

Figure 4.4:

Relative spectral response of the four Boomerang channels. The peak response in each

bandhasbeennormalized to unity. The signal seenbelow-35dB isthought to be rectied

noise.

4.10 Blue Leaks

Blockingeach bandwith a high pass lter (thick grilllter) with a cut-o frequency just

above the band allows a search for spectral leaks at high frequency. Since this test is

sensitiveto integrated leaks,amuchhighersignalto noisemeasurementcan bemadethan

with theFTS. The signalsproducedbya chopped LN

2

source viewed withand withouta

thick grill high pass lter in the beam were compared. Table 4.10 lists the results. The

thick grill lter reduces the throughput of the beam, so a conservative factor of two was

included to correctforthiseect.

A high frequency leak in the bandpass can potentially make a channel more sensitive

to galactic dust emissionthan to CMB anisotropy. Therefore, itis usefulto determinethe

signaldueto a sourcewitha dust spectrum.

(46)

R RJ = R B 300 B 77 t l eak ()d R (B 300 B 77 )t band ()d (4.8)

The desired quantityis theratioofin-band to out-of-bandpowerfrom adust source:

R dust = R B dust t l eak ()d R B dust t band ()d (4.9)

Without detailed spectroscopy, assumptions must be made aboutthe spectral

charac-teristics of the leak and aboutthe spectrum of dust. We assume that the spectral leak is

atinresponse from thecuto of thehighpass lterto the cuto ofthe alkali-halidelter

(1650GHz). The amplitudeof theleakistherefore:

T l eak = R RJ R band B 300 B 77 t band ()d R 1650 GHz 0 ( B 300 B 77 )t band ()d (4.10)

For a dust spectrum, we choose a single-component model with a frequency-varying

emissivity:

B

dust =

B( ;T

dust

) (4.11)

We choose favoredvalues ofthe emissivityspectral indexand the dusttemperature,

= 1.7 and T

dust

= 20 K [21 ]. The estimated in-band to out-of-band ratios are shown in

Table 4.10. While thenumbersappear highforthelowest frequencychannels,they are no

callfor alarm. Roughlya quarter of thesignal dueto dust in the90 GHz channels comes

fromtheout-of-bandleakratherthanfromtheband. Asshownlater,theabsoluteresponse

of the90 GHz channelsto dust isvery weak.

4.11 Load Curves

Currentversusvoltage curvesweremeasuredforeachofthedetectorsunder\ight"loading

conditionswhere a300 Kblackload wasviewed throughthe1.5% neutraldensitylters.

The loadcurvesweretaken automatically;each detector wasbiasedwitha DC current

which wasrampedbetween0A andtwice thecurrentat whichpeakvoltage wasobtained.

(47)

0

Thickgrillltercuto out-of-bandpower out-of-band power

(GHz) (GHz) (R-J) (dust)

90 150 1.7% 23%

150 sm 230 0.5% 3.1%

150 mm 230 0.9% 5.7%

240 300 0.8% 2.6%

400 540 0.5% 0.8%

Table4.4:

The integratedpowerfrom above-band leaksin each channelfora sourcewitha

Rayleigh-Jeansspectrumandwithadustspectrum. Theresultsshownaretheaverageoverchannels

at eachfrequency. Because ofdierentlteringschemes, the150GHz channelsaredivided

into single-mode (sm)and multi-mode(mm) here.

The thermistormaterial(NTD Germanium)givesa resistanceasa functionof

temper-ature asfollows:

R=R

0 exp

0

@ s

T 1

A

(4.12)

TheparametersandR

0

aresetbythematerialpropertiesandgeometryofthethermistor.

In thiscase R

0

=300 and= 30 K.

Figures 4.5 through 4.8 show the load curves of all of the detectors measured on the

ground. The thermal conductivity, G, is measured from the slope of temperature versus

electrical power (Table 4.11). The electrical responsivity is the derivative of the voltage

withrespectto electrical power.

The biasatwhichpeakresponsivityoccursisthebiasusedinight. To verifythatthis

biasvalueprovides peakresponsivity,responsetothecalibrationlampwasmaximizedasa

functionof bias.

