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Balloon-borne observations of the anisotropy of the cosmic microwave background on angular scales of 10' to 5°

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B alloon-borne O bservations of th e A nisotropy o f th e Cosm ic
M icrowave Background on Angular Scales of 10' to 5
°
by
C eleste D iane W in an t
S.B. (M assachusetts In s titu te of Technology) 1995
M.A. (U niversity of C alifornia, Berkeley) 1999
A d issertatio n su b m itte d in p a rtia l satisfactio n of th e
requirem ents for th e degree of
D o cto r of Philosophy
in
Physics
in th e
G R A D U A T E D IV ISIO N
of th e
U N IV E R S IT Y of C A L IFO R N IA , B E R K E L E Y
C om m ittee in charge:
Professor Paul Richards, Chair
Professor Marc Davis
Professor Donald Backer
S pring 2003
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UMI Number: 3105405
UMI
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B alloon-borne O bservations o f th e A n isotrop y o f th e C osm ic M icrowave
Background on A ngular Scales of 10' to 5°
C opyright © 2003
by
C eleste D iane W in an t
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1
A b stract
B alloon-borne O bservations of th e A nisotropy of th e Cosm ic M icrowave
B ackground on A ngular Scales of 10' to 5°
by
C eleste D iane W in an t
D o cto r of Philosophy in Physics
U niversity of C alifornia, Berkeley
Professor P au l R ichards, C h air
We have built the Millimeter-wave Anisotropy eXperiment IMaging Array (MAX­
IMA) to make p artial sky maps of the cosmic microwave background (CMB) tem perature
anisotropy
and
to
measure
the
power
spectrum
over
spherical
multipoles
of
50 < I < 1000.
The MAXIMA experiment is an off-axis Gregorian telescope m ounted on an a tti­
tude controlled balloon platform. The receiver consists of 16 photom eters: eight operating
at 150 GHz, four at 230 GHz and four at 410 GHz. All have 10' FW HM beams. CMB ra­
diation is detected w ith spider web bolometers operated at 0.1K. The combined sensitivity
of the eight 150 GHz photom eters for MAXIMA-1 was 36 pK-y/sec.
MAXIMA-1 was flown on August 2, 1998, from the National Scientific Balloon
Facility in Palestine, Texas. The CMB anisotropy was measured in two overlapping ob­
servations over 3.1 hours. Approximately 122 square degrees of the sky were observed in
a region of low dust contrast. MAXIMA-2 was flown on June 17, 1999. Again, two over­
lapping CMB observations were made over 4.6 hours. Approximately 255 square degrees
of the sky were observed, w ith roughly 50 square degrees of overlap w ith the observations
of MAXIMA-1.
For both flights, a full beam calibration of the 150 and 230 GHz photom eters was
obtained from th e CMB dipole. A calibration uncertainty of 4% and 3% in tem perature
was obtained for MAXIMA-1 and MAXIMA-2, respectively. Beam contour maps and were
obtained from observations of planets (Jupiter in MAXIMA-1, Mars in MAXIMA-2).
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2
We present tem perature maps from the MAXIMA-1 observation. We estimate
a power spectrum from the map with 13 bins spanning the range 36 < I < 1235. The
power spectrum shows a clear peak at I ~
2 2 0
. and is statistically consistent w ith peaks at
higher I. The MAXIMA-1 power spectrum constrains a variety of cosmological param eters,
including the to tal density, Cl = O^ijj'];®, and the baryon density, Clf,h2 = 0.033 ± 0.013,
of the universe. A joint likelihood analysis w ith d ata from recent measurements of high
redshift supernovae constrain our estimates of the dark energy content and m atter density
to Qa = 0.651q'i6 and
= 0 .32 ^0 ^. Limits are quoted at the 95% confidence level. We
subject the results to a variety of systematic checks.
Professor Paul Richards
Dissertation Committee Chair
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To my fath er, C lin to n D in an t W in an t.
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Preface
in*? ntap rrapb 1
y p irj T’iiQ in ’ rroym ‘js r r a ? an so p DTOn 2
’’ nstTT^.ifj?^ nV1?] -iofc y’5: Di’V tfp 3
obtp m
’“?3 onrT p«i " la rp s 4
□rrs b rir a fc wmb orp^n b 3n n y p a i m p
yn&rty 5
To the chief Musician, a Psalm of David
The heavens declare the glory of God, and the firmament his handiwork.
Day to day pours out speech, and night to night reveals knowledge.
There is no speech, nor are there words, b u t their voices are heard among them.
Their sound is gone out into all the land and their words into the ends of the world.
Psalm 19:1-5
Set as a canon for 4 voices and chamber orchestra by Steve Reich, Tehillim. mvt. 1 (1981)
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V
C ontents
Dedication
List of Figures
List of Tables
Acknowledgements
1 History & General Overview
1.1 Experim ental History ................................................................................................
1.2 M otivation ....................................................................................................................
1.3 Personal C o n trib u tio n s................................................................................................
2 Science
2.1 The Cosmic Microwave Background ......................................................................
2.2 The Expansion of an Isotropic Homogeneous U n iv e r s e .....................................
2.2.1 In fla tio n ............................................................................................................
2.3 Evolution of S tr u c t u r e ................................................................................................
2.3.1 Adiabatic Inflationary M o d els.....................................................................
2.3.2 Isocurvature M o d e ls .....................................................................................
2.4 CMB A n is o tro p y ..........................................................................................................
2.4.1 Prim ary Anisotropies ..................................................................................
2.4.2 Secondary A n is o tr o p ie s ...............................................................................
2.4.3 F oregrounds......................................................................................................
2.4.4 P o la riz a tio n ......................................................................................................
2.5 M otivation for MAXIMA .........................................................................................
3 Instrumental Overview
3.1
3.2
3.3
3.4
3.5
3.6
iii
viii
x
xi
1
2
3
4
6
6
7
9
10
10
11
11
12
15
16
19
19
21
O p t i c s ................................................................................................................................. 2 1
D e t e c t o r s ...........................................................................................................................27
The C r y o s t a t .................................................................................................................... 30
D ata A c q u is itio n ..............................................................................................................31
Gondola and B a llo o n ....................................................................................................... 31
The A ttitude Control S y s te m ................................................................................... 32
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vi
4
Optics
36
4.1 MAXIMA O p tic s ..............................................................................................................37
4.2 Pre-flight C h aracterizatio n ............................................................................................. 44
4.2.1 Spectral S en sitiv ity.............................................................................................. 44
4.2.2 Optical Efficiency................................................................................................. 46
4.2.3 F ocusing..................................................................................................................47
4.2.4 Far-sidelobe M e a s u re m e n ts ..............................................................................48
4.3 In-flight C haracterization of Beam P a t t e r n s .............................................................52
4.3.1 M e a s u re m e n t........................................................................................................ 52
4.3.2 Results ..................................................................................................................54
5
Bolometers
58
R e q u ire m e n ts .................................................................................................................... 59
MAXIMA B o lo m e te rs .................................................................................................... 60
Bolometer Noise and O p tim iz a tio n ............................................................................. 63
Readout E le c tr o n ic s ....................................................................................................... 6 6
5.4.1 Radio Frequency Interference F ilte rin g .......................................................... 6 8
5.4.2 RFI Sensitivity M e a su re m e n t.......................................................................... 70
5.5 Detector C h a ra c te riz a tio n ......................................................................................... 73
5.1
5.2
5.3
5.4
6
Observations
77
6.1 Scan S tr a te g y .................................................................................................................... 78
6.1.1 CMB Observation S t r a t e g y .......................................................................... 78
6.1.2 Foreground Rejection ....................................................................................... 80
6.2 F lig h ts ................................................................................................................................. 82
6.2.1 C a lib r a tio n ........................................................................................................... 85
7
Data Analysis and Results
88
7.1 D ata Analysis P ip e lin e ................................................................................................ 8 8
7.1.1 Processing Time Ordered D a t a ....................................................................... 89
7.1.2 Noise E s tim a tio n ............................................................................................. 90
7.1.3 Pointing R ec o n stru c tio n .................................................................................... 92
7.1.4 Map M a k i n g ........................................................................................................92
7.1.5 Power Spectra E s tim a tio n .................................................................................94
7.1.6 Param eter E s tim a tio n ................................................................................... 95
7.2 R e su lts................................................................................................................................. 96
7.2.1 Maps ..................................................................................................................... 96
7.2.2 Power Spectra .....................................................................................................96
7.2.3 Param eter E s tim a te s .........................................................................................100
7.3 Systematic T e s t s ............................................................................................................ 103
7.3.1 S im u la tio n s ......................................................................................................... 103
7.3.2 Comparison and Null T e s t s ............................................................................103
7.3.3 F oregrounds......................................................................................................... 106
7.3.4 G a u s s ia n ity ......................................................................................................... 108
7.3.5 Comparisons with O ther E x p e r im e n ts ........................................................ 108
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Bibliography
109
A p p en d ices
113
A The M AXIM A Collaboration
114
B Thermal design of the MAXIMA cryostat
116
B .l
The Therm al C ir c u it....................................................................................................116
B.1.1 3He R e f r ig e r a to r.............................................................................................. 116
B .l.2 A D R ............................................................................................................ ... . 118
B.2 W irin g .............................................................................................................................. 119
C Amplifier Noise Contributions to Detector NEP for MAXIPOL 150 GHz
Bolometers
123
C .l
C.2
C.3
C.4
M ethod
....................................................................................................................... 123
Results and D iscussion................................................................................................ 126
Comparison w ith Measured N o ise .............................................................................129
C o d e s ..............................................................................................................................130
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viii
List o f Figures
2.1
2.2
2.3
2.4
2.5
2.6
The measured CMB frequency emission s p e c tr u m ............................................
7
The therm al evolution of the u n iv e rse ...................................................................
8
The power spectrum of prim ary a n iso tro p ie s ...................................................... 13
The effect of varying f Ibh2 on the power s p e c tr u m .................................................14
The emission and anisotropy spectra of radio, far-infrared and sub-mm
foregrounds ................................................................................................................ 17
M easurements of the CMB tem perature power spectrum through 1998 . . 20
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
MAXIMA-1 map ........................................................................................................... 22
MAXIMA-1 power s p e c tr u m ........................................................................................23
Measurement of CMB s ig n a l........................................................................................24
Cross-section of MAXIMA o p t i c s ..............................................................................26
Photograph of feedhorns and bolometer a r r a y .......................................................28
MAXIMA observation b a n d s ........................................................................................29
MAXIMA focal p l a n e .....................................................................................................29
MAXIMA gondola ........................................................................................................ 33
A ttitude Control S y s te m .............................................................................................. 35
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
Cross-section of cooled optics and p h o to m eters....................................................... 39
MAXIMA focal p l a n e .....................................................................................................40
150 GHz and 230 GHz back-to-back F eedhorns....................................................... 42
MAXIMA observation b a n d s ........................................................................................45
MAXIMA sidelobe m easurem ent................................................................................. 49
MAXIMA-1 sidelobe m e a su re m e n ts ...........................................................................50
MAXIMA-2 sidelobe m e a su re m e n ts...........................................................................51
Planet s c a n s ..................................................................................................................... 53
MAXIMA b e a m s ........................................................................................................... 54
Asymmetry in MAXIMA-1 b e a m s .............................................................................. 57
5.1
5.2
5.3
5.4
5.5
Schematic diagram of a MAXIMA b o lo m eter.......................................................... 59
Photo of MAXIMA b o lo m e te r.................................................................................... 61
Bolometer noise spectrum ........................................................................................... 65
MAXIMA bolometer readout circuit ....................................................................... 6 6
R FI p ro te c tio n ......................................................
69
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ix
5.6
5.7
R FI filter c irc u it..........................................................................................................
R FI measurements ....................................................................................................
6.1
6.2
6.3
6.4
Azim uthal m odulations in MAXIMA-1 .................................................................... 79
MAXIMA-1 overlap w ith DIRBE map ....................................................................81
MAXIMA-1 & MAXIMA-2 o b s e rv a tio n s .................................................................84
MAXIMA-2 dipole c a lib r a tio n .................................................................................... 8 6
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
MAXIMA d ata analysis p ip e lin e ............................................................................. 89
Maximum-likelihood 3' pixel MAXIMA-1 tem perature m a p ................................. 97
Composite power spectrum from 5' and 3' pixelized m a p s ................................... 98
Interleaved power spectra from the full MAXIMA-1 3' pixelized map . . . 101
C onstraints on flm plane from combined MAXIMA-1 and COBEDMR d a t a s e ts .............................................................................................................. 102
Combined and difference maps for four p h o to m eters...........................................104
Combined and difference power spectra for four p h o to m e te rs .......................... 105
Dark bolometer angular power s p e c tr u m ...............................................................106
Spectral consistency of observations w ith CMB........ ............................................. 107
B .l
B.2
MAXIMA cryostat therm al c irc u it............................................................................117
Low-tem perature bolometer w i r i n g ........................................................................ 121
C .l
Bolometer noise simulation w ith measured INFRARED LABORATORIES
TIA JF E T amplifier n o i s e ........................................................................................126
Bolometer noise simulation with NJ-132 JF E T amplifiernoise measured
at room te m p e r a t u r e ................................................................................................. 127
Bolometer noise simulation with NJ-132 JF E T amplifier noise as measured
by the ACBAR ex p erim en t........................................................................................128
C.2
C.3
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70
72
X
List o f Tables
3.1
Base tem peratures and holdtimes for the MAXIMA cryostat measured in
f l i g h t .................................................................................................................................30
4.1
4.2
4.3
4.4
4.5
4.6
Predicted optical load during f l i g h t .......................................................................... 37
MAXIMA observation b a n d s ........................................................................................46
Optical efficiencies for the MAXIMA receiver .......................................................47
MAXIMA planet specifications ................................................................................. 53
MAXIMA beam F W H M ..............................................................................................55
Sources of beam error for one 150 GHz c h a n n e l ....................................................57
5.1
5.2
5.3
Measured therm al conductance of MAXIMA b o lo m e te r s ................................... 6 6
Bolometer characterization for MAXIMA-1 ............................................................. 74
Bolometer characterization for M A X IM A -2............................................................. 75
6.1
MAXIMA-1 and MAXIMA-2 flight tim e ta b le s .......................................................83
7.1
7.2
7.3
Ranges and sampling for param eter e stim a tio n .......................................................96
Power spectrum measurements from the MAXIMA-1 m a p ................................99
Bayesian param eter estimates from MAXIMA-1 and COBE-DMR d ata . . 101
B .l
Housekeeping therm om etry d e v i c e s ........................................................................ 122
C .l
Optical and electrical power for MAXIPOL-O 150 GHz bolometers during
day-time s c a n ...........................................................................
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125
A cknow ledgem ent s
I would like to thank the members of the MAXIMA collaboration, listed in Ap­
pendix A, without whom this project would have not been possible. I worked closely with
Shaul Hanany, Adrian Lee and fellow graduate student, B ahm an Rabii. The combined
influence of these three has taught me th a t physics research is far from arcane. O ut in the
wilds of Palestine, Texas, we brought new meaning to the term “cowboy physics” , mak­
ing miracles happen w ith garden hose, aluminum tape, car batteries, illogical late-night
arguments, the occasional lab fire and a liberal sprinkling of colorful language.
The two flights of MAXIMA would not have been possible w ithout Danny Ball
and the staff at the National Scientific Ballooning Facility. D ata analysis was facilitated
w ith access to the National Energy Research Scientific Computing Facility at LBNL and
the M innesota Supercomputing Institute at the University of M innesota. MAXIMA was
supported by funding from the NASA Sub-orbital Program and by the NSF through
the Center for Particle Astrophysics at UC Berkeley. My personal contributions were
supported in p art by the NASA G raduate Student Researchers Program.
I would like to thank Donald Backer, Julian Borrill, Marc Davis, Shaul Hanany,
Adrian Lee and Bahm an Rabii for their technical help and personal encouragement in
writing my dissertation.
The technical and support staff at UC Berkeley and LBNL have been dedicated
to both the MAXIMA experiment and collaboration. Armando Baeza, Patrick Bonnefil,
John Davis, John Gibson, Brian Nunn, and George Weber built integral systems of the
experiment.
Caryl Esteves, Lydia Puller, Donna Sakima, Anne Takizawa and Bertha
Zambrano have valiantly helped me contend w ith the bureaucracy at UC Berkeley.
W hen engaged in scientific research, one is constantly reminded th a t we fail
at pursuing these questions with perfect objectivity.
At times, this can be incredibly
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frustrating.
Yet, to let go of our hum anity entirely would be tragic.
My co-workers
remind me of the humor we bring to our work. The camaraderie in the Richards Group
has been a saving grace. For th at, I would like to thank Jeff Collins, W arren Holmes,
Trevor Lanting, Bahm an Rabii, Dan Schwan, Jesse Skidmore and Huan Tran.
My father, Clint W inant, is a physical oceanographer, and has been my role
model. Our similar approach towards people and problems makes his advice indispensable.
My mother, Irene de Watteville, is both passionate and pragm atic, and has helped me
champion the demons of procrastination and endless self-reflection.
My sister, Chloe
W inant, is my best friend and partner in crime. All three are infinitely creative, and
remind me th a t there is no one solution to a given problem.
My friends outside of work, Regina Burris, Michael Feola, Chelle Gentemann,
Eddie Kohler, David Morris, Kim Rankin, Lisa Spivak and Gerry W iener have been un­
conditionally supportive. They know th a t the key to my happiness is eating a good meal,
and have provided me w ith such basic enjoyment on many occasions. My housemate,
David, has kept me from starving while writing my dissertation, and G erry’s open invita­
tion to watch Six Feet Under w ith friends at his home every Sunday recharges my social
battery.
My not-so-secret life outside of work centers around music making. I thank my
co-workers for supporting my extracurricular interests. I have participated in intellectually
and emotionally satisfying musical projects with the UC Berkeley Cham ber Chorus and
Vox Populi Renaissance Vocal Ensemble. The friendships I have formed through these
groups are lasting because of the collaborative nature of music making. I would especially
like to thank my teachers and mentors, Cheryl Keller and Marika Kuzma, for fueling my
skill and confidence in my development as an artist. They have helped me find my voice,
both literally and figuratively, which has strengthened my ability to communicate as a
scientist.
Finally, I would like to thank my advisor, Paul Richards. In allowing me to
take my time in finishing my research and dissertation, he has shown tru st in my process.
He took great care in editing my dissertation, in spite of his wise advice th a t I need not
re-invent the wheel through this endeavor. He has given me wide b erth to both err and
succeed on my own terms, while never failing to step in and directly advise when called
for.
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1
C h a p ter 1
H istory &; G eneral O verview
In the last half century, cosmology has become a quantitative science. We can
directly measure the am ount of luminous m atter in the universe through large scale galaxy
redshift surveys.
We can determine the acceleration of the universe by studying the
recessional velocities of type IA supernovae as a function of redshift. We can estim ate the
dark m atter content of the universe by studying the dynamics of galaxies and through
large scale gravitational lensing surveys. We can uncover an image of the early universe
through observations of the cosmic microwave background.
The cosmic microwave background (CMB) is an electromagnetic radiation back­
ground which fills the universe. Its discovery in 1965 by Penzias and Wilson (see section
1.1) gives credibility to the Big Bang theory of the origin of the universe; th a t the universe
began about 15 billion years ago in an extremely dense and hot state. According to the
Big Bang theory, the universe expands in time, which cools the radiation. The cooling
governs nuclear reactions which yield the baryonic and dark m atter present today in the
universe. The radiation has now cooled to a tem perature of 2.73 K.
The CMB contains the structural im print of the early universe. At the tim e of
recombination, when the universe was approximately 300,000 years old, CMB photons
decoupled from baryons and have been free stream ing ever since. A small fraction of
CMB photons have since undergone secondary interactions w ith hot galaxy clusters, and
portions of the sky are obscured by galactic emission and point source contamination.
By observing the CMB in foreground free regions of the sky, we are able to characterize
density fluctuations from the time of recombination. C hapter 2 presents a more thorough
discussion of the scientific background.
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2
1.1
E xperim ental H istory
The CMB was first postulated by Gamov (1948) and Alpher Sz Herman (1948).
They realized th a t nucleosynthesis could only have taken place in a hot background. The
CMB was discovered by Penzias and Wilson in 1965 w ith the Bell Telephone Laboratory
Telescope in Holmdel, New Jersey (Penzias & Wilson (1965)). The telescope used a Dickeswitch radiom eter (Dicke (1946)) which compared the sky w ith a liquid 4He cold load.
They detected an isotropic signal corresponding to a tem perature of T — 3.5K at 4.08
GHz. Their discovery was not motivated by a dedicated search for an isotropic radiation
field of prim ordial origin. The result was first correctly interpreted by the observational
cosmology group at Princeton which was concurrently attem pting a dedicated observation
of the background radiation (Dicke et al. (1965)). Penzias and W ilson were awarded the
Nobel Prize in physics in 1967 for their discovery. For more details on the early history
of CMB observations, refer to Peebles (1993).
Since its discovery, attention has turned towards measurement of the frequency
spectrum and the tem perature anisotropy of the CMB. Technological advances in electron­
ics, detectors, cryogenics, computers, telescope platforms and space flight have yielded a
diversity of instrum ents and approaches.
Measurements of the CMB emission spectrum below 100 GHz have been made
with microwave heterodyne receivers which chop between the sky and a cold black-body
load. The accuracy of the experiment is usually limited by the construction of the cold
load. Pioneering measurements were made by Wilkinson (Uson &; W ilkinson (1988)) and
Howell & Shakeshaft (1966). The spectrum becomes increasingly difficult to measure for
frequencies above 100 GHz. The quantum noise limit of narrow band heterodyne receivers
above ~ 100 GHz becomes im portant. Bolometers are more sensitive, b u t are broad-band
devices, and require spectral discrimination. This can be provided by a series of band­
pass filters or w ith a Fourier-transform spectrometer. A discussion of the tradeoffs of
different detectors can be found in C hapter 5. Woody & Richards (1981) were the first
to definitively show th a t the spectrum of the CMB decreased with frequency beyond a
peak near 180 GHz using a balloon-borne bolometric telescope w ith a polarizing Michelson
interferometer. The most precise measurement of the CMB emission spectrum over 0.1 to
10 mm was made by the FIRAS instrum ent on the Cosmic Background Explorer (COBE)
satellite, which observed between 1989 and 1993 (M ather et al. (1994)).
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The COBE-
3
FIRAS measurement, shown in Chapter 2, confirmed th a t the CMB spectrum follows
th a t of a unit emissivity 2.73 K black-body.
The COBE satellite made an unambiguous measurement of the tem perature
anisotropy of the CMB. D ata from the Differential Microwave Radiom eter (DMR) instru­
ment yield a definitive map of tem perature anisotropy over the entire sky (Gorski et al.
(1996)). The DMR strategy was to measure the difference between signals from two het­
erodyne receivers th a t were pointed a fixed 60° apart on the sky w ith a resolution of 7°.
Over the course of six months, the pair of receivers swept over the entire sky, yielding
a full-sky map of difference points. The DMR instrum ent had 3 receiver pairs, covering
frequency bands centered at 31.5, 53 and 90 GHz. The COBE-DMR instrum ent measured
the CMB power spectra over the range of spherical multipole moments from 2 < I < 40.
A satellite experiment like COBE requires large resources and much time to
undertake. Logistically simpler ground-based, balloon-borne and aircraft-borne measure­
ments save on time and resources.
These alternative platforms dictate a decrease in
the quality and quantity of data, but allow for rapid turnaround in d ata collecting and
instrum ent development. Of great im portance to the development of MAXIMA is the
Millimeter-wave Anisotropy Experiment (MAX), which was developed at UC Berkeley
and UC Santa B arbara (Devlin et al. (1994), Clapp et al. (1994), Tanaka et al. (1997)).
MAX was a balloon borne bolometric telescope th a t observed in four frequency bands,
centered at 90, 150, 230 and 410 GHz. MAX flew five times between 1989 and 1994, and
was one of the first experiments to report detections of tem perature anisotropy, albeit with
greater uncertainties th an COBE-DMR (Alsop et al. (1992)). The measured anisotropy on
half degree scales was higher th an upper limits set at larger angular scales giving the first
indication of an acoustic peak. O ther im portant experiments during the COBE era are
Saskatoon (Netterfield et al. (1997)) and MSAM (Cheng et al. (1997)). These experiments
measured tem perature anisotropy at smaller angular scales th an COBE-DMR.
1.2
M otivation
Adiabatic inflationary models predict a series of harmonic peaks in the CMB
angular power spectrum above I ~
100
, which corresponds to angular resolutions of a
few degrees or smaller. Improvements in detector sensitivity and optical resolution were
needed to b etter explore CMB tem perature anisotropy at small angular scales. Bolometric
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4
detectors were being developed th a t made such measurements possible. The strategy of
the MAXIMA experiment was to use these detectors to measure anisotropy on angular
scales of 10' < 9 < 4°, or at multipoles of 50 ;$ i < 1000. Tem perature anisotropy is
quantified through maps and power spectra, which can be used to estim ate fundamental
cosmological param eters.
The MAXIMA experiment uses an off-axis Gregorian telescope mounted on an
attitu d e controlled balloon platform. The receiver consists of 16 photom eters operating
at frequency bands centered at 150, 230 and 410 GHz. All have 10' FWHM beams. CMB
radiation is detected with spider web bolometers (Bock et al. (1995)) operated at 0.1K.
MAXIMA has observed twice (MAXIMA-1 in 1998, MAXIMA-2 in 1999). The combined
sensitivity of the eight 150 GHz photom eters for MAXIMA-1 was 36 /rK-^/sec. D ata from
MAXIMA-1 have been used to generate maps power spectra of the CMB, from which we
can estimate cosmological param eters and constrain cosmological models.
1.3
Personal C ontributions
The complexity of the MAXIMA experiment has made it so th a t no one sub­
system could have been designed, developed and tested by a single person. Throughout
this dissertation, most efforts are attrib u ted to the ubiquitous “we” , in reference to the
MAXIMA collaboration, the members of which are listed in A ppendix A.
My personal effort on the experiment was concentrated in three areas: I was
the principal graduate student responsible for assembling and testing the receiver. I in­
tegrated the bolometers, cooled optics and electronics and sub-Kelvin refrigerators in the
MAXIMA cryostat. I designed and supervised the building of the cooled Lyot stop and
the cryostat wiring. I upgraded the MAX experiment housekeeping readout electronics for
the MAXIMA receiver. I designed and implemented radio frequency interference shield­
ing for the receiver. I was responsible for characterizing the bolometers and the optics.
This includes measurements of the therm al conductance and resistivity of the bolometers,
the optical efficiency and spectral sensitivity of each photom eter, and the noise for each
detector. These tests and results are described in C hapters 4 and 5.
I was a core member of both the MAXIMA-1 and MAXIMA-2 field campaigns
(Chapter 6 ). Both campaigns involved 6 - 1 0 weeks of integration of the scientific payload
prior to launch at the National Scientific Ballooning Facility in Palestine, Texas.
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5
I was responsible for a subset of the preliminary d ata analysis for both MAXIMA1 and MAXIMA-2 (C hapter 7). I determined the transfer functions for the electronic filters
from the detector read-out electronics and for the bolometer tim e constants. I determined
the final dipole and planet calibrations and analyzed the two-dimensional beam profiles for
each detector. I was an active participant in group discussions and decisions concerning
the overall d ata analysis effort, and am co-author on publications of MAXIMA-1 results,
most of which are discussed in this dissertation.
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C h a p ter 2
Science
In this chapter, we discuss the scientific background of the CMB tem perature
anisotropy. We describe the CMB and the expansion of the universe. We present brief
history of the evolution of cosmological structure and describe the CMB anisotropy. We
present the scientific goals of MAXIMA.
2.1
T he C osm ic M icrowave Background
The CMB is an electromagnetic radiation background of prim ordial origin th a t
fills all space. The CMB is homogeneous and isotropic, with the exception of the dipole,
to one p art in 105. The CMB has a blackbody emission spectrum , which presently cor­
responds to a blackbody tem perature of 2.736 ± 0.017 K with a peak at a frequency of
~ 180 GHz. The measured CMB frequency emission spectrum is shown in Figure 2.1.
The present day density of the CMB is ~ 400 photons per cm 3 .
