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Medium-scale microwave background anisotropy: Measurement and detectors design

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T H E UNIVERSITY OF CHICAGO
MEDIUM SCALE MICROWAVE BACKGROUND ANISOTROPY:
MEASUREMENT AND D ETECTO RS DESIGN
A DISSERTATION SUBM ITTED TO
THE FACULTY O F THE DIVISION OF THE PHYSICAL SCIENCES
IN CANDIDACY FO R THE DEGREE OF
DO CTO R O F PHILOSOPHY'
DEPARTM ENT OF ASTRONOM Y AND ASTROPHY'SICS
BY
ALEXEY GOLDIN
CHICAGO, ILLINOIS
DECEM BER 1999
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A lot of people, more then. I can nam e here, made this work possible. I would like to
thank at least some of them . I thank my advisor Steve Meyer for getting me interested
in the subject and helping me to keep the right a ttitu d e to m any tilings. I am grateful
to M att Kowitt and Casey Inman for teaching m e more about experimental science
in the only right way — by showing the example. I thank Dave Cottingham and Dale
Fixen for many insightful comments and for impression they had on me. I am very
grateful to Michael Sazhin from Moscow State University and Andrey Brukhanov
from RELUCT team for helping me to keep interest in science in difficult time.
1 also want to thank my wife Tanya for her infinite patience and for support and
love I got from her during all this tim e. And. finally. I want to thank my m other for
all her selfless help that I can not even hope to m atch.
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TABLE O F C O N T E N T S
LIST OF TABLES
v
LIST OF FIGURES
vi
ABSTRACT
I
1
INTRODUCTION
1.1 M otivation for Studying C M B ......................................................................
1.2 The Challenge of Detecting CMB Brightness F l u c t u a t i o n s .................
2
3
5
2
INSTRUM ENT DESCRIPTION
2.1 G o n d o la ...........................................................................
2.2 O p t i c s ................................................................................................................
2.3 R a d io m e te r ......................................................................................................
2.4 Noise and offset sources ...............................................................................
2.4.1 Sidelobe contam ination.......................................................................
2.4.2 Mirror therm al fluctuations................................................................
2.4.3 Atmospheric effects...................................
2.4.4 Cosmic ray' hits......................................................................................
2.4.5 Fundam ental detector n o is e s ............................................................
10
10
12
14
14
14
15
15
10
16
3
DATA ANALYSIS
3.1 Data Description................................................................................................
3.2 Summary of A n a ly sis ......................................................................................
3.3 D e g litc h in g ......................................................................................................
3.4 D e m o d u latio n ...................................................................................................
3.5 Binning and D e d riftin g ...................................................................................
3.6 C a l i b r a t i o n ......................................................................................................
3.7 Spectral D ecom position..................................................................................
3.8 CMBR anisotropy'...........................................................................
3.8.1 Gaussian autocorrelation function....................................................
3.8.2 Bandpower e s tim a te s .........................................................................
3.5.3 Analysis of all three MSAM f l i g h t s .................................................
18
IS
20
20
24
29
32
37
39
42
43
45
4
OBSERVATIONS OF JU PIT E R AND SATURN
4.1 D ata Analysis
.........................................................................................
4.2 P o in tin g .............................................................................................................
4.3 Detector D ata R e d u ctio n ...............................................................................
4.4 Error A n aly sis...................................................................................................
4.5 Wliole-Disk Brightness Tem perature Ratios ...........................................
48
4S
49
49
51
52
iii
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IV '
4.6
4.7
5
M ars M odels......................................................................................................
Brightness T e m p e ra tu re s..............................................................................
52
55
FREQ U EN CY SELECTIVE BOLOMETERS
5.1 M o tiv atio n .........................................................................................................
5.2 FSB design ......................................................................................................
5.3 Frequency Selective Surfaces( F S S ) ............................................................
5.4 Opticiil M o d e l.......................................................................
5.5 O ptical tests of b a c k s h o rts ...........................................................................
5.6 FSB Radiom eter D e s i g n ..............................................................................
5.6.1 Heat capacity, therm al conductivity and tim e constant . . . .
5.7 Bolornetric detectors performance................................................................
5.7.1 Im pact of 1 / / noise on bolometer performance.............................
5.7.2 D etector performance in FSB prototype ......................................
5.7.3 Spectral components s e n s itiv ity ......................................................
5.8 Advantages of FSB ra d io m e te rs .......................................................
57
57
58
59
59
61
62
62
64
66
67
67
78
A SPECTRA L DECOM POSITION AND CHOOSING RA D IO M ETER SPEC­
TRAL CHANNELS
79
B
D E T E C T O R MANUFACTURING
82
C
BOLOM ETER IM PLANT SCHEDULE
86
D
ABSORBER
89
BIBLIOGRAPHY
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93
LIST OF TABLES
3.1
3.2
3.3
3.4
3.5
3.6
Short sum m ary of MS AM-1 1995 f l ig h t .................................................. .
Observation Circum stances for planet observations ...............................
D ata Loss sum m a r y . .................................................................................
24
x 2 f°r drift fits ................................................................................................
37
Calibration coefficients (counts/K elvin)...............................................
Upper and lower lim its to CMBR anisotropy assuming Gaussian auto­
correlation function
3.7 Power spectrum estim ates for three flights of M S A M l...................
47
4.1 Ratios of Target Planet Flux to Jupiter Flux .........................................
51
4.2 Ratios of Planet Tem perature to Jupiter T em p eratu re ...................
4.3 Tem peratures of planets (K)...................................................................
56
63
Dimensions of FSB bolom eters.............................................................
Therm al param eters of FSB bolometers. Materials heat capacities are
taken from [8].............................................................................................
64
5.3 FSB prototype sensitivity in presence of foregrounds (assum ing spec­
tral d eco m p o sitio n )
5.4 Radiometer performance assuming loading in Table 5 . 5 ................
68
5.5 Loading for all channels of FSB prototype (in pYV)..........................
78
19
19
32
43
50
5.1
5.2
C .l Therm istor im plant doses for dose 1.0 (as used in GSFC D etector De­
velopment L a b )
87
D .l Resistance per square for thin gold sam ples.......................................
D.2 Thin film constant C ( fOhm m2) .......................................................
v
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90
91
68
LIST OF FIGURES
1.1
A summary of CMB anisotropy d a t a .............................................
2.1
2.2
11
G o n d o la .................................................................................................
Cold optics ......................................................................................................
3.1
3.2
3.3
3.4
3.5
3.6
Diita Analysis P ip e lin e .......................................................................
20
Wiener filters used for d eg litch in g ....................................................
23
Histograms of removed spikes..............................................................
2-5
Idealized single and double demodulations as function o f tim e . . . .
Beam position as a function of tim e .................................................
27
Single and double demodulations for first channel actually used in anal­
ysis
29
30
Right ascension as function of time (in m in u te s ) ..........................
Single dem odulation drift in all channels..........................................
33
Double dem odulation drift in all channels........................................
34
Single dem odulation beam m ap...........................................................
35
Double dem oduhition beam m ap.........................................................
36
Spectral response of individual channels for MS A M - 1 ........... .....
CMB c o m p o n e n t.................................................................................
40
Dust com ponent......................................................................................
41
Limit on total RMS anisotropy for Gaussian autocorrelation function,
from MSAM1 1995 flight......................................................................
44
Power spectrum estim ates for three flights of MS AM ...........................
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
6
13
27
38
46
4.1 Whole-disk brightness temperatures for J u p i t e r ......................................
4.2 Whole-disk brightness temperatures for S a tu r n ..........................................
53
54
5.1 Illustration of scattering m atrix concept ...................................................
5.2 Transmission of one layer capacitive resonant mesh com pared to f s s
prediction..................................................................................................
69
5.3 Transmission of three layer capacitive mesh compared to f s s prediction
5.4 Phase averaged current density distribution in one cell of periodic ca­
pacitive m e s h
71
5.5 Backshort for channel 3....................................................................................
5.6 Bolometer for channel 3....................................................................................
5.7 Sample FSB stack of three bolometers tuned to different frequencies
with three backshorts e a c h .................................................................
74
5.8 A complete five channel FSB radiometer prototype....................................
5.9 Performance of FSB detector for channel one as function of loading. .
5.10 Predicted spectral response of prototype FSB stack...................................
60
vi
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70
72
73
75
76
77
vii
B .l
B.2
Therm istor im plant...........................................................................................
L ifto ff.................................................................................................................
84
85
C .l
To vs. implant d o s e .........................................................................................
88
D .l
Bulk resistivity of th in gold films a t 4.2 K as function o f film thickness. 92
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A BSTRA C T
This thesis describes three areas of research, all of them closely related to measuring
the anisotropy in cosmic microwave background (CMB). In the first part of the thesis
th e results of analysis of the third flight of MS A M I (Medium Scale Anisotropy Mea­
surem ent) telescope are reported. The instrum ent is balloon-borne telescope with a
28' beam and 3 position chopper with ± 4 0 ' throw. It has radiom eter with bands cen­
tered at 5.6. 9.2. 16.5. and 22.5 cm-1 . The d a ta from all channels are used to simul­
taneously fit the m ajor foreground source — therm al emission from interstellar dust.
The first flight in 1992 yielded a detection of anisotropy confirmed by second 1994
flight. The third flight measured a new region giving lcr lim its for CMB fluctuations
bandpower am plitude ST[ = 50i[® fiK for single difference demodulation at mean
I = 160 and cST) = GSlJ® fiK for double difference dem odulation at mean I = 270 with
calibration errors included. The results of the analysis of all three MSAM1 flights are
also reported.
The second part is the analysis of the observation of Mars. Jupiter and Saturn
cross-calibrated in four bands are reported. This cross-calibration improves the un­
derstanding of Jupiter as calibrator using the b etter understood Mars flux. The mea­
sured tem peratures of Jupiter are 169 ± 2. 165 ± 2. 133 ± 2 and 129 ± 2 Kelvin in
our bands w ithout taking into account closely correlated for all bands Mars emission
model uncertainty ±10 K. This is the most precise measurement of Jupiter microwave
brightness tem perature at these frequencies to date.
The last part describes ongoing work on new generation multifrequency bolometric radiom eter for far infrared astronomy. T he design promises much better optical ef­
ficiency compared to traditional multifrequency radiom eters and. because of its com­
pactness. mnkes multipixel bolometric cam eras with many frequency channels much
easier to design. Such an instrum ent can be useful in next generation CMB or Far
Infrared Background (FIRB) experiment.
1
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CH APTER 1
IN T R O D U C T IO N
“You don't seem to give much,
thought to the matter at hand". I
said at last, interrupting Holmes's
musical disquisition.
"No data yet". he answered. "It is a
capital mistake to theorize before
you have all the evidence. It biases
the judgment."
A Study in Scarlet
A r t h u r C on an D o y le
The story of Cosmic Microwave Background Radiation (CMB) begins in 1940s.
when theorists George Gamow. Ralph Alpher and Robert Hermann, studying nucle­
osynthesis in the early Universe, predicted relic radiation with blackbody spectrum
and tem perature ranging from 5K to 50K. Since the discovery of CMB in 1965 [44]
by Arno Penzias and Robert Wilson it has proven to be an extremely valuable tool
th a t turned cosmology into science overnight. We finally had the evidence rath er then
speculations. The very existence of this background was predicted by "Hot model of
the Universe” and was satisfactory explained in most other models.
The remarkable uniformity of background on large angular scales raised the hori­
zon problem — how could the universe be so uniform if the parts th a t we now observe
to have the same tem perature where beyond the event horizon at the time of recom­
bination and had no chance to interact in the past? This question was one of the
m ajor motivations for inflation introduced by Alan G uth and Alexey Starobinskiy.
The frequency spectrum of CMB is closer to th a t of an ideal blackbody spectrum
then any other spectrum observed in nature [16], which puts strong constraints on
9
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3
energy production in the Universe before recombination and puts limits on theories
predicting elementary particles that could decay at this time. Measurements of CMB
gave a wealth of cosmologiccil information even before any anisotropy was detected.
1.1
M otivation for Studying C M B
This thesis describes CMB experiments th a t measure CMB anisotropy — sm all fluc­
tuation in microwave sky tem perature. T h ey are the signature of initial density per­
turbation th at developed into large scale structures observed today in galaxy surveys.
Anisotropy experiments ruled out many large scale structure form ation theories even
before any anisotropy was detected and gave strong boost to the current favorite —
Cold Dark M atter theory (CDM) [24].
In this theory, primordial density p erturbation (of possibly quantum mechanical
origin) in dark m atter started to grow d u e to gravitational instability. Before redshift
~ % 1000. CMB photons were abundant and hot enough to ionize hydrogen [58].
Baryons and electrons were tightly coupled to photons via Com pton scattering- Pho­
ton pressure resisted gravitational compression and set up acoustic oscillations. The
photon-bciryon fluid was coupled to dark: m atter by the force of gravity only. Den­
sity perturbation in baryon m atter s ta rte d to grow only after photons and baryons
decoupled at the time of recombination. These early perturbations in density grad­
ually grew and finally gave birth to intricate structure of the Universe from large to
smallest scales — from clusters of galaxies down to stars and planets.
At recombination, the universe becam e transparent rather abruptly exposing the
structure formed before this moment. Regions of compression and expansion show
up as hot and cold spots. Photons also suffer gravitational redshift climbing out of
potential wells as well as Doppler shift o n the last scattering surface.
In Gaussian theories, like CDM. w here fluctuations are linear combinations of
modes with Gaussian distributed am plitudes, the power spectrum of the anisotropy
or two point correlation function have aLl the inform ation about model param eters.
O ther theories of structure formation, like topological defects theories, have nontrivial
higher order correlations.
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4
Assum ing the CDM model (this is an assum ption th at can be tested by detailed
study of CM B). a wealth of information is available from precisely measured CMB
anisotropy angular spectrum . The large scale spectrum can give valuable inform ation
on m atter power spectrum and on the shape of inflation potential. Regions separated
by angular distance of more than couple of degrees had no chance to interact in period
between inflation and recombination and therefore no physical process could sm ooth
out the large scale primeval perturbations. This anisotropy, detected by COBE [2] and
confirmed by FIRS [18]. probes the earliest processes, possibly the result of quantum
mechanical processes a t the time of inflation.
At sm aller angular scales, the physics of gas - radiation interaction, well studied
in the laboratories, sta rts to play a role. At angular scale below one degree th e largest
standing acoustic wave reaches maximum am plitude at the m oment of recombination.
In anisotropy spectrum it shows up as Doppler peak (acoustic peak), whose exact
location depends on many cosmological param eters. A precise m easurement of the
angular spectrum of CMB anisotropy would allow the determ ination of a range of
cosmological param eters [25].