4.12 Time Constant

The transfer function of a bolometer can be modeled as a low pass lter with transfer

function g = 1

1+i!

. The measured amplitude of the signal and the modulation frequency

can bet to thefunctionjgj= 1

p

1+! 2

2

where thetimeconstant isa freeparameter.

(48)

Figure 4.5:

Load curvesof 90 GHz and 150 GHz detectors measured pre-launch. The lower left panel

shows therawvoltage versuscurrent. Theupperleftpanel showsresistance plottedversus

electricalpowerdissipatedinthedetector. Theupperrightpanelshowstemperatureplotted

versus bias power. The slope of thiscurve givesthe thermal conductivityG (summarized

inTable4.11). The lowerrightpanel shows electricalresponsivityversus biascurrent.

rapidlyaspossible. Theprimaryexperimentalgoalof Boomerang isthemeasurement of

therst acoustic peakwhichappears at anangularscaleof 1 Æ

. Thissignal mustappear

in the bolometer time stream at a frequencywellabove the 1/f knee of the detector, but

(49)

Channel target G G

(pW/K) (pW/K)

90A 60 81

90B 60 82

150A 60 81

150B 60 88

150A1 60 88

150A2 60 104

150B1 60 90

150B2 60 73

240A1 180 181

240A2 180 180

240B1 180 195

240B2 180 202

400A1 360 519

400A2 360 412

400B1 360 422

400B2 360 424

DarkA 360 377

Dark B 60 28

Table4.5:

Thermalconductivityofeach detectormeasuredintheloadcurves,comparedto thetarget

conductivity.

knee(whichappearsat around5 mHz). ForatypicalBoomerang scanspeedof 1 Æ

/s,the

rst acoustic peak appears at 0.4Hz. The target bolometer time constants(see Figure

3.9) whichare all lessthan 25 ms (corresponding to a cut-o at 6.3 Hz)allow a decade of

bandwidthabove the1/f knee.

The time constant of the detectors in Boomerang were measured by measuring the

responseto a modulatedthermalsource. The modulation frequencywasvariedindiscreet

steps and a signal wasrecorded foreach. The signal as a function of frequency was t to

the above transfer function. It was found that in order to get a good t to the transfer

function, itis necessaryto have dataat a frequencywellbelowthetime constant cuto.

The rst column of Figure6.8 shows the bolometer timeconstants measured with this

(50)

Figure 4.6:

Loadcurvesof 150 GHzdetectors measured on theground. ChannelDarkA isa 400 GHz

detector and has a much higher thermal conductivity than the other bolometers in this

gure.

4.13 Noise Performance

Beforecoolingtheinstrument,noisespectra weremeasured(Table4.13). Asectionoftime

stream datawas recordedusingtheDAS and Fouriertransformed insoftware.

At room temperature, the impedance of the bolometers is 1 k, so bolometer noise

(51)

Figure 4.7:

Loadcurvesof 240 GHz detectors measuredonthe ground.

whitespectrumwithJFETnoisevaryingbetween6and10nV/ p

Hz. Thenoiseofthebias

monitor channels was 4-5nV/ p

Hz, so between 4-9nV/ p

Hz of the noise in the detectors

is due to JFET noise. The resistor channelwas measured to have noise at the levelof 30

nV/ p

Hz.

With the detectors at 0.280 K and viewing a 300 K source through the neutral

den-sity lters, noise spectra were taken again. Most channels have some excess noise at low

(52)

Figure 4.8:

Loadcurvesof 400 GHz detectors measuredonthe ground.

Channelsshownwithupperlimitsinthe1/fknee columnwerenotseento haveanyexcess

noiseat frequencies down to thelowestmeasured.

Severalchannelsalsohadexcess whitenoise: 240B2, 400A1,and DarkB.Swappingthe

JFETs, the bolometers, and the readoutelectronics of these channels with good channels

hadnoeectonthenoiseperformance. Therefore,thesourceofthisexcessnoiseisthought

tobeinthecoldwiring. Duetotimeconsiderations,thesechannelswerenotrepairedbefore

Figure

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References