The CMB was discovered in 1965 by Penzias and Wilson of Bell Telephone Lab­
oratories. Their discovery verified one of the cornerstones of the Big Bang Theory, th a t
the universe began in an extremely hot and dense state. The CMB has since cooled with
the expansion of the universe to its present day tem perature of 2.73 K. The cooling gov­
erns nuclear reactions which yielded the baryonic and dark m atter present today in the
universe. A schematic of the therm al history of the universe is shown in Figure 2.2.
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7
400
500
£
200
100
5
10
15
20
Frequency (cm"')
Figure 2.1: The CMB emission spectrum , as measured by the COBE-FIRAS instrum ent
(Fixsen et al. (1996)), plotted as a function of wavenumber (cm - 1 ). The error bars
encompass a small fraction of the plotted line width. W ithin the errors, the curve fits a
blackbody spectrum perfectly. The peak emission of the CMB frequency spectrum occurs
at ~ 6 cm - 1 (180 GHz).
2.2
T he E xpansion of an Isotropic H om ogeneous U niverse
Einstein, LeMaitre, Friedmann, and de Sitter showed th a t we lived in a dynamic
universe where space can shrink or expand with time.
Following the rules of general
relativity, they derived the expansion of the universe as a function of time, content, density,
and curvature. The notion of an expanding universe was accepted after Edwin Hubble
observed th a t astrophysical objects at great distances uniformly receded from the observer.
The Friedm ann equation describes the expansion of an isotropic, homogeneous
universe;
( - ) 2 = H$(nma-S + nra~4 + nA + nka-2),
(2.1)
&
where a is the scale factor, Hq is the present Hubble constant, Om is the m atter density,
Qr is the radiation density, (lA is the dark energy (A) density, and Qk is the curvature
density. The universe is open for f}k < 0, and is closed for
> 0. All variables are
time dependent. The density variables are defined such th a t the sum of their present day
values is unity (ft 0 (tp re se n t) = !)■
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LEPTON DESERT
log(T)
-15
Decay of baryons
-10
Today
Reionization
Temperature decoupling
Recombination
Proton neutron
10
\
Matter dominated
era begins
_ ____ ^
Nucleosynthesis
Electron-positron annihilation
Neutrino
decoupling
Formation of baryons
from quarks
Symmetry breaking between
weak and electromagnetic
interactions
Baryogenesis
20
Reheating
INFLATION
Figure 2.2: The therm al evolution of the universe: This chronology gives the history of
the universe as a function of tem perature. Time increases from bottom to the top.
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9
The early universe was radiation dominated. The scale factor reduces to approx­
imately
a(t) ~ \J lH § t oc fT
(2 .2 )
Presently, the universe is m atter dominated. The expansion of the universe can
be described as
Q
a(t) ~ { - H 0t ) 3 oc <3 .
(2.3)
In the scenario of a dark energy dom inated universe, the scale factor increases
exponentially.
a(t) ~ a0eHot.
2.2.1
(2.4)
Inflation
The expansion of the universe can not have been governed by the Friedmann
equation alone. The universe is presently homogeneous over too large a distance scale.
We know th a t regions th a t are separated by a distance larger th an the horizon have the
same tem perature. Also, models predict th a t any derivation from flo(f) = 1 diverges. In
order for the universe to be as flat as it is observed today requires \Qo(t =
0
) —1 | < 1 CT60,
which seems arbitrarily fine-tuned. A possible explanation for the homogeneity and the
flatness of the present universe would be if the universe early on underwent a brief period
of superlum inal expansion, otherwise known as inflation.
There are currently well over 100 published inflationary models (Wu (2000)). The
common feature of these models is th a t quantum fields at high tem peratures (
TeV)
tem porarily create a negative-pressure equation of state th a t mimics the effect of a cos­
mological constant.
Such models generate expansion factors of ~ 106 0 over a time of
10- 3 4 sec. It is then possible for the entire universe fit w ithin the horizon before inflation,
solving the horizon problem.
So far, there has been no direct observational confirmation
of inflation.
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10
2.3
E volution of Structure
The universe presently is not perfectly smooth. On distance scales
< lOO/i- 1 Mpc x, the homogeneity of the universe is disrupted by the presence of structures
like clusters, galaxies, and stars. The question is, w hat can we learn from the CMB about
the evolution of structure? Before the recent CMB results, the evolution of structure
was explained by two competing classes of models; adiabatic inflationary models and
isocurvature models.
A d iab atic Inflationary M odels
2.3.1
Adiabatic inflationary models assume th a t the structures present in the universe
today evolved from prim ordial density fluctuations. The Heisenberg Uncertainty Princi­
ple dictates th a t the homogeneity of a field is limited by quantum fluctuations. If the
only m atter component in the universe at the time of inflation is the scalar field, <f>, the
spectrum of prim ordial density perturbations is scale independent; 5p/ p oc <fi2. This re­
markable result lays the foundation for the coherence in the present CMB power spectrum.
Assuming the universe undergoes inflation at its inception, the “fabric” upon which these
fluctuations manifests themselves stretches over scales beyond the horizon. After inflation,
fluctuations separated by a distance larger th an the horizon no longer interact with each
other.
In time, the horizon grows, and a given distance scale eventually re-enters the
horizon. After this time, fluctuations on th a t scale begin to interact. The dom inant mech­
anism for the evolution of baryonic m atter density fluctuations in the early universe for
times between a tim e of 2 psec and 300,000 years was pressure oscillations in the coupled
radiation and baryon fields. The physics of this will be described in §2.4. These oscilla­
tions greatly amplify fluctuations on certain scales. At recombination (t = 300,000 years,
z
=
103), the radiation field decouples from the baryons. Prom this point on, bary­
onic m atter density fluctuations evolve through gravitational interaction. By a red-shift
of z ~
2
, the perturbations become large enough th a t they evolve nonlinearly and begin
to collapse into the structures we observe today; stars, galaxies, clusters, and groups of
clusters. Presently, there are still fluctuations on distance scales larger th a n the horizon.
l h = T-rr:---—9-r , where ft is th e dimensionless H ubble param eter. W hile redshifts can be m easured
100km s ~ 1 M p c- 1 ?
directly, cosmological distances cannot.
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11
These fluctuations have never interacted since the time of inflation.
Adiabatic inflationary models dictate th a t structures present in the universe to­
day evolved from prim ordial quantum density fluctuations via standard physical interac­
tions. The initial distribution of quantum density fluctuations is Gaussian. The universe
is presently homogeneous and flat due to the brief period of superlum inal expansion at its
inception.
2.3.2
Isocurvature M odels
Isocurvature models dictate th a t density fluctuations in the universe overwhelm­
ingly arise from cosmic defects (monopoles, cosmic strings and walls).
A local defect
creates a m inim um /m axim um in the potential. Fluctuations in the density field are set
up to eliminate the local potential (hence the term isocurvature).
These fluctuations
evolve under the same physical forces as adiabatic fluctuations. The initial distribution
of isocurvature fluctuations depends on the given defect model, b u t is presumably nonGaussian.
2.4
C M B A nisotropy
The CMB contains a record of density fluctuations throughout the history of the
universe. The following sections largely summarize pedagogical articles of Hu et al. (1997)
and Tegmark (1995). The pattern of CMB anisotropies th a t we observe are best discussed
quantitatively by considering their effect on the power spectrum of CMB tem perature
anisotropy.
CMB Power Spectrum
The tem perature angular power spectrum is the spherical m ultipole moment
transform of a two-dimensional spherical surface map of mean square tem perature. It is
conventionally plotted as £(£ -I- 1 )Q , where I is spherical multipole moment. Increasing
I corresponds roughly w ith decreasing angular scale, through the approxim ate relation,
I ~
where 0 is in units of degrees.
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12
2.4.1
P rim ary A nisotropies
CMB tem perature anisotropies can be divided into two groups; those th a t orig­
inated before recombination (primary anisotropies) and those th a t originated after (sec­
ondary anisotropies). Before recombination, Thomson scattering between CMB photons
and free electrons coupled the radiation (CMB) and baryonic m atter fields. At this time,
the density fluctuations in both fields were perfectly correlated.
Fluctuations evolved
through pressure oscillations in the baryon/radiation fluid, driven by two opposing forces;
radiation pressure and gravity. Tem perature fluctuations arose from two mechanisms;
density and velocity fluctuations.
Fluid in overdense regions was hotter than fluid in
underdense regions, generating the former. The photons in the fluid flowing from an underdense to an overdense region were Doppler shifted, depending on the velocity of the
fluid. These two effects produced periodic fluctuations, density and Doppler “peaks” in
the CMB power spectrum th a t are 90 degrees out of phase.
At recombination, the photons and baryons decoupled, and CMB photons have
been free-streaming ever since. Fluctuations no longer evolved through pressure oscil­
lations. The relative fluctuation am plitudes at recombination are presently observable
in the CMB. These are called prim ary anisotropies. We observe the p attern of prim ary
anisotropies which originated from the spherical surface in space th a t is d = c A t =
6000h_1 Mpc away from the observer, where A t = tpresent —t r e combination ■ This is often
called the surface of last scattering. The p attern of prim ary anisotropies is determined
by many factors, notably the source of initial fluctuations, the relative density param eters
before recombination, and the geometry of the universe.
The source of initial prim ordial fluctuations determines the distribution and co­
herence of prim ary tem perature anisotropies. In adiabatic inflationary scenarios, structure
evolves from quantum fluctuations. Initially, they obeyed a Gaussian distribution on the
sky. The power spectrum of such a distribution would be white. C ertain adiabatic infla­
tionary models introduce a tilt, n s, in the power spectrum of the gravitational potential.
This tilt will correspondingly increase the slope of the angular power spectrum , Cp. As
the horizon grows, fluctuations on increasingly larger angular scales began to oscillate.
Adiabatic inflationary models predict th a t fluctuations on a given scale w ithin the horizon
subsequently oscillated perfectly in phase. The time delay between the onset of pres­
sure oscillations in fluctuations on different distance scales leads to a relative phase shift
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13
R ecom bination
250
/H o rizo n
200
^
150
100
50
0
t
tim e
200
150
I
—
100
<o
50
0
200
400
600
800
Figure 2.3: The power spectrum of prim ary anisotropies: The top panel is a schematic of
the evolution of tem perature fluctuations as a function of time on four different co-moving
scales, corresponding to multipoles (£i, ...£4 ). Fluctuations began to oscillate when they
enter the horizon, and stopped at recombination. The phase of the fluctuation on each
mode at recombination is preserved in the angular power spectrum (bottom panel). The
tem perature fluctuations are arbitrarily scaled. Note- the simplified power spectrum in
the bottom panel does not include the Doppler “peaks” .
between their respective fluctuation amplitudes. Assuming th a t pressure oscillations of
fluctuations on all modes stop instantaneously at recombination, the power spectrum of
prim ary tem perature anisotropies would be a series of harmonic peaks as a function of
angular scale. The am plitude of the spectrum at a given I corresponds to the phase of each
oscillation on th a t scale at the tim e of recombination. This is illustrated in Figure 2.3.
Density fluctuations oscillated via the same mechanism in isocurvature models,
but the initial distribution of fluctuations differed (See §2.3.2). If initial fluctuations have
a non-Gaussian distribution, they will evolve incoherently. We would not observe the same
periodicity in the power spectrum.
The relative density param eters affect the evolution of prim ary anisotropies. Be­
fore recombination, the magnitude of radiation pressure and self-gravitation in the photonbaryon fluid was determined by the photon and baryon densities, respectively. The pres­
sure oscillation can be modeled as a harmonic oscillator with an effective mass, m ef f , that
is proportional to the ratio of baryon and photon densities. The effective mass sets the
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14
10
a) Hbh 2 D e p e n d e n c e
n bh*
—
d*
H-
-■o
—
—
-
'//
0 .0 2 5
0 .0 1 5
0 .0 0 7 5
0 .0 0 2 5
n =1 h = 0.5
10
100
I
Figure 2.4: The effect of varying f ^ /i 2 on the power spectrum: The baryon-photon ratio
R oc Qbh2 determines the speed of sound and the “zero point” of oscillation in the baryonphoton fluid. Increased R leads to gravitational enhancement of the odd peaks in the
power spectrum . Figure borrowed from Hu & W hite (1996).
speed of sound in the fluid, and determined the frequency of oscillation and the relative
heights of the density and Doppler peaks. A high baryon to photon density ratio slowed
the oscillations and suppressed the Doppler peaks.
A large effective mass shifts the “zero point” of oscillation in density fluctuations.
This introduced an asymm etry in the relative am plitude of the tem perature power for
positive and negative density fluctuations, which translates into an asymm etry between
the heights of the odd and even density peaks in the CMB tem perature power spectrum for
adiabatic inflationary models. The larger the baryon density param eter, fl^h2, the larger
the asymmetry. Figure 2.4 illustrates the effect of varying f\ h 2 on the power spectrum.
The geometry of the universe affects the overall observed scale of prim ary tem ­
perature anisotropies. In an open universe, light travels on convex geodesics, and in a
closed universe, light travels on concave geodesics. Curvature presents the surface of last
scattering to the observer through a lens. Structure is magnified through a closed universe,
and is compressed through an open universe. The harmonic peaks in a CMB anisotropy
power spectrum in adiabatic inflationary models shift towards higher multipoles in an
open universe. The location of the first density peak, £\, in an adiabatic inflationary
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15
CMB power spectrum is
(2-5)
Recombination did not occur instantaneously (although the event did not last
long, by cosmological standards). The tim e At recom over which recombination occurred
determines the thickness of the surface of last scattering along the line of sight, A d =
c A trecom , which smears prim ary anisotropies on smaller physical scales. The CMB tem­
perature anisotropy power spectrum damps exponentially for multipoles larger th an the
angular scale set by this thickness (above multipoles I ~
2.4.2
103
).
Secondary A nisotropies
After recombination, the CMB photons we observe travel a co-moving distance
of 6000/i_1 Mpc from the surface of last scattering. Subsequent perturbations to CMB
tem perature fluctuations are called secondary anisotropies. These perturbations arise from
time variations in the gravitational potential, from local Thomson scattering, from global
reionization, and from the earth ’s peculiar velocity.
Photons th a t fall into a potential well will appear blue-shifted. If the potential
does not vary in time, the photon will climb out of the potential and will be subse­
quently red-shifted, resulting in no overall tem perature shift. If the potential varies in
time (4> 7 ^ 0), then the photon tem perature will change. The overall tem perature shifting
of a CMB photon traveling through a time varying gravitational potential is called the
Integrated Sachs-Wolfe (ISW) effect. To good approximation, the gravitational potential
remains constant after recombination, with two exceptions. Soon after recombination,
the radiation density of the universe was still significant, and the gravitational potential
decayed in time. This blue-shifts CMB photons, which boosts the power spectrum at large
angular scales (to the left of the first density peak), and is called the early ISW effect. If
A > 0, then the universe becomes increasingly vacuum dominated, which also causes the
gravitational potential to decay. This occurs at smaller red-shift, thus peaks at the largest
scales, and is referred to as the late ISW effect.
Tem perature fluctuations can also change if CMB photons travel through a lo­
cally reionized area, like a hot galaxy cluster. Such distortions are called the SunyaevZeldovich (SZ) effect. Thomson scattering of hot free electrons inside the cluster distorts
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16
the blackbody spectrum of the CMB by boosting the energies of low-frequency photons.
This appears as a red-shift below 218 GHz and a blue-shift above 218 GHz in the frequency
spectrum , which is called the therm al SZ effect. The peculiar velocity of the cluster along
the line of sight generates an overall tem perature shift in the CMB. This is known as
the kinematic SZ effect. Both effects occur only at small angular (cluster) scales (for
i > > 103), and will not have a large effect on the overall power spectrum . Instead, the
SZ effect is used to study the physical and statistical properties of galaxy clusters.
Global reionization has the effect of suppressing overall CMB tem perature fluc­
tuations on small angular scales. Thomson scattering at later red-shifts smears structure
on an angular scale of
where
2
is the red-shift of reionization. Global reionization is typically discussed in terms
of the optical depth, r c, of the reionized universe. The CMB tem perature power spectrum
on scales smaller than ~ e~Tc (£ > >
10
) will be suppressed by a factor of e“ 2rc.
The earth ’s peculiar velocity through the CMB reference frame produces an
observable tem perature dipole w ith a m agnitude of A T ^ voie = 3.343 ± 0.016 mK towards
(I, b) = (264.4°, 48.4°), as measured by COBE-FIRAS (Smoot et al. (1991)).
2.4.3
Foregrounds
The CMB is a diffuse background. The emission of other far infrared and sub­
millimeter foregrounds is comparable to th a t of the tem perature anisotropy of the CMB
(See Figure 2.5). These other sources include emission from the terrestial atmosphere, from
free-free and synchrotron radiation, from galactic and zodiacal dust, and from extragalactic
point sources.
The earth ’s atmosphere is largely comprised of nitrogen, ozone, and water, all of
which are sources of rotational emission lines concentrated in the far- and near-infrared.
At low altitudes, pressure broadening transforms the emission spectrum into an approx­
imately continuum black body spectrum w ith an emissivity index of
emissivity B( v) oc
, lending an overall frequency scaling of
~
2
, where the
in the Rayleigh Jeans
limit of the spectrum (for A > 250 pm ).
The galaxy is a strong source of free-free (therm al brem sstrahlung radiation),
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17
■ '
'
- V , !.
r i !
><■>X
1000
jr f
M A X IM A
N
X
o
100
COBE D m {*
..MAP
10
-
r
l
U
'
L
Al,i.
10
100
1000
104
Figure 2.5: The emission and anisotropy spectra of radio, far-infrared and sub-mm fore­
grounds: Diffuse galactic emission from dust manifests it self over the upper region of
the plot (red, upwards diagonal cross-hatchings). Radio and far-IR point source emission
manifests itself over the right-hand v-shaped region of the plot (green, downwards diag­
onal cross-hatchings). Synchrotron and free-free emission is manifest over the lower left
hand corner of the plot (Synchrotron: blue, vertical cross-hatchings; free-free: magenta,
upwards diagonal cross-hatchings). The observational ranges of MAXIMA, COBE-DMR,
the WMAP satellite (MAP) and the Planck satellite are outlined in black. Figure courtesy
of M artin W hite.
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18
synchrotron, and dust emission. Free-free and synchrotron emission peak at 0.5-1 GHz,
and both drop with increasing frequency, w ith respective emissivity indices of -2.15 and
~ —3. The physics of dust emission is more complicated. Pressure broadened vibrational
emission lines give rise to a monotonically increasing emission spectrum as a function of
frequency w ith an emissivity index of /3 = 1.5 —2, peaking at A ~ 1000 /j,m assuming a
dust tem perature of ~ 20 K. Emission lines from rotating dust may boost the emission
spectrum at frequencies between 10 and 100 GHz (Draine & Lazarian (1998)).
These foregrounds have been studied in radio and far-infrared surveys.
Syn­
chrotron radiation has been m apped by the 408 Hz radio survey (Halsam et al. (1982)).
No good free-free map exists, but its distribution is thought to be highly correlated with
H a regions (Smoot (1998)), and dedicated research is underway to investigate this corre­
lation (Jaffe (1997)). The Berkeley-Durham dust map (Schlegel et al. (1998)) combines
IRAS surveys at 100 gm and COBE-DIRBE surveys at 100 and 240 /jm , and has an
angular resolution of ~ 4'. From these measurements, it is clear th a t emission from these
sources falls off rapidly at latitudes above the galactic plane (for \b\ > 15°). MAXIMA
observes in low dust regions at lower galactic latitudes.
The last foreground of issue is emission from extragalactic radio and far-infrared
point sources. Higher resolution experiments are increasingly sensitive to this foreground.
In the far-infrared, point source foreground contributions dominate over diffuse galactic
foregrounds if the beam size of the experiment is smaller th a n 0.5° (Toffolatti (1995)).
By studying the IRAS 1.2 Jy survey, Gawiser k, Smoot (1997) have determ ined th a t the
infrared background is manageable at frequencies lower than 300 GHz, for experiments
with 10' or larger beams. One can account for foreground contributions from the largest
point sources (those w ith an effective tem perature greater th a n a few
) by removing
those pixels from the map in d ata analysis. Information on radio sources comes largely
from the VLA 1.5 GHz survey. It is difficult to extrapolate the microwave emission spec­
trum for extragalactic radio sources considering uncertainties in our knowledge of elliptical
galaxies and quasars. Optim istic estimates state th a t fluctuations from the extragalactic
radio background above 30 GHz, for experiments with 10' or larger beams, should be less
than 10~ 5 if 5cr events are first removed (Toffolatti (1995)).
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19
2.4.4
P olarization
Adiabatic inflationary models predict th a t the CMB is fractionally polarized,
with a rms polarization of 10% .
Thomson scattering produces a local polarization
quadrupole. Before recombination, CMB polarization anisotropy evolved via the same
pressure oscillations as tem perature anisotropy, and these gradients (E modes) are spa­
tially correlated with velocity-induced tem perature fluctuations (the Doppler peaks). De­
tection of the E modes would isolate the peculiar velocity of the the surface of last scatter.
Thomson scattering from global reionization occurs at smaller red-shifts, and boosts po­
larization anisotropy at large angular scales.
During inflation, quantum fluctuations in the spacetime m etric produced grav­
itational waves which introduced bo th a scalar and tensor component to the potential.
A tensor component would manifest itself as a curl (B modes) in the CMB polarization
spectrum. Observations of the B modes would give a direct confirmation of inflation.
The Doppler peaks in the polarization power spectrum are predicted to be a
factor of
102
smaller th an the density peaks in the tem perature polarization spectrum.
The B modes are predicted to be an order of magnitude smaller th an the E modes.
MAXIMA is designed to detect tem perature anisotropy, and has neither the sensitivity
nor the polarizers necessary to isolate and detect these weak signals. Experiments like
MAXIPOL, Boomerang-2002, DASI, POLARBEAR, MAP and Planck have the capability
of discovering and characterizing polarization anisotropy. MAXIPOL is a balloon-borne
bolometric polarim eter currently under development at UC Berkeley and the University
of Minnesota. We expect d ata from MAXIPOL in the spring of 2003.
MAXIPOL is
described in Rabii (2002) and Richards et al. (2002). Further discussion of the detectability
of polarization anisotropy can be found in Kamionkowski & Kosowsky (1998) and Jaffe
et al. (2 0 0 0 ).
2.5
M otivation for M A X IM A
Before MAXIMA, the CMB tem perature power spectrum had been measured
over a range of multipoles from 2 < I < 500. The COBE-DMR measurements continue
to be the best constraint on the power spectrum for I < 20. Results from concurrent
experiments such as MAX (Tanaka et al. (1997)) and Saskatoon (Netterfield et al. (1997))
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20
O b s e rv a tio n a l D ata on P u b lish ed CMB T e m p e r a t u r e F l u c t u a t i o n s t h r o u g h 1 9 9 8
1 0 0
80
^
60
p?
40
<0
20
0
1
10
100
1000
10000
Figure 2.6: Measurements of the CMB tem perature power spectrum through 1998: Shown
here are all published measurements of the rms CMB tem perature fluctuations, ST^eff with
l a errors, plotted as a function of effective multipole, £eff- Not shown is the w idth of the
multipole bin for each measurement. The combined measurements suggest a rise in power
for I > 50, a peak at I ~ 200, and hint at a decline in power at higher multipoles. These
d ata are reproduced from Novosyadlyj et al. (2000)
indicate th a t the power spectrum rises monotonically from 50 < I < 200, b u t give no
strong evidence for the existence of a density peak. See Figure 2.6 for a compendium of
measurements before MAXIMA.
A low-noise measurement of the power spectrum on sub-degree scales (I < 103)
would probe for the existence of multiple density peaks. Such a measurement can constrain
the set of viable cosmological models, can probe the Gaussianity of CMB tem perature
fluctuations and can place strong constraints on il , Ga , Cl^h2, n, and r c.
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21
C h a p ter 3
Instrum ental O verview
MAXIMA’S scientific mission is to measure the CMB power spectral density
from 50 < I < 1000 w ith errors of order ~ 10% in tem perature. This power spectrum is
computed from a map of roughly
100
square degrees w ith a resolution of
10
' as determined
by the beam size. The MAXIMA-1 map and power spectrum are shown in Figures 3.1 and
3.2, respectively. This measurement is calibrated using the CMB dipole as measured by
COBE and a solar system planet (Jupiter for MAXIMA-1 (1998) and Mars for MAXIMA-2
(1999)). It is uncontam inated by sidelobes or far-infrared and sub-millimeter foregrounds.
This is accomplished w ith the following strategy.
We use a balloon-borne telescope w ith an angular resolution of 10' and pointing
accuracy of 3' to make multi-color observations w ith a receiver of sensitive bolometers.
Maps are made from compact, cross-linked observations w ith deep integration on multiple
timescales. M ultiple observations are made w ith rapid turnaround. We give a descriptive
overview of the instrum ent in this chapter. The optics and detectors are described in
greater detail in Chapters 4 and 5. We discuss the scan strategy and observations in
Chapter
3.1
6
.
O ptics
The MAXIMA telescope is an off-axis Gregorian system, consisting three mirrors.
The prim ary mirror is a 1.3 m diameter off-axis section of a paraboloid. It is underfilled to
minimize sidelobes due to the diffraction at the edges. The secondary and tertiary mirrors
are off-axis ellipsoids
(21
and 18 cm in respective diameter) w ith aspheric corrections
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22
Figure 3.1: The Wiener filtered 10' resolution MAXIMA-1 map. This map is made from
the combined d ata of three 150 GHz and one 230 GHz detectors, and contains 15,000
5' x 5' pixels. Pixel boundaries have been smoothed using interpolation. This map is
taken from Hanany et al. (2000).
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23
The MAXIMA^ C o l l a b o r a t i o n
^Hanany e t al 3000)
M A X IM A -1
6000
B e s t f it Model
ACDM----*—1 4000
^
3000
0
200
400
600
800
1000
I
Figure 3.2: MAXIMA-1 power spectrum: Measurements of the power spectrum from
the combined map of three 150 GHz channels and one 230 GHz channels are shown
in red/filled circles w ith la error bars, overlayed w ith a best fit model (solid line) and
ACDM model (dotted line). The models have (fl&, Clcdm,
n, h) = (0.1,0.6,0.3,1.08,0.53)
and (0.05,0.35,0.1,1.0,0.65), respectively (Balbi et al. (2000)). The power spectrum of the
difference map of two 150 GHz channels is shown in blue/open circles, w ith lcr error bars.
This figure is taken from Hanany et al. (2000).
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24
CMB Photons
Primary Mirror
Cooled optics:
{Secondary & Tertiary
mirrors,
Lyot stop)
Horns
Band-defining
filters
Bolometer
JFET
Analog bias & readout
electronics
Data Acquisition System
Modulate & broadcast
data from balloon
Receive data
at Ground Station
Archive
Data
Real-time
display
Figure 3.3: Measurement of CMB signal: this block diagram outlines the detection and
telemetry of CMB signals. Information is communicated via three media: photons from
the sky (dotted line), analog and digital signals (solid line) and radio telem etry (dasheddotted line).
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25
which compensate for aberrations. They are baffled and cooled by pum ped liquid 4He to
reduce the optical load on the detectors. A 1 % neutral density filter can be inserted in
the optical p ath at the interm ediate focus, between the secondary and prim ary mirrors,
for tests using 300 K loads. See Figure 3.4 for a schematic of the optics.
During observations, the prim ary mirror is rotated in azim uth by a large dc servo
motor about the optical axis with an am plitude of 4° p-p, at a frequency of 0.45 Hz. The
position of the mirror is read by a Linear-variable-differential transform er (LVDT), and
the position is controlled by a proportional-differential feedback system.
We observe the CMB over a range of frequencies from 125-430 GHz, which covers
the peak of the CMB emission spectrum. The MAXIMA receiver has sixteen channels
in three frequency bands, allowing for spectral discrimination between the CMB and
known astronomical foregrounds. Eight channels have bands centered at 150 GHz, four
at 230 GHz, and four at 410 GHz, with bandw idths of 40, 70, and 30 GHz respectively.
The bands are shown in Figure 3.6, and the detector arrangem ent is shown in Figure 3.7.
The 10' FWHM beam is defined by a Lyot stop and by feedhorns leading to each
photometer. The secondary and tertiary mirrors, Lyot stop, and feedhorns are cooled
to 1.6 K in flight. The geometry of the feedhorns is determ ined by the frequency of the
photometer. In order to have beams with a full w idth at half m aximum (FWHM) of
10’, the 150 GHz channels are at the diffraction limit of the telescope. Correspondingly,
the feedhorns for these channels are single-mode smooth cones. The 230 and 410 GHz
channels allow for multi-moded feedhorns w ith a W inston geometry because of the Lyot
stop. The sidelobes of the feedhorns are not critical.