The cosmological information is also available from galaxy surveys, stu d y of
Lym an-a lines forests in quasar spectra, observations of supem ovae in rem ote galax­
ies and other sources. However microwave background is uniquely effective probe
because Universe was much simpler in days it was formed. One needs only to know
well tested physics — general relativity in weak field limit and details of interaction
of hydrogen w ith radiation at few thousand degrees to predict CMB spectrum as­
suming primeval density perturbation spectrum and certain cosmological model. The
required physics is understood, can be tested in a lab, and all perturbations are well
in linear regime — density perturbations for the scales of interest in dark m a tte r are
Sp/p ~ 10-3 or less at the moment of recombination. A sim ple linear theory is an
excellent model for physical processes a t this tim e.
Unlike CMB experiments, interpreting results of galaxy surveys requires many
assum ption about evolution of complex dynamical systems in nonlinear regime. Su­
pernova surveys [45] also require some assumptions, for instance, about interstellar
media absorption spectrum . On the other hand, galaxy, supernova and CMB data
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are complementing each, other very well and results from combining results from these
programs promise to be much more precise then from any one program .
1.2
T he C hallenge o f D etecting CM B B rightness
Fluctuations
Measuring am plitude of CMB fluctuations is a difficult task. The tem perature of
radiation is low and the fluctuations on top of it have relative am plitude close to
1 x 10~°. In spite of these difficulties many research groups sta rtin g with famous
1992 COBE DM R announcement published results of successful CMB anisotropy
measurements.
The Figure 1.1 dem onstrates the multitude of CMB experim ents analyzed to date.
The vertical axis is band power in microkelvins. horizontal — num ber of multipole
(inversely proportional to angular scale). The designers of these experiments took
different approaches to sim ilar and very difficult problems which are worth mention­
ing.
Some of the top issues th a t CMB experiment designer m ust address are:
• sidelobe contam ination
• contamination of d a ta by G alactic foregrounds
• atmospheric emission (not an issue for space based experiments)
• scanning strategy to maximize sensitivity to chosen region of spectrum
• Surface based, balloon-borne or space-based? Each choice has some advantages.
• choice of detectors
One of the most difficult problems is far sidelobe (tens of degrees from line of sight)
contamination. While tem perature of microwave background we try to observe is only
3 K. and variations in tem perature (which are the prim ary goal of experiment) are in
tens of microkelvins. E arth and Moon have tem perature about 300K. Sun — about
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6
T eg m a rk 1998
SK
BAM
MSAM
VIA
i
PYTH .
IRING
QMAP
40
20
OBE
0
\ J
............................................................... ■ > . » « ■
10
>
MAX
SP
EN
>
>
i
i
i
i
« i i
................................................................................
100
"
M
1
m ."
M
m
1 00 0
M ultipole 1
Figure 1.1: A sum m ary of CMB anisotropy d ata (figure supplied by Max Tegmark)
6000 K. W hile designing an instrument, a great care is taken to minimize spilling of
beam beyond prim ary mirror. In MSAM-1, the prim ary m irror is underillum inated,
which significantly reduces diffraction controls beam spillage by projecting it on the
sky rather then warm E arth or parts of the instrum ent. Single mode experiments
like MSAM-2 or MAP are often using scalar feed horns w ith exponentially decaying
sidelobe response.
Bright sources are kept as far away as possible from the main
beam. MSAM-1 could be launched only on moonless nights. MAP. taking an extreme
approach, will be launched into Earth-Sun L2 Lagrange point. This will assure that
all m ajor sources of sidelobe contamination (Moon. E arth and Sun) are located in the
same direction, at least 87 degrees from the beam. Most experim ents have extensive
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(
system of shields assuring th a t as little as possible direct, reflected or diffracted light
from these m ajor sources ever reaches detector. Balloon experiments are sometimes
suspended on very long (up to thousand meters) cable to assure th at balloon has as
small angular size as possible.
Another source of concern is contamination by G alactic foregrounds such as syn­
chrotron radiation, free-free radiation, and therm al radiation from interstellar dust.
D ata from some regions, such as Galactic plane, are hopeless and should be cut out. If
the experiment (like TopH at. MSAM or MAP) has m any spectral channels, the data
from relatively contam ination free region can be fit to model m ulticom ponent model
assuming we know the frequency spectra of CMB anisotropy and foregrounds. Single
frequency instruments, like Python, have to rely on sky surveys to find relatively
uncluttered regions.
An im portant foreground for all but space based experiments is atm ospheric emis­
sion. Time dependent random fluctuations from changing transparency along line of
sight introduce low frequency noise with properties which are difficult to characterize.
Such noise is often called 1 / / noise, although its power spectrum is not always exactly
proportional to / ~ l. T he tem porally constant part makes scanning sky in vertical
direction difficult as it introduces signal changing synchronously with scan. For this
reason most balloon and surface based experiments scan in horizontal direction.
To avoid excessive atm ospheric loading and associated noise and gain loss, many
CMB experiments are done from balloons operating at altitude 35000 - 39000 meters.
E arth based experiments are flocking to high altitude places w ith low humidity, such
as South Pole or Chilean Andes. W hen possible, line of sight is placed close to zenith
(it may be difficult in case of balloon experiment because of huge balloon directly
above the instrum ent).
A very im portant issue, influencing the design of the instrum ent, is the choice
of scanning strategy. In a case of very low* noise and no long tim e drifts operating
telescope w'ould be as simple as pointing detector at points of interest in random
order and analyzing m ap. Unfortunately operating instrum ent is greatly complicated
by slow drifts and offsets, wrhose amplitude is often orders of m agnitude am plitude
th at of signal we try to observe.
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8
For this reason all CMB anisotropy experiments are differencing experim ents —
they measure tem perature difference between points on the sky rather then tem per­
ature of the sky itself- The simplest example of differencing experim ent would be a
chopping telescope th a t rapidly switches between two points on the sky. T h is is an
idea of classical Dicke switching radiometer- As tem perature difference is m odulated
with frequency of switching and slow' drifts and gain variations are not. simple Fourier
transform will reveal d a ta otherwise masked by low frequency noise. If instrum ent
switches between m any points, the good way to separate signal from drifts noise is to
fit differential data to model with two prim ary components — position dependent sky
signal and time dependent, slowly changing drift. To improve quality of this solution,
each pixel on the sky should be connected with as many other pixels as possible in all
possible directions. If this condition is not satisfied, strong noise correlations between
pixels appears.
While some experiments attem p t to get detailed distribution of tem perature fluc­
tuations on the sky (COBE. FIRS. MAP. TopHat). most are lim ited to probing sep­
arate regions of anisotropy angular spectrum . Data of m apping experim ents contain
more information (not only am plitude, but phase of every m ultipole). These d a ta is
easier to compare with theories and combine with results of o th er m apping exper­
iments. Maps are easier to analyze for nongaussian fluctuations predicted in some
theories wdth topological defects. Even in case of map. data analyst should be aware
of possible nondiagonal pixel to pixel noise covariance.
Chopping experiments, like MSAM. measure response to synthesized beam p at­
terns which are linear com binations of beam patterns chosen to have £is little sensitiv­
ity to offsets as possible while still retaining sensitivity to tem perature fluctuations at
chosen angular scale. In some cases it is possible to build a tem perature distribution
map from d a ta of experiment not originally designed for m apping, in most cases it is
difficult and resulting m ap would have nontrivial pixel to pixel covariance.
This thesis describes analysis of the d ata from the third flight of MSAM-1 tele­
scope.
T his is a chopping, balloon-borne, bolometric, m ultifrequency instrum ent
specifically designed for m easuring CMB angular anisotropy spectrum a t h alf de­
gree scale. The goal of this experiment wras detection of m edium scale anisotropy.
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9
not extraction of cosmological param eters, for which, this instrum ent did not have
enough sensitivity or angular frequency range. This is a task for the next generation
of anisotropy experiments. From experience with MSAM system a design for new
generation of bolometric radiom eters was born, which is described in second part of
the thesis. This is a potential detector system for these future experim ents. This de­
sign attem pts to address some of the issues mentioned above by packing multichannel
radiom eter in sm all volume and having reasonable frequency dynamic range to allow
scanning over large angular distances to allow mapping experiments. It m ay be useful
for future CMB experiments as well as for other submillimiter surveys.
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CHAPTER 2
IN ST R U M E N T D E SC R IPT IO N
The telescope used for 1995 flight of MSAM (MSAM1-95) flight has a bolometric
receiver with four channels a t 5.6. 9.0. 16.5 and 22.5cm-1 (170. 270. 500 and 680
GHz) with approximately 1 cm -1 bandwidth in each channel. It was used in three
flights: MSAMl-92 in 4-5 Ju n e 1992, MSAM 1-94. 1-2 June 1994 and MSAM1-95.
1-2 June 1995.The first two flights observed the same patch of the sky to confirm the
detection of anisotropy. The results are reported in [7. 6]. They covered an arc at a
declination of +82°. The last flight added an arc at a declination +80.5°.
Both the gondola and the radiometer had flowm in previous experiments. The
gondola was used with different telescope and radiom eter to map the G alactic plane
[21]. The radiometer had been flowm for the Far Infrared Survey (FIRS) [37. 18. 17].
which experiment confirmed the anisotropy detection by COBE mission [3].
2.1
G ondola
The telescope is schematically shown in Figure 2.1. The gondola is attached to the
balloon by a cable system (the figure shows tubular structure, but it was replaced by
cables for 1994 and 1995 flights). The entire gondola is servoed in cizimuth during the
flight. The telescope structure (primary m irror, the secondary m irror and chopper
assembly, the star camera, the dewrar and signal electronics and gyroscope) is servoed
in elevation by two motors.
The observing strategy provides three levels of modulation to aid in separating the
weak sky signal from large drifts and to minimize motion relative to E arth. T he first
level of m odulation is provided by the nutating secondary (chopping) at 2 Hz (above
the 1 / / knee of detectors and electronics). The second level of m odulation results
from triangular wave slow azim uthal scan w ith 1.5° amplitude and 1 m inute period.
10
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11
Cables to Balloon
Jitter Bar
Mechanism
Primary Mirror
1 meter
Secondary Mirror
Chopper
Detector Electronics Box
Star Camera
Elevation Motors (2)
Cryostat
Metering Truss
("strongback")
Gondola Electronics Box
Gondola Frame
NSBFCIPs (2)
Crush Pads
Azimuth Motor
and Wheel
Figure 2.1: Gondola
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12
20 such scans are executed and followed by sta r camera observation and a shift of
0.75° to the west. The star camera observations are used to get fix on slow gyroscope
drifts. T he scans overlap provides the th ird level of modulation (see Figure 3.7). Such
complex three level m odulation is introduced to shift sky signal into frequency range
where gain variations and instrum ent are less im portant and to aid in sep aratin g
position dependent sky signal from tim e dependent noises and drifts.
The center of the scan is close to true N orth. This way elevation changes very
little over the time of scan and is close to maximum all the time.
2.2
O ptics
The telescope is a 51°off-axis Cassegrain system with nutating secondary'. T he pri­
m ary m irror is a 1372 by 1518 mm parabola, focal length is 1473 mm. T he effective
beamsize is 37'. Full W idth Half M aximum (FWHM) size (where beam sensitivity is
half of its peak sensitivity) is 28'. the secondary' throw is ± 40'. The prim ary m irror
is machined from a single piece of alum inum (6061-T6) and lightened by m achining
pockets out of the back leaving a 10 m m thick "skin". Its total weight is 75 kg. The
secondary is 276 by 315 mm convex hyperbola with 1 mm thick skin (to ta l weight
550 g). It is undersized to limit illum ination of the edge of the primary' an d to spill
any' sidelobe power from the radiom eter (at large angles) to cold sky. To move the
beam by ±40' on the sky', the secondary rotates by7 ±1.69°.
The beam is formed byr elliptical W inston cone concentrator cooled to liquid helium
tem perature. Its design etendu is 0.5cm2 steradian. Geometric optics suggest (via
raytracing) that all radiation em itted from the horn will be scattered on primary7
m irror and then on cold night sky. W hen diffraction is taken into account. ~ 10%
of the radiation is coming from outside the secondary m irror in lowest frequency7
channel. In shorter wavelength channels up to ~ 4% of radiation is scattered beyond
secondary7.
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13
Internal
Shutter
4.2K
LHe Shield
Outer Jacket
Channel 2
77KLN2 Shield
Channel 1,
cold p/afe
4.2K
\ 0.24K\
cold plate
0.24K
4.2K
Polypropylene
Window
Elliptical C oncentrator
Channel 4
Fluorogold
Channel 3
Black Polyetheylene
Aluminized Mylar MLI
Dichroic Beam Splitters
Figure 2.2: Cold optics [14]
The input horn, elliptical concentrator and first beam splitter are m aintained a t 4.2K.
The rest of the optics and detectors are a t 0.24 K.
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14
2.3
Radiometer
The cryostat and filter bandpasses are described in [41. 43. 42]. T hey were slightly
modified for MSAM experiment because of different observation strategy.
The filter block (structure supporting detectors and filter system) is made of
copper1. The high frequency IR radiation is blocked by black polyethylene at 4.2 K
and then split twice using capacitive grid dichroics [42] to form four channels. Each
channel has a W inston cone concentrator feeding a silicon bolometer [13] along with
band defining filter and fluorogold high frequency blocker.
The bolometer signals are amplified by cold JFET source followers and external
pream ps. All lines going into cryostat are fed through low-pass RF filters to eliminate
the effect of detectors heating from external RF sources.
2.4
N oise and offset sources
2-4-1
Sidelobe contamination .
W hile most of beam energy is concentrated well within one degree from the center
of the beam (FWHM is 28'), a sm all part of the beam is spilled beyond the prim ary
m irror. Control of this spillover is necessary' since signals are few microkelvin, while
the gondola, earth, balloon and every thing else but the sky is close to 300K. Sidelobe
contam ination concern is the reason why we chose to fly the telescope on a moonless
night.
According to [26], the chopped response (section 3.5) is —80 dB to —90 dB for
angles > 20° from the m ain beam. Unchopped far sidelobe response is —60 dB to
—70 dB. It is difficult to measure far sidelobes to level lower then —100 dB.
If tem perature of the Moon assumed to be 300K, the signal from the Moon in far
sidelobe without additional rejection provided by chopping can be as high as 3 x 10-4
Iv (taking into account th at Moon angular diameter is close to beam FW HM ) which
1Ox\-gen Free Hard Copper OFHC 101. hot rolled in hydrogen atmosphere. If processed in
oxygen atmosphere, oxide will greatly increase heat capacity at low temperatures. This will increase
cooldown time and cryogen consumption.
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15
is higher than expected CMB signal by a t least order of m agnitude. A dditional —10
to —20 dB from chopping bring th is contam inant to a level comparable w ith expected
signal — still too high. This is why observations during moonless night are preferable.
2-4-2
M irror thermal fluctuations.
