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Observations of cosmic microwave background radiation anisotropy

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OBSERVATIONS OF COSMIC MICROWAVE
BACKGROUND RADIATION ANISOTROPY
by
Jonathan M. Nicholas
A dissertation subm itted to th e Faculty o f th e University of Delaware
partial fulfillment of the requirem ents for the degree of Doctor o f Philosophy
Physics
December 1996
(c) 1996 Jo n ath an M. Nicholas
All Rights Reserved
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OBSERVATIONS OF COSMIC MICROWAVE
BACKGROUND RADIATION ANISOTROPY
by
Jonathan M. Nicholas
Approved:
^
j
C jL - j
---- -
Henry Glyde, Ph.D
Chairm an of D epartm ent of Physics
Approved:
John (C Cavanaugh, Ph.D .
Inierfm Associate Provost for G
d u ate Studies
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I certify th a t I have read this dissertation and th a t in m y opinion it meets
the academ ic an d professional standard required by th e U niversity as a
dissertation for th e degree of Doctor of Philosophy.
(
Signed:
Lucio Piccirillo, Ph.D
Professor in charge of dissertation
I certify th a t I have read this dissertation and th a t in m y opinion it meets
th e academ ic an d professional standard required by th e U niversity as a
dissertation for th e degree of Doctor of Philosophy.
Signed:
'a d iu of.
B arbara W illiam s, Ph.D
M em ber of dissertation com m ittee
I certify th a t I have read this dissertation and th a t in m y opinion it meets
the academic an d professional standard required by th e U niversity as a
dissertation for th e degree of Doctor of Philosophy.
Signed:
CL
Qaiser Shaft, Ph.D
M em ber of dissertation com m ittee
I certify th a t I have read this dissertation and th a t in m y opinion it meets
the academ ic and professional standard required by th e U niversity as a
dissertation for th e degree of Doctor of Philosophy.
Signed:
David Colton, Ph.D
M em ber of dissertation com m ittee
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ACKNOWLEDGMENTS
I would like to thank everyone who helped m ake this project possible. Thanks
to the people a t IAC for th eir support during th e observing cam paign, their galaxy
models and helpful advice during d a ta analysis. Thanks to Nishrin Kachwala and
Michele Limon for their kind assistance both during and after th e campaign. Thanks
to Bob Schaefer and Lucio Piccirillo for their expertise and guidance, especially
during d a ta analysis. Finally, thanks to my wife Carol for her love and support
throughout this project.
iv
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DEDICATION
This dissertation is dedicated to Gordon Risch, who taught m e th a t physics
is fun and interesting.
v
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TABLE OF CONTENTS
L IST O F F I G U R E S ...........................................................................................
L IST O F T A B L E S ..............................................................................................
viii
x
C h a p te r
1
I N T R O D U C T IO N .......................................................................................
1.1
1.2
1.3
2
Scientific I n v e s tig a tio n ..................................................................................
M odern C o sm o lo g y ........................................................................................
I n f la ti o n ...............................................................................................
3
5
B A C K G R O U N D .........................................................................................
8
2.1
2.2
2.3
2.4
3
1
T h e o r y ................................................................................................................
O bservational P a r a m e t e r s ...........................................................................
C o n ta m in a n ts ...................................................................................................
O bserv atio n s......................................................................................................
14
15
17
H A R D W A R E ................................................................................................
20
3.1
3.2
3.3
3.4
3.5
4
1
8
A n t e n n a ............................................................................................................
Cold O p t i c s ......................................................................................................
Bolometers ......................................................................................................
C ry o g en ics.........................................................................................................
E lec tro n ic s.........................................................................................................
21
24
27
31
34
3.5.1
3.5.2
3.5.3
D e te c to r ...............................................................................................
H o u se k e e p in g .....................................................................................
C om puter In te rf a c e ...........................................................................
34
35
37
C A L I B R A T I O N .........................................................................................
39
4.1
L aboratory
......................................................................................................
vi
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39
4.2
4.3
O b s e rv a tio n .....................................................................................................
G alactic Plane Crossing .............................................................................