The band edges for each channel are defined by metal-mesh filters built at Queen
Mary and Westfield College, and are located between the feedhorns and the entrance
horns to the detectors. The low frequency edge of the 150 GHz channel band is defined
by the cutoff of the circular waveguide at the back of the feedhorn. High frequency leaks
in all channels are dangerous due to the rising emission spectrum of the atmosphere and
galactic dust. Three additional filters (two metal-mesh and one alkali-halide embedded
in polyethylene) are used to block resonant high-frequency leaks through the metal-mesh
filters.
The filter and detector assemblies are built into an aluminum plate cooled to
100 mK, which is supported by three low therm al conductive Vespel SP-22 plastic tubes
mounted to a 1.6 K coldplate. The feedhorns are supported by an aluminum plate cooled
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Mirror Rotation Axis
Figure 3.4: MAXIMA optics: A cross-section of the prim ary mirror and receiver. Ra­
diation from the sky reflects off the prim ary mirror and enters the cryostat through a
2.5 /rm thick polypropylene window. It then reflects off baffled secondary and tertiary
mirrors th a t are cooled to 4 K by liquid 4He in flight. The FWHM beam size of 10’
is defined by a cooled Lyot stop and feedhorns leading to each of the 16 single-color
photometers.
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27
to 1.6 K. A 0.5 mm gap separates the two plates. The 100-mK side of the gap is covered
with absorber to prevent stray light from entering the detectors. A photograph of the
feedhorns and the array is shown in Figure 3.5.
3.2
D etectors
The detectors are absorber-coupled semi-conducting bolometers. The detector
element is made from neutron transm utation doped germanium (NTD), a semiconducting
material whose electrical resistivity varies as R oc exp —y / A / T , where T is the bolometer
tem perature.
The NTD chips are mounted on metalized silicon nitride (SiaN ^ mesh
absorbers. The absorbers have a spider-web geometry which reduces the cross-section of
cosmic-ray hits by two orders of magnitude, and are built using optical lithography (Bock
et al. (1995)). The bolometers have measured time constants of order
t
~ 10 msec. The
fast response time is necessary to prevent the distortion of signals by the rapid prim ary
mirror m odulation. In addition to the sixteen optical photom eters, the MAXIMA receiver
has three dark channels used to m onitor noise during flight. The performance of these
detectors will be described in more detail in C hapter 5.
The bolometers are AC current biased to avoid 1/ f noise in the amplifiers. The
frequency is tunable from 200 to 500 Hz, and is set to avoid microphonic resonances
in the system.
The bias am plitude is tunable for each channel. Typical currents are
~ 1 nA. The bolometer signals are first amplified by cooled JF E T amplifiers inside the
cryostat.
This reduces the output impedance of the bolometers, which minimizes the
microphonic sensitivity of the receiver. The signals are further amplified and rectified in
analog electronics outside of the cryostat. The detector signals are protected from stray
radio frequency interference (RFI) w ith a variety of filters. A more detailed description of
detector signal processing and RFI filtering is found in C hapter 5.
We perform two absolute calibrations of the detectors in flight. Observations of
the CMB dipole provide an absolute calibration of the 150 and 230 GHz channels th a t has
the same spectral morphology as the CMB tem perature anisotropy, and is independent
of beam shape. We measure beam patterns for all channels in flight and calibrate the
410 GHz channels by mapping a bright solar system planet.
A relative calibration is
obtained during CMB anisotropy observations by periodically flashing an internal optical
stim ulator directly into the feedhorns. The stim ulator is a composite bolometer used in
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28
Figure 3.5: Photograph of feedhorns and bolometer array: T he feedhorns (top of pho­
tograph) are assembled into a gold-plated aluminum plate supported by three aluminum
legs. The band-defining m etal mesh filters and bolometers for each photom eter are stacked
inside aluminum holders (bottom of photograph). The holders are assembled into a goldplated aluminum plate th a t supported is by three thin-walled Vespel SP-22 legs. The
horn and bolometer arrays are separated by a 0.5 mm gap at room tem perature. The cold
JF E T amplifier modules are shown behind and to the right of the feedhorns.
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29
1.5
1.0
2 . 7 3 K blockbrfdy
0 .5
1 p 0 GHz
410
2 3 0 GMz
0.0
0 .5
0
200
100
300
400
F r e q u e n c y [GHz]
500
600
Figure 3.6: MAXIMA observation bands: Shown above are the m easured normalized spec­
tral response transm ission spectra for a detector of each color. The solid curve represents
a 2.73 K blackbody. The spectra were measured before flight w ith a Michelson Fourier
interferometer.
150 GHz
230 GHz
410 GHz
J J O CO101
•too
• JO O
2.5 cm
Figure 3.7: MAXIMA focal plane: The schematic above illustrates the layout of the
sixteen sky beams on the focal plane. They are arranged in a 4 x 4 grid, covering roughly
1 deg 2 on the sky. There are eight 150 GHz photom eters (dark blue/black), four 230 GHz
photom eters (white), and four 410 GHz photom eters (light blue/grey). The nominal
FWHM of each photom eter beam is 10’. During flight, the prim ary mirror scans in
azimuth, which moves the focal plane across the sky.
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30
Stage
Liquid N 2
Liquid 4He
3He sorption
ADR
Base Temp.
(K)
~ 60
0.300
Holdtime
(hours)
36
42
36
0 .1 0 0
12
1 .6
Table 3.1: Base tem peratures and holdtimes for the MAXIMA cryostat measured in flight:
The MAXIMA receiver has a flight hold-time of 36 hours at 300 mK and 12 hours at
100 mK. The ADR can be cycled remotely during flight, with a duty cycle of roughly 80%
(3 hours to cycle for 12 hours of holdtime).
emission whose bias current is stable w ithin 0.1%. More details on calibration are found
in C hapter
3.3
6
.
T he C ryostat
The detector array is cooled to 100 mK during flight via a four-stage refrigeration
process. The array is housed inside an evacuated cryostat, and is cooled by an adiabatic de­
m agnetization refrigerator (ADR), which dumps its heat to a single-shot charcoal-pumped
elosed-cycle 3He sorption refrigerator, a pum ped liquid 4He bath, and a pum ped liquid N 2
bath. The ambient tem perature of the outside of the cryostat during flight is ~
200 K.
The cryostat can m aintain a base tem perature of 100 mK for twelve hours, and 300 mK
for 36 hours (see Table 3.1). The ADR is a Ferric Am m onium Alum (FAA) salt pill, and
a Nb-Ti magnet generates 2.5 T for a peak current of 6.2 A. T he ADR can be cycled
remotely during flight. The 3He refrigerator and the ADR will be described in more detail
in Appendix B.
The cryostat was m anufactured commercially by Infrared Laboratories (model
HDL14). It has an outer diameter of 15.95 inches and a length of 44.3 inches. Liquid N 2
and 4He are held in 13 and 20 liter stainless steel wall tanks, which are structurally
supported by G-10 stand-offs. The coldplate for each tank is made of 0.75 inch thick
gold-plated OFHC copper, which provides excellent therm al contact.
The cryostat houses the array of detectors, the secondary and tertiary mirrors,
the Lyot stop, the feedhorns, the detectors, the 3He refrigerator and the ADR. The optical
entrance to th e cryostat is vacuum sealed w ith a 25 pm polypropylene window. Gaseous
4He which permeates through the window is trapped by an activated charcoal “getter”
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31
th a t is cooled to 1.6 K in flight. The detectors are wired with low therm al conductivity
51 fim diam eter 5 cm long platinum -tungsten (Pt-W ) wire varnished to G-10 straws to
minimize microphonic response. A modular “wire insert” carries all wiring from 300 K to
the liquid 4He coldplate at 1.6 K. More details on the therm al design of the wiring can be
found in Appendix B.
3.4
D ata A cquisition
Once the analog bolometer signals are amplified and rectified, they are digitally
sampled and inserted into a d ata frame which is broadcast during flight at a rate of one
frame per 19.6 msec from the payload to a ground station via a 1.8 GHz downlink. House­
keeping d ata including instrum ent tem perature readouts, two prim ary mirror position
sensors, and voltage and current monitors for the bolometer readout and d ata acquisition
electronics are also incorporated in the frame. Each bolometer output is sampled four
times per frame. The stages of bolometer signal processing are diagrammed in Figure 3.3.
3.5
G ondola and B alloon
The telescope, receiver, electronics, and power are all housed in a gondola th a t is
shown in Figure 3.8. It measures 4.5 m in height (from floor to pivot), and has a footprint
of ~ 2 x 2 m. The gondola is constructed of lightweight aluminum angle and honeycomb
paneling. The entire scientific payload is designed to w ithstand inertial loads of 10 g when
the parachute opens. It weighs 3600 lbs without ballast.
The inner frame of the gondola supports the cryostat, the prim ary mirror, and
the prim ary m irror modulator.
The inner frame can rotate in elevation w ith respect
to the rest of the gondola, and is controlled by a dc servo motor and ball screw. The
outer frame of the gondola provides the mechanical framework for two electronics boxes,
batteries, pointing sensors, the pivot and two reaction wheels. The two electronics boxes
contain the attitu d e control, d ata acquisition, and command electronics. The experiment
is powered in flight by lithium battery packs which are housed at the bottom of the gondola.
Rollbars and paneling make up the outerm ost layer of the gondola. The rollbars protect
the innards of the gondola from damage upon landing. The paneling is constructed from
lightweight aluminum coated builders foam. It protects the receiver from stray optical
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32
and RF radiation. The paneling is not shown in Figure 3.8.
The payload is flown on a balloon-borne platform designed for ~ 12 hour night­
time N orth American flights. Such observations require 1-2 months of field preparation
once the instrum ent is built, and consume less resources and manpower th an a satel­
lite mission. It is possible to fly the telescope and observe once a year, w ith time for
instrum ental upgrades between flights.
The 40-million cu ft zero-pressure balloon is made of polyethylene film and is
m anufactured by Raven Industries (U.S.A.). The balloon is filled w ith ~ 107 STP liters of
4He gas. At launch, the 4He gas occupies a small fraction of the balloon volume because
of the atmospheric pressure at sea level. The payload typically achieves a float altitude of
125,000 ft. The balloon and pivot are connected with a long flight line which consists of a
parachute and a steel cable ladder th a t is designed to provide significant torsional rigidity
during flight.
3.6
T he A ttitu d e Control System
In order to achieve the desired angular resolution, the telescope requires pointing
control of ~ 3' to avoid significant smearing of the 10' beams.
The orientation of the telescope is controlled by the attitu d e control system
(ACS). The ACS also provides detailed attitu d e information used for pointing reconstruc­
tion. This system is a feedback controlled loop w ith four m ain components: pointing
sensors, a central feedback-loop computer, pointing actuators, and d ata relay. The central
processor controls the pointing actuators using information from pointing sensors. The
feedback loop is diagrammed in Figure 3.9.
The telescope’s attitu d e is m odulated by two azim uth control motors, a linear
actuator, and passive pendulation dampers. One azim uth control motor drives a reaction
wheel and the other drives directly against the flight line. The feedback of the reaction
wheel motor is proportional to azimuthal velocity measured by an azim uthal rate gyro­
scope. The feedback of the direct drive motor is proportional to the reaction wheel velocity
as measured by a tachometer. A ball screw and small dc servo m otor control the angle
between the inner and outer frames of the gondola, and thus controls the elevation of
the telescope. The elevation range of the telescope is 20° to 50°. Pendulations during
flight are stabilized with two passive dampers, whose resonance frequency is set to the
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33
Figure 3.8: MAXIMA gondola: The telescope, cryostat, electronics, and batteries are all
housed in a gondola, which measures 4.5 m in height, and has a footprint of ~ 2 x 2 m.
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34
0.6 Hz rocking frequency of the gondola. These dampers, built by the Geneva Observa­
tory (Switzerland), consist of a spherical weight rolling in a spherical cup in an oil-filled
vessel.
Two CCD video cameras, three rate gyroscopes, and a m agnetometer measure the
attitu d e of the telescope. Most of these sensors provide feedback inform ation to control the
azimuth of the gondola. For both MAXIMA flights, the feedback controlling the elevation
of the telescope was disabled. The CCD cameras can track two stars each, down to
6
th
magnitude. The CCD images are processed on-board by a pressure-cooled video digital
signal processor (DSP). The camera with the 14.34 x 11° field of view and ~
1
' sized pixels
tracks Polaris. This information is fed back into the control loop. The other camera is
boresighted w ith the telescope at the center of the scan, and tracks stars in the observing
region. It has narrower field of view of 7.17 x 5.5° w ith 0.69' sized pixels. Information from
this higher resolutions camera is used exclusively for pointing reconstruction. Three rate
gyroscopes measure accelerations of the gondola, which are fed back into the control loop.
A two-axis magnetometer is used for pointing reconstruction during azim uthal rotations
which are used to calibrate from the CMB dipole.
D ata from the pointing sensors, actuators, and the feedback loop processor are
inserted into a frame sampled every 96 msec, which is sent to the ground station during
flight via a 2.4 GHz downlink. Raw video images from both CCD cameras are broadcast
via a 2.4 GHz downlink and images from the DSP are transm itted via a 1.8 GHz downlink.
The performance of the ACS is described in detail in Rabii (2002).
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35
Reconstruction and Feedback sensors
: Star sensors
: (2 CCD cameras)
|
&
1 Digital Signal
j
Processor
i
:
!
j
j
f------------------ j
j Rate Gyroscopes j
f
j Magnetometer j
’------ 1---1
------- 1
'
Elevation angle
encoder
Feedback Loop
Controller
CPU
D-
j Reaction wheel
IP
Elevation
drive
Actuators
S Azimuth control
___ J
Attitude Control Ground Station
Elevation control
Figure 3.9: A ttitude Control System: this block diagram outlines the m ajor functions of
the telescope pointing
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36
C h a p ter 4
O ptics
In order to achieve the desired sensitivity to CMB tem perature fluctuations up
to multipoles of I ~ 1000, the beams must have 10' full width at half maximum (FWHM).
To facilitate d ata analysis, the beams must have a symmetric Gaussian profile along any 1dimensional cut and should all have a uniform shape across the array and over all observing
bands. To make sure th a t local sources such as the earth, the moon and the balloon do not
contam inate the measurement, we require a near- and far-sidelobe response of ~ —20 dB
at 2 degrees off the center of the beam, and ~ —60 dB at 30 degrees off the center of the
beam.
We require cooled, baffled secondary and tertiary mirrors and feed horns to
minimize the loading on the bolometers.
To minimize cryostat size, we require fast,
compact optics designed without excessive geometrical aberrations. We place the aperture
(Lyot) stop of the telescope w ithin the cryostat, which apodizes the illum ination of the
prim ary mirror and term inates the excess detector field of view at ~ 3 K. We also require
feedhorns which optimize beam shape without compromising focal plane geometry and
mapping speed, and band defining filters with no appreciable high or low frequency leaks.
The end-to-end optical efficiency of the telescope and receiver should be as high
as possible. We also require a 1% transm itting neutral density filter (NDF) to facilitate
laboratory tests w ith a 300 K background.
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37
Source
CMB
Prim ary Mirror
Atmosphere
Optics Box
Total
-P i 50
P230
P410
[pW]
0.16
0.25
< 0 .0 1
[PW]
0.16
0.83
< 0 .0 1
0.16
1.15
[pW]
0.025
2.15
2.15
0.05
4.38
0 .1 2
0.53
Table 4.1: Predicted optical load during flight for the three CMB bands, the prim ary
mirror, the atmosphere at 125 kft and the optics box (which consists of the secondary
and tertiary mirrors, the Lyot stop, the feedhorns and blackened baffles). The calculated
emissivity of the aluminum surface of the prim ary mirror at T = 250 K is 0.5 ± 0.1% over
the entire set of observation bands.
4.1
M A X IM A O ptics
The Telescope
The MAXIMA telescope is an off-axis Gregorian system, consisting of a 1.3 m
diameter underfilled prim ary mirror with cooled, baffled ellipsoidal secondary and tertiary
mirrors. The reimaging optics are cooled to reduce the instrum ental optical load on the
bolometers, which is necessary to achieve the required sensitivity. We cool all optical
elements except the prim ary mirror and the cryostat window. Table 4.1 shows th a t the
CMB contributes a significant fraction of the expected total optical load for the 150 and
230 GHz channels as long as the prim ary m irror is underfilled and has low emissivity and
the subsequent optical elements are cooled.
The prim ary mirror is a off-axis section of a paraboloid. It has an off-axis angle
of 38° and a focal length of 1.3 m from the center of the m irror to the prim ary focus.
The m irror was constructed by Dornier Satellitensysteme (Germany) from a light-weight
graphite-epoxy honeycomb to facilitate m odulation (as discussed in C hapter 6 ) and weighs
~ 20 kg. The reflecting surface is a thin layer of sputtered aluminum. The mirror was
fabricated from the p attern made for the 3m Cologne mm-wave telescope to reduce fab­
rication costs. As a result, the off-axis angle is larger than optim al, b u t this has been
compensated for in the design of the secondary and tertiary mirrors.
During observations, the prim ary mirror is rotated in azim uth by a dc servo mo­
tor and solid state PID controller about the optical axis with an am plitude of 4° p-p at a
frequency of 0.45 Hz. The position of the mirror is read by a Linear-variable-differential
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38
transformer (LVDT). The motor was purchased commercially, and the controller was de­
veloped at UC Berkeley.
The choice of a reimaging system was driven by a need for a cooled aperture
(Lyot) stop.
We also create a well baffled intermediary focus w ithin the cryostat by
adding two cooled mirrors with ellipsoidal surfaces to the telescope before the cooled Lyot
stop and feedhorn coupled photometers. A cross section of the cooled optics along w ith a
geometrical ray diagram are shown in Figure 4.1. This fast Gregorian system also has the
advantage of b etter sidelobe rejection than a Cassegrain system of similar dimensions.
The focal ratio is / = 1.5 at the opening of the feedhorns. The focal plane has an
area of ~ 1 x 1°. We used CODE 5 (a software package by Optical Research Associates)
to simulate the optical design, which allows us to investigate geometrical aberrations. We
introduced aspheric corrections to the ellipsoidal surfaces of the secondary and tertiary
mirror. We minimized the geometrical spot diagram using the diffraction Airy pattern at
150 GHz as a figure of merit.
The secondary and tertiary mirrors have respective diam eters of 21 and 18 cm.
They are diamond turned from solid aluminum which gives an optical quality surface. The
back of each mirror is lightweighted to reduce the mass and heat capacity of the cooled
optics. The mirrors were manufactured by Speedring Systems (U.S.A.).
The secondary and tertiary mirrors are housed in a baffled optics box within the
MAXIMA cryostat, which is cooled to ~ 4 K by liquid 4He during flight. The interior
baffles of the optics box are blackened w ith a ~ 0.5 cm thick layer of combined Stycast
2850 F T black epoxy, carbon lampblack, and 175 /im diam eter glass beads, which has
been dem onstrated to be an effective far-infrared absorber (Bock (1994)).
The image of the beams covers an area of 1° square on the sky, and consists of
a 4 x 4 array of sixteen 10' FWHM gaussian beams. See Figure 4.2 for a schematic of the
beams on the sky.
The MAXIMA telescope has three foci; one at the entrance of the cryostat be­
tween the prim ary and secondary mirrors, one between the secondary and tertiary mirrors,
and one at the entrance of the feedhorns. The focal plane has significant curvature. We
account for this in the placement of the feedhorns.
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39
3He Fr idge •
THe Tank
ADR■Opti cs Box
Bolometers
S u p p o r ts
100 mK Stage
-Feed Horns
Secondary■
— Lyot
Stop
■Terti ary
Pr im e Focus
Figure 4.1: Cross-section of cooled optics and photometers: Light enters the bottom of
the cryostat through a thin polypropylene window, then reflects off a cooled secondary
and tertiary mirror. A cooled Lyot stop apodizes the illum ination of the prim ary mirror.
Light is detected by 16 feedhorn-coupled single channel photom eters. The band defining
filters and bolometers are cooled to 100 mK by an adiabatic dem agnetization refrigerator
(ADR).
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40
150 GHz
230 GHz
410 GHz
• 'JOO>
•too
•
t
o
o
I-----------------
1
2.5 cm
1
1
Figure 4.2: MAXIMA focal plane: The schematic above illustrates the layout of the
sixteen sky beams on the focal plane. They are arranged in a 4 x 4 grid, covering roughly
1 deg 2 on the sky. There are eight 150 GHz photom eters (dark blue/black), four 230 GHz
photom eters (white), and four 410 GHz photom eters (light blue/grey). The nominal
FWHM of each photom eter beam is 10'.
Lyot Stop
We locate the liquid 4He cooled Lyot (aperture) stop after the tertiary mirror
and before the entrance to the photom eters to apodize the illum ination of the prim ary
and to term inate the excess field of view at ~ 3 K. The Lyot stop is fabricated from a
0.25 inch thick sheet of Eccosorb MF-124, a commercially available microwave absorber
manufactured by Emerson & Cuming Microwave Products (USA). Eccosorb MF-124 is
a machinable solid composite of epoxy and iron particles. The absorptive properties of
Eccosorb are quoted in Halpern et al. (1986). We require this thickness of m aterial to
achieve adequate absorption of excess radiation.
The Lyot stop has an elliptical opening w ith semi-major and semi-minor axis
lengths of 2.04 and 1.75 cm. We achieve a well focused beam despite the thickness of the
material by tapering the opening to a knife edge at an angle of 30 degrees. The tapered
face points towards the sky and is covered w ith a layer of
0 .0 0 1
inch aluminum foil which
reflects radiation th a t would otherwise be transm itted through the thinnest section of the
taper. The Lyot stop is mounted on a blackened 0.030 inch thick aluminum baffle.
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41
Feedhorns
We use a feedhorn coupled array as compared to a bare pixel array to better
shield the bolometers from instrum ental optical load and from RFI. Feedhorn coupled
arrays are inherently easier to use in fast optical systems. The tradeoffs are discussed in
greater detail in Griffin et al. (2002).
The optical signal from the sky is fed to 16 individual photom eters through
back-to-back circular aperture copper feedhorns. The antenna p attern of a feedhorn is de­
term ined by the cross sectional geometry of the walls and the opening diameter. The angle
of the feedhorn walls strongly influences the beam profile. At 150 GHz, 10' FWHM beams
are at the diffraction limit of the telescope. Consequently, we use single mode straight
wall feedhorns at 150 GHz. The theoretical beam patterns for a single-moded straight
wall feedhorn are well understood (Olver et al. (1994)). The higher frequency channels
are multi-moded, and have W inston feedhorns. The properties of W inston feedhorns are
explained in Welford & W inston (1978). All feedhorns are designed to create 10' FWHM
beams. The MAXIMA straight wall and W inston feedhorns are shown in Figure 4.3.
The opening diam eter of the feedhorns is quantified in term s of N F X , where
A is the wave length of observation, F is the focal ratio (f-number) at the focal surface
opening and N is a numerical factor. F is determ ined by the beam FWHM and the
reimaging scheme. A is fixed for a given observation. The larger N is, the b etter control
one has in defining the beam. However, increasing N will separate the beams centers in
the sky, which degrades spatial sampling. We have chosen N F X = (6.10:4.47) mm for
the (150:230) GHz channels ( N ~ 2). The telescope scan p attern is chosen to ensure
overlapping observations with large degeneracy, as discussed in C hapter
6
.
We use back-to-back feedhorns to collimate the radiation before filtering. In
doing so, the signal b etter approximates a plane wave, which is easier to filter.
The feedhorns are fabricated by machining aluminum mandrils of the interior
surface. The mandrils are then electroplated with copper, and the aluminum is etched
away in a b ath of NaOH. The exterior surfaces of the copper feedhorns are then trim m ed
on a lathe, and the interior surface is polished.
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42
Figure 4.3: Cross-section of 150 GHz (left) and 230 GHz (right) back-to-back feedhorns:
Radiation from the sky enters the feedhorns from the top, with respect to the schematic.
The 150 GHz channels are diffraction limited, and have straight-walled feedhorns. The
230 GHz and 410 GHz (not shown) channels have a multi-moded W inston geometry. All
feedhorns produce 10' FWHM beams given a properly focused telescope. After the beam
defining portion at the top, the feedhorns expand to collimate the radiation before filtering.
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43
F re q u e n c y Bands and Filters
MAXIMA observes in frequency bands at 150, 230 and 410 GHz. The 150 and
230 GHz bands are prim arily used to measure the CMB. The 410 GHz band monitors
emission from the atmosphere, galactic dust, and extragalactic infrared point sources.
D ata from all three observation bands can be used to discriminate spectrally between
various signal sources.
MAXIMA’S frequency bands are prim arily defined by metal-m esh filters located
between the feedhorns and the bolometers. The 230 and 410 GHz channels have both
high-pass and low-pass metal-mesh filters. The 150 GHz channels only have a low-pass
metal-mesh filter. The section of circular wave guide between the back-to-back straight
cones acts as a high-pass filter.
The filters are built from thin metallic meshes supported on Mylar film substrates
by P. Ade at Queen Mary and Westfield College, London. The transm ission of the filter
is determined by the p attern and geometry of the film, and the number and spacing of
the stack of meshes. A th in copper substrate is evaporated onto a ta u t ~ 1.5 /jm thick
ta u t Mylar sheet suspended on a stainless steel ring. The m etal is patterened via photolithograpy in either a capacitive (low pass), inductive (high pass), or resonant (band
pass) geometry. The steepness of the cutoff is improved by stacking multiple meshes sepa­
rated by Ao/4, where Ao is the cutoff frequency of the filter. These filters can be repeatedly
cryogenically cycled w ithout any stress fractures or significant performance change. They
have been dem onstrated to have high transm ission and sharp cutoffs (Lee (1997)).
The band defining filters leak slightly at harmonics of the cutoff frequency due to
Fabry-Perot fringing. Three low-pass filters between the cryostat window and the entrance
to the feedhorns fill in the tranmissive gaps in the spectra of the band defining-filters, and
provide overall rejection at higher frequencies. Two of these filters are low-pass metalmesh filters with cutoffs at 480 and 570 GHz. The last is an alkali-halide filter, and has a
cutoff frequency of 1650 GHz.
Detector Backshort
After the signal from the sky is filtered, it is concentrated by a W inston horn and
detected by the bolometer. The bolometers are suspended in resonant optical cavities with
a characteristic depth of A0&s/4, created by a flat brass backshort. In laboratory tests, we
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44
determined th a t the flat A/4 backshorts yield higher optical efficiencies th an spherical or
tilted backshorts.
Neutral Density Filter
We place a 1% transm itting neutral density filter (NDF) at the interm ediate focus
between the secondary and tertiary mirrors for optical tests w ith a 300 K load. The NDF
is made by evaporating a thin continuous metal film onto a ta u t Mylar sheet stretched over
a stainless steel ring, and was provided by P. Ade of Queen Mary and Westfield College,
London. The NDF is mounted on an aluminum slider which can be manually moved in
and out of the beam. The slider is pulled by a steel cable which is driven by hand with a
vacuum-sealed linear actuator during cryogenic tests.
4.2
Pre-flight C haracterization
We measure the spectral response and optical efficiency of each channel in the
laboratory before flight to characterize the instrum ent and to diagnose potential problems.
We measure the beams and the far-sidelobe response of each channel ju st before flight in
order to verify proper focusing and baffling of the telescope.
4.2.1
S p ectral S en sitiv ity
We measured the transm ission spectrum of each channel in the array before the
flight of MAXIMA-1 to verify performance of the band defining filters. The transm ission
spectra enable us to check th a t our observations are spectrally consistent w ith the CMB
and inconsistent w ith other astrophysical foregrounds. They are also used to check the
consistency of calibrations from the CMB dipole and a solar-system planet.
We measure the optical response of each photom eter w ith a Michelson Fourier
spectrom eter which is described in Richards (1967). The output signal of the spectrom eter
is chopped at 7 Hz so th a t signals appear above the 1 /f knee in the bolometer noise. We
couple the output of the spectrom eter to the cryostat with a brass light pipe, which can
be positioned in front of the cryostat window for maximum signal. Bolometer signals are
rectified w ith a lock-in amplifier referenced to the chopped o utput of the spectrometer.