Chopping the secondary m irror causes the radiometer to illum inate different p arts of
prim ary mirror. Because of nonuniform tem perature distribution.the integral o f tem ­
perature over the beam pattern is changing synchronously w ith chopping, contribut­
ing to the demodulated (see section 3.4) signal. This dem odulated signal is changing
slowly with time and is correlated in ail channels (it has Raieigh-Jeans spectrum with
correction on aluminum absorption coefficient changing with frequency). T he drift
was changing by as much as 1.5 mK in some channels during the flight (see Figures
3.8. 3.9). Of course, this is ju st one of possible drift mechanisms.
During the observation period the tem perature of m irror was dropping by ~
1.25Iv/hr. The longest tim e constant for thermal gradients was ~ 30min. A nother
sort of offset can arise from nonuniform ity of reflection coefficient (which is close to
99.5% on average).
2-4-3
Atmospheric effects.
Neglecting the curvature of atm osphere, the number of molecules of air in the line of
sight of telescope is proportional to
N oc P / sin(0)
(2.1)
where P is pressure. 0 is elevation. For small optical depth the loading from atm o­
sphere is proportional to N . If loading changes slowly, these effects are rejected by
demodulation however large loading can change detector responsivitv. S = d V / 8 Q .
where V - detector output voltage, Q - radiative loading, and so changes to ta l system
gain.
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16
T he Equation 2.1 explains im portance of chopping in a horizontal direction. In
a case of coupling between elevation and azim uth (possibly because of gyroscope
m isalignment), angle 9 changes synchronously with chopping and will contribute to
dem odulated signal (see Section 3.4). Its spectral signature depends on atm ospheric
absorption lines distribution but the signal is likely to be correlated in all channels.
Scans In elevation set an upper limit to signal induced by elevation motion a t ~
3m K /arcm in. A misalignment in scanning axis relative to local horizon by 6' results
in to ta l change in sky tem perature of % 540/rK. This offset is m itigated by three level
scanning strategy.
2-4-4
Cosmic ray hits.
Cosmic rays hitting the bolometers deposit energy th at heats the bolometer effectively
instantly. The signature of such event is fast rise in tem perature, followed by an
exponential cooldown2. It is impossible to identify all cosmic ray hits, as significant
p art of them has am plitude below noise level (Figure 3.3). however most strongly
non-Gaussian events are likely to be results of cosmic ray hits.
A small percentage of high am plitude events appear to have negative energy. T he
m ost likely source of these events are energetic particles hitting preamplifier JF E T
[27].
These events are not correlated between different channels. They are best identi­
fied in tim e domain before dem odulation.
2.4-5
Fundamental detector noises
T he model of detector performance is considered in great detail in [33, 34, 35]. To
sum m arize, the following term s contribute to detector noise: Johnson noise from
finite resistance, therm al noise from finite heat conductivity from detector to therm al
bath, transistor amplifier noises. All these sources look essentially as white noise
uncorrelated between channels.
2Because of limited amplifier bandwidth the exact shape o f the tail is not exactly exponential,
see section 3.3
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17
All silicon bolometers dem onstrate another low-frequency noise also known as 1 / /
resistance noise. There is no definite theory of this noise that fits d ata well. A good
experim ental study is published in [20]. In a case of MSAM-l experiment, however,
this noise source was not a dominant one.
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CHAPTER 3
DATA ANALYSIS
3.1
D ata D escription.
The third flight of the MSAM- 1 experiment took place from the National Scientific
Balloon Facility in Palestine. TX during the night of June
1
- June 2, 1995. The
package was launched at 23h47m UT. After th e balloon is launched it took a few
hours to reach an altitude where observations were possible. The first raster scan
over Jupiter was used to locate the center of th e beam, the second (before CMBR
observations) and third (after) were used to carefully measure beam map. The first
CMBR scan was started at 4h20m UT. The to tal time spent observing the C’MB was
5h01m. The observed region on the sky spans right ascension from 14.2 hours to 19.5
hours, and declination from 80 to 80.5 degrees.
Jupiter scans (one-dimensional motions across the planet) and rasters (two-dimensional
observations of a rectangular patch centered on the planet) were used for instrum ent
calibrations in previous flights of MSAM-1. However tem perature of Ju p iter is not
very well known in MSAM - 1 bands so the prim ary calibration was done by observing
Mars and fitting data from Mars scan to beam m ap constructed from Ju p iter raster
(section 3.6). Saturn was also observed for possible use as a calibrator in future
experiments.
At the beginning of the flight, we performed a raster scan across Ju p iter to de­
termine the antenna pattern, and then performed horizontal calibration scans across
Jupiter and Mars for flux calibration. For the next 5 hours, the telescope executed
deep scans above the N orth Celestial Pole to m easure CMB After the CM BR obser­
vations, the telescope was again slewed to Jupiter. Another raster was performed to
re-check the antenna pattern, followed by another calibration scan on Jupiter. Fi­
nally, a calibration scan was performed on Saturn. The general sum m ary is given in
18
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19
Table 3.1. while th e detailed circumstances for each of the four calibration scans are
given in Table 3.2.
O f particular note is th at, for these observations, the S atu rn ring inclination angle
to E arth is nearly zero (—0i37): thus, we are measuring only the radiation em itted
by the planet disk.
The beam size is close to 28' FWHM and is moved ± 4 0 ' on the sky by chopping
the secondary. T h e four frequency channels are placed at 5.7. 9.3. 16.5 and 22.6 cm -1 .
The following table briefly summarizes observations.
Table 3.1: Short summary of MSAM - 1 1995 flight
tim e
Event
J u p ite r raster
Ju p ite r raster2
F irst Mars scan
Second Mars scan
CM BR observations (scans 1-15)
J u p ite r raster 3
J u p ite r scan
S aturn scan
03h02m -03hl0m
03h26m-03h35m
03h53m-04h04m
04h06m -04hl2m
04h20m.-09h.20m
09h34m-09h41m
09h47m-09h54m
lO h llm —10hl7m
After each CM BR scan a few minutes were spent obtaining images w ith the star
camera. Stars were m atched to catalog of bright stars to provide exact pointing. This
data was used to su b tract gyroscopes drift over the time of the scan. T here were 15
CMBR scans to ta l each lasting about 18 minutes.
Scan
Ju piter - 1
Mars
Ju piter - 2
Saturn
Table 3.2: Observation Circumstances for planet observations
Elevation
Alt. (km)
UT
Lat.
Long.
25° 32' - 26°30'
34.9
03:41:51 -03:49:12 31° 19' N 95°41' W
32° 55' - 30°09'
36.1
03:59:01 - 04:11:47 3 i ° i r N 95°44' W
18° 56' - 17° 48'
37.6
09:47:05 - 09:53:49 31° 28' N 98° 2 7' W
30° 07' - 31°15'
37.3
10:11:03 - 10:17:13 31° 23' N 98° 39' W
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20
3.2
Summary o f A nalysis
The diagram in Figure 3.1 dem onstrates simplified data analysis pipeline. The detec­
to r d a ta are cleaned from identifiable contam inants, such as cosmic ray hits, binned,
cleaned from drifts and decomposed into CMB and dust com ponent. The following
sections describe the analysis in detail.
.on
Detectors
timescream
Cosmic ray
hits
ider.t.
Demodulation
Spectral
decomposi cion
ISM dusc
data
CM3R anisotropy
data
Maximum
.ikelyhood
analysis
Figure 3.1: Data Analysis Pipeline
3.3
D eglitching
This part of d a ta analysis was done by Lloyd Knox as p a rt of MSAM collaboration.
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21
Before fitting time ordered data to a sky model, it is necessary to cut out regions
affected by cosmic rays. Cosmic ray particles deposit energy in a bolometer and
produce spurious signals having no relation to CMBR.
Unlike previous flights ([27. 47]) where individual cosmic ray tem plates were fit
to tim e ordered data, in this analysis deglitching was done by first applying Wiener
filter (for popular treatm ent see [46]) to localize cosmic ray signature.
W hen the cosmic ray particle deposits heat in a bolometer, for all practical pur­
poses power P is equal to Qd(t — t0). where Q is the to ta l heat deposited by the
particle. d(t) is delta function. The response in the tim e-ordered d a ta is
\'i — ^ 2 Q jT i-j
j
(3.1)
where T is the transfer function. Tj-j = 0 for i < j . j is a sample number when a
particle hit the bolometer, depositing energy Q j .
W hile to tal deposited energy Qj may be significant. V] is not significantly higher
than noise at each given sample as response is spread out over many samples. This
makes identifying cosmic ray hits difficult.
One possibility to handle this is to "collapse" all response in one sam ple by deconvolution of transfer function T — reconstructing signal before it was low-pass
filtered by bolometer and amplifier. Significant hits can th an be easily identified.
The simplest obvious answer is a strict deconvolution — make a Fourier transform
of data, divide by spectrum of transfer function and Fourier transform result back.
U nfortunately in a presence of noise if transfer function is not known precisely and
close to zero at some frequencies, noise at these frequencies is amplified by a large
factor. The answer is to use Wiener filtering which gives a least square approximation
to a noisy signal in the case when the signal and noise spectra are both known.
The first step was to construct a transfer function. In frequency space
(3.2)
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2 2
E ( f ) is the amplifier transfer function measured with a spectrum analyzer prior
to flight. S ( f ) is a sampling function due to discrete integrated sam pling of d ata.
S(f)
where 5 =
1
(3.3)
=
“J
/32sec is the sampling period.
The bolometer transfer function. B ( f ) . is a low pass filter
B(f) = ■
.■v- " ,
1 -r- l l - a J T
where r is bolometer therm al time constant.
<3 -4 )
It was found by fitting the inverse
Fourier transform of T( f ) to a large cosmic ray hit with r as free param eter.
The cosmic ray hit signal is a delta function in tim e convolved with transform
function T (t). Therefore the W iener filter
« (/) = ^
(3.5)
\C(f)\2
where C' (f) is the spectrum of d ata because
|C (
/ ) | 2
=
\T{f)\2 + |-V (/)i
2
(3.6)
where N ( f ) is noise spectrum.
The filtered output can be w ritten as
F-F.T. {V,ilured) = H i L i l l o
(3 .-)
Due to our scanning strategy detectors are repeatedly looking at the same points
on the m irror and sky at the same chopping cycle phases, therefore offsets are close
for samples in different cycles with the same phase, but very different for different
phases in the same chopping cycle. Each sample is assigned two num bers — i an d n
where n is number of chopping cycle a n d i is number w ithin a cycle (i = 1..16) then
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counts
23
V
0.5
Channel
Channel
Channel
Channel
5
1
2
3
4
S\
v'\
10
frequency (Hz)
Figure 3.2: W iener filters used for deglitching
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15
24
averages and RMS for each. 16 values of i within 512 seconds (1024 chopping cycles)
are calculated.
A fter this all cosmic ray spikes above 3.0cr and a region around them proportional
to the spike am plitude were deleted- The num ber of neighboring samples to be deleted
was chosen to be am plitude of spike divided by RMS of cleaned data. T his procedure
was iterated twice.
D ata in an entire chopper cycle (0.5 sec length) was deleted when any part of it
was lost because o f cosmic ray signal or telem etry dropout.
In addition to cosmic ray hits, a total of about 35 minutes of data were discarded
because of anomalously high instrum ental noise of unknown origin. T his excessive
noise was observed simultaneously with excess noise in 3He stage tem perature sensor
suggesting problem with readout electronics.
The Table 3.3 show's a sum m ary of d a ta cut due to cosmic rays hits and other
reasons. In this table r is the corresponding detector time constant. The Figure
3.3 dem onstrates histogram of fitted spikes.
For obvious reasons, no spikes w ith
am plitude less then 3.0er could be found by this procedure.
Channel
Channel 1
Channel 2
Channel 3
Channel 4
I
0 . 1 2 0
0 . 1 0 0
0.058
0.025
t
percent of d ata cut due to cosmic rays
23%
2 1 %
25%
1 1 %
total datci loss
33%
31%
34%
23%
Table 3.3: D ata loss summary.
is detector tim e constant for given channel.
3.4
D em odulation
The experiment observing strategy provides 3 levels of sky signal m odulation. This is
necessary to reject the DC signals and slow* l / f drifts w'hich exceed the am plitude of
anisotropy by m any orders of m agnitude. The first level comes from
2
Hz secondary'
m irror motion (chopping). Linear combinations of the detector signals are constructed
to synthesize nearly' orthogonal beams.
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25
1200
1000
Ii i i i Ii i i i !i i i i Ii ii i Ii i i i !i
I i i i i I i i : I ! ! i I i I i i I '
1200
—
1000 —
800—
800—
600 —
600—
400—
400—
Channel 1
200
1000
-15
i
I
i
I
I
I
i
i
I
rTftTI
n
i ---- 1 i j i'i ; i ; i
-10
i
Channel 2
200
I
-20
1 2 0 0 — ^
-5
i
i
i
i
I
0
i
i
i
i
!
5
i
i
i
i
I
—
i
-20
i i~f~!~[~l i ii i't ; ; i
-15
-10
-5
_1
I I | I I I [
i_
1200
—
1000—
800 —
800—
600—
600—
r
400—
2o o
-20
i i i; ii
0
II I 1 I I I i I I I
5
I I i i t I I I
400Channel 3
-
I i i i r i
m T P 1 1n1 15
Channel 4
200
-10
-5
IIIIII *
0
rr
r-t
o -jTTn | : i
-20
-15
i l! O
| i Ii
-10
“i i [ i i i r~j i p
-5
0
5
Figure 3.3: Histograms of removed spikes. Note th a t number of negative spikes
(positive energy deposited on bolometer after a cosmic ray hit should give a negative
spike) greatly exceeds number of positive spikes. Horizontal axis is am plitude of spike
divided by RMS of filtered signal, vertical — number of spikes with given amplitude.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
26
Detectors were sampled at 32 Hz giving 16 samples across each chopper cycle.
The position of the beam on the sky relative to the center of the chopper is shown
on the Figure 3.4.
If a detector makes three tem perature measurements at left, center and right T L. To
and T-i there is an obvious way to represent each measurement as linear com bination
of three orthonormal tem plates. DC average, single difference and double difference:
T qc — (Ti-{-To-hT z)/\/Z
(3-8)
T sd
(3.9)
=
T qd =
(TL - T 3)/y/2
(Ti — '2To 4- T ^ )/\/z
(3.10)
By not using TDC in analysis we get rid of DC signal without losing any anisotropy
d ata. T od is not sensitive to gradients. Using this approach one can build naive
dem odulations for the experiment shown in figure 3.4.
demodulated data t can be w ritten as
(3.11)
where n is the chopping cycle number, i is the phase number of sample in a chopping
cycle. S is the detector signal and d is demodulation template.
Unfortunately these tem plates neglect many time-dependent effects an d are not
optim ized for lowest signed to noise ratio. First, detector tim e constant is not zero.
W hen chopper switches to the next position, the d ata acquisition system (DAQ) reads
out a linear combination of tem peratures at previous and current positions. Second,
simple templates have power at all frequencies up to 16 Hz while signal electronics
effectively rolls off signal a t
8
Hz. T hird, times at which data are read by DAQ system
are not known exactly although synchronous to chopper motion. The exact tim ing is
determ ined from the flight data.