42
46
5 DATA A N A L Y S IS ........................................................................................
50
5.1
5.2
5.3
5.4
Lock-In ............................................................................................................
Atm ospheric R e d u c tio n .................................................................................
Correlation A n a l y s i s ....................................................................................
W indow F u n c tio n ...........................................................................................
50
55
69
72
6 C O N C L U S IO N S ...........................................................................................
75
A p p en d ix
DATA
............................................................
77
C alibration .....................................................................................................
Lock-In ............................................................................................................
B i n n i n g ...........................................................................................................
A tm osphere S u b t r a c t i o n .............................................................................
D ata R e j e c t i o n ..............................................................................................
S ta c k in g ...........................................................................................................
C orrelation A n a l y s i s ...................................................................................
77
79
98
106
116
128
139
R E F E R E N C E S ....................................................................................................
150
A .l
A.2
A.3
A.4
A.5
A.6
A.7
ANALYSIS P R O G R A M S
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LIST OF FIGURES
2.1
CM B Power Spectrum with C o m p o n e n ts ..............................................
14
3.1
A n ten n a and. Radiation S h i e l d ...................................................................
21
3.2
M irror S y s te m .................................................................................................
22
3.3
A n t e n n a ...........................................................................................................
23
3 .4
W inston C o n e ................................................................................................
25
3 .5
Cold O p t i c s ....................................................................................................
26
3 .6
F ilte r R e s p o n s e .............................................................................................
27
3 .7
B o l o m e t e r .......................................................................................................
28
3.8
C ry o g e n ic s .......................................................................................................
32
3 .9
H elium T em perature vs Vapor P r e s s u r e .................................................
33
3.10 D ata A cquisition C i r c u i t ............................................................................
35
3.11 H ousekeeping E le c tro n ic s............................................................................
36
4.1
L aboratory Calibration S e t u p ..................................................................
40
4.2
A lgorithm used to evaluate response to th e m oon................................
43
4.3
Moon O b se rv a tio n .........................................................................................
44
4.4
G alactic Plane Crossing - 2 B e a m ...........................................................
47
4.5
G alactic P lane Crossing - 3 B e a m ...........................................................
48
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4 .6
Spectral Analysis of G alactic P l a n e ............................................................
49
5 .1
D ata From Good O bserving C onditions After L o c k -In ..........................
51
5 .2
D ata From Bad O bserving C onditions After L o c k -In ..............................
52
5 .3
D ata From Typical O bserving Conditions A fter L o c k -In .......................
53
5 .4
Fourier Analysis of Typical D a t a ..................................................................
57
5.5
Fourier Analysis of Internal N o i s e ...............................................................
58
5 .6
Fourier Analysis A fter A tm ospheric S u b tr a c tio n ....................................
59
5 .7
D ata From Good O bserving A fter Atmosphere Subtraction . . . .
5 .8
D ata From Bad O bserving A fter Atm osphere S u b tr a c tio n ...................
5 .9
D ata From Typical O bserving A fter Atm osphere Subtraction . . .
5 .1 0
D ata From Good O bserving A fter R e j e c t i o n ..........................................
65
5 .1 1
D ata From Typical O bserving A fter R e j e c tio n .......................................
66
5 .1 2
Final Data: Two B e a m ...................................................................................
67
5 .1 3
Final Data: T hree B e a m ...............................................................................
68
5 .1 4
Theoretical C orrelation Functions Normalized To 1 .............................
69
5 .1 5
Correlated D ata w ith T heory for x 2 F i t ....................................................
70
5 .1 6
x 2 F H .................................................................................................................
71
5 .1 7
Window Functions w ith CDM M o d e l .......................................................
73
6 .1
Observations w ith CDM Model
76
.................................................................
ix
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60
61
62
LIST OF TABLES
3.1
C haracteristics of C h a n n e l s ........................................................................
26
4.1
Observational C haracteristics of the M o o n ...........................................
45
5.1
Lock-in P a r a m e te r s ......................................................................................
54
5.2
Noise thresholds for accepting d a ta ..........................................................