The spectrum as a function of frequency is computed for each channel in the MAXIMA
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45
to
c
2 . 7 3 K b ia ck bg d y
<
>,
0.5
cQ)
to
C
o
u
>0 GHz
2 3 0 Gmz
0.0
CL)
CL
CO
0.5
0
100
200
300
400
F r e q u e n c y [GHz]
500
600
Figure 4.4: MAXIMA observation bands: Shown above are the measured normalized spectral response transm ission spectra for a detector of each color. The solid curve represents
a 2.73 K blackbody. The spectra were measured before flight w ith a Michelson Fourier
interferometer.
receiver from the measured interferograms. We then measure the ou tp u t spectrum of the
spectrom eter and lightpipe w ith a separate detector which is designed to have a frequency
independent responsivity. It is a composite NTD bolometer cooled to 4 K. The ratio of
these spectra gives our best estimate of the frequency dependence of the responsivity of
MAXIMA.
We measure the spectral response from 4.8 GHz to 1.2 THz, w ith a resolution of
4.8 GHz. One such spectrum from each of the three frequency bands is shown in Figure
4.4. The noise in the spectrum rises significantly below 90 GHz and above 1 THz due to
the reduced efficiency of the beam splitter. We also see increased noise at 540 GHz due
to a strong water absorption line. We estim ate a statistical error of 2% for the 150 GHz
bands, 14% for the 230 GHz bands, and 7% for the 410 GHz bands.
The spectral response for all photometers of a given frequency band are morpho­
logically similar. The band widths for each color, averaged over each set of photometers,
are listed in Table 4.2.
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46
Vnom
< U l >
[GHz]
150
230
410
[GHz]
124
199
393
< Au >
[GHz]
40
59
30
<Vh>
[GHz]
164
258
423
Table 4.2: MAXIMA observation bands: Listed are the FWHM frequencies (vi) and
(vh) and the bandw idth (A u) averaged over each set of detectors of a given nominal
mean observation frequency (vnom), as measured before MAXIMA-1. Note- the bands are
referred to by their nominal band centers. The measured band centers may vary. In the
case of the 150 GHz channels, the measured bands are asymmetric, leading to a slight
underestim ate in the frequencies of the band edges.
4.2.2
O ptical Efficiency
The ratio of optical power detected to th a t which enters the telescope is less than
unity. We call this frequency dependent quantity the optical efficiency, e(i') . The total
optical power detected,
P d etected
P d etected
= AQ
, can be expressed as
f e(v)I{v)dv = A n
JV
< e(u) >
f
J VI
I {v) d v ,
(4.1)
where AQ is the throughput of the telescope (0.0041 cm2Sr for MAXIMA) and I{v) is the
spectral intensity of the observed source. The average optical efficiency is defined between
FWHM frequencies ui and
In the laboratory, we determine the average optical efficiency, < e(v) >, for each
channel over its effective bandwidths. Using the NDF to avoid saturation, we measure
the load curve of each bolometer (R\,0io vs’ Pelec) w ith a 300K optical load filling the
throughput. We repeat the same measurement w ith a 77K load.
The resistance of the therm istor is determ ined by the bolom eter tem perature
which depends on the the sum of the electrical and the optical power which is absorbed.
We assume th a t for points of equal resistance on the two load curves, the bolometer is
heated by equal power. The difference in measured electrical power for this resistance
is the same as the difference in detected optical power. We calculate the power which
enters the photom eter from a given optical load, assuming an effective bandw idth and a
throughput. From these numbers and the measured transm ission spectra of each channel,
we can calculate the average optical efficiency for each channel of the array.
We only measure the optical efficiency of the bolometers and the telescope ele-
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47
Channel
b l4
b l5
b24
b25
b34
b35
b44
b45
< v>
[Hz]
150
150
150
150
150
150
150
150
< e(F) >
[%]
18.4
8.4
Channel
2 0 .2
2 2 .8
14.2
-
16.8
15.0
b l3
b23
b33
b43
b l2
b2 2
b32
b42
< v>
[Hz]
230
230
230
230
410
410
410
410
< e(^) >
[%]
3.9
13.9
9.6
24.2
3.8
3.9
3.9
5.6
Table 4.3: Optical efficiencies for MAXIMA bolometers: This table lists the mean observa­
tion frequency (< u >) and mean optical efficiency (< e(v) >) for each channel measured
before MAXIMA-1. D ata are missing for the one channel which was not functioning at
the time of the measurement.
ments th a t are w ithin the cryostat as it is im practical to fill the prim ary mirror with a
calibrated diffuse source. The prim ary mirror has an absorptivity of order 0.5% over all
observation bands, and should degrade the overall optical efficiency minimally.
We made this series of measurements twice before MAXIMA-1. Between mea­
surements, we polished the feedhorns and implemented the detector backshorts to improve
the optical efficiencies. The efficiencies achieved are listed in Table 4.3. The optical effi­
ciency degrades w ith increasing frequency of observation. We are not concerned about the
low numbers for the 410 GHz channels as the spectral intensity of all astronomical sources
of interest (dust, atmosphere, planets) rises w ith increasing frequency and are predicted
to generate detectable signals even with ~ 5% efficiency.
4.2.3
Focusing
The telescope is focused through proper alignment of the prim ary mirror with
the cryostat. The cryostat houses the remaining optical elements (secondary and tertiary
mirrors, Lyot stop, the feedhorns and the photometers, as show in Figure 4.1). The prime
focus of these combined elements is at the optical entrance into the cryostat.
Focusing is achieved by bringing the prime foci of the prim ary mirror and the
cryostat together along a unique optical axis.
The mounting plate of the m irror was
located by the m anufacturer to be perpendicular to a line passing through the prime focus
of the primary. We can establish the location of the prime focus of the cryostat on a
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48
similarly perpendicular “lens cap” th a t can be mounted on the window. We check the
relative alignment by measuring the distance and angle between the m ounting plate and
the “lens cap” w ith a focusing bar and a laser.
We then measure the two-dimensional beam profiles of each channel in the array
by performing a raster scan with the telescope over a 7' diameter source. The source is a
halogen lamp mounted at the at the focus of a 1 m diameter / / I paraboloid mirror. The
source is chopped at 5 Hz so th a t signal appears above the 1 /f knee in the bolometer signal
bands. We create the beam profiles by combining bolometer d ata w ith sensor d ata from
the gondola elevation encoder and the prim ary mirror azim uth encoder (LVDT). We focus
the telescope iteratively until 10' FWHM beams are measured in lab (taking in account
the diameter of the halogen source). We estim ate an approxim ate uncertainty of 2' in this
process.
4.2.4
Far-sidelobe M easurem ents
We measure the far-sidelobe response of the telescope before flight to verify that
sources such as the earth, the moon, the balloon, and the gondola will not contaminate
our measurements of CMB tem perature fluctuations.
We aim a 150 GHz 20 mW Gunn oscillator at the assembled and baffled payload
from a distance of ~ 20 m. The oscillator is chopped at 7 Hz so th a t the signal appears
above the 1/ f knee in the bolometer signal band. We carry out the measurement outdoors
to minimize secondary reflections off building walls. This was b etter accomplished for the
measurement before MAXIMA-2 th an before MAXIMA-1. We measure the far-sidelobe
response in bo th elevation and azimuth.
Before MAXIMA-1, the source was mounted on the top of a 35 m building for
sidelobe measurements as a function of elevation angle. Before MAXIMA-2, the source
was mounted at the end of the arm of a “cherry picker” truck, as shown in Figure 4.5.
We scan the telescope in elevation with the source a fixed angle and distance from the
payload.
M easurements as a function of azim uth were carried out as follows; we aimed
the source at the telescope at a fixed elevation. We varied the azim uthal position of the
source by driving the “cherry picker” around the gondola in a circle of fixed radius, without
varying the height or angle of the source.
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49
Figure 4.5: Photograph of far-sidelobe measurement before MAXIMA-2. The 150 GHz
source is mounted to the edge of the basket of a “cherry picker” truck, allowing us move
the source in both azim uth and elevation around the assembled and baffled payload. We
make the measurement outside, as far as possible from structures th a t could contaminate
the measurement w ith secondary reflections.
The response of the bolometers is linear for signal changes less th a n 20 dB. We
attenuate the o utput of the source with both a dial-attenuator and
1
inch thick sheets
of plywood to keep the response linear over the 80 dB range of the measurement. We
corrected for the attenuation of the source by measuring bolometer voltages before and
after each change in attenuation at a fixed angle.
The far-sidelobe response of the telescope measured prior to MAXIMA-1 and
MAXIMA-2 are shown in Figures 4.6 and 4.7. For MAXIMA-1, the telescope response
in elevation drops by 20 dB at 2 degrees and 40 dB at 5‘degrees, w ith a noise floor of
-50 dB. In azimuth, the response drops symmetrically by 40 db at 10 degrees and 60 dB at
30 degrees, and below the noise of -75 dB at 60 degrees. We suspect th a t the rise in power
at +180 degrees is due to reflections off a nearby building. For MAXIMA-2, the telescope
response in elevation drops by 20 dB at 2 degrees and 40 dB at 5 degrees, w ith a noise
floor of -60 dB. In azimuth, the response drops symmetrically by 40 db at 10 degrees and
60 dB at 20 degrees, and tapers off to -78 dB at 180 degrees. See Figure 4.7 for a plot of
the measurement.
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50
o
-10
-30
-40
-20
-30
-4 0
-70
•50
-5
-10
-1 5
0
El ev at io n Angle f r o m s o u r c e [ d e g . ]
-200
-1 0 0
0
100
200
A zi m u th Angle f r o m S o u r c e [ d e g . ]
Figure 4.6: The measured far-sidelobe response of the telescope before MAXIMA-1 as a
function of elevation (left plot) and azimuth (right plot) angle off the center of the beam
for one 150 GHz detector. The signal in dB is calculated as follows: PdB = 20 \og(Vg/Vo),
where Vg is the rms off-axis bolometer voltage per VWz, measured an angle 0 from the
center of the beam, and ho is the rms bolometer voltage per \/H z measured w ith the
source on axis. The measured points are connected w ith straight lines.
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51
M A X I M A - 2 , E le v a t io n
M A X IM A -2, A z im u th
0
-20
13
CD
-60
80
-80
30
20
10
0
A n g le [ d e g ]
10
- 2 0 0 -1 0 0
0
100
200
A n g le [ d e g ]
Figure 4.7: The measured far-sidelobe response of the telescope before MAXIMA-2 as a
function of elevation (left plot) and azimuth (right plot) angle off the center of the beam
for one 150 GHz detector. The signal in dB is calculated as follows: P^ b — 20log(Vg/Vo),
where Vg is the rms off-axis bolometer voltage per \/H z, measured an angle 9 from the
center of the beam, and Vq is the rms bolometer voltage per s/Hz measured w ith the
source on axis. The measured points are connected w ith straight lines.
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52
4.3
In-flight C haracterization of B eam P attern s
We measure the beam patterns of each channel in the array during flight to
determine the beam function, B i , which is the spherical multipole moment expansion of
the beam. The accuracy of our knowledge of the beam function is one of many constraints
on the sensitivity of the instrum ent to probe power at higher multipoles. The exact form
of the beam function depends on the shape, symmetry, and w idth of the beam, but in
most cases, the beam function drops sharply for £ > tt-1---- • The noise in the power
”
f w h m
spectrum at a given multipole moment, C f 0lse, is inversely proportional to the square of
the beam function. For 9fwhm = 10', this cutoff is £ ~ 1080. Knowledge of the beam is
also necessary for calibrating the detectors from the planet, which underfills the beam.
4.3.1
M easurem ent
The beam patterns were measured in flight by observing Ju p iter for MAXIMA-1
and Mars for MAXIMA-2. These planets are both small in angular size compared to
the beam FWHM, and can thus be treated as point sources. They are bright enough to
generate a detection w ith S/N of ~ 100 when observed at the center of the beam. See
Table 4.4 for details on both planets.
We point the telescope so th a t all the channels in the array are initially pointed
~ 0.5° below/above the rising/setting planet. The prim ary m irror modulates w ith an
am plitude of 4° p-p in azimuth at 0.45 Hz, scanning the array quickly across the planet.
A single sweep of the mirror produces a measurement of the beam in azim uth (See Figure
4.8). Sky rotation scans the planet slowly in elevation across the beams. The bolometer
tim e stream s are combined with the pointing solution (generated from the boresight CCD
camera and the prim ary mirror position sensor) to generate two dimensional beam contour
maps in azim uth and elevation. The angular offset between the center of the beam and
the boresight CCD camera determines the position of the beam center on the array.
We analyzed the d ata as follows; we first prepared the detector time stream by
removing an offset and gradient, then deconvolved the independently measured electronic
and bolometer response filter. High frequency noise was suppressed by filtering the de­
tector tim estream w ith a phase preserving
8
pole digital low pass filter w ith a cutoff of
30 Hz. We reconstructed the pointing solution about the p lan et’s position in azimuth
and elevation, as described in Rabii (2002). We then combined detector and pointing
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53
Observation
Planet
MAXIMA-1
MAXIMA-2
Jupiter
Mars
de
[”]
47
13
T
[K]
(169,165,133) ± 2
196
< beam dilution >
3.9 ± 0 .5 x 10~ 3
3.75 ± 0.65 x 10- 4
Table 4.4: MAXIMA planet specifications: The table above gives d ata for each of the
planets observed during the two MAXIMA flights. The planet tem peratures are taken
from Goldin et al. (1997). The observed tem perature of Jupiter is listed for the 150, 230
and 410 GHz observation bands, respectively. The beam dilution is the ratio between the
normalized area of the planet and the beam. We quote the mean beam dilution for all
150 GHz channels.
,-4
1 .5 x 1 0 '
i“ 4
>
o
c
g>
,-5
5 .0 x 1 0 '
in
150 GHz
- 5 .0 x 1 0
150 GHz
2 4 0 GHz
4 1 0 GHz
,-5
-8 0
-6 0
-4 0
-2 0
0
C hopper Position [ a r c - m in ]
20
40
Figure 4.8: Planet scans: Plotted above are bolometer d ata from four adjacent detectors
from one row in the array during the Jupiter planet scan in MAXIMA-1. The d ata are
plotted against the corresponding position of the prim ary m irror (as m odulated by the
“chopper” ) in time. The labels underneath each peak denote th e frequency of the given
detector.
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54
F o c a l P la n e
0.6
40
0 .4
20
0.2
0.0
0
-0 .2
-2 0
-0 .4
-4 0
-0 .6
-0 ,6
•0 .4
-0 .2
0.0
d e g re e s
0.2
0 .4
0.6
A z im u th ( o rc m in )
Figure 4.9: MAXIMA beams: Left: MAXIMA-1 beam contour plots for all channels.
The contours, from the center of each beam out, represent the 90%, 70%, 50%, and 30%
levels respectively. Lower contours produce considerable overlap in this figure. Right:
MAXIMA-2 beam contour plots for all channels. The contours, from the center of each
beam out, represent the 90%, 70%, 50%, 30% and 10% levels respectively. Two of the
230 GHz channels were dead during the MAXIMA-2 flight.
timestreams to generate two-dimensional beammaps for each channel in the array. The
detector d ata were averaged in fixed azim uth and elevation bins over a prescribed area
and resolution through three-point linear interpolation. We measured the beam FWHM
from the 50% contour of the beammap. We used binning and plotting routines from the
IDL d ata analysis software package (Research Systems, Inc. (U.S.A.)).
4.3.2
R esu lts
We measured the beams for all of the functioning channels during bo th MAX­
IMA observations. Two-dimensional beam contours for all channels for MAXIMA-1 and
MAXIMA-2 are shown in Figure 4.9. We can generate individual beam maps for each
channel over a range of 2 degrees in azim uth and elevation. The FWHM as measured
along the m ajor and minor axes of each beam are listed in Table 4.5.
Symmetry
It is useful th a t the beam be rotationally symmetric about its center. During
flight, the telescope revisits regions of the sky at different times so th a t the angle of the
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55
Channel
b l4
bl5
b24
b25
b34
b35
b44
b45
b l3
b23
b33
b43
b l2
b2 2
b32
b42
<v>
[GHz]
150
150
150
150
150
150
150
150
230
230
230
230
410
410
410
410
M l:$ f w h m , m a j
[arcmin]
11.3
1 0 .8
1 0 .8
1 0 .8
1 0 .8
1 0 .0
10.5
1 0 .8
1 0 .2
1 1 .0
11.3
11.5
1 2 .0
1 0 .2
13.6
1 1 .0
M l:$ f w h m , m i n
[arcmin]
9.0
9.0
8.4
8.4
8.4
8.4
9.2
9.0
8.4
8.4
7.7
8.4
8.3
9.0
7.9
7.7
M 2 : 9 f w h m ,m a j
[arcmin]
1 0 .0
1 0 .1
9.5
9.7
9.5
9.8
1 0 .1
1 0 .0
M2 '■&f v ) h m , m i n
[arcmin]
9.3
9.1
9.2
9.3
9.5
9.4
9.3
9.4
-
8.7
8.7
-
8.4
8 .8
8 .1
8.3
8.5
9.5
7.5
8 .2
8 .1
7.4
Table 4,5: Measured FWHM for individual beams for both MAXIMA-1 and MAXIMA-2:
The FWHM for the m ajor (9 f w h m , m a j ) and minor axes ( 9 f w h m , m i n ) are listed for each
flight. These values were determined by measuring the w idth of the 50% contour in both
azimuth and elevation for each beam. Two of the 230 GHz channels were dead during the
MAXIMA-2 flight.
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56
scan varies due to sky rotation. Beam symmetry ensures th at the same region of the sky
is observed upon revisitation, regardless of angular orientation. Rotational asymmetry in
the beams would also introduce an error in the beam function, B[. Correction requires
th a t the beam function be expanded in m. The predicted CMB power spectrum , Ci , for
an adiabatic inflationary cosmology is Gaussian, and is not a function of to. Our approach
to this problem is to transform the B i m for a given I into a Bi w ith an error.
Comparing the two panels in Figure 4.9, the beams in MAXIMA-1 are noticeably
less symmetric than those in MAXIMA-2. We have reason to believe th a t for MAXIMA-1,
the telescope was not perfectly focused. Figure 4.10 shows a close-up of three of the 150
GHz beams and one of the 230 GHz beams (labeled 240 GHz) in MAXIMA-1. The major
axis of the 10% contour is roughly twice as long as is its minor axis. We developed a
formalism to interpret asymmetric beams in the d ata analysis, which finds the optimal
circularly symmetric equivalent for easy adaptability into existing analysis methods (Wu
et al. (2001a)). We determined th a t the beam size uncertainty causes less th an 4% and
11% uncertainty in the Ct estimates for I < 410 and 785, respectively, given the bands
used in Hanany et al. (2000). This error is small compared to the overall error in the power
spectrum (see C hapter 7). We also determined th a t the 50% contours were symmetric for
all 150 GHz channels, even in the most extreme cases of asymmetry.
Sources of Error
The statistical uncertainty in our estimates of the shape and the beam FWHM
for each channel in the array is affected by numerous sources of error. These sources are
the uncertainty in the pointing reconstruction, the noise in the detector tim e streams,
the uncertainty in the bolometer electronic filters and time response, and the area and
resolution of the beammap. We list the contributions to the to tal error from these sources
in the measured beam FWHM for one 150 GHz channel in Table 4.6. Assuming th a t the
sources of error are independent of each other, the total error is the sum of the individual
errors in quadrature.
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57
0.4
0.2
0
-
0.2
-
0.4 (1) 150 G
(2) 150 GHz'
0.4
0.2
0
-
-
0.2
0.4 (3) 150 GHz
- 0.4
- 0.2
0
(4) 240 G
0.2
0 . 4 - 0.4
-
0.2
0
0.2
0.4
degree
Figure 4.10: Asymmetry in MAXIMA-1 beams: Shown are the 90%, 50%, 10% and 1%
iso-contours for 4 different beams.
Source of error
W hite noise in the detector time stream
Bolometer electronic filters
Bolometer time constant
Phase preserving low-pass filter
Pointing reconstruction (differential err.)
Resolution of beammap
Area of beammap
Total
Qfwhm
[arcmin]
0.09
0.13
0.06
0.14
0.05
0.17
0.15
0.32
Table 4.6: Sources of beam error for one 150 GHz channel, listed in the order in which
they enter the analysis. These term s are defined in §4.3.1. Assuming th a t the sources of
error are independent of each other, the total error is the sum of the individual errors in
quadrature.
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58
C h a p ter 5
B olom eters
A bolometer is a therm al detector whose electrical resistance varies as a function
of tem perature. A thorough review of bolometers can be found in Richards (1994). The
bolometer is heated by radiation from an infrared source. In practice, the therm istor
element is coupled to an absorber (e.g. m etal mesh), which optimizes the fraction of
radiation absorbed by the bolometer. The bolom eter’s resistance is read out electrically.
The bolometer is thus heated both by the optical source and by electrical bias power. A
schematic of a bolometer is shown in Figure 5.1.
Far-infrared and mm-wave observations can be made by two methods: coherent
and direct detection. W ith the former, the signal from the sky is coherently received by
an antenna, mixed down in frequency if necessary, amplified and then directly detected
by a diode. Phase information is preserved by the mixer and amplifier. HEM T (High
Electron Mobility Transistor) amplifiers are used in coherent receivers. HEM T amplifiers
are typically used w ithout mixers in CMB experiments to observe at frequencies between
10 and ~ 100 GHz. At frequencies below ~ 60 GHz, the noise is w ithin a factor of 3 of
the quantum limit.
To observe above ~ 100 GHz, one must abandon the route of coherent amplifica­
tion in favor of direct, or square-law detection. We choose bolometers over HEMTS given
their superior sensitivity at 150 GHz, where far-infrared and sub-millimeter backgrounds
are minimized in comparison to the spectral intensity of the CMB. M easuring the tem ­
perature anisotropy of the CMB does not require spectroscopic precision. The CMB has
a smoothly varying black body spectrum , and spatial anisotropy of the CMB is correlated
over all frequencies. For square law detectors, the output voltage is a measure of the
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59
P b ias
P ra d
Figure 5.1: Schematic diagram of a MAXIMA bolometer: The composite bolometer (NTD19 therm istor and SisN 4 + metal absorber) is therm ally coupled to the tem perature bath
by a weak link w ith therm al conductance G. The b ath has a tem perature of To- The
therm istor and absorber have a combined heat capacity of C. Two sources of power heat
the therm istor: Radiative power, Prad, from the sky and from the radiative load of the
receiver, and electrical power, Peiec, from the bolometer bias. Assuming constant bath
tem perature and power, the bolometer has an equilibrium tem perature, Tf,.
square of the input signal amplitude. All phase and frequency inform ation from the input
signal is lost, b u t the bolometer inherently has a wide bandw idth and large throughput.
Semiconductor bolometers, which are commonly used in astrophysics experi­
ments, have a smoothly b u t non-linearly varying resistance th a t decreases as a function of
increasing tem perature. It is common practice to read out the bolom eter’s resistance with
a constant current bias and a voltage amplifier. Non-linearities of the device limit the
dynamic range, which is adequate for measuring the predicted range of CMB tem perature
fluctuations.
5.1
R equirem ents
We estim ate th a t for a time of observation of
balloon flight) and an area of observation of
a detector sensitivity of 100 pK
32
10
x
10
=
8
100
hours (typical for an overnight
deg2, w ith a
10
' beam, we need
to detect 20 pK rms tem perature fluctuations. This
sensitivity can be achieved by operating the detector at cryogenic tem peratures.
Improvements in sensitivity can be achieved by using an array of detectors. Pro­
viding the beam profile error and noise for each detector are similar b u t uncorrelated,
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60
the d ata can be combined in a straightforward m anner (see C hapter 7 for further discus­
sion). If these conditions are met, the total sensitivity of the array can be determined by
combining the individual sensitivities, s*, of N detectors in quadrature:
_ 1V
Stotal — (I
N
s^ J
I •
(5.1)
The Tspace coverage in the measurement of the power spectrum depends in part
on the bandw idth of the bolometer signal, which is determ ined by the 1 / /
knee and the
high frequency roll-off in the signal spectrum . The cosmological signal appears between
the prim ary mirror m odulation frequency at 0.45 Hz and the roll off due to the telescope
beam window function at ~ 20 Hz. l / f
noise causes striping in the maps, which must
be removed by cross-linking. The bolometer response time, which is defined below, can
constrain the high-frequency cut-off of the signal band. This, in turn, can limit the choice
of scan speeds for the telescope.
A bolometer has a
heat capacity C and is coupled to the therm al b ath by a weak
link with a therm al conductance G. If the bolometer is heated a tem perature A T above
the b ath tem perature To, its subsequent tem perature relaxes exponentially;
T(t) = T q + AT(1 - exp(—t / r ) ) where r = C/G.
(5.2)
The frequency response of the bolometer tem perature is th a t of a single pole
low-pass filter w ith a characteristic frequency of f s d B = 1/(27rr).
A slow detector response compared to the telescope scan speed has the effect of
smearing the beams on the sky, distorting the window function. Hanany et al. (1998) show
th a t a bolometer speed which is at least 2.5 times faster than the speed of the telescope
modulation prevents significant distortion. In order to achieve the desired range of scan
speeds, we require detector response times of order 10 msec or less for MAXIMA.
5.2
M A X IM A B olom eters
We use composite bolometers w ith metalized mesh absorbers and neutron trans­
m utation doped germanium (NTD-Ge) therm istors obtained from J. Bock at JPL, as
shown in Figure 5.2. This design is a result of years of optim ization by research groups at
UC Berkeley, LBNL, CalTech, and JPL.
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Figure 5.2: Photo of MAXIMA bolometer: The absorber is a layer of 1 pm thick SisN 4
and a thin layer of An. The sheet resistance of the Au layer is chosen to be 37712/D to
match the impedance of free space. The absorber is etched in a “spider-web” p attern
th a t has a 2.5 mm diameter w ith a 5% filling factor. The radial components w ithin the
spider-web p attern are 160 pm long and 4 pm wide. The therm istor, a cube of NTD-19
whose sides measure 250 pm , is bum p bonded to the center of the web. The chip is
powered through two gold electrical leads th a t are lithographed over the absorber. The
absorber and chip are supported by the electrical leads and by sixteen SisN 4 legs th a t are
1 mm long and 5 pm wide. Photograph courtesy of J. Bock.
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62
Intrinsic semiconducting materials, like Si and Ge, are not well suited for de­
tectors at operating tem peratures below 1 K. The resistance of a semiconductor varies
exponentially with tem perature, and is governed by the Boltzmann factor. Conduction
in pure semiconducting materials is determined largely by therm al excitation of carriers
across the gap. The tem perature dependence of the electrical resistance has the form
R{T) =
R q exp
(Eg/T), where the energy gap. E g > 1000 K, and gives rise to imprac-
tically large impedances in devices operated at cryogenic tem peratures. Resistances can
be lowered by doping the material. The introduction of im purities in the m aterial creates
donor and acceptor states near the edges of the conduction and valence bands, yielding
conduction in the m aterial by variable range hopping. The tem perature dependence of
the electrical resistance of the material then has the form, R{T) =
R q exp
(A /T ) 2 , where
A ~ 10 K and is determined by the type and level of doping in the material. A more
thorough discussion of this phenomenon can be found in Richards (1994) and Efros &
Shklovskii (1984).
Suitable low tem perature therm istors can be made through neutron transm uta­
tion doping of germanium (NTD-Ge) which has more uniform and reproduceable im purity
distribution th an melt-doped semiconductors. Transm utation of the four stable isotopes
of germanium yields isotopes of gallium, arsenic, and selenium. The level of doping in
the m aterial and thus the tem perature dependence of the electrical resistivity of NTD-Ge
is determined uniquely by the neutron fluence. The characteristic tem peratures for the
various types of NTD-Ge allow for operation between tem peratures of 20 mK to 4.2 K.
MAXIMA bolometers are made from NTD-19, which is optimized for operation at 100 mK.
More inform ation on neutron transm utation doping can be found in Haller (1985).
Electrical contacts on the NTD-Ge chips are made through ion im plantation,
followed by a therm al annealing process. NTD-Ge is sliced into th in wafers, which are
dosed w ith 25-100 keV P ions for n-type Ge, 101 4 — 101 5 /cm 2 produces a degenerately
dosed n layer. The wafers are annealed, then metalized with a ~ 20 nm-thick layer of
Cr or Ti, followed by a ~ 150 nm layer of Au for easy attachm ent of wires. The wafers
are then diced, etched, and passivated. Gold leads are indium bum p-bonded onto the
metalized edges of the therm istor.