All these effects introduce phase shifts and affect different frequencies in different
way. Although Wiener filtering (see section 3.3) reduces this effects to som e degree
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27
I i i i i I i i i i 1 i i i i I i i i i I i i i i I_
0.6
0.6 _J I I I I I I I I I I I I I I I I I I I I I ! 1 I l_
0 .4 —
0 .4 —
0. 2 —
cn
3
3 o.o— '
0 .0 —
o
-0. 2 —
-0 .4 —
-0 .4 —
-0 .6 —]i i i i i | i i i i | i i i i I i i i i I i i i i i
0.0
0-1
0.2
0.3
0.4
-0 .6 —j | I l ! | | | 1 ! | | I | I I 1 | I I | I I ! I [~
0.0
0.1
0 .2
0.3
0.4
0.5
0.5
time (sec)
time (sec)
Figure 3.4: Idealized single and double dem odulations as functions of time. Demod­
ulation tem plates are normalized so th a t sum of squares of tem plate is one.
1.0 _ ! i i i i I i i i i I i i i i I i i i i I i i i i L
2
0. 0 —
O-0-5-
-1 -0 —]
0.0
I
I
I
I
|
0.1
[
l
I
I
|
0 .2
I
I
I
I
|
0.3
I
I
I
i
|
0.4
!
I
I
I
J-
0.5
time (sec)
Figure 3.5: Beam position as a function of time
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2 8
it does not eliminate them com pleted. To get maxim um signal to noise ratio in
dem odulated data we have to
• determine which frequencies have useful signal and which do not. In the result­
ing tem plate each frequency should have weight proportional to S/X ratio in
this frequency.
• for each frequency carrying useful signal keep only one phase with highest S /X
ratio and discard phase shifted by
tt/ 2
(quadrature phase) with zero S/X" ratio.
Templates constructed from quadrature phases can be used for estim ating noise
in demodulated signal.
To build such a tem plate, data from the Jupiter scan were used. First, an average
was subtracted from each chopping cycle to compensate for possible drift. O utliers
beyond 3<r where deleted to remove cosmic rays hits. Sophisticated deglitching is not
very im portant in this measurement because of the high signal to noise ratio. T hree
regions where selected: center — when Ju p iter was within 0.035 degrees of chopper
central position, right and left — when Jupiter was within 0.035 degrees within left
or right chopper position.
(3.12)
c e n te r
(3.13)
In idealized case of infinite amplifier bandw idth, no phase shift and zero bolometer
tim e constant this method would give us idealized demodulations shown in Figure
3.4. Constructed from real signal filtered by amplifier and detectors with finite tim e
constant these templates will have properties close to ideal properties described above.
As the next step all frequencies but 4 Hz in single demodulation tem plate or 2 Hz
and
6
Hz in double demodulation tem plate were set to zero.
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29
Channel 1. Single demodulation.
0 0_!
i i i i I
i
Channel 1. Double demodulation.
i i i I i i i i I i i i i I i i i i I__
0 g _ !
0.4—
I
I 1 I I I 1 I l f !
1 l
I
i
I I 1 I I ! 1 l
l L
0.4—
0.2 —
5 o.o—
5 0.0—
-0.2 —
-
-0.4—
-0.4—
-0.6—j i i i i [ It i t | i i i i | i i i i |
0.0
0.1
0I2
0.3
ei
0.4
i i [—
0 .2 —
*0 -6 —| 1 > 1 1 |
0.5
0.0
1 1 1
0.1
!|
1 1 1
0.2
I[1
0.3
1 1
:[
0.4
1 1
:1(
0.5
time (sec)
time (sec)
Figure 3.6: Single and double demodulations for first channel actually used in analysis.
Note how shape and phase changed compared to naive demodulations in Figure 3.4.
3.5
Binning and Dedriffcing
In section 3.4 I described dealing with first level of m odulation. The experiment had
three levels of modulations total. The second and the third level were provided by
scanning the telescope back and forth on the sky.
The Figure 3.7 shows right ascension cts a function of time for a period of forty
minutes.
One can see that on top of the fast chopping motion of the secondary
mirror the whole gondola was slowly (with a period close to
and forth in azim uth for a period of
2 0
1
minute) scanning back
minutes, followed by a short period of sta r
observations to determine exact pointing and correct for gyroscope drifts. The next
CMBR scan starts at a new center, but half of it overlaps with the previous one. This
strategy of using overlapping scans helps to separate space-dependent sky signal and
tim e-dependent 1 / / drift, signal from atmosphere, prim ary mirror therm al drifts and
other non-astronomical sources.
The observed region of sky was divided into bins sm all compared to the bearnsize.
The bins size is 0°12 degrees in declination and $ 0 5 7 in right ascension. Because of
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30
I
i
I
i
I
i
I
i
I
i
I
t
1
i
i
I
i
1
i
I
i
I
i
Time (UT)
i
14.4
14.6
14.8
15.0
15.2
15.4
Right ascension
Figure 3.7: Right ascension as function of time (in minutes)
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I
31
earth rotation some points are observed with different angular orientation o f the beam
throw on the sky. For this reason the data are also divided by angular orientation
(twist) with a bin size
1 0
°.
The d ata was then fitted by the following model:
H = £ aaH ai = £ TsBai + £ cKK Ki
a
3
k
(3.14)
where aa are model param eters. Xj is tem perature in the bin. 3 is bin number, i
is dem odulated sam ple num ber in time-ordered data. /vKI is a complete system of
natural cubic splines with knots far enough ap art to avoid overfitting d a ta (in this
case the time between knots was
2
minutes w'hich is much longer than one chop cycle).
3 runs over all bins in the three-dimensional space of right ascension, declination and
twist. Bins writh less then 10 chopper cycles of d a ta (5 seconds) in any channel after
cuts were discarded. B ai =
1
if record i lies in the bin ,3 and 0 otherwise. This model
does not include pressure-dependent term as in [26] because no significant correlation
between drift level and pressure was found (unlike MSAM-1 1994 data). T he solution
for this equation is found by minimizing least square sum of deviation of d ata from
model:
Wij ^
X* = E ( l < - E
where
11
- y
a3H , ) j
(3.15)
V, is the weight m atrix - inverse of the noise m atrix of the dem odulated d ata.
The solution for this m inim ization problem is
aQ = £ (HaiWtJHJ0r l H akW klTL
ijaki
(3.16)
The covariance of the fit param eters cov(aQ. a 3 ) is
t ad = £
(3.17)
ij
The covariance of binned d a ta is given by upper iY&j-n by A'&£-n square of m atrix
tad -
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32
The Figures 3.8. 3.9 show fitted drifts iu all four channels. It is evident that drifts
in single dem odulation are much more correlated than in double demodulation.
Channel
1
2
3
4
Single dem odulation
23564
24365
23162
27941
Double dem odulation
23274
24160
22898
27539
Degrees of freedom
23887
24498
23210
27706
Table 3.4: \ 2 for drift fits
The table 3.4 shows the x 2 (see 3.15) for all channels and demodulation. Number
of degrees of freedom is a number of chopper cycles in every channels less the number
of fitted param eters. T he fact th at x 2 is close to number of degrees of freedom in
unfitted d ata suggests th a t the distance between knots is not too small.
3.6
Calibration
Just like in previous MS AM flights, in this flight observations of Jupiter were used
to find the beam m ap and calibrate radiometer. However, because tem perature of
gas giant planets is not very well known in our bands and because we were lucky to
be able to observe Ju p iter, Saturn and Mars in one flight, a hybrid approach was
used. The tem perature of Jupiter was found by cross-calibrating it to Mars, which
tem perature is known better, but Jupiter is used for beam m apping as it provides
better signal to noise ratio. For details of cross-calibration see chapter 4.
The next step was to construct beam maps from the Ju p ite r raster d ata. The third
Jupiter scan (see Table 3.1) was used where Jupiter was scanned 9 times in cross­
elevation from —1.5° to 1.5° at elevations varying uniformly from —0.6° to 4-0.45°
relative to Jupiter.
Elevation, cross-elevation and dem odulated tem perature were
fitted to cubic splines as a function of time for each of the nine scan lines. After this
the demodulated tem perature was interpolated in elevation and cross-elevation with
0.05° steps.
The calibration coefficient can be found in the following way:
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33
C hannel L
C
O
1
02
o
6
7
8
9
8
9
8
9
8
9
T im e (UT)
C hannel
5
6
2
7
T im e (UT)
ChanneL 3
o
6
7
T im e (UT)
C h a n n el 4
02
I
5
6
7
T im e (UT)
Figure 3.8: Single dem odulation drift in all channels. The vertical axis is tem perature
in mK. the horizontal axis — time in hours. Note that there seems to be some long
term correlation between channels. The large feature between UT ShOOm a n d 8h20m
is bogus and is due to big d ata cut at this point. This is the best fit to d a ta with
very low significance.
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34
C hannel 1
CO
E
u
r
CO r
7
T im e (UT)
C hannel 3
T im e (UT)
C hannel 4
in
cn
5
6
7
8
9
T im e (UT)
Figure 3.9: Double dem odulation drift in all channels. T here seems to be much less
correlation between channels then in Figure 3.8. The am plitude of drift is also smaller.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
f B f(x .y ) d x d y — f B f(x .y )d x d y
Ci =
x <0__________________ x>0_______________
T /Q j
(3.18)
where C£ is counts to Kelvin conversion factor for channel i.x and y are cross-elevation
and elevation in radians w ith reference frame centered a t Jupiter. B f is single demod­
ulation beam m ap in channel i (see Figure 3.10). T { is tem perature of Jup iter in our
channels (see chapter 4). Qj is solid angle subtended by Ju p iter at the time of obser­
vation (see Table 3.2). The radius of Jupiter in subm illimeter bands was taken from
[22] and is equal to 71495 km. The distance to Jupiter was approxim ately 4.3248
astronom ical units at the moment of observation [4. 12].
Figure 3.10: Single dem odulation beammap. This is a beam m ap for antisym m etric
dem odulation of channel 2. To fit tem peratures of planets the response of the planet
scan was fitted to this beam m ap.
The signal from detector contained spikes due to cosmic rays striking the detec­
tors. Because of high signal to noise ratio of these d a ta the procedure described in
section 3.3 could not be applied to the planets scans. T he d a ta reduction was iden-
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36
Figure 3.11: Double dem odulation beammap. This is symmetric dem odulation of
channel 2. See caption of Figure 3.10 for explanation.
tical to the procedure described in section 4.3 except that the same dem odulation
tem plates (section 3.4 as those used for the rest of analysis were used. In chapter
4 simplified ("naive") tem plates were used as this part of analysis was done when
optim al demodulation tem plates were not available yet.
Calibration errors were estim ated using a Monte-Carlo m ethod as follows. Sub­
tracting temperature, elevation and cross-elevation from time-dependent sm ooth fit­
ted splines residuals were found. It was determined th at they have Gaussian distribu­
tion. The standard deviation for coordinates was 015. for dem odulated tem perature 0.28. 0.32. 0.54. 0.64 counts respectively. From existing datasets sim ulated d a ta were
constructed by adding both to pointing and tem perature data Gaussian distributed
random numbers with the above RMS. These data were used to find calibration coef­
ficients Ci (equation 3.18) for 1000 different realizations of beam m aping experim ent.
T he resulting set was used to find covariance matrix cov(C i,C j). As it turns out. the
m ajor contributor to covariance is pointing uncertainty rather then detector noise,
therefore noise calibration error in different channels is nearly completely correlated.
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37
The errors in Table 3.5 are diagonal elements of covariance m atrix which can be used
for order-of-magnitude error analysis.
The generated sets of C\ and full covariance m atrix cov^Ci.Cj) was used to esti­
m ate errors in spectral decomposition (section 3.7).
Channel
1
2
3
4
Ct
494 ± 6
505 ± 6
650 dz 8
575 ± 7
Table 3.5: Calibration coefficients (counts/Kelvin). System atic uncertainties are not
included.
3.7
Spectral D ecom p osition
To extract the CMB anisotropy data the binned data (equation 3.14) are fitted to
the following two component spectral model (appendix section A):
(3.19)
where TA is the dem odulated d ata in units of W /m 2 sr (section 3.6). S-L(v) is the
spectral response of the instrum ent (Figure 3.12). B„(T) is the Planck function at
tem perature T, Xb = 20 K is the dust tem perature, a = 1.5 is the spectral index of the
dust (more on this subject later). uQ= 22.5 cm - 1 is the reference frequency, Tcmb =
2.728 K is the tem perature of the CMB [16], and rk and 5T k are free param eters —
interstellar media (ISM) dust optical depth and CMB anisotropy. The result of the
fit is a component sensitive to CMB anisotropy and a com ponent sensitive to dust
with corresponding covariance matrices.
Varying the spectral index a from 1.3 to 2.0 has alm ost no effect on the CMB
results, but significantly affects dust results. The x 2/D O F ra tio of spectral decompo­
sition fit (equation 3.19) fit is 505/548 for single difference dem odulation and 533/548
for double difference demodulation, consistent with a x 2 distribution.
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__ CMBR
.... Dust
1.0 —
MSAM responce
0.8
—
0 .6 —
/
0 .4 —
0.2
—
0.0
5
10
15
20
frequency (cm-1)
Figure 3.12: Spectral response of individual channels for MSAM - 1
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39
T he plots 3.13 and 3.14 show the result of decomposition. For clarity the largest
eigenmodes of covariance m atrix are removed from the d ata. This procedure can
be explained as follows. The result of the analysis is difficult to represent on the
plot: there are a large number of d a ta points (275). it has significant non-diagonal
covariance m atrix and it is function of three coordinates — declination, twist and
right ascension. To plot the figures, the eigenmodes of the covariance matrix with the
largest eigenvalues ( «
1 0
) are projected out from both d a ta and covariance. In this
way a few large angular scale eigenvectors elim inated, and and the resulting covariance
m atrix is close to diagonal. The d a ta is then rebinned ignoring declination and twist
and using coarser RA bins. All CMB anisotropy analysis is done with original full
d ataset, this step is performed only to make visual representation of data.
D ust plot (Figure 3.14) has IRAS signal (IRAS Sky Survey Atlas a t 100 /.im. or
ISSA [54]) convolved with our beammap overplotted for comp<irison. If we fit our
m easurements in channel 4 (wavelength 444 /xm) to ISSA data, the effective dust
spectral index is a = 1.46 ± 0 .2 8 . consistent with previous MSAM data ([7. 6 ]) and
FIRAS and DIRBE all-sky results [48]. T he * 2/D O F ra tio of this fit is 449/273 for
the single difference demodulation, and 356/273 for double difference. This indicates
significant correlation, but the d a ta is not in complete agreement wiiich is not very
surprising for such a large range in frequencies.