64
x
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ABSTRACT
In this dissertation we will describe and discuss observations of Cosmic Mi­
crowave Background Radiation A nisotropy made at El Teide observatory in the
C anary Islands during the sum m er of 1994. The observations were m ade using a set
of 4 bolometers operating at wavelengths of 1.1 mm, 1.3 m m , 2.1 m m and 3.1 mm
over a strip of sky at a declination of +40°. We detect an anisotropy of
m ultipole moments of I =
3 3 t ?3
A' for
an upper limit of QOfiK for m ultipole m om ents
of / = 5 3 t^ . The spectral characteristics of the anisotropy indicate a cosmological
origin.
xi
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Chapter 1
INTRODUCTION
T he question., “W here did it ail come from?” is probably as old as thought
itself. Certainly, th a t p articular question predates literacy. V irtu ally every culture
on E arth has developed its own version of how the universe cam e to be. In Egypt,
th e universe began as an infinite realm of w ater inhabited by th e god P tah . The
god P ta h conceived th e world as a thought and created it through th e spoken word.
All other gods axe m erely m anifestations of the thoughts an d words of P tah . In
Scandinavia, th e world was envisioned w ith a tree at the cen ter of a round disk
which was surrounded by ocean. The sun traverses the sky in a great chariot during
the day, returning to the east by means of a ship underneath th e tree a t night. In
Greece, the universe begins in chaos, and from chaos springs th e E arth , Night, Day
and the Sky. T he E a rth and the Sky m ate and give b irth to K ronos, R hea and the
rest of the T itans which proceed to produce the rest of the known world. Often two
cultures would interm ingle and their cosmologies would m erge into a new (and not
necessarily consistent) whole. In this dissertation, we wish to continue investigation
into possible answers to this question of the origins of the universe.
1.1
Scientific In v estig a tio n
In the vast m ajo rity of the early cosmologies the E arth rem ained at the center
of th e universe and heavenly objects traveled across a celestial sphere above. For the
m ost p art, this is a reasonable view of things since the e arth is seemingly motionless
while th e stars move across the sky every night. Everything seem s to move except
the E arth.
1
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This was the view adopted by A ristotle which we will consider scientific not
because of its correctness, but rath er because o f its interest in consistency w ithin
itself and w ith observations. According to A ristotle, th e world was constructed of
five elem ents; earth , w ater, air, fire and ether. N othing which happened was random
or accidental. Everything had a cause. T he sun, planets and stars were attach ed
to rigid spheres which revolved about th e e arth in perfect circles. This view was
eventually adopted by the Catholic church and persisted in Europe for alm ost 2000
years.
T he problem th a t arose with this view of th e universe was th e m otion of the
planets. The relative motions of the stars, m oon and sun could easily be described
by these rigid spheres w ith each on a separate sphere. However, the planets, while
going around th e earth, would not do so w ith th e sam e regularity as th e others.
Most of the tim e th e planets would go around th e e arth faster than the stars, but
som etim es they would slow down to a rate slower th an th e stars and then speed up
again. Through the years a num ber of m echanical devices were devised to explain
this discrepancy w ith varying degrees of success.
In 1543, Nicolas Copernicus, a Polish astronom er, published On the Revolu­
tions o f the Heavenly Spheres. In this work he proposed th a t the sun was at the
center of the universe, w ith the planets going around th e sun in circular orbits.
This was a much sim pler solution to th e discrepancies of planetary m otion th an
the m echanical devices of the past 2000 years. D uring th e next 150 years th e Aristotilian view was abandoned in favor of a new universe in which the planets moved
around th e sun in elliptical orbits caused by th e gravitational attraction between
the sun and the planets. Since there were no longer spheres to hang things on, the
stars becam e distan t objects in infinite space. This view would rem ain essentially
unchanged until the beginning of the
2 0 th
century and E instein’s theory of general
relativity.