The bolometer absorbing structure is fabricated via optical lithography starting
with a silicon on insulator (SOI) wafer coated with a 1 pm layer of silicon nitride (SiaN ^.
The top of the SiaN 4 is coated with a layer of gold whose thickness is selected to obtain
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63
an average sheet resistance of 377fl/D. The absorber is then patterened in a “spider-web”
geometry w ith photoresist. A dry-etch is used to remove the gold and SigN4 around the
pattern. The SOI is dry etched from the back side of the wafer w ith deep trench Si etcher.
See Figure 5.2 for a photograph of a MAXIMA bolometer.
The spacing of the absorber legs is small enough to trap millimeter-wave radia­
tion, but is large enough to let high energy cosmic rays pass through. The absorber has
a 5% filling factor, which diminishes cosmic ray hits by ~ 90%. While the filling factor
and the geometry the web affects the absorptivity of the absorber, it has been calculated
th a t for an absorber w ith a 5% filling factor, if A >
<, where g is the spacing of the
10 7
legs, a “web” will absorb w ith the same efficiency as a continuous sheet. A web with a
sheet resistance of 377Q/D absorbs 50% of the incoming radiation in one pass (Bock et al.
(1995)). The optical efficiency can be further increased by placing the bolometers in an
integrating cavity with a characteristic depth of A/4 (see C hapter 4).
5.3
B olom eter N oise and O ptim ization
The m ajor contributors to bolometer noise are photon noise, Johnson noise, and
therm al fluctuation noise. We also consider noise from the first stage of amplification
(amplifier noise). A thorough discussion and derivation of each noise term is found in
Richards (1994). Bolometer noise is generally discussed in the context of noise equivalent
power (NEP), which is defined as the incident signal power required to generate a signal
equal to the noise in a one Hz bandw idth, and is a measure of the ratio of signal to noise.
Photon noise, or optical power fluctuations from a black body source, can be
calculated from the variance of the number of photons per mode per second per Hz of
bandwidth. Photon noise can be significant, but is independent of bolom eter param eters
aside from the throughput and absorption efficiency. Both optical signal from the sky and
stray emission from the experiment contribute to the overall optical load, and subsequently
to photon noise. MAXIMA’S secondary and tertiary mirrors, Lyot stop, and horns are
baffled and cooled to 3 K in flight to minimize the optical load on the detectors. Optical
signals at frequencies outside the desired bands are aggressively filtered by a series of
metal mesh and alkali-halide filters in the optical path.
The photon noise for a real
optical system is complicated to express. Given an estim ate of the detected optical power,
Popt, the photon noise can be expressed as
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64
( N E P ) p hoton = 2hDPopt,
(5.3)
where v is the mean observation frequency.
O ther significant noise term s arise from the bolometer and the readout circuit.
The Nyquist noise in a resistor in equilibrium at a tem perature T is called Johnson noise.
Therm al fluctuation noise arises from fluctuations in the energy in a bolometer. These
noise term s can be analytically expressed as;
*hTR/\S\\
(5.4)
( N E P ) 2Tk, rmFluA = 4k T 2G,
(5.5)
W E P f j d . „ ,o n
=
where T is the bolometer tem perature, R is the bolometer resistance, S is the bolometer
G is the therm al conductance of the link between the bolometer
responsivity (in V /W ) and
and the tem perature bath.
High impedance bolometers are typically used with JF E T preamplifiers. We re­
quire an amplifier with a low noise tem perature (TV < T^0i0). The noise tem perature
of the amplifier is expressed as T/v = (VA + I AR 2) / 4 R k [K], where Va and I a are the
respective voltage and current noise of the amplifier. The only low noise devices avail­
able for Tboio = 0.1 K are JF E T and SQUID amplifiers. The bolometer
chosen to minimize the
resistance is
noise tem perature of the amplifier. The amplifier is located near
the bolometer to minimize noise and microphonics. The best JF E T amplifiers have a
minimum noise tem perature of approximately 0.1 K for frequencies above 10 Hz, which
is unfortunately close to the bolometer tem perature so there is little noise margin. The
NEP of the amplifier is given as
( N E P ) 2Amplifier = (U | + I 2a R 2)/\ S\ 2.
(5.6)
The individual noise sources are uncorrelated. The to tal noise is given by the
sum of each term in quadrature.
( N E P f total = (.N E P f Photon + { N E P f Johnson + ( N E P ) 2Th erm .F luct. + ( N E P ) 2Amplif ier (5.7)
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65
,-17
B o l o m e t e r Noise Equivalent P o w er (NEP)
Measured NEP
NEP total
NEP photon
NEP amplifier
NEP therm al fluctuatio n
~NEP johnso n
0
0.1
1.0
1 0 .0
100.0
Frequency (Hz)
Figure 5.3: Bolometer noise spectrum: Shown above is the m easured noise equivalent
power (NEP) spectrum for a 150 GHz MAXIMA bolometer plotted along w ith theoretical
NEP contributions from photon
Johnson (long dash), therm al fluctuation (short
dash) and amplifier (-.-) noise. The solid line is the estim ate of the total NEP. Low
frequency noise below 0.4 Hz arises from tem perature drifts in the detectors. Electronic
filters in the readout circuit cause the signal to roll off above 20 Hz
The estim ated contribution of each noise term compared to a measured noise
spectrum is shown in Figure 5.3. We optimize the bolometer and receiver so th a t photon
noise is the dom inant term . This is done by selecting the tem perature of the b ath To and
the param eters defined in the equations above.
Given the interdependence of all of these variables, a rigorous optimization, such
as described in G rannan et al. (1997), is complex. First, we design the experiment to
minimize the background power outside of the nominal observing bands. We choose the
therm al conductance G required to operate the bolometer with a tem perature rise of ap­
proximately (T —T0)/To = 0.5. This, in combination w ith a low b ath tem perature reduces
the contribution of therm al fluctuation noise compared to photon noise. The higher the fre­
quency of observation in a given channel, the larger the optical power. We correspondingly
increase the therm al conductance of the bolometer as a function of observation frequency
(see Table 5.1). The heat capacity must be small enough to produce bolometers with a
fast enough response time ( r = C/G). We operate the bolometers at a b ath tem perature
of To = 100 mK, as low as practically possible, taking into consideration available refriger­
ation technology. We select the lowest noise JF E T pre-amplifiers commercially available.
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66
<v>
[Hz]
150
230
410
<G>
[pW/K]
71
290
320
<f >
0.51
0.29
0 .2 1
Table 5.1: Measured therm al conductance of MAXIMA bolometers: Listed are the ther­
mal conductance (G) and fractional tem perature rise above the b ath tem perature ( jjf )
averaged over each set of 150 GHz, 230 GHz and 410 GHz bolometers.
Freq -200 Hz
Ampl -100 mV
Ainplifi<
Low Pass Filter High Pass Filter
pair
Pre-amp
per JFET pair
Figure 5.4: Block diagram of the bolometer analog readout circuit: The bolometer re­
sistance is determ ined from the am plitude of the AC voltage across the bolometer. The
bolometer is biased w ith an AC voltage with a frequency of 212 Hz (MAXIMA-1). Low
noise JF E T amplifiers near the bolometers convert the signal impedance from ~ 1MQ
to ~ 1 kSl. Amplification and dem odulation of the signal are provided by ambient tem ­
perature electronics mounted on the side of the cryostat. Signals are then digitized and
inserted in a d ata frame by the d ata acquisition system (C hapter 3).
A straightforward example of bolometer optim ization for the MAXIPOL experiment is
presented in Appendix C.
5.4
R eadout E lectronics
We design the bolometer readout electronics to minimize electronic noise, to max­
imize the linearity of the detector responsivity, and to provide adequate signal bandwidth.
A schematic of the readout circuit is shown in Figure 5.4.
The bolometers are AC-biased to minimize low frequency noise contributions
from the electronics (e.g. 1 / f
noise in the JF E T amplifiers). We have previously de­
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67
term ined th a t if bolometers are biased at a frequency th a t is ~
10
times larger than the
characteristic detector response frequency (~ 20 Hz for MAXIMA bolometers). As a re­
sult, the AC bias does not cause fluctuations in the the bolometer tem perature, assuming
constant optical power. All detectors are biased at the same frequency by a sine wave
oscillator which can be tuned from 200 to 500 Hz. We select this frequency to minimize
microphonic noise.
The bias voltage am plitude for each detector is set between 50 and 100 mV
by a potentiom eter. We achieve a linear relation between the voltage responsivity, S,
of the bolometer and the derivative of the resistance of the therm istor w ith respect to
tem perature,
by minimizing the bias current fluctuations across the bolometer. Bias
current variations are adequately controlled by two 40 MO load resistors in series with
each bolometer. The largest fractional change in bias current was observed during the
planet scan and was of order
10
ppm.
We minimize the microphonic sensitivity of the receiver by reducing the output
impedance of the bolometers. This is achieved w ith a matched pair of cooled monolithicdual silicon EJ-TIA JF E T amplifiers (Infrared Laboratories (USA)) in a m atched em itter
follower circuit. The JF E T pairs, cooled by a weak therm al link to the 1.6 K liquid 4He
bath, operate at 150 K. Each JF E T pair consumes 300 /iW of power and contributes
6
— 10 n V /\/H z to the total noise per channel. Details on bolom eter electronics wiring
can be found in Appendix B.
The bolometer signals are further processed by ambient readout electronics. They
are pre-amplified w ith an AD624 op amp, band pass filtered around th e bias frequency,
then are each rectified with an AD630 lock-in amplifier referenced to the bias signal.
We are interested in measuring the resistance fluctuations of the bolometer. This
signal appears in the side bands of the bias frequency, as determined by the speed of the
telescope modulation. Given the prim ary mirror m odulation frequency of 0.45 Hz and
peak velocity of 4 deg/sec (or ~ 25 beam FWHM per second), we are interested in the
band th a t is 0.1 - 30 Hz around the bias frequency. Signals outside the band are suppressed
by a four pole B utterw orth filter with a characteristic frequency of 19.96=t0.61Hz, averaged
over all
20
read-out channels.
Finally, the rectified signal is amplified by a gain of 1800 and split to two outputs.
We remove the offset from one signal stream with a single pole high pass filter with a
characteristic frequency of 14.9 ± 0.7 mHz, averaged over all 20 read-out channels. This
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68
signal is further amplified by a factor of 36, yielding a net gain of 65,000. Overall, the
warm readout circuit has a gain stability of < 10 ppm /deg C. Both signal outputs are
then fed to A /D converters, which sample the high gain and low gain analog outputs at
4.8 and 19.6 msec, respectively.
5.4.1
R adio Frequency Interference F iltering
It is essential to shield the detectors from ambient radio frequency interference
(R FI). The bolometers used in the MAXIMA program are sensitive to femtowatts of heat
input. The telem etry provides a m ajor source of R FI during flight. Seven transm itters
which radiate ~ 20 W in the frequency range from 1.4 to 4 GHz are located 2-3 meters
away from the receiver. R FI can enter the receiver through two main paths: the wiring
and the optical window. We have implemented many different strategies in the MAXIMA
receiver to reduce R FI reaching the detectors. Figure 5.5 is a schematic showing all of the
RFI filtering strategies.
We encase the receiver, including the receiver electronics, in R FI-tight enclosures.
All signals between the cryostat, the ambient electronics, and the d ata acquisition system
pass through Amphenol E M I/R F I filtered connectors, which provide -60db insertion loss
at 1GHz. All wiring inside the cryostat is potted in Eccosorb CR-124 (Emerson & Cuming
Microwave Products (U.S.A.)) before reaching the bolometers. Eccosorb CR-124 has a
measured insertion loss of -30db at 1 GHz and -60db at frequencies > 2 GHz (Halpern
et al. (1986)).
The optical window acts as a high pass filter for ambient RFI, which has a mea­
sured cut-off of ~ 2.5 GHz. The cooled optics and the feed-horns are encased in Faraday
cages. Higher frequency RFI which enters the optical p ath can leak between the cylindrically concentric radiation shields. We block these leaks by taping a cylindrical sleeve
made from multiple layers of
0 .0 0 1
inch sheets of aluminized mylar around the perime­
ter of the optical p ath near the cryostat window w ith aluminum tape (See Figure 5.5).
This attenuates the coaxial transm ission of RF between the shields w ithout significantly
compromising the therm al isolation between the different tem perature stages inside the
cryostat.
Each individual bolometer is enclosed in a RFI-tight cavity. The optical open­
ing into the cavity is small enough to prevent R FI at frequencies below 100 GHz from
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69
Cryostat
Warm
Electronics
Liquid Nitrogen
Liquid Helium
Bolometers
Feed horns
Amphenol EMI/RFI
f i l t e r e d co n n e c t o r s
B o l o m e t e r LC filters
Optics
E c c o s o r b CR - 1 2 4
A l u m i n i z e d m y l a r s e pta
Window
Figure 5.5: R FI protection: The bolometers (shown w ith resistor symbols) are shielded
from electrical RFI pickup by three different types of filters in series, shown as filled rect­
angles (see key). RFI is prevented from coaxially transm itting between the tem perature
baffles by contiguous layers of aluminized mylar placed around the optical p ath at the
cryostat window. The cryostat and the warm electronics shield act as Faraday cages.
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70
Cl
ssz.
- v/
^ I+ b ia s
s /m d
W TH
Ll
_q V+ bolo (to jfet gate)
Rbolo
-OV- bolo (to jfet gate)
Bolometer
cavity
Cl
_
vVMD h bias
Rload
Figure 5.6: R FI filter circuit: Each bolometer is encased in a R FI tight cavity, represented
by the dashed line. The schematic above illustrates the filter and its interaction with the
bolometer signal. The values of L l and C l are chosen to maximize the attenuation of RFI
signals w ithout modifying the bolometer bias and output. For the MAXIMA 2 receiver,
L l = 47 nH, C l = 10 pF and Rload = 80 MOhm, and we assume th a t Rbolo ~ 1 —5 M Q
at 100 mK. The components were fabricated by M urata M anufacturing (Japan).
radiatively coupling onto the bolometers. The bolometer signal is filtered at the cavity
wall by LC feed-through filters, as shown in Figure 5.6. This circuit presents the lumped
element view of the filters. Calculations of the high frequency performance of these filters
including distributed reactances were made by Hristov (1999).
This set of measures was only partially implemented before MAXIMA-1. We
discovered measurable RFI leakage in the receiver during ground tests before MAXIMA1, but have good reason to believe th a t RFI did not contam inate the published MAXIMA-1
data. The aluminized mylar septa and bolometer cavity LC filters were incorporated after
MAXIMA-1 and before MAXIMA-2. We characterized the improvements in RFI shielding
in laboratory tests before MAXIMA-2. These results are presented below.
5.4.2
R FI S en sitiv ity M easurem ent
We have measured the RFI sensitivity of the MAXIMA receiver (cryostat and
analog read-out electronics) before and after implementing the aluminized mylar septa
and bolometer cavity LC circuits in a series of cryogenic runs between April and May,
1999. We implemented neither improvement (but all MAXIMA-1 RFI safeguards) in the
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71
first run. We introduced the septa, only, in the second. We implemented both the LC
filters in a subset of detectors and the septa in the last.
In each run, we cooled the bolometers to 100 mK, then irradiated the cryostat
with a Hewlett Packard 86360A RF sweeper coupled to a 10 x 10" copper sheet bowtie antenna w ith a SMA connector. The antenna was mounted against the window of the
MAXIMA cryostat. A sheet of cardboard was used to isolate the antenna ground from the
cryostat chassis. We swept the receiver w ith 10 MHz to
of the output from -26 to
+ 6
6
GHz RF varying the am plitude
dbm. The output of the sweeper was m odulated w ith a 15 Hz
square pulse, placing the R FI into the bolometer signal band. The bolometers were biased
w ith 100 mV AC at 212 Hz, identical to MAXIMA-1 flight settings. We measured one
detector output at a time. The detector output was split between a lock-in amplifier in
series w ith a paper analog x-y recorder (y = rectified detector output, x = R FI frequency)
and a digital spectrum analyzer to facilitate calibrating the output.
The first run (no septa or LC circuits) revealed the following; the receiver was
susceptible to RFI frequencies greater than 2.5 GHz for all bolometers; light and dark. This
radiation came in through the window. This was very apparent w ith -26 dbm RFI signals.
The bolometers were susceptible to isolated lines between 1 < / < 2.5 GHz, dependent on
the bolometer and the position of the antenna. If we disassembled the shielding axound
the analog read-out electronics, the bolometers were measurably susceptible to RF from
100 to 500 MHz. See the top panel of Figure 5.7
In the second test, measurements with the septa only revealed less RFI suscep­
tibility in all detectors. In the third test, the subset of detectors w ith LC filters showed
dram atic improvement, as shown in Figure 5.7.
The LC filters appeared to suppress
pickup at 1 < / < 2 GHz in these detectors. Given the limited dynamic range of the
lock-in amplifier, we determined th a t the septa and LC circuits contributed at least - 2 0 db
suppression of pickup in this frequency regime. Independently, the LC circuits were shown
not to introduce measurable suppression or phase shifts in the signal band of the detectors.
The R FI susceptibility of the dark bolometer likewise diminished in each test.
This evidence supports the model th a t prior to the installation of the septa and the
LC filters, RFI leaked in through the window, around the tem perature baffles, and then
coupled into the bolometer wiring. Based on these results, the aluminized mylar septa
and LC filters were implemented in all channels.
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72
MAXIMA bolometer response: no RF filter: -6 dbm
0
1
2
3
4
5
Frequency (GHz)
MAXIMA bolometer response with RF filters: - 6 dbm
0
1
2
3
4
5
RF frequency (GHz)
Figure 5.7: R FI measurements: These two plots give the frequency spectra of the RFI
signal detected by one 150 GHz detector before and after the im plem entation of RFI
shielding strategies discussed in §5.4.1. The test RF is produced by a bow-tie antenna
coupled RF generator set to sweep between 10 MHz and 6 GHz at - 6 dbm. We plot the
detector output in arbitrary units, but he two plots have identical vertical scales.
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73
5.5
D etector C haracterization
Measurements of the bolometer response times and noise were made during both
the MAXIMA-1 and MAXIMA-2 flights. We determined the response times by deconvolv­
ing a single pole low pass filter, whose characteristic frequency is a free param eter, from
bolometer tim e stream s while scanning the prim ary telescope back and forth in azimuth
across a planet. The bolometer time constant param eter is adjusted until the left and
right going scans spatially overlap. This measurement has a statistical error of 0.50 msec.
The measurements are presented in Tables 5.2 and 5.3 for MAXIMA-1 and MAXIMA2, respectively. We switched detectors in many channels between the two flights, which
explains the larger discrepancy between the two measurements in many channels. In all
cases, the measured bolometer response tim e is small enough to prevent significant beam
smearing from the telescope modulation.
We determ ined bolometer noise by computing the power spectrum of the bolome­
ter time stream measured during the CMB observations. Given the three independent spa­
tial modulations of the telescope on the sky, we assume th a t CMB signals will not appear
at any fixed tem poral frequency. We also assume stationarity of the noise. Character­
izing bolometer noise is a critical step in the overall determ ination of CMB tem perature
anisotropy, as will be explained further in C hapter 7. We select uninterrupted sections of
the bolometer time stream s th a t are free of non-Gaussian trends which can be attributed
to events such as cosmic ray hits, telemetry drop-outs or the periodic flashing of the inter­
nal calibrator. We divide the signal by the gain of the readout electronics, and compute
the frequency power spectrum out to the Nyquist frequency of 104 Hz. A typical noise
power spectrum is shown in Figure 5.3. The spectrum can be divided into three frequency
ranges. For frequencies below ~ 400 mHz, the spectrum decreases as 1/ / . At intermedi­
ate frequencies, the noise spectrum is white. At frequencies above ~ 20 Hz, the spectrum
decreases because of the electronic low-pass filter and bolometer tim e constant.
We present noise and bolometer time constant measurements for all functioning
channels for MAXIMA-1 in Table 5.2 and for MAXIMA-2 in Table 5.3. We include the
overall N EP and NET for the detectors grouped by channel and observation frequency.
The noise was calculated from a ~ 10 minute tim e-stream segment from each detector
during one of the CMB scans.
In bo th flights, the performance of the bolometer array was not uniform. The
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74
Channel
bl4*
bl5*
b24*
b25
b34
b35*
b44
b45
< 150GHz >
b l3
b23
b33
b43
< 230GHz >
b l2
b2 2
b32
b42
< 410GHz >
<v>
[GHz]
150
150
150
150
150
150
150
150
150
230
230
230
230
230
410
410
410
410
410
Vn
[nV/VHz ]
15.2
10.9
17.9
1 1 .1
10.9
2 2 .1
37.0
10.9
4.8
12.9
13.3
1 0 .2
23.4
6 .6
16.8
18.7
24.2
33.8
1 0 .6
NEP
[x 1Q-17W/VH z]
2.73
2 .1 2
3.87
2.29
1.73
4.51
6.71
2 .1 2
0.90
3.27
5.94
5.27
9.65
2.44
6.56
10.9
7.5
19.2
4.38
N E T cmb
[yuKVsec]
129.4
81.2
169.2
79.5
74.5
199.5
229.5
81.4
35.8
382.8
184.5
137.6
343.5
101.3
r
[msec]
1 2 .6
12.5
12.3
1 0 .0
7.0
9.5
10.4
8.9
10.3
7.1
9.3
8 .8
-
-
1 2 .0
-
8 .6
-
-
-
5.9
5.2
-
Table 5.2: Bolometer characterization for MAXIMA-1: This table lists for each detector,
from left to right, the frequency band, the voltage noise (Vn) measured above the 1 /f knee,
the noise equivalent power ( N E P ) , the noise equivalent tem perature given a 2.73 K black
body spectrum (N E T cmi,). The final column lists the measured bolom eter response time,
r . D ata from the channels in b o ld were used for the final MAXIMA-1 d ata analysis.
Channels w ith prominent microphonic noise are marked with an asterix. The combined
sensitivity for all detectors of a given color is listed below the list of individual sensitivities.
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75
Channel
bl4**
b l5
b24**
b25**
b34
b35
b44
b45
< 150GHz >
b l3
b23
b33
b43
< 230GHz >
b l2 *
b2 2
b32
b42
< 410GHz >
< v >
[GHz]
150
150
150
150
150
150
150
150
150
230
230
230
230
230
410
410
410
410
410
Vn
[nV/VHi]
26.5
9.0
9.3
9.7
NEP
[x lO - 1 7 W /a/Hz]
7.51
2.38
8 .6
2.49
2.28
8.74
8.3
28.2
10.3
3.65
2 .8 8
2 .6 8
2 .6 6
1 .0 2
N E T cmb
[/iKy'secj
344.9
65.1
99.4
81.7
100.7
91.3
353.3
83.5
34.0
T
[msec]
12.5
11.5
10.25
11.9
6.25
7.75
8.25
8.25
-
-
-
-
-
1 0 .1
7.97
5.99
164.0
170.5
5.0
8.5
1 1 .8
-
-
-
-
7.68
18.8
12.4
11.7
18.9
7.17
4.79
17.5
15.0
13.1
23.6
8.08
118.2
-
-
14.0
6.5
2.5
3.0
-
-
-
Table 5.3: Bolometer characterization for MAXIMA-2: This table lists for each detector,
from left to right, the frequency band (< v > ), the voltage noise (Vn) measured above
the 1 /f knee, the noise equivalent power ( N E P ) , the noise equivalent tem perature given
a 2.73 K black body spectrum ( N E T cjnf)). The final column lists the measured bolometer
response time, r. Channels with prominent microphonic noise are marked with an asterix.
Channels with overwhelming low-frequency noise are marked w ith two asterices. The
combined sensitivity for all detectors of a given color is listed below the list of individual
sensitivities.
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76
combined NEP for channels of a given observation frequency is largely determ ined by the
subset of the best performing bolometers. For MAXIMA-1, we used the d ata from three
150 GHz and one 230 GHz channel to make maps of CMB tem perature anisotropy. D ata
from these channels and from one 410 GHz channel were used for system atic tests, notably
spectral discrimination of the signal from different foregrounds.
Most of the channels for MAXIMA-1 exhibited stationary noise throughout
the CMB observations.
The computed noise for each bolometer is Gaussian between
~ 500 mHz and 20 Hz for the healthiest channels. A bad solder connection in the analog
electronics produced interm ittent noise in all bolometer tim estream s at isolated times.
This issue affected less than 2% of the CMB data. These d ata were not analyzed. A
subset of the channels had high microphonic noise throughout the observation. These
channels were not included in the final analysis. Most tim estream s exhibited some degree
of low frequency noise which was correlated w ith the spatial m odulation of the prim ary
mirror. The higher observation frequency channels were more susceptible to this noise,
which suggests th a t the source of this signal is atmospheric emission. This mirror syn­
chronous signal proved to be stationary over long enough time scales, and we developed a
formal tem plate subtraction in subsequent analysis (Chapter 7).
For MAXIMA-2, non-stationary noise at low frequencies appeared in all chan­
nels.
The source of the noise is unknown.
The mirror synchronous noise appears in
the higher observation frequency channels, especially during the beginning of the second
CMB observation. The 1 / / knees in the respective noise spectra range from 1-6 Hz. The
150 GHz channels th a t were most affected are indicated in Table 5.3. The reported N E P
and N E T for these channels, which are calculated from the noise averaged over the signal
band from 7.0 ± 0.2 Hz, are not an accurate reflection of the overall noise performance.
Nonetheless, the combined sensitivity for each set of same observation frequency channels
is computed from these estimates.
The m agnitude of the low-frequency noise for each channel varies over the course
of the CMB observations.
Prelim inary analysis reveals th a t the d ata from the lowest
noise channels are still worth investigating if we marginalize over low frequencies. This
strategy im pacts the sensitivity w ith which the power spectrum can be estim ated on large
angular scales. At present, the power spectrum for I < 200 has been well constrained by
MAXIMA-1 and by other experiments. We hope to use the MAXIMA-2 data to better
constrain the power spectrum at higher multipoles.
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77
C h a p ter 6
O bservations
MAXIMA’S observation strategy is to make compact, crosslinked observations
of the CMB tem perature anisotropy over regions of the sky w ith low galactic and extragalactic dust contrast. We require an observation region of roughly 100 deg 2 in order not
to be sample variance limited at I = 80. These measurements are made during 4-8 hour
night time observations using a balloon borne telescope. The telescope is flown at an alti­
tude of 115-125 kft to minimize foreground contributions from the terrestrial atmosphere.
We observe at night to avoid detection of sunlight. The telescope is constrained to move
within elevation range of 20-55 deg to prevent detection of the earth, atmosphere, balloon
and gondola in the near sidelobes. The beam undergoes four distinct spatial modulations;
three from the attitu d e of the telescope and one from sky rotation. These modulations
carry CMB signal into the frequency signal band of the detectors (0.1 - 20 Hz).
We must generate an absolute calibration of the detector signals from an astrophysical source w ith a known tem perature and emission spectrum . We calibrate the 150
and 230 GHz detectors by observing the CMB tem perature dipole which COBE measured
to be 3.343 ± 0.016 m K . We calibrate the 410 GHz detectors and measure the beams
of all channels by scanning a solar system planet. We observed Jupiter for MAXIMA-1
and Mars for MAXIMA-2. A shift in the calibration caused by tim e dependent drifts in
detector responsivity is corrected by a periodic measurement of the relative calibration.
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78
6.1
6.1.1
Scan Strategy
C M B O bservation S trategy
Two competing factors determine the size of our scan region. The region must be
large enough to ensure th a t we are not sample variance limited at th e lowest multipoles we
seek to measure. The scan region must be small enough to allow adequate integration time
per pixel, assuming fixed observation time and detector sensitivity. According to Tegmark
(1997), the best strategy is to pick a sky area th a t yields a signal to noise ratio per pixel of
order unity. We maximize the angular resolution of our measurement by avoiding oblong
observation areas which are narrower than a few degrees.
roughly square, at least
10
x
10
MAXIMA observations are
° in area, which yields low sample variance in anisotropy
measurements down to I = 80. The size of the scan area also affects correlations between
multiple bins in the power spectrum . We can generate bins as narrow as A£ = 75 without
significant correlation w ith observations of this geometry.