3.8
C M B R anisotropy
We are only capable of predicting statistical properties of CMB anisotropy rath er
then detailed tem perature distribution on the sky. T he o utput of most cosmological
theories is the angular correlation function
C (0 ) = C ([xL—Xo|) ( A T ( X l) A T ( x 2)>
wrhere x L and x 2 are positions on the sky,
0
is the angle between them.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(3 .2 0 )
40
C^MBF^ te m p e r a tu r e (yttK)
NO —*•
^
M U
O
O
O
O O
o
o
o
o
o
o
^ MB R ( te m p e r a tu r e (p X )
—-*•
do
o
o
o
o
o
o
o
o
o
nj
..
cn
V
cn
Two
CD
CD
>
CL
CD
demodulation
33
beam
cr
CD
a
3
33
3
o
CL
c_
Q
o'
o
CO
CD
CD
CD
Figure 3.13: CMB component. Beam profile is overplotted for clarity.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
D ust Optical Depth
l
—»
oI
o
o
o c n o c n
)
I I
- p ^ M O r o - P ^ c n
CiT1
(x10
Dust Optical Depth
cn
Two
beam
demodulation
,1
i
* iw h I
CD
■4—1
■+-4 **
. ** *
■.4~1*
i—£*&• tp»
.
*
*
>
IH-i?
.1—nP***-«■ *
dust
l—i—it#%
n —i—i * £* *
00
data
f—I—I
***•**
1
(
*
■*fr *• 1 -M
CD
*w ;
i - -
i— i— i
^f-*—H
Figure 3.14: Dust com ponent. Asterisks: fitted IRAS d a ta [54j.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to IRAS
*3* I I
♦ * 111
* w
j- tnn
^
H*H*
compar ed
i nP *
XI
1-
Here I briefly outline the m ethod used for comparing results o f all three MSAM
flights with theoretical prediction.
The observations are binned on the sky in right ascension, declination and twist.
Each of them is the convolution of the signal on the sky w ith the instrum ent beam m ap
Bi, which is the translated and rotated measured beam m ap B . T he predicted covari­
ance of the signal on the sky is
To compare measured and sim ulated skies, the likelihood ratio [32] is used as a
statistic:
where Tk is the measured signal. V = V'v + V XI, W = V L. V M and W x[ are
covariance and inverse covariance of the model (excluding noise). I A is the noise
covariance m atrix (section 3.5).
If measured value of the likelihood ratio is XM, and probability density function
for given correlation function C is pc(X), the cumulative probability
(3.23)
P = fpc(X)dX
Jo
can be used to set confidence intervals for correlation function param eters. If it can be
param etrized by single am plitude param eter C q (like in eq. 3.24). the 95% confidence
lower limit on
Cq
and 95% confidence upper limit on
Cq
are values of
XM
for which
P = 0.05 and P = 0.95.
3.8.1
Gaussian autocorrelation function.
The often assumed tem perature distribution is described by two-point correlation
function.
C (|x L- x 2|) = ( A r ( x 0 A r ( x 2)) = Co exp
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(3.24)
43
where 6C is the model param eter which is often interpreted as the angle of peak
sensitivity for a given beam pattern. It is not a realistic tem perature distribution,
but it was a popular model in early days of CMB research. T he results of GMB
experim ents were often reported in terms of this model, so it is still useful to estimate
most likely power of anisotropy in Gaussian correlation function as in Equation 3.24
for comparison with, other experiments.
The Table 3.6 shows lower and upper 95% confidence limits for x/Co for this and
previous MSAM-I flights (1992 and 1994 results are taken from [261).
Flight
MS AM 1-92
MS AM 1-94
MSAMl-95
Double difference
0 C = 0.3°
Upper bound Lower bound
(A*K)
(a*k )
97
50
34
78
118
63
Single difference
0 C= 0.5°
Upper bound Lower bound
(/iK)
(a*K)
116
53
79
30
104
47
Table 3.6: Upper and lower lim its to CMBR anisotropy assuming Gaussian autocorrelation function.
C alibration errors are not taken into account.
If both demodulations are taken into account, the to ta l RMS CM BR anisotropy
(v/Co) is between 61 and 10 1 [iK for ©c = 0.3° and between 64 and 122 qK for
0 C = 0.5°.
3.8.2
Bandpower estimates
In article [5] Bond suggested reporting CMBR experiments results using correlation
function which in spherical harmonic basis would have power
Ci = 6C2/l(l + 1 )
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(3.25)
44
1 0
,-4_J
i t t • i i i »i I
i
I I r I t I I If I I I I I
I
5
<
2
1 0 ' 5
n0.1
I
I
0.2
I
I I I I I [ ■I
0.5
0c
1.0
(degrees)
Figure 3.15: Limit ou total RMS anisotropy for Gaussian autocorrelation function,
from MSAM l 1995 flight.
Each line is a 95% confidence level. Dashed lines: single demodulation, dotted: double
demodulations, solid lines: both demodulations. Because Monte-Carlo integration is
used for estim ating integral 3.23. single demodulation limits are sometimes more
restrictive then both demodulations limits. This problem would go away if more
samples were used in Monte-Carlo simulations.
where I is number of spherical harmonic (approximately corresponds to angular scale
k /I).
C% is quadrupole amplitude. Such correlation function has the same power at
ail angular scales. The band power param eter is
m = J l{l
)C‘ = V 'M Vir
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(3.26)
45
l a limits for this correlation function (84% upper and level bounds) an d m edian
(50% confidence level bound) are 5Ti — 50 l[f /J.K for single difference dem odulation
at mean I = 160 and 5Ti = 651 [ 3 (J.K for double difference dem odulation a t mean
I = 270 with calibration errors included.
The double difference results from 1995 flight are significantly higher th en results
from 1994 flight; th a t measurement, converted 1995 bandpower estim ates is STi =
40~|o f.iK. or 1.78cr lower. The probability of such (or more significant) difference is
7.5%. not small enough to call this an inconsistency. The MSAM1-95 m easurem ent
at I = 270 is consistent with results of other experiments at this angular scale, such as
SK95 (see [40] . STi = 8 5 if | fJ-K a t I = 240. error bars adjusted to include calibration
uncertainty). The M SAM l-94 and MSAMl-92 measurement, altough statistically
consistent, is rather smaller. The MSAMl-95 d a ta without taking MSAM l-92 and
MSAMl-94 into account suggest a moderate rise in power, predicted by standard
CDM theory.
3.8.3
Analysis of all three MS A M flights
W hen looking at Figure 1.1, one is immediately seduced to combine results of all re­
ported CMBR anisotropy measurements and find much more strict limits on anisotropy
power spectrum then it is possible from single experiment d ata. Unfortunately, this
task is not straightforward. These experiments are different in m any obvious and sub­
tle ways — they are using different sources for calibration, have different frequency
coverage and different beam maps, some of them are overlapping in their sky coverage
and some not. They usually report anisotropy level in terms of Gaussian autocorre­
lation function which has little in common with a physically m otivated spectrum of
anisotropy and system atics errors are very' different . Finally (and this m ay be the
most im portant obstacle), there is no person intim ately fam iliar with the details of
every experiment. While such a task is possible, the effort required is probably b etter
spent on preparing more sensitive next generation experiments.
Combining d a ta from three MSAM l flights is easier in comparison. T he beam m ap
is very similar in all three flights (save for differences caused by reassembly and
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46
I
I I I [ 1 i t i t I
o
8000 — A
*
□
V
O
CM
^ 0 0 0
o
A
+
□
CM
V
c> 000
_+
♦
£ <
— I
—I
2000 - ^ 1
t
l i t i l
( t i l l
i t i t
DMR
SK95
MAT98
MAT97
OVRO
QMAP
CAT98
SP91
BAM
Python
sp89
CAT
MAX
Argo
SP94
Tenerife
FIRS -r-
Ix -
o —i
5.
I III
i i i i
10.0
20.
I 1 I 1| t i l l
50.
100.0 200.
500. 1000.
left
Figure 3.16: The M SAM l band-power estim ates for all three flights is shown by
shaded rectangles compared to other experiments to date (1999). The solid line is
stan d ard CDM. normalized to fit COBE DM R data.
realignm ent of telescope and different analysis method in 1995 flight). MSAM l d a ta
are heavily oversampled, partially as the prim ary goal of MSAM l-94 flight was to
confirm MSAM l-92 anisotropy detection an d the same region of the sky was observed
twice. Because of this, the d a ta contain inform ation about the power spectrum on
angular scales somewhat sm aller than beamsize.
The m ethod is described in [55]. The analysis was done by G rant W ilson and
Lloyd Knox as part of MSAM collaboration. The spectrum of anisotropy is assumed
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
to be flat (Equation 3.25) in every one of three bands. The bands were chosen to be
as narrow as possible, w ithout m aking 5T[ (Equation 3.26) errors too high.
z_
39
131
284
leff
84
2 0 1
407
1+
130
283
453
m
( fxK )
3oZtX
1 6
Table 3.7: Power spectrum estim ates for three flights of MSAMl. lef f is the average
value of I over the filter function for given band.
The Figure 3.8.3 shows MSAMl b<ind-power estim ates for all three flights. The
delta from I = 20 llfo band are somewhat smaller then predicted by CDM theory and
as reported by other experim ental groups. This is mainly due to low 1992 a n d 1994
flights data with higher then 1995 flight combined statistical weight. In 1992 and
1994 flights the telescope was observing the same region with intent to verify CMB
detection.
It is possible th at MSAMl-92 and MSAMl-94 flights observed statistically unusual
area with smaller then usual CMB anisotropy.
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CHAPTER 4
OBSERVATIONS OF JU P IT E R A N D S A T U R N
Wliole-disk brightness tem perature measurements of the planets are frequently used
as calibrators for radio and infrared astronomy. For instruments w ith beam size larger
than ~
1
\ planets are bright, unresolved sources ideal for m apping the shape of the
far-held antenna pattern as well as providing an absolute calibration. In particular, for
studies of anisotropy in the cosmic microwave background radiation (CMB). precise
common calibration targets are needed to permit comparison of experim ental results
with each other and with theories.
A new feature in this flight of MSAM-1 as opposed to flights on 1992 and 1994
was using Mars for cross-calibration of Jupiter and Saturn.
Jupiter and Saturn, w'hile bright and frequently observable, have complicated
atmospheres w'hich introduce substantial uncertainties in modeling their brightness
tem peratures. Mars, however, has only a tenuous CO-> atm osphere which, for broad­
band millimeter and submillimeter observations, can be safely neglected compared
with thermcd emission from the M artian surface [19. 56]. Observation and cross­
calibration of these
3
planets provided us with more precise calibration com pared to
other experiments including earlier MSAM- 1 flights and w-as of interests to non-CMB
members of astronomical community.
4.1
D ata Analysis
These planet observations have a high signal-to-noise ratio, even in the raw' tim eordered data. The d a ta reduction requires a somewhat different approach th an th a t
previously reported for CMB anisotropy [7, 6 , 27, 26]. Systematic effects, particularly
with regards to precise telescope pointing, are the lim iting factors.
48
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49
4.2
Pointing
The accurate determ ination of the telescope orientation is critical for this measure­
ment. T he telescope pointing is found by m atching sta r cam era images against a
sta r catalog. This fixes the position of the cam era frame a t the time of the exposure:
between exposures, pointing is interpolated w ith the gyroscope outputs. Typically,
the pointing drifts about 2! between successive camera exposures. The residual errors
from interpolating between exposures is p re s u m a b ly several times sm aller than this.
The position of the m ain telescope beam within the cam era fram e is determ ined from
the raster scan across Jupiter. Note th at for the planetary observations, the image
of the planet itself is deleted from the CCD frame, and background stars are used
to establish the celestial coordinates of the beam. This ensures that blooming in the
CCD due to the bright planet does not compromise the a ttitu d e solution. Noise in
the gyroscope readout leads to a random RMS pointing uncertainty of 017.
4.3
D etector D ata R ed uction
In this analysis, only the "naive” double-difference dem odulation of the d a ta is used
as proper dem odulation tem plates were not available yet, while signal to noise ratio
is high enough. For each complete cycle of the secondary m irror, the d a ta for the
two side beam s are averaged and subtracted from the average of the central beam
data, producing a single dem odulated value every 0.5 s for each of the four radiom eter
bands. T his results in a symmetrical, three-lobe antenna p a ttern th at is well suited
to absolute flux determ inations.
Slow offset drifts are present in the data, and must be removed. For each observa­
tion listed in Table 3.2, a single linear drift in tim e is fit to those portions of the d a ta
corresponding to times when the telescope was pointed well away from the target
planet. T his linear drift is then subtracted from the data. Since the observations are
short and the drifts are slow, this simple model is adequate for dedrifting.
The detector signal contains transient spikes due to cosmic rays striking the de­
tectors. In previous CMB analysis, the very low' instantaneous signal-to-noise perm it-
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50
B and
1
2
3
4
Table 4.1:
Jupiter - 1
1.036 ± 0 .0 1 6
1.016 ± 0.015
1 . 0 1 1 ± 0 .0 1 6
0.985 ± 0.019
Ratios of Target P
Mars
(256 ± 2.2) x 10~ 4
(263 ± 2.3) x 10" 4
(325 ± 2.8) x 10~ 4
(335 ± 2.9) x 10~ 4
anet Flux to Ju p iter Flux
Jupiter — 2
S aturn
0.979 ± 0 .0 1 6 ( 1 1 1 ± 1 .0 )
0.994 ± 0.015 (101 ± 0.9)
0.993 ± 0.016 (109 ± 0 .9 )
1.044 ± 0.016 ( 1 1 2 ± 1 .2 )
x 10"3
x 10~ 3
x 10~ 3
x 10~3
ted the identification and removal of these transients directly from the time-ordered
d a ta . The presence of large signals from the target planets frustrates this procedure:
instead, a sm ooth spatial model is fit to the data, and cosmic ray spikes are identified
as significant outliers from the fit. For the raster observations, each of the 9 horizon­
tal scans was fit to a cubic spline with 30 uniformly-spaced knots. An initial noise
estim ate a is formed from the RMS of the residuals from the fit. and then 3cr outliers
are deleted. The fit is then repeated, and vertical splines are used to interpolate
between the scan lines to form a 2^8 x 0?9 beammap. Finally, raw detector noise is
estim ated from the RMS of a subset of the data pointed at least 1°4 away from the
target planet.
The calibration scans were analyzed in a similar way. except th a t instead of free
splines, the fit model was constructed from the beammap derived in the raster analy­
sis. For each datum in a calibration scan, the telescope pointing is used to determine
a planetocentric A". Y coordinate, which is then referenced to obtain the beammap
am plitude. A single free param eter, the overall scan-to-raster flux ratio, is then fit
to the data. Again. 3a outliers are deleted, and the fit is repeated. Between 2% and
8
% of the d ata are removed this way. depending on scan. For this procedure, the
early Jupiter raster is used for fitting the two scans at the beginning of the flight,
while the late Jupiter raster is used for the two scans at the end of the flight. A sys­
tem atic check on this processing is provided by the Ju p iter calibration scans, which
should yield a scan-to-raster flux ratio of 1 (within errors). The fit results are given
in Table 4.1.