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1.2
M o d e rn C osm ology
In 1917, A lbert E instein published a theoretical p ap er on cosmology using his
new theory of general relativity. E instein’s paper m ade two im portant assum ptions:
the universe is static and homogeneous. In 1922 A lexander Friedm ann, a Russian
m athem atician, proposed cosmological models for a changing universe. This led to
what was later called th e big bang m odel of the universe. However, observations
were incapable of m aking any definitive statem en t about eith er of these assum ptions.
A m ajor problem in cosmology is how far away any particular object m ight
be. We cannot tell ju s t by looking at it if a sta r is dim and close or bright and far
away. Distance to relatively close stars (less th an 10 parsecs away) can be m easured
through parallax, b u t for objects fu rth er away th e distance is unknown.
In 1912 H e n rietta Leavitt discovered an interesting property of a class of
bright, variable lum inosity staxs known as Cepheid variables. By analyzing a cluster
of Cepheids which were known to be at th e sam e distance, it was found th a t th e
period of the lum inosity variation was a function of the s ta r’s average luminosity.
A fter calibration w ith a nearby Cepheid of known distance and lum inosity, we can
find the distance to any Cepheid. In 1924 Edwin Hubble used observations of a
Cepheid star in th e A ndrom eda nebulae to determ ine th a t it was a group of stars
which was not p a rt of o u r galaxy.
Hubble continued his observations and, in 1929, determ ined (by Doppler
shift) th a t the further away an object was, the faster it was moving away. Further­
more, the velocity was directly proportional to its distance, ju st w hat one would
expect for a uniform ly expanding universe. This is conclusive evidence against a
static universe.
Since the universe is not static, it is reasonable to assume th a t gravity is
the dom inant driving force in its evolution. W hen considering the final fate of th e
universe, we need to know how much m a tte r is in th e universe slowing its expansion.
If there is a high enough m a tte r density in th e universe, it will eventually stop its
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4
expansion and contract. Such a universe is known as a closed universe. A universe
with insufficient density to halt expansion is an open universe, and one with the
critical density (any m ore and it would be closed) is a flat universe.
C urrent observations of th e expansion and density of th e universe would
suggest an open universe. However, there are significant difficulties in calculating
both the expansion and th e density.
Cepheid stars can only be resolved up to
distances of about 30 million light years. Distances to galaxies fa rth e r th an th a t
can only be regarded as crude estim ates based on lum inosity and w hat we expect a
galaxy to be like. However, galaxies are not uniform , nor are th ey static. So, as we
look at a distant galaxy, not only are we looking a t a galaxy which m ay be different
in some im portant respect from th e nearby benchm ark galaxy, th e galaxy we are
looking a t is much younger and m ay be deceptive in appearance.
As for the density of the universe, again, we can only infer th e mass in any
region from the suspected masses of observed galaxies. T he m ass of an individual
galaxy is often uncertain, and the galaxies do not have a uniform d istrib u tio n , mak­
ing estim ation extrem ely difficult. Nevertheless, sufficient m ass has been identified
to make a t least 10 percent of th e critical density. F urtherm ore, a density of twice
the critical density would indicate a universe younger th a n te rrestrial objects, so we
can place these definite constraints upon th e density of th e universe.
If we consider a sim plistic view of the universe’s developm ent, it would start
as a very hot, very dense region of space. As th e universe expands, it cools and,
eventually, electrons and protons combine to form hydrogen.
universe becomes transparent to photons.
At this point, the
T h a t is, th e free electron population
decreases to the point where the free mean p ath of a photon is effectively infinite.
Meanwhile, the various particles in the universe gradually clum p into regions of
higher density due to gravity. Eventually, these clum ps will form w hat are now
recognized as stars and groups of stars (galaxies). If we take th e tim e now to look
as far away as we can, we will see photons coming to us th a t cam e from a hot electron
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gas th a t existed before the electrons and protons combined into hydrogen. Photons
com ing from this tim e are referred to as com ing from the surface of last scattering.
Photons from before this tim e would n o t have been able to propagate through th e
free electrons, and thus would not arrive a t th e earth at this tim e. Photons from
th e last scattering surface would exhibit th e spectral characteristics of a blackbody
rad iato r at approxim ately 4000 K. As th e universe expands, the photons undergo
a redshift due to the Doppler effect. T hus, we arrive at th e cosmic background
radiation from a 2.7 K black body which we observe today.