Rapid modulations of the beam on the sky circumvents noise introduced by low
frequency drifts in detector response. Previous CMB tem perature anisotropy experiments
made detections through differencing (otherwise known as “chopping” ). These experi­
ments compared the signal on the sky against th a t of a calibrated load, or by rapidly
m odulating the telescope over two positions in the sky separated by a fixed angle. The
former m ethod significantly im pacts integration time on the sky and makes the d ata sen­
sitive to signals from sources such as the m odulator, the cryostat window and the atmo­
sphere. The latter m ethod only delivers information about the power spectrum at specific
multipoles. The MAXIMA telescope scans in a total power mode, which means the de­
tectors integrate w ithout interruption as the beams are swept continuously across the sky,
maximizing the tim e spent observing the sky and enabling one to measure tem perature
anisotropy over a continuous range of angular scales.
The beam is m odulated by four independent motions. First, we m odulate the
prim ary m irror in a periodic sawtooth scan w ith a 4 degree peak-to-peak throw in azimuth
at 0.45 Hz. This hardware is described in C hapter 4. The motion of the prim ary mirror is
superimposed on a similar but slower azimuthal scan of the entire gondola, actuated by the
two reaction wheels on the top of the gondola. These wheels are controlled by the attitude
control system (Rabii (2002)). The gondola scans in azim uth about a stellar target set
a fixed distance away from the NCP. A schematic of these two superposed modulations
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79
1+ 2
1+4
1+8
Tsiescope Beam Azimuth
Figure 6.1: Azimuthal modulations in MAXIMA-1: The azim uthal position of the tele­
scope on the sky is plotted as a function of time. Azimuth is defined as increasing clockwise
with respect to the NCP. This p attern is generated by the superposition of two periodic
sawtooth modulations from the prim ary telescope (2.2 sec period) and gondola (40-85 sec
period) modulations.
as a function of tim e and azimuthal angle is shown in Figure 6.1. For MAXIMA-1 and
MAXIMA-2, the gondola azimuthal throw varied from 4.5° to 9° p-p at speeds varying
from 12 - 25 mHz.
We consider sky rotation about the NCP w ith respect to the fixed elevation of the
telescope to be the third m odulation of the beams. The target and throw for the gondola
azimuth scan is selected such th a t sky rotation produces over
10
degrees of change in
elevation over the course of the scan while still yielding beam overlap between adjacent
azimuthal throws of the prim ary mirror. The resulting scan on the sky resembles th a t
shown in Figure 6.1, w ith elevation replacing time on the vertical axis, if we ignore slight
rotational corrections in elevation.
After the desired area on the sky is observed, we reset the scanning param eters of
the telescope back to the initial target and scan the same region again, yielding the fourth
spatial m odulation of the beams. Due to sky rotation, the azim uthal m odulation of the
telescope scans the sky at a different angle ( AO /A t = 15 deg/hr). The combination of the
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80
two scans produces a crosslinked map of the observed region of the sky. This significantly
reduces the effect of detector 1 / / noise on the subsequent maps.
6.1.2
Foreground R ejection
Far infrared and sub-millimeter astrophysical foregrounds introduce spurious sig­
nal into measurements of CMB tem perature anisotropy. We are concerned about contri­
butions from galactic and zodiacal dust, free-free and synchrotron radiation, the terrestrial
atmosphere, and radio and far-infrared point sources. Our choice of observation frequen­
cies (is > 150 GHz) lessens the foreground contributions from free-free and synchrotron
radiation, whose respective emission spectra each peak below 1 GHz and drop w ith increas­
ing frequency (see C hapter 2). Estim ates of brem sstrahlung and synchrotron radiation
(Bouchet h G ispert (1999)) predict contributions of less th a t 1 pK at 150 and 230 GHz.
By making partial sky observations, one can chose an area th a t is relatively
clear of known astrophysical foregrounds. Dust emission, synchrotron radiation and freefree emission are strongest along the galactic plane. We constrain our observations to
galactic latitudes higher than |6 | > 30. W ith the aid of the CMB experiment design
software tool FORECAST (Jaffe et al. (1999)), which extrapolates dust tem perature as
a function of frequency from the Berkeley-Durham IRAS-Dirbe map (Finkbeiner et al.
(1999)), it has been possible to select observation targets w ith 3.0 pK and 2.7 pK rms
dust tem perature variation at 150 GHz (assuming a dust emissivity index of 1.6) for
MAXIMA-1 and MAXIMA-2, respectively. The overlap of the MAXIMA-1 observation
w ith the IRAS-DIRBE map extrapolated to 150 GHz is shown in Figure 6.2.
By flying the telescope at an altitude of 115,000 - 125,000 feet, at a pressure of
~ 2.5 mbar, the column density of atmosphere reduces by a factor of 250. Atmospheric
emission is greatly reduced, but not completely. Three other properties allow for sys­
tem atic discrimination between CMB and atmospheric signals. First, the atmosphere is
essentially isotropic on angular scales less th an 1°. Second, the atmosphere is assumed to
be stationary on time scales of the telescope m odulation and of sky rotation. Last, the
410 GHz channels, which are significantly more sensitive to atm osphere th an the CMB,
serve as foreground monitors. We can use d ata from the 410 GHz detectors to develop
a tem plate subtraction of atmospheric signals in the tim e domain, as was done for the
MAXIMA-1 dipole calibration.
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81
Figure 6.2: MAXIMA-1 overlap w ith DIRBE map: The MAXIMA-1 CMB observation
scan (white) is plotted over the Berkeley-Durham IRAS-Dirbe map of the northern galactic
hemisphere dust emission extrapolated to 150 GHz (Finkbeiner et al. (1999)). Areas of
the sky w ith low dust contrast are shown as dark regions of the map. The MAXIMA-1
CMB observation region is constrained to b > 30°.
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82
The last foreground of issue is emission from extragalactic radio and far-infrared
point sources. Higher resolution experiments are increasingly sensitive to this foreground.
Point source foreground contributions dominate over diffuse galactic foregrounds if the
experim ent’s beam size is smaller than 0.5° (Toffolatti (1995)). By studying the IRAS
1.2 Jy survey, Gawiser & Smoot (1997) have determined th a t the infrared background is
manageable at frequencies lower than 300 GHz, for experiments w ith 10' or larger beams.
One can account for foreground contributions from the largest point sources (those with
an effective tem perature greater th an a few microkelvin) by removing those pixels from the
map in d ata analysis. Information on radio sources comes largely from the VLA 1.5 GHz
survey. It is difficult to extrapolate the microwave emission spectrum for extragalactic
radio sources considering uncertainties in our knowledge of elliptical galaxies and quasars.
Optim istic estimates state th a t fluctuations from the extragalactic radio background above
30 GHz, for experiments with 10' or larger beams, should be less th a n 10- 5 if 5a events
are first removed (Toffolatti (1995)). No connections were made to the MAXIMA-1 data
for any source of foreground emission.
6.2
Flights
MAXIMA-1 was launched at 00:58 UT on August 2, 1998 from the National Sci­
entific Ballooning Facility (NSBF) in Palestine, Texas (latitude 31.8°N, longitude 95.7°W).
The payload reached a flight altitude of 38.4 ± 0.4 km at 4.6 UT. Table 6.1 lists observa­
tion activities, including starting times and length of observation, for bo th flights. High
winds at float during MAXIMA-1 shortened projected observation times considerably. We
correspondingly performed the dipole calibration during ascent (see §6.2.1). We next con­
ducted two overlapping cross-linked CMB observations near the Draconis constellation.
The first CMB observation (CMB-1) began at 4:21 UT and lasted 1.6 hours. The second
(CMB-2) began at 6:00 UT and lasted 1.4 hours. The combination of these observations
covered a nearly square region of the sky w ith an area of 124 square degrees of which
~ 45% is crosslinked at an angle of ~ 22°. The average integration time per beam-size
pixel was 2.5 seconds. The flight concluded w ith an observation of Jupiter for purposes of
measuring beam maps and calibrating the 410 GHz detectors.
MAXIMA-2 was launched at 00:07 UT June 17, 1999 from the NSBF in Palestine,
Texas. The payload reached a float altitude of 38 km at 4:34 UT. Two overlapping CMB
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83
Observation / Activity
MAXIMA-1
Launch
Dipole
CMB 1
CMB 2
Jupiter
Termination
Total time at float
Total time of flight
Starting Time
U.T.
00:58
03.36
04:21
06:00
7:30
8:06
Observation / Activity
MAXIMA-2
Launch
Mars
CMB 1
CMB 2
Dipole
Daytime scan tests
Term ination
Total time at float
Total time of flight
Starting Time
U.T.
00:07
03:14
05:22
07:38
09:40
10:18
-
-
1 2 :2 1
-
-
D uration
[hr]
-
0 .6
1 .6
1.4
0 .6
3.5
7.1
D uration
N
-
0 .6
2.4
2 .2
0 .6
0.7
7.8
1 2 .2
Table 6.1: MAXIMA-1 and MAXIMA-2 flight timetables: The starting times (in U.T.) and
duration for each observation activity are listed for MAXIMA-1 (top table) and MAXIM A2 (bottom table). The CMB dipole observation for MAXIMA-1 took place during ascent.
observations were made again near the Draconis constellation. The first CMB observation
(CMB-1) began at 5:22 UT and lasted 2.4 hours. The second scan began at 7.38 UT
and lasted 2.2 hours.
The combination of these observations covered a nearly square
region of the sky with an area of 255 square degrees of which ~ 60% is crosslinked at an
angle of ~ 27° w ith roughly 50 degrees of overlap w ith the observations of MAXIMA-1.
The average integration tim e per beam-size pixel was 2.2 seconds. Both MAXIMA-1 and
MAXIMA-2 observations are shown in Figure 6.3. Observations of the CMB dipole and
Mars provided absolute calibrations and beam measurements of all photom eters. After
sunrise, a brief third CMB observation was made to test the daytime performance of the
experiment.
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84
64
62
<8 6 0
<
P
k_
U1
3
c
58
*-p
56
o
o
c
t- A
cu 5 4
Q
52
50
13
14
15
16
Right A sce nsion ( h o u r s )
17
Figure 6.3: MAXIMA-1 & MAXIMA-2 observations: The telescope scans for bo th flights
are displayed as a function of right ascension (RA) and declination (DEC) on the sky. The
MAXIMA-1 scans are shown in yellow (light grey) and the MAXIMA-2 scans are shown
in red (dark grey). Boxes are drawn around the two respective scans for each flight.
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85
6 . 2.1
C alibration
For bo th flights, full beam calibrations of the 150 and 230 GHz photometers
were obtained from the CMB dipole. We perform the calibration in flight by spinning
the gondola continuously w ith the telescope at fixed elevation and observing the dipole
for approximately 40 minutes. The gondola performs 360° azim uthal rotations, which
generates a circular scan on the sky. The gondola spin speed is set at 3.3 rpm, so th a t the
observed sinusoidal signal falls w ithin the signal band of the detectors. The elevation is set
such th a t telescope scans over a significant gradient of the CMB dipole. For MAXIMA-1,
we observed an effective tem perature dipole am plitude of 4.08 mK p-p and for MAXIMA-2,
3.30 mK p-p.
In order to determine the calibration, we analyze the d ata as follows; an offset,
gradient and quadratic term are removed from the relevant bolometer timestreams. We
deconvolve the measured electronics response function from the data.
We generate a
pointing solution during the observation from the pointing sensor data. Using this solution,
we generate a simulated tim estream of the CMB dipole and dust tem perature for each
photom eter using the FORECAST CMB observation planning software package.
Given a projected observing time at float altitude of less th an 4 hours for
MAXIMA-1, we observed the CMB dipole early on in the flight before achieving float
altitude (38 km). The MAXIMA-1 CMB dipole observation occurred during ascent, at an
altitude of 32-38 km. Observing at these lower altitudes resulted in correlated atmospheric
signal in all detectors. In the analysis, we assume th a t all of the signal in the 410 GHz
channel comes from high frequency foregrounds such as galactic dust and the atmosphere,
and use the tim estream from a a selected detector as the measurement of the atmospheric
contribution.
We regress the dipole and dust models and the measured signal from a 410 GHz
channel from the 150 and 230 GHz channels. Galaxy crossings produce large spikes in the
bolometer time streams. Given th a t the 10' FWHM beams significantly smear the struc­
ture in the galaxy, it is difficult to accurately regress the dust model from the bolometer
signal. We chose instead to cut out d ata at galaxy crossings, using an 2a deviation from
the mean of the bolometer signal as a threshold. The regression coefficient for the dipole
model gives us a calibration in units of Volts/K. We do not need to factor in any spectral
band power corrections since the spectral morphology of both the dipole and higher order
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86
1 .5 F
1 . 0 Er
0.
0.
0,
1
1
0
20
40
60
80
100
120
Time [s]
......... ....
111!
E
i:
1
E
mi
E
fill
III!
0
20
40
60
80
100
120
Time [s]
Figure 6.4: MAXIMA-2 dipole calibration: The top line of the top plot is d ata from
one of the 150 GHz channels, and the bottom line is out best fit model containing the
COBE-DMR measured dipole and IR A S/D IR B E dust maps. The bottom plot shows the
difference between the two. The difference is statistically consistent w ith zero, except at
the galaxy crossings. We do not include the d ata near galaxy crossings in our calibration
regression.
spatial fluctuations of the CMB are identical. Plots of a bolometer time stream , the model
and the difference of these two are shown in Figure 6.4. More details about the analysis
can be found in Rabii (2002).
C alibration uncertainties of 4% and 3% in tem perature were obtained respec­
tively for MAXIMA-1 and MAXIMA-2 from the CMB dipole observation. A secondary
calibration and beam contour maps for all detectors were obtained from observations of
planets (Jupiter in MAXIMA-1, Mars in MAXIMA-2). Refer to C hapter 4 for more detail
on beammaps. To calibrate, we assume th a t the bolometer voltage when the observed
planet is in the center of the beam is a measurement of the beam -diluted tem perature of
the planet. The tem perature of Jupiter is 169 K at 150 GHz, 165 K at 230 GHz and 133 K
at 410 GHz. The tem perature of Mars is a constant 196 K across the observation band.
Both planets are effectively Raleigh-Jeans sources for the observation bands. We apply a
spectral band power correction to the planet calibration, K pianet, to calculate an effective
calibration, K cmb, for a black body source w ith a tem perature of 2.73 K;
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87
K a n t = K ru „ ,
f
^
’
\Tplanej ( v ) d v
(<U)
where B(v ) is the spectral intensity of the CMB or the planet, r(u) is the measured spectral
transm ittance for a given photom eter, and K is in units of Volts/K. Sources of uncertainty
in the planet calibration include the beam, the planet tem perature and emission spectrum,
the photom eter transm ittance spectra, and noise in the bolometer tim e stream.
A relative calibration is obtained during CMB anisotropy observations by peri­
odically firing an internal calibrator directly into the feedhorns. The internal calibrator is
an em itting composite bolometer whose bias current is stable w ithin 0.1%. We can com­
pare the two absolute calibrations (which occur at different times in each flight) through
extrapolation using the relative calibration. We determine th a t the dipole and planet
calibrations are consistent w ithin error for both MAXIMA-1 and MAXIMA-2. Refer to
Rabii (2002) for more detail on in-flight calibration.
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C h a p ter 7
D ata A nalysis and R esu lts
We generate tem perature maps from the MAXIMA data. From these maps, we
can estimate the tem perature power spectrum , Cg, as a function of multipole moment, I.
In turn, we can constrain the set of viable cosmological models by comparing the measured
power spectrum with those computed analytically from various predictions. We can also
constrain the values of cosmological param eters assuming general classes of cosmological
models.
The published results for MAXIMA-1 are presented in this chapter, as well as
an overview of the entire d ata analysis pipeline. Results from the 3' pixel analysis of
MAXIMA-1 (Lee et al. (2001), Stompor et al. (2001)) are prim arily discussed. Results
from the earlier 5' pixel analysis (Balbi et al. (2000), Hanany et al. (2000)) are presented
as a cross-check of the analysis methods. Also presented are the results of systematic
tests on bo th final and intermediary results, which allow us to test for the presence of
non-Gaussian instrum ental noise and astrophysical foregrounds in our detections. The
analysis methods are also subjected to rigorous testing with sim ulated d ata and through
other cross-checks.
7.1
D ata A nalysis P ipeline
The MAXIMA-1 data set consists of approximately 2,300,000 measurements from
each of the 16 photometers.
These d ata are of low signal to noise.
The analysis of
this d ata set requires specialized, com putationally efficient algorithms for determining the
maximum-likelihood map from the data. The validity of the result is determ ined through
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89
Raw time ordered
detector data
Raw time ordered
pointing sensor data
Generate pointing
solution
Process time ordered
detector data
Estimate detector
noise power spectrum
Map making
Pixel based
noise correlations
Power spectra
Parameter Estimation
Systematic Tests
Figure 7.1: MAXIMA d ata analysis pipeline: The flowchart above breaks down the major
tasks involved analyzing MAXIMA data, from raw time stream s to maps, power spectra
and cosmological param eter estimates. Arrows indicate the task order. A dotted line
denotes th a t the tasks at the intersection of two lines are not connected.
both iterative analysis methods and an exhaustive set of system atic tests.
The procedure for generating maps, power spectra and cosmological param eter
estimates from the MAXIMA d ata is described below and is visually summarized in Figure
7.1. We applied these analysis techniques to both MAXIMA d ata sets. In this section,
we discuss both intermediary results and specific analysis examples from the published
MAXIMA-1 d ata set.
7.1.1
P rocessin g T im e Ordered D ata
We begin w ith the raw detector time stream s and pointing sensor data. We first
identify the sections of each detector time stream th a t are corrupted by readily identifiable
non-Gaussian noise or by telem etry drop-outs. We flag data th a t deviate by > 4cr due
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90
to cosmic ray detections, transient fluctuations in the bolometer read-out electronics and
telemetry drop-outs. Overall, we flagged 2 - 3% of the MAXIMA-1 d ata from the six
detector tim e stream s analyzed for publication. These d ata were removed, creating gaps
in the respective detector time streams. We filled these gaps w ith a constrained noise
realization as estim ated from the neighboring d ata (see §7.1.2).
Each detector time stream was divided into two parts corresponding to the two
CMB anisotropy observations made at different fixed elevations (CMB scan 1 and CMB
scan 2). The map-making and noise estim ation techniques require th a t the noise of the
detector time stream s be Gaussian and stationary. For both MAXIMA-1 and MAXIMA2
, the assum ption of stationarity is only valid if we divide the time stream s into shorter
segments ranging in length from ~ 2 - 20 minutes (30,000 - 250,000 samples).
D ata
between segments were removed to minimize correlations between segments. D ata from
the two MAXIMA-1 CMB observations were divided into 11 and 10 segments, respectively.
During observations, bolometer signal was filtered by the low-pass filter due to
the bolometer time constant and the band filters in the bolometer read-out electronics.
These complex filters are phase-shifting and do not preserve the am plitude of the output
signal. We characterized the read-out electronics high-pass and low-pass filter response
functions in the laboratory between MAXIMA flights. We determ ined the bolometer time
constants using the in-flight detector response to a known source (Jupiter for MAXIMA1, Mars for MAXIMA-2). These measurements are described in C hapter 5. The errors
in the filter measurement were small and were neglected. The filters were deconvolved
from the detector time streams during the map-making procedure. We marginalized over
frequencies lower th an 0.1 Hz and higher th an 30 Hz where we did not expect appreciable
optical signals.
We calibrated the detector output during the flight from known astrophysical
sources, as described in C hapter
6
. We obtained an overall calibration uncertainty of 4%
and 3% in tem perature for MAXIMA-1 and MAXIMA-2, respectively.
7.1.2
N oise E stim ation
The detector time streams consisted mostly of noise. This noise must be precisely
characterized in order to correctly extract signal from the d ata during the map-making
stage of analysis.
We assumed th a t the noise in the detector tim e stream s could be
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91
separated into the following uncorrelated terms; white (Gaussian) noise arising from a
combination of photon, Johnson, therm al fluctuation and amplifier noise in the bolometers
(Chapter 5), 1 / /
noise arising from fluctuations in the operating tem perature of the
cryostat, spatially correlated'm irror synchronous” noise occurring over tim e scales of the
prim ary mirror throw, and non-Gaussian transients due to telem etry drop-outs and cosmic
ray hits.
We presumed th a t the “mirror synchronous” component of the detector noise
was due to large scale gradients in atmospheric emission over th e angular range of the
azimuthal throw of the prim ary mirror (4° p -p). This periodic signal was stationary over
the length of each CMB observation segment (2 - 20 minutes), and has an am plitude of
~ 100 fiK in the 150 GHz channels. For each segment, we generated a tem plate for the
spurious signal which was subsequently subtracted.
We filled the gaps in each detector time stream using a constrained realization
of the measured detector noise. We generated these realizations by taking averages of the
estim ated power spectra of pre-whitened gap-free segments of the detector time streams.
These segments were longer than the expected noise correlation length. We then verified
th a t the power spectrum of the restored time stream matched th a t of the subsegments.
Both the pre-whitening and instrum ental filters were then deconvolved from the detector
time streams.
Formally, we require the full time-time noise correlation m atrix to generate the
maximum-likelihood map. For an idealized time stream of finite length, the circulant noise
m atrix is expressed as
(7.1)
where P ( f ) is the power spectrum of the time stream and A is the d ata sampling interval.
If the noise correlation length, Ac, is shorter th an the length of the tim e stream , n, we can
assume a band diagonal noise correlation m atrix, Nt, where
N ct {i, j) , if \ i ~ j | < m in (n / 2 , Ac),
0
, else
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(7.2)
92
7.1.3
P o in tin g R econ stru ction
We reconstructed a time ordered pointing solution for each photom eter using ob­
servations of guide stars by two optical CCD cameras and measurements of the azimuthal
throw of the prim ary mirror during flight. The relative offset between the beam for each
photom eter and the center of the prim ary mirror on the sky was measured w ith respect
to a known astrophysical source (the planet) during flight. We obtained an overall un­
certainty of V in the pointing solution for bo th MAXIMA-1 and MAXIMA-2. Pointing
reconstruction is described in greater detail in Rabii (2002).
The detector time stream s and pointing reconstruction were then combined. We
assigned the detector d ata to fixed sized spatial pixels. Given the small angular size of
the observing regions, we used simple square pixels. The flagged sections of the detector
time stream s were assigned to a fictitious pixel w ith zero weight, which was not considered
in power spectra or cosmological param eter estimation. The highest angular resolution
analyses were performed on 3' pixel maps. Most systematic tests were performed on 8 '
square pixel maps to minimize com putational time.
7.1.4
M ap M aking
The detector time stream , dt, can be expressed as
dt = A m p + n t ,
(7.3)
where A is a pointing m atrix assigning each time sample to an appropriate pixel, m p is the
sky signal given by a pixelized map, and nt is the noise in the tim e domain. The maximum
likelihood estim ate of the map, m p, and the pixel domain noise correlation m atrix N p are
m p = (AT N f 1 A) ~ 1 A TN f 1dt ,
(7.4)
N p = (AT N f 1A ) - \
(7.5)
where N ^ 1 is the inverse time-time noise correlation m atrix. Usually, the inversion of the
time domain noise m atrix is the most com putationally intensive step in the maximumlikelihood map-making procedure. C om putational tim e savings can be made if rather than
explicitly inverting the noise m atrix, one uses th a t approxim ation th a t
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93
,,
I N r } ( i , j ) , if \i - j\ < m in(n/2, Ac), I
N f (i, j) ~
ctX , Jh
1
J' ~
?.
[ 0 , else
J
(7.6)
This approxim ation was introduced by Ferreira & Jaffe (2000), was incorporated into the
MADCAP package by Borrill (1999). The approxim ate inverse noise m atrix, lVt~ 1 (i,j),
can be computed element by element with FFT s in n lo g n operations, where n is the
number of tim e domain samples, assuming band diagonality of the noise matrix.
Comparison of exact and approxim ate m ethods yielded results th a t are broadly
consistent at the noise level of MAXIMA-1 maps (Stompor et al. (2002a). The relative
differences of maps were of order
10
%, which am ounts to less th an
10
% of the rms noise
level predicted per pixel, on average. While the noise correlation length could vary over
the course of observation in a given data segment, maps generated by the approximate
m ethods are generally insensitive to the choice of Ac if it is sufficiently large.
An exact inversion of the pixel-domain noise correlation m atrix is possible assum­
ing th at it is band diagonal. Noise inversion in the pixel domain requires n p steps, where
np is the number of pixels. We assume th a t n p <C n. Such inversions are com putationally
feasible for the MAXIMA-1 d ata set, where the maps have ~ 105 pixels.
The m irror synchronous signal was removed from the map by amending the
pointing m atrix. The extra signal was assigned to fictitious spatial pixels which were
later marginalized over in the estim ation of the maximum-likelihood map. The flagged
regions of the time stream were similarly marginalized over. This procedure is explained
in Stompor et al. (2002a).
The above m ethod assumes th a t the time stream signal is dom inated by noise.
We relaxed our requirements on this assum ption by estim ating noise iteratively.
We
computed a map by the above method, which is then used to estim ate the signal in the
time stream . In the next iterative step, the estim ated signal was subtracted from the time
stream, and the map-making procedure was repeated. We have found th a t iterative noise
estim ation combined with marginalization effectively removes sources of non-stationary
noise and extraneous (non-CMB) sky signal from the resulting map.
The different segments were co-added with the correct offset removal by requiring
th a t the same underlying p attern be displayed in overlapping segments. The crosslinked
scan pattern yields overlap in 14 of the 21 CMB observation segments for MAXIMA-1.
The 7 remaining disconnected segments were not used is the final analysis. Maps from
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94
different photom eters were combined with a weighting th a t is inversely proportional to the
respective noise correlation matrices. We produced an effective beam for the combined
map from the noise weighted averaging of the individual beams. We assumed the largest
single detector calibration error for the calibration uncertainty of the entire map.
7.1.5
Pow er Spectra E stim ation
The conditional probability for a power spectrum Ci, given a map to, can be
expressed as a Gaussian likelihood;
P(Ci\m) oc exp
j —^ ( m T M ~ 1m + T r[In M ])| .
(7.7)
M is a map correlation m atrix th a t is treated as a param eter to be varied until P is
maximized. The m atrix M — S + T is the sum of contributions from a sky model S
and from measured pixel-pixel noise correlations T . The sky model S is generated from
a candidate power spectrum Ci and is convolved w ith the measured experimental beam.
Maximizing P over possible M ’s results in finding the maximum likelihood Ci, given to.
We have implemented algorithms for calculating maximum-likelihood power spec­
tra th a t use massively parallel processing based on the work of Bond et al. (1998) and
Ferreira & Jaffe (2000). These algorithms are implemented in the MADCAP CMB data
analysis package (Borrill (1999)).
Precise understanding of the beam is im portant in determ ining the power spec­
trum accurately for I > 300, a range which includes the theoretical location of the second
and third density peaks in flat adiabatic inflationary models. Beyond I ~ 1000, the pre­
dicted power spectrum falls roughly as I2. The MADCAP im plem entation assumes that
the beams are axially symmetric. Beam characterization is discussed in C hapter 4. The
pixelization of the maps smears features on angular scales smaller th an the pixel size. We
deconvolve a pixel window function while estim ating the power spectrum of the map to
account for the extra smoothing introduced by the pixel.
We calculated the MAXIMA power spectrum using bins of finite w idth in i
assuming a constant £(£ + l)Ci /2n = C b band power in each bin. We use bins of finite
width, L, to minimize correlations between bins and to increase the signal to noise of the
measurement per bin.
Given MAXIMA’S limited sky coverage, we could not meaningfully calculate Ci
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95
for t < 30 given sample variance. We marginalized over low and high £ (I < 35, £ > 785
in Hanany et al. (2000), £ < 35,1? > 1235 in Lee et al. (2001)). We also marginalized over
the CMB monopole and dipole. We had the choice of diagonalizing the t'-bin correlation
m atrix to fully uncorrelate the measurements in different bins, which has the trade-off of
distorting the window function of each bin from a simple top-hat w ith w idth L.
7.1.6
Param eter E stim ation
The power spectrum of the CMB can be analytically com puted from theoretical
cosmological models. We estim ated cosmological param eters from the set of measured
{C b ) through a maximum-likelihood comparison with theoretical spectra com puted over a
multi-dimensional param eter space. We used a Gaussian likelihood in the offset lognormal
form ln(CB + x b ), w ith x b related to the noise properties of the instrum ent, following
Bond et al. (2000).