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51
4.4
Error Analysis
D etailed Monte-Carlo sim ulations were used to estim ate the errors on the scan-toraster flux ratios.
Each realization was generated by starting w ith the measured
bolometer and pointing data, and adding normally distributed random num bers with
variances corresponding to the estim ated bolometer and position-readout noise, re­
spectively. An additional random linear position drift, corresponding to the slow
absolute pointing uncertainty, was also added to the sim ulated pointing d ata. Note
th a t pointing noise and drift were sim ulated in both azimuth and elevation. For each
sim ulated dataset, the beam m aps and scan-to-raster flux ratios are reconstructed ac­
cording to the procedure described above. Final error estim ates for the scan-to-raster
flux ratios are determined from the standard deviation of the sim ulated ratios. In
contrast to CMB measurements, here the uncertainty is dom inated by the position
readout noise, and not the bolometer noise.
Among the Jupiter scan results in Table 4.1 two values out of eight (Jupiter - 1
band
1
. and Jupiter-2 band 4) have greater than 2a deviations from unity. This
has ~ 3% probability (based on y 2 = 17 for
8
degrees of freedom), and so may be
evidence of an additional unaccounted systematic error in the data. T he estim ated
uncertainties th at follow are conservatively inflated by a factor of 1.46. which forces
the reduced \ 2 ° f the Jupiter scans to unity.
Table 4.2: Ratios of Planet Temperature to Jupiter Tem perature
Mars
Saturn
Band
1
1.158 ±0.015 0.833 ±0.012
2
1.189 ±0.015 0.758 ± 0.010
1.470 ± 0.019 0.818 ± 0 . 0 1 2
3
1.515 ±0.019 0.840 ± 0.012
4
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4.5
W hole-D isk Brightness T em perature R atios
The raw flux ratios determined in section 4.3 are converted to whole-disk brightness
tem perature ratios using the effective m m /sub-m m band planetary equatorial radii
and eilipticities of [22]: Z?eq (c) = 3397 (0.006). 71495 (0.065). and 60233 km (0.096)
for Mars. Jupiter, and Saturn, respectively, along with th e ir geocentric distances and
polar inclinations a t the epoch of observation.
These constitute the primary results reported here, a n d are given in Table 4.2.
The errors reported in the table reflect the total uncertainty, as determ ined in §4.4.
and include the extra scale factor (1.46).
4.6
Mars M odels
To convert the brightness ratios into whole-disk brightness tem peratures, an epochdependent therm al model of Mars is needed to provide an absolute calibration. Two
distinct models were used for this purpose.
The first model considered ([56], [57]) is extensively used in the literature (see,
e.g., [22] and [19]), and is based on 10-20/im radiom eter observations of Mars by the
M ariner 6 &c 7 spacecraft. Following the example of [22], this m odel is truncated
assuming T(A > 350/im) = T (A = 350/im). The estim ated model uncertainty at long
wavelengths is ± 10K ([56]).
The second model used ([49], [50], [39]) is based on a physical model of the dielec­
tric properties of the upper m eter of the M artian surface, constrained by polarized
flux measurements obtained from V L A observations at A = 2 and
6
cm. Some extrap­
olation is needed to estim ate the properties of the regolith at MSAM wavelengths:
dielectric constant assumed to be e = 2.25 ± 0.25, and a power absorption length
lu =
( 1 1
± 4 ) A ([39]). The model uncertainty due to the in p u t param eter uncertain­
ties (± 3 K) is somewhat smaller than that due to neglecting the effect of scattering
(estim ated at A = 2.7 mm to be
± 6
K), giving a total m odel uncertainty of ± 7 K.
Both of these models involve substantial extrapolations in wavelength to reach our
bands. It is reassuring, however, th at the two models, tu n ed to substantially different
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53
200
NHo
PH3
CO I
v
180
.E
160
>
CD
±3
140
• This work
O Griffin et al. (1986)
120
□ Hildebrand et al. (1985)
X Ulich (1981)
100
20
30
Frequency (cm'1)
Figure 4.1: Whole-disk brightness temperatures for Ju p iter. The Wright thermal
model of Mars is used to determ ine the calibration. T he vertical bars reflect the
relative photom etry errors, while the horizontal bars show the bandw idth of the mea­
surements. The plotted errors do not include the M ars m odel uncertainty of ±5%.
The model spectra shown are from [19], and assume clear-sky (dashed) or NH3 cloud
with particle size 100 fj,m and a particle scale height to gas scale height ratio of 0.15
(dotted). The molecular lines from which they are calculated are shown at the top of
the figure.
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54
160
i
i
i i i
i
i
i i i r
nh 3 I
*
140 -
.£
_>
i i i i i [ i I i i i i i i i i i |
ph 3 I
>
*A
A
*\N
*- V
\ \
\ \
\ V
120
-m -
CD
cc
100
-
• This work
8060
□ Hildebrand et al. (1985)
X Ulich (1981)
I
0
I
I
I
I
I
I
l
I
I
10
!
I
I
I
I
I
I
I
I
I
1
I
20
I
I
1----- 1----- 1----- 1----- L
30
Frequency (cm*1)
Figure 4.2: Whole-disk brightness tem peratures for Saturn. The W right therm al
model of Mars is used to determ ine the calibration. The vertical bars reflect the rela­
tive photom etry errors, while the horizontal bars show the bandwidth o f the measure­
ments. The plotted errors do not include the Mars model uncertainty of ±5% . The
model spectra shown are from [2 2 ], and assume an NH3 mixing ratio o f 2 x 1 0 - 4 in the
deep atmosphere, and PH 3 mixing ratios equal to 1.5 x 10- 6 (dashed) or 1.0 x 10“ °
(d o tted ). The m olecular lines from which they are calculated are shown a t the top of
the figure
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oo
observations at very different wavelengths, give predicted brightness tem peratures
th at agree well within th eir estim ated uncertainties.
4.7
Brightness Tem peratures
The modeled Mars tem peratures, along with the derived whole-disk brightness tem­
peratures for Jupiter and Saturn, are presented for both models in Table 4.3. Note
th at the errors listed reflect the uncertainty in the brightness ratios described in §4.4.
but do not include the ~5% Mars model uncertainties which are common to all the
points.
Figures 4.6 and 4.6 plot the brightness tem peratures for Ju p iter and Saturn using
the Wright model for Mars: this is chosen to perm it easy comparison with the earlier
measurements of [52]. [22]. and [19]. Also plotted in the figures are two representative
model tem perature spectra, together with the series of molecular lines from which they
are derived. The Jupiter models are from [19]. and assume clear-sky (dashed) or NH 3
cloud cover with particle size
1 0 0
fim and a particle scale height to gas scale height
ratio of 0.15 (dotted). T he Saturn models are from [22]. and assume an NH 3 mixing
ratio of 2 x 10- 4 in the deep atmosphere, and PH 3 mixing ratios equal to 1.5 x 10- 6
(dashed) or
1 .0
x
1 0
”° (dotted).
Note that results at 16.4 cm - 1 for both Jupiter and Saturn are significantly lower
than previous m easurements th at cover this band. While we do not completely un­
derstand the cause of this, we offer several observations: The bandw idth of 16.4 cm - 1
filter is significantly narrower than the previous measurements (due to [22]). This
band is nearly coincident w ith the first expected strong dip in the spectra of the giant
planets, near the ~ 19 cm - 1 NH 3 and PH 3 resonances. Additionally, the measure­
ments reported here had essentially 100% atmospheric transmission. The earlier mea­
surements were made from the ground on Mauna Kea, and were corrected to a fixed
value of the line of sight w ater vapor before taking ratios of unknown to calibration
signals.
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56
Band
1
2
3
4
Wright
Mars
196
196
196
196
model ( T = T35Qfim)
Jupiter
Saturn
169 ± 2
141 ± 3
165 ± 2
125 ± 2
133 ± 2
109 ± 2
129 ± 2
109 ± 2
Rudy model (extrapolated)
Saturn
Mars Ju p iter
141 ± 3
169 ± 2
196
166
±
2
126 ± 2
198
1 1 2 ± 2
137 ± 2
2 0 1
1 1 2 ± 2
134 ± 2
203
Table 4.3: Tem peratures of planets (Iv).
The tabulated errors do not include the M ars model uncertainty of ±10K (Wright)
or ± 7K (Rudy).
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CHAPTER 5
F R E Q U E N C Y SELEC TIV E BO LO M ETER S
5.1
M otivation
M onolithic silicon bolometers [13] are the most sensitive wideband detectors in the
range of interest to CMB researchers from 150 GHz to approxim ately 600 GHz. The
current scheme for building a multimode radiom eter with this kind of detectors usu­
ally involves a W inston cone concentrator, a lightpipe optics, a series of dichroic
beam splitters followed by IR blockers, band defining filters and W inston cones with
bolometers in a cavity (see. for example. Figure 2.2 — MS AM optics schematics).
This m ethod works, but it is not w ithout disadvantages.
To begin with, the filter system is large. Its size is much larger then the size
of the bolometers. As it should be kept cold to reduce bolom eter loading, it is the
m ajor design driver for cryogenic system size (and therefore mass, strength and heat
conductivity of support structure) as experience of TopHat project showrs. The bulky
filter system complicates building a focal plane densely packed with bolometers.
The second problem with the MSAM style radiom eter design is th at every de­
tector is illum inated by a beam which passed through a band defining filter, layer of
fluorogold and dichroic beam splitter (or was reflected from last) with cutoff frequency
close to center frequency of band defining filter. The splitter inevitably has high losses
at frequencies close to cutoff.
The alternative approach wras chosen by designers of SCUBA [23] system who
chose to put all bolometers behind a large common filter w-heel. However this design
makes impossible to do observations in all channels sim ultaneously wiiich is reduces
effective observation time and introduces additional system atic errors in case of obser­
vations from the ground through variable atm osphere. It is also impossible to reduce
57
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58
atm ospheric emission noise by fitting a n d subtracting atmosphere spectrum as this
m ethod require observing in all bands simultaneously.
The design o f Frequency Selective Bolometers (FSB) [301 m itigates some of the
problem m entioned above. In this chapter I present the work done on the concept
since publication o f article [30} and its advantages.
5.2
F S B design
Each FSB element consists of a resonant bolom eter followed by several resonant band
stop mesh filters.
Bolometers are prepared on silicon wafers1, back-etched to ap­
proxim ately 5 fim thickness and then reactive ion etched to leave only a thin silicon
grid (see appendix B for details of bolom eter m anufacturing). Identically shaped,
periodic m etal features are deposited onto the bolom eter and filter planes to form a
capacitive-type resonant mesh. Silicon m icrolithography is used to produce the m etal
features, assuring the sharp feature edges necessary for good filter performance. For
the bolometer plane, the thickness of the conductor, and thus the resistance, is set
to achieve optim al absorption. The subsequent meshes have several skin depths of
m etal deposited to make them nearly a pure reactance. They are built by depositing
gold on 0.75 /.im thick silicon nitride film by Hvpres [1 ].
The power absorbed by the bolometer element is measured using a therm istor
im planted near th e center of the grid. On the bolometer element, ~80% of the therm al
gradient is taken up by the four support legs, leaving the grid nearly isotherm al. By
thinning and etching the silicon, the effective dielectric constant of the substrate is
greatly reduced, improving the impedance m atch to free-space.
The bolom eter element is a resonant, frequency selective resistive grid absorbing
power in a broad band centered at design frequency. Following the bolom eter by
a backshort consisting of three resonant reflectors separated by A/4, where A is de­
sign wavelength sharpens its absorption band which improves precision of spectral
decomposition (see A). Impedance m atch is also improved, with peak absorption at
LSOI wafers, where 5 /zm and 380 fim layers of silicon are separated by
oxide
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0 .2
fim layer o f silicon
59
resonant frequency approaching 100% as compared to maximum of 50% possible w ith
no backshort.
T he bolom eter and backshort filters are stacked on top of each other, therefore
distance between filters and bolometers is defined by thickness of the wafer, from
which reflective filters are m anufactured.
5.3
Frequency Selective Surfaces (FSS)
A numerical m ethod for analyzing periodic conductive surfaces was described in [38.
9]. This m ethod agrees well w ith measurements for a variety' of periodic geometries,
including the sim ple crosses we use here [9]. The method perm its calculations of the
current distribution on periodically spaced arbitrary shaped patches, with infinite or
finite conductivity, induced by incident radiation. A numerical program implementing
this m ethod was also used to design filter system for TopHat experiment.
5.4
O ptical M odel
A simple one-dimensional model described in [31. 53. 51. 11] works remarkably well
to predict optical properties of a stack of FSS and other planar elements assembled
in a lightpipe.
An incoming electrom agnetic wave is scattered on every transition u'here refraction
index is changing or where a partially reflective surface (FSS for example) is placed.
Let's use index
1
for direction of incoming wrave. 2 for wave traveling in opposite
direction. E for am plitude of wave in front of transition, E ' for am plitude on the
other side of transition. Then
where T is cascade m atrix
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60
Figure 5.1: Illustration of scattering m atrix concept — see equation 5.2
E
1
W
E ->
E\
FSS
T can be found from the following equations
~ tv z E i
Eo =
-F
roiE'o
(5.2)
t o i E - y "F r 1 2 E 1
From this
T =
t l 2 — r L 2 ^ 2 l/ i'll
r 2 L/ ^ 2 1
—r L2 A 2 1
(5.3)
l/^2i
where Uj is the complex transmission coefficient and rtj is the z reflection coefficient
for wave traveling in direction from medium i to m edium j .
A cascade m atrix for a continuous medium with thickness S and refraction index
n is
Tc (6) =
eiknS
0
0
e— i k n S
(5.4)
Here a refraction index can be complex if the m edium is absorbing. If absorption
coefficient is a, n = Re (n) -F ia /k , where k = 2tt/A is the wave vector. A is the
wavelength..
Cascade m atrix of few transitions separated by distances
61
, S1: etc. is
T = TiTc{6 i)T 2 Tc{S2 )T3...
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(5.5)
61
From, this cascade m atrix one can find transmission and reflection coefficients for
the whole composite system assum ing th a t all system is one-dimensional (neglecting
diffraction on FSS and scattering on the walls). Assume E!, =
0
in equation 5.1. The
transm ission coefficient
t = 511 —S 0 1 S 1 2 / S 0 2
and reflection
r = —S 2 1 / S 2 2 .
5.5
(5-~)
O ptical tests o f backshorts
Resonant backshorts sim ilar to ones th a t will be used in FSB prototype were produced
by Hypres [1]. Their transm ission was measured on the Chicago Fourier Transform
Spectrom eter (FTS) to compare calculations described in Section 5.4 w ith measure­
ments. The Chicago FTS is not equipped for measuring reflection spectra (which
m atter in FSB design), but it is possible to measure transmission spectrum and com­
pare it with spectrum predicted by numerical calculation. In a case of lossless surface
the sum of the reflection and transm ission spectra is one for frequencies below c/g
where g is period of the mesh. At higher frequencies some energy is scattered in
non-zero diffraction orders at non-zero angle to incoming beam.