1.3
Inflation
W hile the standard m odel of universal expansion was sound in principle, it
failed to explain a num ber of observable item s. The cosmic background radiation
showed a high degree of isotropy, even betw een regions of th e sky which are too
far a p art to have established a th erm al equilibrium in the tim e of th e universe’s
existence. W hile big bang nucleosynthesis was very successful a t predicting th e
abundances of light elem ents, particle th eo ry would indicate large num ber of stable,
heavy particles, most notably m agnetic monopoles, which is inconsistent w ith ob­
servations. Furtherm ore, it fails to explain th e relative abundances of m a tte r and
a n tim a tte r. Last, as the universe evolves, th e density will tend to deviate from th e
critical density. For exam ple, if the universe is closed, it will become m ore apparent
as tim e goes on th at the universe is closed, until th e expansion stops, when any
m a tte r density at all will result in a closed universe. For the current observed lim its
of th e m a tte r density to exist, the initial m a tte r density m ust have been w ithin one
p a rt in
1 0 15
of the critical density one second after th e big bang.
A round 1980, cosmologists developed a new theory for describing th e first
m om ents of the universe using new theories of high energy particle physics. T he
theory requires a special set of fields known as Higgs fields. As th e universe cools,
it reaches a point (well before last scattering) where the Higgs field reaches a phase
transition. Since the phase transition is slow com pared to th e cooling ra te a t this
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6
tim e, th e universe begins supercooling and approaches a peculiar state o f m a tte r
known as a false vacuum predicted by quantum field theory. This false vacuum
has a pressure which is both large and negative. In general relativity, th is causes
a large repulsive gravitational force which in tu rn causes an exponential increase
in the size of th e universe. This is known as th e inflationary phase of th e m odel
and where th e model gets its nam e from. T his expansion causes regions which
were previously in therm al equilibrium to become d istan t from one another. Thus,
later observation of these regions would show a high degree on isotropy betw een
regions w hich previously could not be causally connected. T he inflationary e ra also
drives th e density of th e universe tow ard th e critical density, regardless of th e initial
conditions.
As the phase transition ends, the energy stored in th e false vacuum
is released, resulting in a trem endous am ount of particle production. U nder these
circum stances, the particles produced would be consistent with observation, b o th in
type and abundances.
O bservations of luminous m ass indicate a baryon density o f about 10 percent
of the critical density. However, observations of th e rotation o f galaxies are not
consistent w ith the observed luminous mass. T he rotation ra te of galaxies requires
more mass th a n has been observed. The n atu ral conclusion from these galactic
observations is th a t there is some m a tte r in th e galaxies which is not lum inous,
or dark m a tte r. Exactly w hat form this dark m a tte r has is a subject of d eb ate
depending on w hat exact properties various particles have (i.e. neutrino m ass).
W ith this dissertation, we wish to continue this investigation of th e origins
of the universe. C urrently, there are m any unresolved questions about th e initial
conditions of th e universe. In particular, there is no t a com plete understanding of
how stru ctu res (galaxies and galactic clusters) in th e universe form . These stru c tu re s
m ust have h a d prim ordial precursors a t th e tim e of last scattering which can be
m easured as anisotropy in the cosmic microwave background radiation. The levels of
anisotropy observed a t various angular scales (i.e. th e spectrum of the fluctuations)
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/
will also serve to b e tte r define constraints on th e cosmological param eters (m atter
density, baryon density, Hubble constant, am ount o f c o ld /h o t dark m atter, etc.). We
will present a discussion of th e theory of anisotropy, our in stru m en t and observing
strategy, our d a ta analysis and calibration, and finally th e results of our observations.