For MAXIMA-1, we considered only adiabatic inflationary models. At the time
of publication, alternate models were in poor agreement with previous measurements of
CMB anisotropy and galaxy clustering. Angular power spectra are straightforward to
calculate for adiabatic inflationary models for given cosmological param eters, especially
w ith the availability of com putational packages like CMBFAST (Seljak & Zaldarriaga
(1996)) and CAMB (Lewis et al. (2000)).
We com puted models over a seven-dimensional param eter space which included
the am plitude of fluctuations at £ —
1 0
physical density of cold dark m atter, Oc d
energy density of the universe, fI = flm +
, C\o, the physical baryon density, fh,/i2, the
m h 2 ,
and cosmological constant,
the total
(where the fractional density of pressureless
m atter is fim = fl&+flcdm), the spectral index of prim ordial scalar fluctuations, n s, and the
optical depth of reionization, r c. We used the ranges and sampling shown in Table 7.1. To
ensure th a t the set of param eters was sampled with enough resolution, we included models
corresponding to values of the param eters th a t were not on the grid by quadratically
interpolating between power spectra. The dependence of th e power spectrum on these
param eters is discussed in C hapter 2. We imposed top-hat priors for the value of the
Hubble constant 0.4 < h < 0.9, the m atter density fim > 0 .1 and the age of the Universe
> 10 Gyr. We included the 4-year COBE-DMR angular power spectrum from Gorski
et al. (1996) in our analysis to normalize models at large angular scales (2 < £ < 34).
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96
Param eter
C'io
n
Qbh?
^cdm fa
Tc
ns
Param eter space
continuous
(0.3,0.5,0.6,0.7,0.75,..., 1.2,1.3,1.5)
(0.00325,0.00625,0.01,0.015,0.02,0.0225,..., 0.04,0.0045,0.005,0.075,0.1)
(0.03,0.06,0.12,0.17,0.22,0.27,0.33,0.40,0.55,0.8)
(0 .0 , 0 .1 , 0 .2 ,..., 1 )
(0,0.025,0.05,0.075,0.1,0.15,0.2,0.3,0.5)
(0.6,0.7,0.75,0.8,0.85,0.875,..., 1.2,1.25,..., 1.5)
Table 7.1: Ranges and sampling for param eter estimation: W ith the exception of C\ q, the
param eters are all dimensionless.
7.2
7.2.1
R esults
M aps
The maximum-likelihood 3' pixel map computed from d ata from three 150 GHz
detectors is shown in Figure 7.2. The map contains ~ 40,000 pixels. The pixel size does
not compromise the resolution of the map (Wu et al. (2001a)). We previously computed a
5' pixel map (Hanany et al. (2000)) from these three detectors and an additional 230 GHz
detector. We exclude the 230 GHz detector d ata in the 3' map because the power spectrum
of difference maps between the 230 GHz d ata and the 150 GHz d ata are inconsistent with
zero above £ = 785. This discrepancy may be explained by the higher level of “mirror
synchronous” noise in the 230 GHz data (larger by a factor of ~ 2).
7.2.2
Pow er Spectra
The power spectrum is calculated from ~ 23,000 pixels from a central square
region of the map (shown outlined in white in Figure 7.2). The central region encompasses
approximately half the area of the entire map (60 deg2) where th e observations are fully
cross linked, the signal-to-noise ratio is highest and the sampling is most uniform. The
downside of using a smaller portion of the map is a rise in sample variance, which increases
the error in the estim ation of the power spectrum prim arily at low £ . We have created
a composite power spectrum , shown in Figure 7.3, using the £ < 335 points from Hanany
et al. (2000), derived from a 5' pixel map.
This choice of transition point limits the
minimum error bar increase to ~ 20%. Correlations are less th a n 10% between dominant
and adjacent bins for each set of measurements.
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97
Figure 7.2: Maximum-likelihood 3' pixel MAXIMA-1 tem perature map: This map was
computed from d ata from three 150 GHz detectors and contains ~ 40,000 pixels. The
resolution of the map is determined by the 10r FWHM beams of the experiment. The
tem perature scale ranges from —800 /zK (black) to +800 fiK (white). We define a square,
central region of the map, outlined in white, covering ~ 60 deg 2 and containing ~ 23,000
pixels, from which we estim ate a power spectrum (Lee et al. (2001)).
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98
8000
MAXIMA—I + DMR (L ee e t al. 2 0 0 1 )
„ „
MAXIMA-I + DMR ( H a n a n y e t a l. 2 0 0 0 )
MAXIMA-I + DMR + SBBN
M
a.
6000
4000
o
+
2000
0
200
400
600
I
800
1 0 0 0
1 2 0 0
Figure 7.3: Composite power spectrum from 3' and 5' pixelized maps: D ata from I < 335
are from the full map w ith 5' pixels (Hanany et al. (2000)) and d ata from I > 335 are from
the central region of the map w ith 3' pixels (Lee et al. (2001)). The points are plotted
with lcr error bars. The best fit adiabatic inflationary model to these d ata is plotted with
a solid line. The best fit model from the 5' square pixel map is plotted w ith a dashed
line. The best fit model from these d ata and estimates of
from BBN constraints are
plotted w ith a dotted line. The l a estim ate of the power spectrum for the expanded bins
are shown as gray shaded rectangles (Stompor et al. (2001)).
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99
^e//
[£m im £m ax ]
77
147
[ 36, 110]
[ 111, 185]
[ 186, 260]
[ 261, 335]
[ 336, 410]
[ 411, 485]
[ 486, 560]
[ 561, 635]
[ 636, 710]
[ 711, 785]
[ 786, 935]
[ 936, 1085]
[ 1086, 1235]
£(£ + l)Ci/2ir
( / ^ 2)
222
294
381
449
523
597
671
746
856
1004
1147
19991 fog
2 9 6 OI 5 5 4
6 0 9 2 l^ f
38301^7
22701 4 7 ?
1468111
19351H
18111111
2 1 0 0 lf H
2189±68q
3104t® !
1084ll20!
rycyq + 2 7 9 1
Beam Error
Pointing Error
(% )
(%)
± 0
± 0
± 0 .6
±1.5
±2.5
±3.5
± 0 .2
±0.4
± 0 .8
± 1 .2
±1.7
±2.3
±3.0
±3.7
±4.6
±5.6
±7.7
± 1 0 .2
+5
- 4 .5
+ 6 .5
-6
+8
-7
+ 9 .5
- 8 .5
+11
-10
+14
-12
+ 18
-1 5
+25
-1 8
ZZO-2 0 2 5
AT
(/+K )
451^
54l®
781®
621®
481®
38l®
4 4 I®
431®
461®
471®
56l£
oq+13
—22
ik +29
—15
0
Table 7.2: Power spectrum measurements from the MAXIMA-1 map: D ata from £ < 335
are from the full map w ith 5' pixels (Hanany et al. (2000)) and d ata from I > 335 are
from the central region of the map with 3' pixels (Lee et al. (2001)). l a errors are quoted
w ith 6 8 % confidence. Uncertainties in the beam and in pointing reconstruction give the
listed correlated errors. We also list the rms tem perature anisotropy, A T, over the listed
£ -bin.
The dominant bins, Ci estimates and tem perature estim ates for the composite
power spectrum are listed in Table 7.2, along with beam and pointing error contributions.
The l a errors are quoted assuming
6 8
% confidence intervals, and do not include contribu­
tions of system atic error from calibration, beam uncertainty or pointing reconstruction.
The Ict calibration error is a constant 8 % of 1(1 + l)Q /2 7 r.
The uncertainty and asymmetry in beam shapes introduces an error in Ct which
is less th an 1% at I — 1000 (Wu et al. (2001a)). The uncertainty in the bolometer time
constants gives an error in Ci th a t increases with I . The error is
6
% at I = 500 at
17% at I = 1000. These errors are correlated in I , which introduces a systematic overor underestim ate of the power spectrum with an am plitude th a t increases w ith I . We
increase the bin size from L = 75 to L = 150 for £ > 800 to suppress these correlations.
Simulations reveal th a t a Gaussian pointing reconstruction error leads to a sys­
tem atic underestim ate of the power spectrum at high £ . The actual pointing error is not
completely Gaussian, so we apply a conservative symmetric random pointing error equal
to the size of the bias which is bCijCi ~
10
% at £ =
1 0 0 0
.
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100
Analytical power spectra computed from adiabatic inflationary models fit the
data well, as will be discussed in §7.2.3. Nevertheless, it is im portant to assess the com­
patibility of the measured power spectrum with general classes of models. The points
shown in Figure 7.3 clearly show a rise in power from I = 77 to I = 222, w ith a subse­
quent decrease in power until I = 449. Beyond this bin, the presence of additional peaks
must be assessed by a statistical likelihood approach (Stompor et al. (2001)). It appears
th a t there is excess power in the bin centered at £ = 860. We com pute the bin powers
for bins, Bo, 411 < £ < 785, B\ , 786 < £ < 925, Bi, 926 < £ < 1235, as shown in the
shaded regions of Figure 7.3. We compute th a t the ratio of the power in B \ versus Bo is
Roi = 0.49±g;|f and is thus lower th an 1 at the ~ 95% confidence level. The statistical
confidence for a drop in power beyond I = 925 falls to ~ 80% due to larger uncertainties.
The excess power appears where one would expect the presence of the th ird acous­
tic peak in an adiabatic inflationary power spectrum , assuming a first peak at £ ~
2 2 0
.
These models also predict the presence of a second peak in the range 410 < £ < 785. The
points in bin B q are well fit by a single flat band power (with x 2 = 1.5), but the presence
of a second peak w ith smaller am plitude than the th ird is still statistically probable.
We have recently computed power spectra from the entire 3' pixel map, as shown
in Figure 7.4 (Borrill (2002)). This figure gives two estimates of the power spectrum for
interleaving sets of £-bins. The two estimates are correlated. Nevertheless, this analysis
yields the suggestion of a second and third acoustic peak in the power spectrum .
7.2.3
P aram eter E stim ates
We compute the likelihood on the seven dimensional grid of param eters for adi­
abatic inflationary models from the measured power spectrum using th e offset log normal
Bayesian approxim ation of Bond et al. (2000). The 95% confidence level (c.l.) estimates
of five cosmological param eters are listed in Table 7.3. A strong degeneracy exists be­
tween estim ates of r c and n B. If we constrain n s to be less th an 1.2, we recover r c < 0.4
(95% c.l.), consistent with recent measurements from the WMAP satellite (Spergel et al.
(2003)). We can constrain n s > 0.8 (99% c.l.) independent of the value of the optical
depth.
The x 2 for the best fit model for all param eters is 30 for all 41 points (combined
MAXIMA-1 and COBE-DMR) and is 4 for the 13 points of MAXIMA-1. We recover best
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101
MAXIMA1 : 3 C h a n n e l, 3 ' P ix e ls, Full M ap, M o n o p o le-D ip o le -D u st-S y n ch ro tro n M arg in a liz ed
8000
6000
2000
-2000
1200
M ultipole
Figure 7.4: Interleaved power spectra from the full MAXIMA-1 3' pixelized map: Shown
in red (solid) and blue (dashed) are two estimates of the MAXIMA-1 power spectrum in
units of jj,K2 w ith l a error bars over ten bins, each bin L = 100 wide (Borrill (2002)).
Param eter
95% c.l. estimate
Q
Qbh2
ttcdmh2
ns
6901^25 mK2
0.9±g;i|
0.033 ± 0.013
0.17tjj;J?
(0.99 ± 0.14) + 0.46rc (rc < 0.5)
“
Table 7.3: Bayesian param eter estimates from MAXIMA-1 and COBE-DMR data: Errors
are quoted at the 95% confidence level (Stompor et al. (2001)).
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102
1. 0
0.8
0.6
<
c
0.4
MAXIMA-1
k+COBE
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Figure 7.5: C onstraints on Dm - Da plane from combined MAXIMA-1 and COBE-DMR
datasets: The contours correspond to the 6 8 , 95 and 99% confidence levels. These contours
are overlaid on the bounds obtained from high redshift supernovae d ata (Perlm utter et al.
(1999), Riess et al. (1998)). The confidence levels of the joint likelihood are shown in black
(Stompor et al. (2001)).
fit model param eters (fib, D^™, Da, t c, n s, h) = (0.07,0.68,0.1,1.0,0.0,1.025,0.63). The
power spectrum of this model is shown with a solid line in Figure 7.3. This model is marked
by a low vacuum energy and high m atter content. However, the strong degeneracy between
Da and Dm allows us to find models which are consistent w ith MAXIMA-1, COBEDMR and supernovae constraints, as shown in Figure 7.5. Using all three d ata sets, we
constrain our estimates of the dark energy content and m atter density to Dm = 0.324q!ii ,
Da = 0.65lg;^ (95% c.l.).
Our estim ate of the total energy density of the universe is consistent w ith models
where the universe is flat (D = 1).
The constraint on Qbh2 is compatible with that
based on measurements of prim ordial deuterium and on calculations of standard BBN;
Dft/j2 = 0.020 ± 0.002. (Tytler et al. (2000), Buries et al. (2001)). It is also compatible
w ith the latest constraints from the WMAP satellite measurements; D&h2 = 0.024 ± 0.001
(Spergel et al. (2003)). If we fix the value for Qbh2 to the allowed valued nearest to the BBN
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103
prediction, 0 .0 2 , we recover a best fit model w ith the param eters (fib, f lcdm->
tc, n s,h)
—
(0.07,0.78,0.0,0.0,1.0,0.53) with x 2 — 7 for the 13 MAXIMA-1 points only. The power
spectrum of this model is shown w ith a dotted line in Figure 7.3.
In Bayesian estimates of cosmological param eters, the outcome depends strongly
on existing priors.
We have made a frequentist estim ate of cosmological param eters,
described in Abroe et al. (2002). which is independent of priors. T he resulting estimates
are consistent with those from Stompor et al. (2001), albeit w ith larger error bars due to
the lack of initial priors.
7.3
7.3.1
System atic Tests
Sim ulations
We test the d ata analysis pipeline by analyzing simulations of CMB data. We
generate simulations of the detector time stream s from Gaussian realizations of the sky
which are calculated from a given adiabatic inflationary model and from realizations of
the measured detector noise. We verify th a t the d ata analysis pipeline recovers the initial
power spectrum used to generate the simulation.
7.3.2
C om parison and N ull T ests
We generate maps and power spectra from the following (combinations of) data
which, in principle, should yield no cosmological signal;
1
. a dark bolometer
2. the d ata from a 410 GHz photom eter
3. the difference between the overlapping regions of the CMB-1 and -2 scans
4. the difference between maps produced by different (set of) photom eters
A difference map is the unweighted difference of pixels common to both maps.
These maps are all consistent with noise, as determ ined by the following statistical tests;
X2
of the noise-weighted map, the one dimensional Kolmogorov-Smirnov test, through
determ ination of the “null-buster” statistic (Tegmark et al. (1999)), and through determi­
nation of the probability enhancement factor (Knox et al. (1998)). For more details, see
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Figure 7.6: Combined and difference maps for four photometers, (Three 150 GHz, one 230
GHz), calculated w ith 8 ' square pixels. The tem perature scale for bo th maps ranges from
-400 fj,K (black) to +400 fj,K (white) (Stompor et al. (2002b)).
Stompor et al. (2002b). The comparison between the 8' pixel sum and difference maps for
four photom eters is shown in Figure 7.6. Note th a t the sum maps are calculated through
the noise-weighted co-addition of the constituent maps.
We can compare detections made from different photom eters by estim ating an­
gular power spectra. The power spectra for the sum and difference maps of different
photom eters are shown in Figure 7.7. The power spectra estim ated from combinations of
different pairs of photom eters are consistent with each other and w ith the
8
' pixel map
from the four photom eter map (indicated by the best fit model). The power spectrum
estim ated from the difference map of two pairs of photometers is consistent with zero with
a measured
%2
— 1 per degree of freedom.
We compare power spectra made from 81 and 3; pixelized maps. The two esti­
mates are in good agreement (within lcr) across the spectrum . For bins w ith I > 800, the
8
' pixelization introduces a systematic overestimate of the power spectrum , which is to
be expected. We test the accuracy of iterative noise estim ation by comparing the power
spectra com puted from bo th iterative and non-iterative estimates of 31 maps. The two
power spectra are nearly indistinguishable.
Another systematic test is to check for the presence of spatially correlated signal
in the dark photom eter data. The dark photom eter has the same type of detector and
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105
10000
8000
^
6000
-2 0 0 0
0
200
400
600
800
i
Figure 7.7: Combined and difference power spectra for four photom eters, generated from
8 ' square pixel maps. The power spectrum for the combined m ap of one 150 GHz and one
230 GHz detectors is plotted with open circles. The combination of the two remaining
150 GHz detectors is plotted with diamonds. The power spectrum for the combined four
photom eter map is plotted with filled (black) circles. The best fit model for the four
photom eter map is shown with a dotted line. The power spectrum of the difference map
of two pairs of detectors is plotted with triangles. All power spectrum measurements are
calculated for bin widths of L = 75 and are plotted w ith la error bars. (Stompor et al.
(2 0 0 2 b))
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106
20 00
1000
a.
w
u
-1 0 0 0
-2 0 0 0
0
200
400
600
800
£
Figure 7.8: Dark bolometer angular power spectrum: The points are calculated for bin
widths of L = 75 and are plotted w ith lcr error bars (Stompor et al. (2002b).
read-out electronics as the 150 GHz photometers, b u t is completely shielded from radi­
ation from the sky. We have estim ated an 8 ' pixel m ap from the dark photom eter data
using the reconstructed pointing solution and therm odynamic calibration from one of the
150 GHz photom eters. We have also estim ated a power spectrum , w ith bins centered from
77 < i
<
742, from this map, shown in Figure 7.8. None of these measured points
deviate by more than 2 a from zero power, with a measured \ 2 — 1 per degree of freedom.
7.3.3
Foregrounds
We can deduce the absence of contam ination from the atmosphere, earth or
balloon in our measurements from the tem poral stability of d a ta (Hanany et al. (2000)).
We verify the spectral consistency of our measurements w ith CMB tem perature
anisotropy as opposed to dust, free-free and synchrotron emission. In Figure 7.9, we plot
the total mean-square power determined from MAXIMA-1 maps made from 150, 230 and
410 GHz data, respectively. These points fit a straight line, and are consistent with the
emission spectrum of CMB tem perature anisotropy. We assume th a t the emission spec­
trum of the spatial anisotropy of the three foregrounds scales linearly w ith each respective
total power emission spectra. We calibrate each model’s emission spectrum (in CMB ther­
modynamic units) to one of the three measured to tal power anisotropy points. We deduce
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107
S p e c t r u m o f D e te c te d P o w e r C o m p a re d to E x p e c te d F o r e g r o u n d s
CO
S y n c h r o tr o n —
5
iai
o
'a
CM
0!
0
p.
V
S
3
r
{2
0
100
2 00
3 00
400
500
F r e q u e n c y |GHz)
Figure 7.9: Spectral consistency of observations w ith CMB: We plot the to tal meansquare CMB tem perature anisotropy and lcr error bars determ ined from MAXIMA-1
maps made from 150, 230 and 410 GHz data, respectively. Models for the to tal meansquare tem perature anisotropy for three foregrounds, converted to CMB therm odynam ic
units, are also plotted; dust (solid), synchrotron (dashed) and free-free emission (dotted).
Lee (2003)
th a t the measurements are spectrally inconsistent w ith the foregrounds since no model
intersects all three measured points.
The spectrum of diffuse galactic emission (dust) is not precisely understood be­
tween 150 and 410 GHz. Nevertheless, we can directly correlate MAXIMA maps w ith the
Berkeley-Durham foreground tem plates compiled by Finkbeiner et al. (1999) from IRAS
and COBE-DIRBE measurements. We conclude th a t the spectrum of dust emission over
150-410 GHz as observed by MAXIMA is consistent with preferred foreground models but
the effect on the CMB power spectrum observations is negligible (Jaffe et al. (2003)).
We are concerned with the presence of far-infrared and radio point sources for
the high-f' region of the power spectrum . A careful catalog search yielded no detectable
known point sources in the observation area, assuming correct extrapolation of the source
brightness in the observed frequency bands. We lessen our reliance on the extrapolation
assumption by removing all pixels from the map w ithin
20
' of the known sources before
estim ating the power spectrum (a removal of roughly ~ 30% of the area of the m ap). The
power spectra from the maps both with and w ithout the pixels removed are consistent
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108
within the la error bars of both measurements. As a final check, the shape of the measured
power spectrum is inconsistent w ith a point source origin, which would give a rising
spectrum w ith increasing i . Instead, the measured power spectrum decreases above
I = 850, and is consistent with zero.
7.3.4
G aussianity
A diabatic inflationary models predict th a t the distribution of cosmological per­
turbations is Gaussian.
Non-Gaussian features may be an indication of the presence
of topological defects. Both foregrounds and the instrum ent can also give rise to nonGaussian noise in the data. It is thus im portant to determine the Gaussianity of the
measured tem perature map.
Wu et al. (2001b) determine through a variety of methods (the methods of mo­
ments, cumulants, the Kolmogorov test, the y 2 test and Minkowski functionals) th a t the
MAXIMA - 1 d ata are consistent w ith Gaussianity. Santos et al. (2001) compute the cos­
mological bispectrum from the MAXIMA-1 d ata and find th a t the estim ate is consistent
with a Gaussian sky signal.
7.3.5
C om parisons w ith O ther E xperim ents
We can compare our estimates of the power spectrum and cosmological param ­
eters w ith those from other experiments. Such comparisons provide an interesting cross­
check, especially if the methodologies of the experiments are complementary.
Jaffe et al. (2001) perform a joint analysis on results from MAXIMA-1 Hanany
et al. (2000) and BOOMERANG-98 (de Bernardis et al. (2000)). Implicit in this analysis
is a comparison of both sets of results. BOOMERANG is a balloon-borne millimeter-wave
telescope designed for long duration flights (~ 15 days) which circumnavigates the south
terrestial pole (Crill et al. (2002)). The BOOMERANG experiment observes in the same
frequency bands as MAXIMA w ith an array of bolometers cooled to 300 mK. The main
tradeoff between the two experiments is photom eter sensitivity versus integration time.
Both experiments observe different regions of the sky with different scan strategies. We
determine th a t the results are consistent with a single underlying power spectrum if the
calibrations and beam profiles for both experiments are rescaled w ithin the respective
errors of each individual measurement.
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109
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Tegmark, M. et al. 1999, Astrophys. J., 474, L77
Timbie, P., Bernstein, G., & Richards, P. 1990, Cryogenics, 30, 271
Toffolatti, L. 1995, Astro. Lett, and Communications, 32, 125
Tytler, D. et al. 2000, Physica Scripta, 85, 12
Uson, J. k Wilkinson, D. 1988, in Galactic and Extragalactic Radio Astronomy, ed.
G. Verchur k K. Kellerman, 603-640, (Berlin: Springer-Verlag)
Welford, W. T. k W inston, R. 1978, The Optics of Nonimaging Concentrators: Light and
Solar Energy (New York, New York: Academic Press)
Woody, D. & Richards, P. 1981, Astrophys. J., 248, 18
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— . 2001b, Phys. Rev. Lett., 87, 251303
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A ppendices
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114
A p p e n d ix A
T he M A X IM A C ollaboration
The members of the MAXIMA collaboration listed below are co-authors of the
seminal MAXIMA-1 results papers (Balbi et al. (2000), Hanany et al. (2000), Lee et al.
(2001), Stompor et al. (2001)). Also included are the undergraduate and graduate stu­
dents who were not co-authors but who made critical contributions to the success of the
MAXIMA project.
The MAXIMA effort was first concentrated at UC Berkeley, w ith key participa­
tion from CalTech, the University of Rome La Sapienza and IROE-CNR (Florence, Italy).
Over time, team members moved to different institutions while remaining affiliated with
the project. I list the most recent institutional affiliation for each member while their
respective involvement in the collaboration was still active.
M atthew Abroe
University of M innesota/Tw in Cities, M inneapolis MN, USA
Peter Ade
Queen Mary and Westfield College, London, UK
Amedeo Balbi
Universita Tor Vergata, Rome, Italy
Domingos Barbosa
Lawrence Berkeley National Laboratory, Berkeley CA, USA
CENTRA, Instituto Superior Tecnico, Lisbon, Portugal
James Bock
Jet Propulsion Laboratory, Pasadena CA, USA
California Institute of Technology, Pasadena CA, USA
Julian Borrill
Lawrence Berkeley National Laboratory, Berkeley CA, USA
Andrea Boscaleri
IROE-CNR, Florence, Italy
Dyezone Chen
University of California, Berkeley CA, USA
Paulo de Bernardis
Universita La Sapienza, Rome, Italy
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115
Pedro Ferreira
University of Oxford, UK
Shaul Hanany
University of M innesota/ Twin Cities, M inneapolis MN, USA
Viktor Hristov
California Institute of Technology, Pasadena CA, USA
Andrew Jaffe
University of California, Berkeley CA, USA
Queen Mary and Westfield College, London, UK
Bradley Johnson
University of M innesota/Tw in Cities, M inneapolis MN, USA
Andrew Lange
California Institute of Technology, Pasadena CA, USA
Adrian Lee
University of California, Berkeley CA, USA
Lawrence Berkeley National Laboratory, Berkeley CA, USA
Oren Levy
University of California, Berkeley CA, USA
Phil Mauskopf
University of Wales, Cardiff, UK
C. B arth Netterfield
University of Toronto, Canada
Sang Oh
University of California, Berkeley CA, USA
Enzo Paseale
IROE-CNR, Florence, Italy
Bahm an Rabii
University of California, Berkeley CA, USA
Paul Richards
University of California, Berkeley CA, USA
Lawrence Berkeley National Laboratory, Berkeley CA, USA
George Smoot
University of California, Berkeley CA, USA
Lawrence Berkeley National Laboratory, Berkeley CA, USA
Celeste W inant
University of California, Berkeley CA, USA
Jiun-Huei Proty Wu University of California, Berkeley CA, USA
Johnny Wu
University of California, Berkeley CA, USA
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116
A p p e n d ix B
T herm al design o f th e M A X IM A
cryostat
This appendix will describe the therm al circuit, the sub-kelvin refrigerators and
the cryogenic wiring. General discussion of cryogenic design can be found in Lounasmaa
(1974) and Richardson & Smith (1988).
B .l
T he Therm al Circuit
The detector array is cooled to 100 mK during flight via a four-stage refrigeration
process. The array is housed inside an evacuated cryostat, and is cooled by an adiabatic de­
magnetization refrigerator (ADR), which dumps its heat to a single-shot charcoal-pumped
closed-cycle 3He sorption refrigerator backed by a pum ped liquid 4He bath, and a pum ped
liquid N 2 bath. A schematic of the therm al circuit is shown in Figure B .l. The holdtimes
for the various tem perature stages are listed in C hapter 3, Table 3.1.
B .1.1
3
He R efrigerator
We have designed and constructed a large capacity 3 He sorption refrigerator for
use in the MAXIMA cryostat. The closed-cycle refrigerator consists of 42 STP liters of 3He
of 99.995% purity, an activated charcoal sorption pump, a copper condenser and a copper
evaporator which is hermetically coupled to the condenser w ith a thin-walled stainless
steel bellows. The bellows is structurally reinforced w ith three thin-walled Vespel SP1
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117
Hermetic Cryostat Shell
Liquid
Nitrogen
O-
Liquid
Helium
3He
Refrigerator
Optics,
Optical
baffles,
77 K
-60 K)
300 K (-200 K)
(-2 K)
QBolometers,
Optical
band filters
HW
A: Mechanical Heat Switch
B: Electrical Heat Switch
Figure B .l: MAXIMA cryostat therm al circuit: The four therm al stages inside the her­
metic cryostat shell are drawn in boxes. Listed inside each box is the type of refrigeration,
the base tem perature of the stage, and the im portant hardware which is cooled to this
tem perature. Both the flight (in parentheses) and lab operation tem peratures of the shell
and liquid cryogen stages are listed. Each therm al stage is connected by a weak therm al
link to adjacent stages, denoted by the resistor symbol. The ADR and bolometers can be
directly coupled to the liquid 4He cold-plate and 3He refrigerator cold-plate by closing a
mechanical heat switch or electrically driven mechanical heat switch, respectively.
tubes connecting the evaporator to the 4He cold-plate. Vespel (DuPont (USA)) has a
tensile strength and therm al expansion coefficient comparable to most metals, but has the
therm al conductance of plastic.