The Figures 5.2 and 5.3 show comparison between calculated and m easured trans­
mission spectra of prototype backshorts. Using existing 200/i thick wafers the cen­
ter of test filters reflection band was set at 12.5cm-1. The distance between meshes
should be equal to 0.25/i/o where u0 is resonant frequency (see section 5.2). To build
backshort assembly with different resommt frequencies wafers with different thickness
were necessary.
T he geometry of filter shown in Figures 5.2 and 5.3 is the following: periodic
capacitive mesh with conductor (5000 A gold) patterned in a shape of cross with
width 52/r and length 390/i. T he period of the grid is 520/i.
T here were many other tests of capacitive backshorts and inductive filters th a t
gave enough confidence th a t FSS (the program used to design filters) predicts spec­
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62
trum of filter systems reasonably well. This program was also used to design inductive
passband filters for TopH at experiment.
One of im portant lessons we learned from these filters is th at quality o f edges
is very im portant- From Figure 5.4 one can see th at the highest concentration of
the current is at the edges of the filter, so the sharper the transition from conductor
to insulator, the less energy transformed into heat due to poor conduction at the
transition.
This effect is especially strong in thin inductive (slot type) bandpass
filter. W hile quality of features is difficult to quantify, a significant improvement in
efficiency in passband filters was after switching to somewhat more expensive method
th at creates sharper transitions — so called lift-off.
5.6
F SB Radiometer D esign
Since the resonant frequency of a single FSB assembly is coupled with thickness of
wafer from which backshorts are etched. I decided to build prototype with the same
bands as TopHat radiom eter. This allowed to place FSB backshorts on the same
wafers and masks as TopHat filters for cost and schedule reasons. More optim al set
of bands has been found without this constraint.
5.6.1
Heat capacity, thermal conductivity and tim e constant
Heat capacity is one of the most important factors determ ining the performance of
bolom eter. Large heat capacity requires high thermal conductivity to the therm al
bath to keep time constant acceptable, but high thermal conductivity increases ther­
mal noise (see [33, 34]). Table 5.2 shortly summarizes the predicted therm al proper­
ties of all five bolometers. For all materials heat capacity as a function of tem perature
is the sum of linear and cubic term s [8 ].
The therm al conductance is modeled with simple rule G (T) = G qT z .
From
INDIGO-2 (TopHat prototype detectors) bolometer tests the coefficient Go is approxim ately
tut
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(5.8)
63
Table 5.1: Dimensions of FSB bolometers
rt a
V0
Channel
Channel
Channel
Channel
Channel
1
5.14
2
6.90
3 12.60
4 14.40
5 21.20
lc w d lxe^ Wx^
9b
1059
940
651
585
415
947
707
366
315
208
14
15
14
13
10
740
740
600
550
470
370
370
300
275
235
Lieg {fi)
1811
2380
1980
1885
1873
“Center frequencyxm - 1
6Grid spacing.^in
“Dipole length, fim
■^Dipole width, fim
“Thermistor length, fim
CThere are two thermistors in each bolometer
^Thermistor width, fim
/lLeg length. Each bolometer has 4 of them
This design assumes leg w idth 30 microns.
w ithin factor of two. In this formula w and t are w idth and thickness of leg, L is length.
The heat capacity of implanted therm istor im plant is C{T) = (2.0 x 10_l3J / K 2)T for
200yu x 400/t therm istor [29].
The Figures 5.6 and 5.5 show masks used for producing bolom eter and backshort
for one of channels.
Each one band element is a stack of bolometer (absorptive mesh) and three reso­
nant reflectors separated by distance of 0.25 resonant wavelength.
The elements are arranged in order of decreasing resonant frequency. This way
radiation in a band belonging to next element is not scattered in non-zero diffraction
maximum.
Each stack of bolometer and filters is preceded by layer of fiuorogold w'ith a thick­
ness calculated to cause 80% absorption of radiation at given stack central frequency.
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64
Channel
1
2
3
4
5
msi
4.76 x 10~8
5.76 x 10~8
6.93 x 10~8
11.6 x 10"8
9.11 x 1(T8
mn
b
4.21 x 10"11
5 .2 0 x n r 11
4.93 x 10“ U
7.66 x 10"11
5.44 x 10_u
m AxL
c
1.25 x 10~9
1.54 x 10"9
1.46 x 10~9
2.28 x 10“ 9
1.62 x 10-9
c Ld
0.90 x i o - L1
1.01 x 1 0 - 11
1.53
1.86
0.94 x 10~LL 2.14
1.43 x 10"lL 3.56
1.01 x 10~11 2.75
C3
x 10~u
x 10~11
x 10~11
x 10-11
x 10_tl
_ e
*e
4 .3
4 .9
3 .8
3 .8
2 .5
“Mass of silicon (kg). For silicon ci = 0. C3 = 2.63 x 1 0 ~ 4 J/k gK 4
6Mass of titam um (kg).
= 71 x 10~ t3 J/kgK2TC3 = 5.4 x 10_ 4 J/kgK 4
“Mass of gold (kg),
= 3.75 x 10- 3 .J/kgK2. c3 = 2.19 x 10_ 3 J/kgK 4
dHeat capacity o f bolometer is C = C {T 4 -C3T3
“Effective tim e constant (in ms) with load shown in table 5.5
Table 5.2: T h erm al param eters of FSB bolometers. M aterials heat capacities are
taken from [8].
5.7
B olom etric detectors perform ance.
FSB prototype is using current-biased thermistors for measuring tem perature. These
therm istors are made by ion implanting m ajority and m inority dopants (phospho­
rus and boron) into silicon (detector substrate). Such therm istors are often used in
subm illim eter band experiments [23. 14. 15]. The resistance of such thermometers is
usually well approxim ated by [13] :
f? = f ? o e x p ( / V T )
(5-9)
These bolom eters are operated in series with load resistor R l - whose resistance is
higher than bolom eter resistance at operating point.
One of the m ost im portant features of current biased bolometers is negative feed­
back: increasing tem perature causes drop in resistance, which decreases electrical
power dissipated on therm istor. This feedback decreases relaxation tim e after a ther­
m al pulse and reduces noise. Because of this measured tim e constant r e is lower then
physical tim e constant r = Cf g, where C is heat capacity and g is heat conductivity.
E lectrotherm al feedback results in some other interesting effects.
Because the
tem perature and resistance of thermistor depend on power P dissipated on it. low
frequency dynam ic impedance Z = d E / d l is different from R. At higher frequen-
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65
cies because tim e constant r can be high by microscopic standards therm istor with
electrotherm al feedback may look like a reactive (inductive) load with fairly high
inductance L.
The standard quantity used to describe bolom eter performance is NEP wrhich is
a noise equivalent power ( spectral density of noise in received power). As bolom eter
is to tal power detector, this is a natural perform ance indicator of detector neglecting
the efficiency of optical train. Another quantity'. N ET (noise equivalent tem perature)
is needed to estim ate total system sensitivity' to given signal.
NEP
NET -
(5.10)
W here AQ is telescope throughput (etendu). B( v ) is signal spectrum . R is detector
spectrum response (including coupling efficiency) .
Compared to TopHat detectors, FSB prototype has som ewhat higher N 'E P which
is hopefully compensated by better coupling efficiency leading to better N E T (see
Table 5.7.3)
The classical references on subject of bolom eter sensitivity and noise are [33, 34,
35]. The total noise is
,2
th e r m a l ~r
Jo hn son
,2
p h o to n
S ( uj) is small signal voltage responsivitv
. ,
1 Z/R -l
1
a-?) — — „
: :
2 1 Z j Z £ -+■ 1 1 4~ iui i e
(5.12)
and Zc(u) is the complex dynamic impedance at angular frequency u
1 -ri lUJi
Z L{ui) = Z
1 -b
i
Z - t-R .
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(5.13)
66
where Z is dynamic low frequency impedance d E / d l . r is physical tim e constant.
r e is effective time constant.
I f f noise was mentioned in passing in [33]. but not much understanding of this
noise was available then. Since then an excellent experimental paper [20]
im portant
m ade many
d a ta available. NEPf/f is the only noise term in equation 5.11 which
increases with decreasing tem perature.
5.7.1
Impact o f l / f noise on bolometer performance.
According to [20] in the case of therm istor strongly coupled to a therm al b ath with
no dependence of resistance on electric field the spectrum of 1 / / noise can be w ritten
as
(ir ) 2 " h
x f
(5 ' 14)
In a case of bolometer with weak therm al link to therm al b a th and dependence of
R on voltage across bolometer (due to non-ohmic effects)
f) R
r)R
5R = A R + ^ ST + ^ 5 V
oT
dv
(5.15)
If bolometer resistance can be approximated by the following expression:
R = R 0(T) exp(v/7V T ) ex p (-V V /T )
(5.16)
where u is non-ohmic effect param eter [28]
Substituting
ST
= Cr
r t-f-^
sp
= i 2^ r ^ d R
I
(3' 17)
- G
r
L£ - r XL
-4
= - l ^
= i l f l o e x p ( v/f / 7 i ) e x p ( - I ' V / r )
F
= J
= vI t
r
W
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(5-18)
(5.19)
( 5
' 2 0 )
67
where P is electrical power dissipated on bolom eter. G is therm al conductivity. C is
heat capacity, I is current through bolometer. V is voltage across bolometer and Rc
is load resistance, one will get following procedure in [36]
R ,T.
= ~~R~l
r .A R
-fl~
F — A 5P + 6Q
T
T { C + i C ) - f4 V
(5.21)
P ( l - R / R L) { F - A )
TG{ 1 -f- I
)
(5.22)
and if loading Q is constant
SV = \
where
rA R
R
1 + F -l- R / R c —
u j t
is bias voltage. This noise should be added in quadrature with noises
discussed in [33].
5 . 7.2
Detector performance in FSB prototype
The Figures on page 76 demonstrate how detector performance changes with changing
radiative load q. For each value of q it is possible to pick the optim al bias voltage Vb
to minimize NEP (equation 5.11). W ith increasing q, tem perature of detector rises,
increasing Johnson, thermal and load resistor noise. Responsivity 5 is going down,
increasing amplifier noise. Photon noise is going up too (as there are more photons).
5.7.3
Spectral components sensitivity
Using above model of detector performance a n d oversimplifying spectral decomposi­
tion process it is possible to estimate sensitivity of the detector to CMB in presence of
foregrounds (see A). The prototype described above will have the CMB tem perature
sensitivity shown in Table 5.3
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68
Model
CMB -t- ISM dust
CMB -F ISM dust -F svnchrotron
CMB -F ISM dust + free-free
CMB 4- ISM dust -F free-free -F synchrotron
CMB sensitivity (in /My/ x/sec)
22
94
152
183
Table 5.3: FSB prototype sensitivity in presence of foregrounds (assuming spectral
decomposition)
Channel
1
2
3
4
5
NEP (W t/\/H z )
6.14
8.55
1.03
2.19
2.98
x
x
x
x
x
10~L7
10-1'
10"16
10-16
10~16
:\E T in
IJK /v/H ?
(CMBR)
36
29
115
ISO
1678
.\E 1 in
fxK/ y/Hz
(RJ)
20.7
10.3
8.9
6.4
6.3
Table 5.4: Radiom eter performance assuming loading in Table 5.5
at frequency 10 Hz.
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69
. i
1.0
0.8
§
—
0 -6 -
CO
E
CO
CO 0.4-
0. 2 —
0.0
5
10
15
20
Frequency (cm-1)
Figure 5.2: Transmission of one layer capacitive resonant mesh, compared to f s s
prediction. The filter parameters are the following: cell period g = 520/um. cross
w idth w = 52/un. cross length I — 390^m. substrate — O.To^m silicon nitride, gold
layer thickness — 5000A. This filter was built by Hyp res [1].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
E
C/D
CO 0.4 —
0-0
1 I I I ! I I I I 1 I I I I I I I I | I |V I t '{ . I . | I I . I I I 1 I I [—
5
10
15
20
Frequency (cm'1)
Figure 5.3: Transmission of three layer capacitive mesh, compared to f s s prediction.
Each FSS has the same param eters as grid shown in Figure 5.2. the distance between
them is 200/im.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
Figure 5.4: Phase averaged current density distribution in one cell of periodic capac­
itive mesh. If we assume uniform surface resistance, this figure shows where resistive
losses are happening.
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72
■ % + - + ■ + + '+ ’ +•
-r + + ++■ + +
+ +■ + +'+■+• +
+
+
+
+
+
+
+
+
+
+ + +- + -8- +
+ + + +■ + +
+ + + ■ + '+ ■ +
+ + + + + +
+ + + + + +
+■+■ + + - + +
+
+ +■+•+'+■+-
+
T + -+ •+ •+ •+ • +
T + + + + • + +■
4 ^ + - r + + +- +
" > '+ - 3 ^ 4 - -
FSB f i l t e r
Figure 5.5: Backshort for channel 3. The circular feacure is not part of the structure,
but an outline of lightpipe. T he lightpipe diam eter is 10mm. The gold crosses are
patterned on half-micron silicon nitride film, the frame is A/4 thick silicon.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
r
i
\
i
t
T
»
_i_
+
i
-ti
~r
—
►
i
-b +
-b +
“T H- +
-b +
-b +
-b +
-b +
-b
~~r
+
T
T
- L .
i
-b -b
-b
+
_j_
i
i
—L
i
t
i
-b
-b
-b +
I
-b
i
“h
+
+ +
“1“ _ji_ +
i
i
~b +
-b
-b
t
1
-b +
+
+
-b
-b ~r ~r ~r
-b -b +
T +
-b + -b
-b _i_
-b -b -b
1
\
~r T
-b
+
-1- -b +
t
:■
t
i
i
+
-b
+
“T -b +
H- -b -b
-b +
-b -b +
-b
+
-b
-b
“f
i
i
-b
i
+
“T
“T
-b -b +
+
*r
“i”
-b -b
-b +
+
-b -b
-J—
-b
+
i
1“
-b
_
t
!
-b
-b
I ~b
T
-b "T -b “T +
F3
Figure 5.6: Bolometer for channel 3. Two rectangular features in the center are
therm istors. The features in the corners are contact pads, at the sides of the frame
— ion-implanted load resistors. T he therm istors in the center are connected with
contact pads by degenerate im plants going through diagonal legs. T he structure is
supported by four legs only. T he thickness of the grid is five microns, the silicon
frame is 381 microns thick. Again, the lightpipe diam eter is 10 mm.
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74
Figure o.i: Sample FSB stack of three bolometers tuned to different frequencies with
three backshorts each. In this figure light is entering from below.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F lu o rog o ld
DEAD LOAD
In c o m in g lig h t
Figure 5.8: A complete five channel FSB radiom eter prototype. The channels are
arranged in order from highest to lowest frequency. Each channel unit is preceded by
a layer of fluorogold. All preceding layers of fluorogold have transmission of 80% an d
the band center of the following channel unit.