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Chapter 2
BACKGROUND
As we design our experim ent, we need to keep in m ind what we are looking
for and expect to be able to observe, how to relate our observations to theoretical
expectations in cosmology, th e possible interference we may receive from sources
beyond our control, and w hat has already been done by other experim ents. In this
chapter, we will first review th e general theories of the evolution of th e universe,
particularly in regards to th e surface of last scattering. Next, we will discuss the
m ethods used to relate observations of anisotropy to theoretical p aram eters. VVe
will then proceed to consider th e problems of contam ination by foreground sources
of microwaves. Finally, we will review observations made by other experim ents.
2.1
T heory
As we look farther into th e sky, we look further back in tim e. E arlier this
century, observations revealed th a t objects further away from us are m oving away
from us. The further away th ey are, the faster they are moving away from us. This
gives rise to the theory of universal expansion. The Hubble constant H a
1
defines
the current rate of expansion.
ffo = i = 100A^
r
Mpc
where r is the distance to an object, h represents the uncertainty in m easurem ents
of the distance of objects far away. It is generally accepted to be betw een 0.4 and
1 In general, a subscript o f o represents current observation and a subscript of * indicates con­
ditions at last scattering.
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9
1.0. T his expansion is not constant and how it varies depends on the evolution of the
universe. If th e universe has a sufficiently large mass, th e expansion will slow and.
eventually, contract. If the universe does not have sufficient mass for contraction,
it will continue to expand indefinitely. The rate of change of th e H ubble constant
depends prim arily on th e mass density of the universe, and cosmological theory finds
it convenient to define the density of th e universe in term s of th e critical density
separating an infinitely expanding universe and a universe which will eventually
contract.
q
_
Puntverse^
^
Pcrxtical
As the universe expands, it cools. So, as we look back into tim e at more
distan t objects we see a t a ho tter universe. We can look back until we reach a tim e
in which th e universe is hot enough to m aintain th e ionization of hydrogen. At
th a t point, the electron population is high enough to m ake th e universe opaque to
photons, resulting in the last scattering surface. T h a t is to say, photons created
before th e universe cools enough for recom bination to occur will scatter through
th e electron cloud until it is absorbed or the universe cools and the photons no
longer have an im pedim ent to their propagation through th e universe. W h at we
perceive as observers is the region in th e sky from which photons last scattered. If
we were to observe this surface in a static universe, it would appear to be a black
body rad iato r a t roughly 4000 K. However, our universe is expanding, causing the
photons to redshift to the point th a t we now observe a black body radiating a t 2.7
K.
In order for structures such as galaxies to form, th ere m ust exist some density
anisotropies in th e prim ordial m a tte r distribution which would be the precursors of
those structures.
If the fluctuations are adiabatic, regions of higher density will
have a higher tem perature, which will be observable as fluctuations in th e cos­
m ic background radiation. Cosmological perturbation theory describes how these
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10
anisotropies arise and develop through tim e. It should also predict w hat will be ob­
served at the last scattering surface as a result of these anisotropies. M any m odels
of the initial density inhomogeneities exist, b u t m ost of the widely accepted m odels
have a num ber of features in comm on.
We define a tem p eratu re pertu rb atio n as
AT
e „ = ~y
(2.3)
where A T is th e deviation from the m ean tem p eratu re of th e sky. If a density per­
turbation (and therefore tem p eratu re pertu rb atio n ) exists, it will oscillate betw een
th e conflicting forces of gravity and photon pressure according to
e Q+ k 2c2sGQ& F
(2.4)
where F is the gravitational force, k is th e wavenum ber (essentially, an indicator of
feature size), cs is the speed of sound, which is a m easure of th e resistance o f the
fluid to compression. All dots are derivatives w ith respect to conformal tim e
= J { l + z)dt
77.
(2.5)
where z is the redshift p aram eter AA/A. We use this notation because th e uncer­
tainty in the actual tim ing is large bu t th e redshift remains relatively well known.
T he gravitational force F is th e driving oscillator of the system at
F = --------------------------------------------------------- (2.6)
3
where $ is the Newtonian gravitational potential, obtained from th e density fluctu­
ations and $ ~ —$ is the pertu rb atio n of th e space curvature.