Due to size constraints w ithin the cryostat, the sealed 3He refrigerator is coupled
to an external tank to prevent overpressurization. The pressure of the combined vessels
at room tem perature is 108 psi; a factor of 4 times smaller th an the elastic limit of the
bellows. The condenser is directly coupled to the 4He coldplate. The 4He b ath must
be pum ped in order to achieve a condensation tem perature of 3.2 K. The sorption pum p
consists of 131 grams of activated charcoal. The charcoal is glued w ith Stycast to a copper
stand consisting of closely spaced fins which maximize the pum p area. Calculations show
th a t optim al sorption is achieved w ith at least 3 grams of charcoal per STP liter of gas
(Duband (1990)).
The pum p is therm ally linked to the 4He coldplate w ith a ultra-high purity tin
wire. The therm al conductivity of the tin decreases rapidly w ith tem perature. The tin
wire is a poor therm al link for tem peratures above 10 K. The refrigerator is cycled by
first heating the charcoal to 40 K for ~ 30 minutes, which desorbs the 3He atoms from
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118
the pump. After heating, the charcoal and tin slowly cool back to the 4He coldplate
tem perature.
Meanwhile, the desorbed atoms condense into liquid and pool into the
evaporator. Once the charcoal has cooled below 10 K, it begins to pum p on the
3
He,
which cools to liquid to ~ 300 mK.
The refrigerator was designed to m aintain a base tem perature of 253/280 mK
for 14/3.9 days, assuming an expected heat load of 13/43 fiW from a continuously
pum ped/unpum ped liquid 4He bath. In practice, the refrigerator has achieved a base
tem perature of ~ 300 ± 20 mK for 1.5-2 days w ith an unpum ped 4He bath. The differ­
ence in actual performance may be explained by parasitic heating of the condenser during
cycling, the lack of optim ization of the cycling and the large heat capacity of the cooled
material.
Specific details on the construction and testing of the MAXIMA 3He refrigerator
and further references can be found in Levy (1995).
B .1.2
ADR
The adiabatic demagnetization refrigerator (ADR) makes it possible to achieve
sub-kelvin tem peratures in a reduced gravity environment (i.e. space). The environmental
conditions in a balloon flight are not as stringent as those on a satellite, b u t we make use
of the ADR developed in Berkeley as a prototype for the Space Infrared Telescope Facility
(SIRTF). This ADR was first flown multiple times on the MAX experiment. The details
of the construction and testing of the MAX/MAXIMA ADR are found in Tirnbie et al.
(1990) and Hagmann & Richards (1995). W hat follows is a sum m ary description of the
ADR and details on its operation in the MAXIMA cryostat.
The ADR consists of a param agnetic salt pill inside a high field electromagnetic
superconducting coil. The salt pill is made from 40 gm of ferric am monium alum (FAA)
and is supported w ithin the shielded coil with a kevlar string suspension th a t is therm ally
intercepted by the 3He refrigerator cold-stage. The 4He cooled superconducting Nb-Ti
coil generates a peak field of 2.5 T with a current of 6.2 A. The magnet shield is made
from vanadium perm endur coated w ith copper to reduce its therm al tim e constant.
The salt pill has a large heat capacity, and has an im practically long cooling
time constant from 300 to 4 K via the weak therm al link provided by the kevlar string
suspension. The salt pill can be directly coupled to the 4He coldplate by closing a me­
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119
chanical heat switch, and can thus be efficiently cooled from ambient tem peratures. The
mechanical heat switch has two gold plated OFHC copper jaws which close by a manually
driven gear around a cold finger which is connected to the salt pill.
We operate the ADR by first magnetizing the coil w ith the salt pill therm ally
coupled to the 4He cold-plate (the mechanical heat switch is closed). This aligns the
magnetic moments of the salt, reducing the entropy of the moments. The heat of mag­
netization is transferred to the 4He reservoir. We then open the mechanical heat switch
and close an electrically driven mechanical heat switch which couples the ADR to the 3He
refrigerator cold-stage, transferring more heat until the salt-pill cools to ~ 500 mK. The
electrical heat switch is opened, and the magnetic field is adiabatically decreased with a
commandable current controller. Entropy is transferred from the lattice to the magnetic
moments, causing the salt-pill to cool. The salt pill is partially demagnetized to ~ 100 mK,
at which point the field is reduced isothermally to compensate for the heat leak. The ADR
has a laboratory tested hold-time of 17 hours and a flight-tested hold-time of 12 hours at
100 mK w ith a ~ 80% duty cycle.
The electrically driven mechanical switch was developed in Berkeley for operation
with the ADR (Hagmann & Richards (1995)), and consists of a commercial linear solenoid
with copper windings th a t closes two m etal jaws around a cold finger with a force of
~ 200 N. The jaws and finger are made from gold-plated OFHC copper. The solenoid
and jaws are therm ally coupled to the 3He refrigerator cold-stage. The finger is therm ally
coupled to the ADR cold-stage. The heat switch can be activated remotely, allowing for
therm al cycling of the ADR during flight.
B .2
W iring
The photom eter array requires a considerable number of wires into the cryostat.
The approxim ate electrical power consumption of the bolometers and JF E T amplifiers is
100 mW (dominated by the JF E T amplifier heaters). Wiring must be carefully designed
to prevent significant heat leaks via therm al conduction and dissipated electrical power.
Bolometer Wiring
Each of the nineteen photom eters (optical and dark) requires seven wires between
the outside of the cryostat and the JF E T module, and four wires between the JF E T
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120
module and the bolometer (100 mK), disregarding shields. A schematic and description
of the bolometer wiring is shown in Figure B.2.
The signals enter the cryostat via hermetic connectors. Once inside the cryostat,
the signals are carried by a harness of low therm al conducting stainless steel wire (Cooner
Wire (U.S.A.)) which is heat-sunk at its midpoint to the liquid N 2 therm al stage. The
signals are then carried in K apton striplines of 2 mil gold plated Ni wire, fabricated by
Tayco Co. (U.S.A.), which are potted in Eccosorb CR-124 (Emerson & Cuming Microwave
P roducts (U.S.A.)). These modules are heat-sunk to the 4He cold-plate and filter radio
frequency interference signals (RFI) from the bolometers.
The wiring between the RFI filters and the JF E T modules is standard Tefloncoated m ulti-strand copper. Teflon can be repeatedly therm ally cycled to 4 K. Each pair of
JF E T amplifiers (Infrared Laboratories (U.S.A.)) is packaged in standard transistor cans
w ith internal therm al isolation and heaters so th a t the amplifiers operate at ~ 150 K.
They are mounted on printed circuit boards w ith copper traces. The JF E T modules are
cooled to 1He tem peratures. The signals are then carried from the JF E T amplifiers to the
100 mK array via formvar coated 2 mil platinum tungsten (Pt-W ) wire (California Fine
W ire (U.S.A.)), which has a low therm al conductance. The wiring between the JFETS
and the bolometers is susceptible to microphonics. We bundle and tw ist the wires for five
bolometers around a thin walled G-10 tu b e th a t is rigidly connected to b o th the JF E T
module and the array. The entire set of P t-W wires required four tubes. The tubes arc
therm ally intercepted by an OFHC copper heat strap from the 0.3 K therm al stage. The
wires are glued to the tubes with GE varnish.
The signals travel from the G-10 tubes to each photom eter on four G - 1 0 printed
circuit boards with 10 mil copper traces. We cover both sides of the circuit board with
electrically insulated aluminum tape to reduce the emissivity of the array. 2-4 cm lengths
of stiff formvar-coated copper wire bridge the term ination of the traces on the circuit
boards and the photom eter terminals.
AD R Wiring
The ADR superconducting magnet coil can be driven by as much as 6.2 A. The
wiring from the outside of the cryostat to the magnet m ust be of minimal resistivity to
minimize electrical power dissipation. The magnet current enters the cryostat via the same
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121
Hermetic connector
300 K
(-200 K)
S t a i n l e s s ste e l (conductor
St b r a i d e d shield)
2 m i l g o l d - c o a t e d Ni w i r e
in K a p t o n striplines,
p o t t e d in E c c o s o r b C R - 1 2 4
18 A W G t e f l o n - c o a t e d Cu
JFET module
2 mil formvar-coated Pt-W
G-10 PCB
(10 m i l C u trace)
Formvar-coated Cu
Bolometer
Figure B.2: Low-tem perature bolometer wiring: Each photom eter requires seven wires
between the JF E T from 300 K and four wires between the JF E T and the bolometer,
shown as solid lines drawn in parallel. Shields are not shown in this diagram. The wire
type, specialized connector an d /o r device at each tem perature stage are listed in the order
they are implemented. The various tem perature stages are distinguished by dotted lines.
The unpum ped/(pum ped) tem perature of each stage is listed in each zone. The actual
tem perature of each wire harness varies across a gradient set by the therm al stage each
end is heat-sunk to. Note- the JF E T s operate at ~ 150 K, b u t are housed in modules
which are cooled to liquid 4He tem peratures.
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122
Base tem perature
[K]
77 (60)
4 (1.6)
0.3
0 .1
Therm ometer
M anufacturer
Si diode
1600 0 carbon composition resistor
R u 0 2 resistance therm om eter
Ge resistance therm om eter (Ge-RTD)
Lakeshore Cryotronics
Allen-Bradley
T.R.I. Research
Lakeshore Cryotronics
Table B .l: Housekeeping therm om etry devices: The unpum ped/(pum ped) tem peratures
are listed for the liquid N 2 and liquid 4He therm al stages.
hermetic connectors as the bolometer signals and is first carried by bundles of standard
22 AWG copper wire which are heat-sunk to the liquid N 2 coldplate. Each bundle of wire
is soldered to a high-Tc superconducting lead (YBCO) (Eurus Monoco (U.S.A.)) which is
clamped between the liquid N 2 cold-plate and the top of the liquid 4He tank. The magnet
current is then carried by formvar coated copper clad Nb-Ti superconducting wire along
the side of the liquid 4He tank. We strip the formvar along a ~ 10 cm length of each
wire, then solder the wire to a ~ 10 x 10 cm square of OFHC copper foil which is glued
with Stycast and a layer of cigarette paper to the side of the tank, providing adequate
heat sinking th a t is electrically insulated. The Nb-Ti leads are p o tted in Eccosorb CR124 before entering the 4He cold-plate area. They are heat sunk to the cold-plate, then
soldered directly to the Nb-Ti leads on the magnet coil.
All of the wiring from the high-Tc leads to the magnet coil is superconducting
during cryogenic operation. Any significant electrical power dissipation is dum ped into
the liquid N 2 , which has a larger latent heat of vaporization th an the liquid 4 He.
Other Wiring and Thermometry
We m onitor the tem peratures of the various therm al stages w ith the devices listed
in Table B .l. The operating principles of these therm ometers are described elsewhere.
The therm om eter signals enter the cryostat through the same hermetic connectors as the
bolometer signals. They are then carried by the same stainless steel wire harness and
Eccosorb RFI filter module into the cold-plate area. Each device is wired to the RFI
module w ith low therm al conducting Teflon coated 5 mil manganin wire (California Fine
Wire (U.S.A.)). The wires for the 0.1 K therm om eter are heat-sunk midway on the 3He
refrigerator cold-stage.
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123
A p p e n d ix C
A m plifier N oise C ontributions to
D etector N E P for M A X IPO L 150
GHz B olom eters
We calculate amplifier noise contributions to the to tal bolom eter NEP. We are
concerned th a t the Infrared Laboratory EJ-TIA JE F T amplifiers dom inate the MAXIPOL
bolometer NEP. We want to explore whether the NEP can be significantly improved by
switching to lower noise JF E T amplifiers, such as the NJ-132 modules used in the ACBAR
experiment (Runyan et al. (2002)).
C .l
M ethod
Using the DC-coupled bolometer output voltages measured during one of the
day-time scans for the test flight of MAXIPOL (September 2002), I was able to calculate
the resistance, tem perature, electrical power, and optical power for each 150 GHz bolome­
ter. The base tem perature of the ADR was 100 ± 3 mK for the given d ata sample. All
bolometers were biased with 100 mV AC, and the average therm al conductance of the 150
GHz bolometers was assumed to be G = 70 pW /K . The latter should be correct within
a factor of 10%: For MAXIMA, the average of the mean therm al conductance for all 150
GHz bolometers was G = 71 pW /K . J. Bock specified G ’s of 70 p W /K at 300 mK for
the new MAXIPOL bolometers. I assume th a t the gain of the DC bolometer electronics
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124
readout, gdc is 1800.
The equations below were used to calculate the resistance, R , the tem perature,
T, the electrical power, Peiec, and the optical power, P0pt, from the bolom eter DC voltages.
These quantities are shown in Table C .l.
(C .l)
Vb0i0 = — ; gdc = 1800
9dc
(C.2)
V b0 lo
;
A = 14.4K, R 0 = 1200
(C.3)
(C.4)
Popt
= G (T — Tq) -
P e l ec',
G — 70pW /K , To = lOOmK
The voltage for channel b43 seems suspiciously large.
channel in further analysis.
(C.5)
I did not include this
I determined the average R, T, Peiec and Popt from the
remaining 150 GHz channels in the array.
I calculate the various contributions to the bolometer N EP using two MATLAB
codes shown at the end of this appendix (Lee (1995)). Our group has used these codes
for bolometer optim ization since MAXIMA was in the design stages. The codes calculate
the Johnson, therm al fluctuation and amplifier NEP, then add the three in quadrature
to generate the to tal NEP (except for the photon NEP, which should be a significant
contribution). I can make a rough estim ate of the photon NEP from the optical load.
N E P photon = \ j ‘l h v P 0pt\
v = 150GHz
(C. 6 )
I assume fixed average therm al conductance, b ath tem perature, therm istor properties, JF E T amplifier voltage noise and optical load for this calculation. I vary the ratio
of the electrical power to the optical power, and generate plots of the various contri­
butions to the NEP as a function of this ratio. I have done the calculation with two
different JF E T noise voltages; en = 10 nV /rt(H z) corresponds to the MAXIMA-style
Infrared Laboratories EJ-TIA JF E T amplifiers currently used in the cryostat. en = 3
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125
Channel
b l3
b l4
b l5
b23
b24
b25
b33
b34
b35
b43
b44
b45
av.
V dc
R
[Volts]
3.88
4.14
3.29
3.90
2.74
[Mfi]
1.76
2 .2 1
3.49
3.53
2.89
7.40
3.45
2.67
3.29
1 .8 8
1.49
1.77
1.24
0.99
1.58
1.60
1.31
3.43
1.56
1 .2 0
1.49
T
[mK]
156
154
162
156
168
177
160
160
167
137
160
170
162
P e le c
P ip t
[PW]
2.63
2.81
2.24
2.65
1.87
1.52
2.38
2.40
1.97
4.93
2.35
1.83
2.25
tpw]
1.31
0.99
2 .1 0
1.29
2.93
3.87
1.82
1.77
2.70
-2.35
1 .8 8
3.05
2.15
Table C .l: Optical and electrical power for MAXIPOL-O 150 GHz bolometers during day­
time scan; This table lists the DC-coupled output voltage (V^), the therm istor resistance
(R) and tem perature (T), and the electrical power (Peiec) and optical power (Popt) across
each bolometer. We calculate the average of these quantities over all 150 GHz bolometers,
excluding channel b43. We measure V^c during flight. The other param eters are calculated
from Vac using the equations listed in the body of this memo. The operating tem perature
of the ADR is 100 mK, and all bolometers are biased w ith 100 mV AC.
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126
T b a s e = 1 0 0 m K , P o p t= 2 .1 5 p W , G = 7 0 E ~ 1 2 , e n = 1 0 rtV/rH z, m a x ip o l7 0 b .e p s
cl 3
Q_
0.5
2 .5
3 .5
2 .5
3 .5
P e le c /P o p t
0.2
0 .1 8
Q 0.16
0 .1 4
0.12
0.1
0 .5
P e ie c /P o p t
Figure C .l: Bolometer noise simulation: The top panel is a plot of the various contri­
butions to the bolometer NEP as a function of the ratio of the electrical power, Peiec to
the optical power, Popt. The various contributions are; Therm al fluctuation noise
Johnson noise (o), Amplifier noise (x), photon noise (.) and these four term s added in
quadrature (solid line). The bottom panel is a plot of the therm istor tem perature as a
function of the same ratio of powers. We assume the param eters for a MAXIPOL 150 GHz
bolometer w ith flight loading using INFRARED LABORATORIES TIA JF E T amplifiers;
an operating tem perature, Tf,ase of 100 mK, an optical load, Popt, of 2pW, an average ther­
mal conductance, G of 70 pW /K , and JF E T voltage noise, en of 10 nV /rt(H z).
nV /rt(H z) corresponds to the measured noise of the NJ-132 JF E T amplifiers used for
ACBAR (Runyan et al. (2002)). We would consider using the same components. In ear­
lier room tem perature tests of these devices, we were only able to achieve a noise voltage
of
6
nV /rt(H z) (Lanting (2002)).
C.2
R esu lts and D iscussion
The measurements are shown in Figures C .l, C . 2 and C.3.
The bottom plots in both figures are not of great im portance, except th a t they
can be compared w ith the measured bolometer tem peratures in Table 1. There seems to
be an underestim ate of the bolometer tem perature by 5 - 10% from those measured.
According to the table, the ratio of electrical to optical power is ~ 1. My con-
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127
x io"17
T b a s e = 1 0 0 m K , P o p t= 2 .1 5 p W , G = 7 0 E -1 2 , e n = 6 nV /rH z, m a x ip o l7 0 m e d n o is e b .i
Z 2
0 .5
2 .5
3 .5
2 .5
3 .5
P e ie c /P o p t
0.2
0 .1 8
0 .5
P e ie c /P o p t
Figure C.2: Bolometer noise simulation: The top panel is a plot of the various contri­
butions to the bolometer NEP as a function of the ratio of the electrical power, Peiec to
the optical power, Popt- The various contributions are; Therm al fluctuation noise
Johnson noise (o), Amplifier noise (x), photon noise (.) and these four term s added in
quadrature (solid line). The bottom panel is a plot of the therm istor tem perature as a
function of the same ratio of powers. We assume the param eters for a MAXIPOL 150
GHz bolometer w ith flight loading using new JF E T amplifiers; an operating tem perature,
Tbase of 100 mK, an optical load, Popt, of 2pW, an average therm al conductance, G of 70
pW /K , and JF E T voltage noise, en of 6 nV /rt(H z).
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128
T b a s e * 1 OOmK, P o p t= 2 .1 5 p W , G = 7 0 E - 1 2 , e n = 3 nV /rH z, rn a x ip o l7 0 Io w n o ise b .e p s
' 0
0 .5
1
1.5
2
P e ie c /P o p t
2 .5
3
3 .5
4
0.2
0 .1 8
0 .1 4
0.12
0 .5
2.5
3 .5
P e ie c /P o p t
Figure C.3: Bolometer noise simulation: The top panel is a plot of the various contri­
butions to the bolometer NEP as a function of the ratio of the electrical power, Pe\ec to
the optical power, Popt■ The various contributions are; Therm al fluctuation noise
Johnson noise (o), Amplifier noise (x), photon noise (.) and these four term s added in
quadrature (solid line). The bottom panel is a plot of the therm istor tem perature as a
function of the same ratio of powers. We assume the param eters for a MAXIPOL 150
GHz bolometer w ith flight loading using new JF E T amplifiers; an operating tem perature,
Tbase of 100 mK, an optical load, Popt, of 2pW, an average therm al conductance, G of 70
pW /K , and JF E T voltage noise, en of 3 nV /rt(H z).
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129
elusions are drawn from the various N E P ’s calculated at this ratio of powers.
The high optical load is puzzling. In fact, the optical load for MAXIPOL-O
is higher th an th a t for MAXIMA-1 by a factor of 1.5-2. One would expect the optical
load to decrease by a factor of 2 w ith the introduction of the wire grid polarizer. The
MAXIPOL-O optical load was calculated from the daytime scan, but it is unlikely that
scattered sunlight increases the optical load by a factor of 3-4. The other postulate is that
the rotating wave-plate is warm enough to contribute significantly to the optical load.
These questions should be further explored.
Assuming the calculated optical load is correct, we calculate a to tal N EP of
3.2
x
10~
17
W /rt(H z) for the Infrared Laboratory JF E T amplifier noise of en
10 nV /rt(H z), a to tal NEP of 2.65
fier noise of en
=
6
x
10~
17
=
W /rt(H z) for the NJ-132 JF E T ampli­
nV /rt(H z) and a to tal NEP of 2.4 x
ACBAR NJ-132 JF E T amplifier noise of en =
10"
17
W /rt(H z) for the
3 nV /rt(H z). The to tal N EP w ith the
3 nV /rt(H z) amplifier noise is 75% th a t of the total w ith the 10 nV /rt(H z) amplifier noise.
The to tal N EP w ith the
6
nV /rt(H z) amplifier noise is 83% th a t of the total w ith the 10
nV /rt(H z) amplifier noise.
C.3
C om parison w ith M easured N oise
From the flight data, I can directly calculate the to tal N EP from the following
equations from Richards (1994);
N E P total = ^
(C.7)
where Vn is the measured noise voltage and l ^ l is the responsivity of each bolometer;
I(d R /d T )
Sa
=
T_
a - P(dR/dT)
Vbolo
R '
t v
/ w
! '
( 0
dR _ —R j A
d T ~ 2 y T3
' 8 )
(n m
( }
For a noise voltage, I use Vn = 11 ± 2 nV /rt(H z). The average to tal N EP I calculate for the
functioning 150 GHz bolometers is NEPtotal = 2 .8 ± 0 .7 x 10~
of NEPtotal = 3.2 x 10~
17
17
W /rt(H z). My calculation
W /rt(H z) falls w ithin th a t error, as does the lower estimate
from using the lower noise JF E T amplifiers. The error is large given the uncertainty in
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130
the measured noise voltages and in my incorrect assumption th a t each bolometer has the
same Rq, A and G.
Nevertheless, this cross-check verifies th a t my calculations are approximately
correct. Since an improvement in JF E T noise lends to a system atic improvement in NEP,
it is still w orth considering.
C.4
C odes
The N EP calculations were done w ith the following codes, optimize2 .m and
NEPcalc3.m, in MATLAB version 6.0.0.08.
optimize.m
/.this is a program to calculate optimal NEP for given parameters
”/.
‘
/.Adrian T. Lee, 4/24/95
’
/.Updated by Celeste Winant, 1997-2003
’
/,optimize2 is used for bolometers that are already built
’
/.uses NEPcalc3.m
global Popt R Rzero Tbase Tntd del en in Af Cin freqratio alpha C SVsq
global SVsqeff G Gabs Geff Gzero T_Gzero phonon_ratio n NEP_phonon
global NEP_johnson NEP_amp
Popt = 2.E-12; ‘
/.optical power in W for 5cm-1 MAXIPOL 10’ beam flight
R; "/.calculated, dc bolometer resistance in Ohms
Tbase = 0.1; ‘
/.base temperature in K
Tntd; ‘
/.temperature of the NTD in K calculated by program
Rzero = 120; '/.Rzero in Ohms for NTD
del = 14.4; ‘
/.del a.k.a. Tzero and A in K-> measured MAXIMA number
en = 6E-9; ‘
/.amplifier voltage noise in V/rHz
in = 0; ‘
/.amplifier current noise in A/rHz
Af = 0; ‘
/.amplifier 1/f noise = en~2 = Af/f Af = Volts~2
Cin = 10E-12; ‘
/.input capacitance in farads
freqratio = 1; ‘
/.for ac bias -> ratio of -3dB freq:freq
n = 1; */,G proportional to T~n , leads dominated over SiN2->n=l
alpha; ‘
/.alpha = - T/R dR/dT (unitless)
C = 30E-11; ‘
/.Heat capacity in J/K
°/.G; “
/.calculated, differential G in W/K
Gabs; ’
/.calculated. delP/delQ -> used to calculate Tntd
Geff; ‘
/.calculated, includes electro-thermal feedback
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Gzero = 70E-12; '/.Differential G in W/K at T_Gzero
T_Gzero = .1; '/,Temperature in K where G = Gzero
Pelec = l*Popt; '/.Bias power in W — start point for optimization
SVsq; '/.calculated, squared responsivity (V/W)“2
SVsqeff; ‘
/.calculated, used Geff .
phonon_ratio; '/.fractional non-equi 1 ibrium reduction in phonon noise
k = 1.38E-23; '/.Boltzmann’s constant
hold off; clg
G = 7E-11;
for i = 1:20
Pelec = Popt*i/5;
p = [G Pelec];
x(i) = Peiec/Popt;
NEP2(i) = NEPcalc2(p);
alpha2(i) = alpha;
Tntd2(i) = Tntd;
NEPG2(i) = NEP_phonon;
NEPJ2(i) = NEP_johnson;
NEPen2(i) = (en~2/SVsqeff)".5;
MEPAf2(i) = (freqratio*Af*2*pi*Cin*R/SVsqeff )~ .5;
NEPin(i) = (in~2*R~2/SVsqeff)~ .5;
NEPamp(i) = NEP_amp;
NEPphoton(i) = (2*6.626e-23*l.5*Popt)“ .5;1.5 -> 150 GHz
NEP2(i) = (NEP2(i)“2 + NEPphoton(i)*2)"0.5
end
subplot(211),plot(x,NEPphoton,’.’, x , N E P 2 , x , N E P G 2 , ’,x,NEPJ2,’o ’,..
x ,NEPamp,’x ’)
xlabel(’Peiec/Popt’)
ylabel(’NEP (W/rHz)’)
title(’Tbase=100mK, Popt=2.OOpW, G=70E-12, en=6 nV/rHz, file.eps’)
subplot(212),plot(x,Tntd2)
xlabel(’Peiec/Popt’)
ylabel(’Temp(NTD) (K)’)
end
N EPcalcS.m
function out = NEPcalc3(p)
'/.This function calculates the NEP of NTD based detectors
’
/.globals are: Popt,R ,Tbase,Tntd,del,en,in,Af,Cin,freqratio,
'/.alpha,C,SVsq,SVsqeff , Gabs, Geff, phonon_ratio, n, NEP_phonon,
'/,NEP_johnson, NEP_amp.
p = [Tb Pelec]
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132
7,4/25/95, original Adrian T. Lee
7,1997-2003, modified by Celeste D. Winant
k = 1.38E-23; 7,boltzmann’s constant
Tb = p(l);
Pelec = abs(p(2));
global
global
global
global
Popt R Rzero Tbase Tntd del en in Af Cin freqratio
alpha C SVsq SVsqeff
G Gabs Geff Gzero T_Gzero phonon_ratio n
NEP_phonon NEP_johnson NEP_amp
Tntd = Tb + (Popt + Pelec)/Gzero; 7,calculated NTD temperature
7,a first approx. only
for i = 1:10
G = Gzero*(Tntd/T_Gzero)~n;
Gabs = G/(n + 1)*(1 - (Tb/Tntd)“(n+1))/(l - (Tb/Tntd));
Tntd = Tb + (Popt + Pelec) /Gabs; 7,calculated NTD temperature
end
7.G, Gabs, and Tntd are functions of each other. Therefore,
7,they are calculated iteratively above.
phonon_rat io=(n+1)/(2*n+3)*(1-(Tb/Tntd)~(2*n+3))/(1-(Tb/Tntd)"(n+1));
R = Rzero*exp ((del/Tntd) ''0.5);
alpha = -0. 5* (del/Tntd) ~ .5;
7.dimensionless alpha ~ 5-10 for NTD
Geff = G - alpha*Pelec/Tntd;
SVsq = Pelec*alpha“2*R/(G~2*Tntd"2);
7,squared responsivity
SVsqeff = Pelec*alpha~2*R/(Geff~2*Tntd~2); 7,squared eff. respons'ty
NEPsq_phonon = 4*k*Tntd~2*G*phonon_ratio; 7,differential G used here
NEPsq_johnson = 4*k*Tntd*R/SVsq; 7.G not Geff used. Work done
7,by ETF reduces spectral
7,density of Johnson noise
7,canceling Geff effect
NEPsq_amp = (en~2 + freqratio*Af*2*pi*Cin*R + in"2*R'2)/SVsqeff;
NEPsq = NEPsq_phonon + NEPsq_johnson + NEPsq_amp;
NEP_phonon = NEPsq_phonon“ .5;
NEP_johnson = NEPsq_j ohnson".5;
NEP_amp = NEPsq_amp".5;
out = NEPsq'.5;
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