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76
-|Q-13_J .1 . I . I t I .1 1 t i l I I .1 I i . I I I .1 < I >I 1
1 0
Total
Johnson
Thermal
io-t4—
1 r 1. I I I . i . ( . I l l
~t0 _ i • 1 . 1. 111
T
”
Total
Ti
. 1 . I . i I (_
___________________
________
r
implant
Au
JFET
10*
“ |
* i
■ i *t i {
0-1
- i
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1.0
11
• t
1 i *f i |
10-0
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100.0
l
* i ' » 11—
tQGQ.
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0.1
‘ E
.1 , l . I t 1
I . I . I 1!
'
- I ‘ I 1 |
10.0
loading (pW)
5 J
• I ' I l\
1.0
* I
• I * ! - [—
1000.
100.0
Loading (pW)
. I , I t 1 .1 . I . I : L
I
1. 0 -
I I
.I
I
I
I
. t :!
i
■ i
I
E
.
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t
.1
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2 0. 6 —
02.
0.4—
ca 0.1
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-
0.01
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i * i ■i i j
1.0
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i ,i i I . i
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Tq =
—
15
W
E,
c
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co
o
©
E
5
0 —j
0-1
- i
■ i
1.0
i
i [
i
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i ■i i |
i
• i >■ i [
10.0
1.0
i 11
10.0
* i 11 i j
100.0
1000.
loading (pW)
loading (pW)
20—
i [
- i
100.0
■ i ■ i i |—
1000 .
Tbath
—
m Ti
—
TTl.-lu
=
m si
—
Go
ct
Co
=
=
=
10 X io 6o
25 X 106f2
25K
0.22K
4.21 x 10- u kg
1.25 x 10-9 kg
4.76 x 10_8kg
2.51 x 10“ 8W K~
8.9 x 10"l2J / K 2
1.52 x 10-LLJ / K 4
loading (pW)
Figure 5.9: Performance of FSB detector for channel one as function of Loading.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 5.10: Predicted spectral response of prototype FSB stack-
Interstellar dust 0. 6 —
CD
cn
c
I
o 0 .4—
Q_
C/)
cd
:
0.2 —
5
10
15
20
f r e q u e n c y (c m '1)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78
channel
1
2
3
4
5
CMBR
1.65
2.23
0.42
0.49
0.60
atmosphere
0.45
0.98
5.37
28.31
54.47
m irror
8.92
24.96
34.99
102.43
142.47
total
11.02
28.17
40.78
131.23
197.00
Table 5.5: Loading for all channels of FSB prototype (in pW). Atmosphere spectrum
was taken from [41]. mirror is assumed Raleigh-Jeans spectrum with tem perature 2.6K
(emissivity 1% and tem perature 260K). Emission from vacuum window is neglected.
5.8
Advantages o f FSB radiom eters
FSB style radiometers promise a better sensitivity then traditional ones due to a
sim pler filter system. However, this higher efficiency has yet to be dem onstrated.
O ther advantage is much more evident: the outer diam eter of FSB radiom eter is just
twenty millimeters. For comparison. TopHat optical block is 150 millimeters wide
and 25 millimeters high.
Small dimensions of FSB radiometer makes possible building an instrum ent with
many radiometers therefore increasing sensitivity by brute force — increasing number
of detectors. The time of observation is decrecised by factor of .V. where iV is number
of detectors. For iV = 10 the same objective can be achieved by two weeks Antarctic
flight instead of much more difficult hundred day balloon mission.
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A P P E N D IX A
SP E C T R A L D EC O M PO SITIO N A N D C H O O SIN G
R A D IO M E T E R SPECTRAL C H A N N E L S
79
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80
L et's consider a simple case of telescope observing N Pixel pixels on the sky with
w ith n-channel radiom eter. T he sky spectral brightness as function as frequency u
and pixel a is defined mainly by m components with spectrum
B(v)
(A.1)
j
each.
Each of n spectral channels has spectral response Si(u) (which includes losses in
filter system and incomplete absorption). The total etendu of the telescope is -4.fi.
The total power registered by z-th channel is
P ia
= -4.fi [ S i(v)B (u )d u = -4.fi [ S d u ) Y TjaB j(u)du
(A.2)
j
where a is num ber of pixel, i - num ber of channel.
One can conveniently rew rite this expression by introducing spectral response
m atrix
Q ij = -4fi j Si(u)B j(u)di/
(A.3)
Pia = Y Q i ^ «
(A -4)
j
T he covariance m atrix between pixels a . 3 in channels i and %' is
COV ( P i a . P j $ ) — i H’ a 3
(often Vtl'a3 =
( A .O)
0fori ^ j as different channels are obsetved by independent
detectors).
If the number of channels n is larger th an the num ber of spectral components
rn it is possible to find param eters Tia by least squares method by minimizing the
following sum
X2 = Y
(Q ijT jc t — Piet) Wrii’a3 { Q i'j'T f p — P t>3 )
ii'jj'ai3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(A.6)
81
where W = V l .
T he solution of this m inimization problem is
If ik.3-t Qij P t7
(-^~~)
-^■ij.ad = 5 1 Q k l^ k l.a a Q lj
kl
(-^-8)
T ia = T
where
and covariance m atrix is
cov(Tka;Tl3) = ( Y i (QI^ V lJ.a3Qjl) \
(A.9)
J
To find the near optimal distribution of spectral channels one may consider the
following simplified but manageable problem. Imagine a telescope observing only a
single pixel on the sky (It may be switching between this only pixel and internal cali­
brated load).
The noise in channel i is Ni W t/H z1/2 and assumed to be independent
in different channels. The covariance m atrix V\j (equation A.o) after t seconds of
integration is
% = Nfdij/t
(A. 10)
The covariance m atrix of tem peratures of different components 7} after spectral
decomposition is
Cki = cov(Tk, Ti) = Y . { Q i k W i/tQ j,)
(A.11)
ij
(see A.9)
and the sensitivity to given component i is
N ETt- = s / c ^ K /H z1/2
(A. 12)
This number can be a convenient figure of merit when designing a detector system.
T he best design will have lowest N ETt-. O f course, other im portant details such as
technological lim itations, atm ospheric emission lines th at would b etter be avoided,
scanning strategy should be taken into account.
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A P P E N D IX B
D E T E C T O R M A N U F A C T U R IN G
82
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83
The technology used to produce detectors is modification of well developed one.
used for decades for integrated circuits production — photolithography. Each step
involves depositing a thin (about l^m ) layer of photoresist. T hen the m ask with
features of device to be made is aligned with existing features on the wafer and
the photoresist is exposed w ith bright ultraviolet lamp. The exposed photoresist is
dissolved in process of developing, while unexposed one stays and protects th e rest of
the area.
Here is a short description of the process with many details o m itted for clarity.
The detectors are built from SOI silicon wafers which are lightly doped (or undoped) silicon wafers with 2000 A thick buried oxide layer. T he thickness of device
wafer is originally 7 /i.the substrate is 381 fj. thick.
The first step is growing the oxide (about 3.7 /j) to protect m ost of the area from
etching. In the following step both sides of the wafer are protected by photoresist.
On the back of the wafer the oxide is patterned by backetch m ask in a shape of hole
in a frame. T hen the wafer is etched in 45% solution of KOH to the thickness of 40-45
microns.
The oxide th at was protecting wafer from KOH is removed and sm all features
used exclusively as a reference for front side features are aligned to back etch pattern
and etched to the depth of 1000 A.
The next step is ion implanting. T he wafer is covered with ISkA thick layer of
alum inum , then m etal is etched away in areas that should be im planted. The implants
are applied successfully for
• heavy phosphorous doses for leads and contacts
• therm istor phosphorous doses
• boron dose for therm istor compensation
The next step stripping protecting m etal and oxide and annealing im plant. The
wafer is baked for 30 minutes at 900 degrees Centigrade in nitrogen or argon at­
mosphere. Im planted ions are diffusing and generate sm ooth and uniform implant
density profile.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
wafer
Phosphorous implant (n-)
boron compensation (p+)
Figure B.l: T herm istor im plant.
T he masks and im plant schedules are picked out in such a wav. th a t m ajority phos­
phorus im plant is completely and reliably enclosed in com pensation boron im plant.
In this way we can assure that small uncom pensated area will not short out the whole
therm istor a t low tem peratures.
A thin protecting layer of oxide is sputtered on top of front side. The device is
etched in KOH until etching stops at buried oxide layer. The oxide is stripped away.
Contact pads are created from 8kA alum inum and activated by heating for 15
minutes in flowing nitrogen at 490 degrees Centigrade.
Then the absorber (gold) is deposited using liftoff m ethod. By special processing
created a profile of photoresist wails which is getting wider closer to wafer. T hen
m etal is deposited from above creating a discontinuous sheet. The parts not sticking
to wafer are washed away while stripping photoresist. This procedure creates b e tte r
defined edges then alternative — covering everything w ith m etal and etching it away
from the areas where it is not needed.
Then the front side is covered with photoresist which is developed to create an
image of free standing silicon mesh and devices are diced up by dicing saw. The final
step is RIE (reactive ion etch) of individual bolom eters to p attern front side. T he
device is ready.
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85
Deposited gold
photoresist
Silicon wafer
Figure B.2: Liftoff.
The gold is deposited from above creating non continuous profile.
sticking to wafer is washed away while stripping photoresist.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The part not
A P P E N D IX C
BO LO M ETER IM P L A N T SCH ED ULE
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
The following table shows surface densities of dopants used to produce therm istorsThe dopants are phosphorus (m ajority implant) and boron (minority, or com pensation
im plant). The penetration depth of implants depends on energy of the particles,
therefore by picking right doses and energies it is possible to create a variety of
implants density profiles. To avoid under-compensated m ajority implant shorting out
the thermistor, the volume occupied by m ajority implant should be a strict subset of
volume occupied by com pensation implant. T he energies picked in such a way th at
minimum and m axim um penetration depth of m inority im plant bracket penetration
depth of m ajority im plant. After annealing in dry nitrogen at tem perature 900 degrees
Centigrade the thickness of im plant is approxim ately 0.3/n
The heavy dose to make the degenerate leads is made w ith a single energy im plant
of phosphorus ions (150 keV P + ) with flux of 5 x 10Xo ions/cm 2.
Im plant
P+
P -r
P+
P+
BBBBB-
Energy (keV)
292
176
115
72
154
105
75
50
29
fluence
1.629 x
6.442 x
3.963 x
2.933 x
5.424 x
2.598 x
2.278 x
2.095 x
1.878 x
(particles/cm 2)
10U
1013
1013
1013
1013
1013
1013
1013
1013
Table C .l: T herm istor im plant doses for dose 1.0 (as used in GSFC Detector Devel­
opment Lab)
To get an im plant schedule with different dose, all particle densities should be
scaled proportionally. T he Figure C .l shows dependence of therm istor param eter To
on implant dose1 . Ro for all samples was close to 2000 —2500 Ohm s per square. The
samples were prepared in GSFC Detector Development Lab.
1Using parametrisation R = R q exp y y T ^ J T j . The resistance of ion-implanted thermistors
closely follows this law. but parameters R 0 and To are strongly correlated when determined from
experimental data. The better parameters (and more relevant to parametrising thermistor as power
detector) would be a = 1 / R c lR /d T and R at operating temperature
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88
vs implant dose
To
2Q
I I I I I I I I I I I I I I I I I I [ I I I I I I I
i i i i L
V
25 —
20
—
15
10
V
—
-j
I
0.65
I
I
I
! |
.
|
I
|
1 |
0.70
1 I
I
I
I
I
I
|
I
I
I
I
1
0.75
Figure C .l: T0 vs. implant dose
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
i 1 i 1 p
0.80
A P P E N D IX D
A BSO R B E R
89
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90
To estim ate thickness of gold absorber necessary to achieve given resistance per
square M att Kowitt from GSFC prepared samples of 4-inch silicon wafers. Half of
wafers had layer of oxide grown on silicon, half had m etal deposited directly on silicon.
The m etal was deposited in electron beam deposition machine in GSFC. First, a 50
Alayer of titanium was deposited on silicon followed by few hundred Angstrom of
gold (because gold does not stick to silicon surface well).
T he measurements of resistance was done for five different gold thicknesses.
thickness (A)
oxide
room tem perature
294
294
145
145
107
107
211
211
594
594
X
Y
X
Y
X
Y
X
Y
X
Y
3.05
4.11
11.93
9.60
17.65
15.05
6.48
5.41
1.69
1.10
K
4.2K
1.96
2.50
10.57
8.10
17.21
11.86
4.82
3.41
0.99
0.59
1.61
2.12
9.76
6.80
16.12
10.97
4.24
2.94
0.77
0.44
/ 1
Table D .l: Resistance per square for thin gold samples
According to [10] thin metal film resistance can be approxim ated by the following
formula:
Pfilm = Pbulk T* C / d
where
(D .l)
is resistance of bulk metal, C is constant with no significant tem per­
ature dependence, d is the film thickness. According to [10] it represents resistance
caused by scattering on grain boundaries.
This article quotes pimik = 2.97 nOhm m for LHe tem perature and 25.09 for room
tem perature, C - from 0.261 to 0.2S4 fOhm m2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
This tests give different pimik for films deposited on oxide and silicon at LHe tem ­
peratures. but the same a t room tem perature. This is probably because at low tem ­
peratures bulk resistance is to low to separate it from surface term cleanly. At room
tem perature pbuik is pretty close (62 and 67 nO hm m) for both types of sam ples—
deposited on oxide and not deposited on oxide. This is num ber significantly higher
then quoted in [10]. C onstant C is not changing significantly with tem perature, b u t
is noticeably different when deposited on silicon or oxide.
Table D.2: T hin film constant C ( fOhm n r )
Oxide
Y
X
1.1
1.1
1.8
1.4
Tem perature
300K
4.2K
The target surface resistance for detectors w ith dimensions in table 5.1 is 1.81 Q/ElLower resistance is preferable to higher as it gives sharper defined band. There is also
uncertainty about how much jagged edges of golden crosses will increase effective
resistance (see Figure 5.4). Taking this into account, the reasonable choise on surface
resistance is 1.5-1.6 Q /O , suggesting depositing 350 A gold thick film.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92
I i i i i I i ii i I i i i i !
.—.1 5 0 —
^
-
ii i i i i i I i i i i I
i i i i I i i
m
I i i ii I i i i i
\
'# ■
E
I
O
-jr|
c
m
\
> 100~
\
□ ---------------------------No oxide
*
'□
Oxide
\
\
co
\
’co
CD
\
CC
50
jiii
100
i | i i i i | i ii i | t i i i | i i i i | i t i i j i i i i | i i i i | i ii i ] i i 1
200
300
400
500
Film thickness (A)
Figure D .l: Bulk resistivity of thin gold films at 4.2 Iv as function of film thickness.
This plot should be flat if surface effects are neglected
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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