If we consider the gravitational potential to be static as a first approxi­
m ation, we have a simple harm onic oscillator. If we assume initial conditions of
an adiabatic universe, we get Oo(0) = —f'F and 0o(O) = 0.
W hich leads to
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11
9o(t?) = ^ c o s ( k c , r j ) — 'I'. As th e photons leave this gravitational well they ex­
perience a gravitational redshift equal to
Thus, we call 0 O + # th e effective
te m p eratu re fluctuation.
€>0 (^7 ) + ’P =
On scales larger than the sound horizon
O
(2.7)
cos(kcsT})
c s j/* ( 77 *
is the value o f
77
at recom bination),
we effectively observe the initial conditions of th e universe. T his is because on scales
larger th a n th e sound horizon, there has not been sufficient tim e for th e forces of
th e oscillation to have an effect. Therefore, no causal connection can exist between
points on these large scales. Fluctuations on these large scales are known as the
Sachs-Wolfe effect.
These prim ordial fluctuations axe a function of the scale of th e fluctuation.
If we assum e, for simplicity, th a t th e functional dependence o f density fluctuations
on scale is a power law, we arrive at
|0 o(fc)|2 oc k n~l
(2.8)
where n is known as the spectral index. C urrently popular inflationary theories
predict a value for n of about 1 (or scale invariant), which is consistent w ith current
observation.
On sm aller scales, th e oscillations will result in larger fluctuations.
The
period of these oscillations is determ ined by th e scale (u; = k c s). As a result, on
certain scales, the oscillations will be peaking (cos(kc, 77*) = ± 1 ), and on o th er scales,
th e oscillations will be nonexistent (cos(fccj77*) = 0). Obviously, th e scale (k) for
these occurances depends on th e age of the universe (77*) and th e com position of the
universe (c3). A younger universe would result in a smaller scale for these oscillation
peaks and troughs since th e sonic compressions and decompressions would have less
tim e to travel. A larger baryon content would reduce the speed of sound and also
reduce th e scale for these oscillation peaks and troughs. A larger baryon content
would also lead to larger peaks and troughs as th e increase in mass increases the
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m om entum of the plasm a. O nce again, it is convenient to define the density of
baryons in the universe as the ratio to the critical density.
ab= ^
ssl
( 2 .9)
P critic a l
O n the angular scales where th e oscillations are close to nonexistent, we ex­
pect th e m ean velocity of the particles to b e peaking. For a photon dom inated
fluid th e contribution from the resulting D oppler effect is equal in m agnitude to the
density fluctuations. T h at is, if th ere is little to no m atter, the density fluctuations
and th e doppler fluctuations would result in th e sam e tem perature fluctuations, and
would be indistinguishable by observation. T h e addition of baryons to th e system
will cause the relative velocities to decrease as the mass of th e fluid increases, due
to conservation of energy. Since th e addition of baxyons results in larger density
oscillations, the greater the m a tte r content, th e m ore we expect to see large fluctu­
ations on the scale where cos{kc3,qie) =
C O S^C sT }*) =
±1
an d little fluctuations on th e scale where
0.
As we continue to still sm aller angular scales, we find th a t photons m ay be
created in one region of the sky, travel to an o th er part and scatter tow ards the
observer. This will sm ear any anisotropy betw een the two points. T he scale of the
sm earing depends on the m ean free p ath of th e photons, which is in tu rn , extrem ely
sensitive to ionization. If the deionization is instantaneous, sm earing would only
exist on the scale of the photon m ean free p a th before deionization. As th e tim e
of deionization increases, the p h o to n ’s m ean free path increases m ore gradually,
allowing th e photons to scatter and sm ear over a larger region. Essentially, th e scale
of sm earing will be the length of th e free m ean p ath when the rate of expansion of
th e m ean free p ath exceeds the speed of light.
As the photons travel tow ards the observer, the universe is expanding and
th e photons m ay suffer further gravitational effects due to the expansion.
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The
13
com bination of this and th e Sachs-Wolfe effect is referred to as th e Integrated SachsWolfe (ISW ) effect.
If the effect occurs a t the tim e of last scattering (such effects would occur
on scales larger than th e sound horizon), it is referred to as th e early ISW. T he
particulaxs of this effect are heavily model dependent and outside th e scope of this
discussion.
If the effect occurs after m a tte r no longer dom inates th e expansion, we refer
to it as late ISW. T hus, th e tim e at which the universe exits th e m a tte r dom inated
stage is recorded in th e CMB by the ISW. This occurs in open m odels of the universe
(indefinite expansion) and models w ith a positive cosmological constant, when th e
universe enters a phase of rapid expansion. Again, th e particulars axe heavily model
dependent and outside th e scope of this discussion.
Obviously, all of th e effects described here take place in som e volume of
space, when w hat we will observe is an anisotropy over a surface (th e sky). So these
effects m ust be converted to an angular scale which depends upon th e distance
to th e last scattering surface and th e geodesics which the photons travel along.
Furtherm ore, one m ust be careful to recognize th a t a one-to-one correspondence
between spatial effects and angular observations only occur if th e sp atial variation
occurs perpendicular to th e line of observation. If it does n o t, th en th e angular
scale of any particular effect m ay be reduced. T he Doppler effect is also direction
dependent and may vanish altogether if the m otion of th e particles is perpendicular
to the line of sight.
T he results of all of these effects can be seen in figure 2.1. Please note th a t the
figure is of an a rb itrary scale, and merely representational of relative contributions
of various com ponents, all of which are model dependent. T h e horizontal axis is
m ultipole m om ents, and the vertical axis is the correlation ensem ble observed for
each m ultipole m om ent (see section
2 .2
for more detail).
As a result of all of this, the developmental history of th e universe will be
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14
3.0
Effective Temperature
Doppler Effect
LateJSW
EarlyJSW
Total
Scattering Cut Off
2.5
2.0
//
1.0
/ /
0.5 /.I / i
l/lii.Mltj
0.0
100
F ig u r e
2
. 1 : CMB Power Spectrum w ith Com ponents
im printed on the CMB anisotropy spectrum . By m easuring the CMB anisotropy we
can set constraints upon th e param eters which cause th e level anisotropy observed
and the scale on which it is observed. For example, d eterm in atio n of scale of th e first
oscillatory peak will set definite constraints on the age of th e universe at th e tim e of
recombination. D eterm ination of the height of th a t sam e peak will set constraints
upon the baryon content of th e universe. Therefore, we m ust m ake observations of
CMB anisotropy to clarify our view of the evolution of th e universe.
2 .2
O b s e rv a tio n a l P a r a m e t e r s
W hen we make observations, we wish to relate our observations to theoretical
values and param eters. In order to do this, we need to construct a common notation
and describe the relationship between theoretical descriptions of universal evolution
and the anisotropy observed in the CMB. It is conventional in CMB work to expand
the tem perature fluctuations in spherical harmonics.
AT
-wr = E
1
Im
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( 2 . 10 )
15
where A T is, again, th e tem perature p erturbation. Since observations are usually
m ade of the difference in tem perature of 2 points in th e sky separated by some angle
0, we work w ith a correlation function
AT
C ( 0 12) = ( —
AT
(n i),-^ -^ )),
( 2. 11 )
where th e average is taken over the observed sky w ith a co n stan t 9. As 9 is constant,
due to th e high degree of isotropy of th e cosmic background radiation, we can w rite
C in term s of the Legendre polynomials
=
( 2 . 12 )
c o s $ )
where we have introduced the rotationally invariant q u a n tity aj =
afm to rep­
resent th a t the m m odes can only be determ ined if we have a preferred direction,
since we do not have a preferred direction, we axe only interested in the m ean for
all correlations conducted at a particular angle. We can rew rite this as
C (0) = 7 " D 2/ + 1)Ci Pi {cqs 9)
47r
(2.13)
where Ci is a dim ensionally convenient representation of th e relative contributions
of the m ultipole m om ents proportional to (A T / T )2.
E quation 2.13 is modified by the fact th a t the experim ent will not be sensitive
to all harm onics. T he sensitivity of the experim ent to various harmonics is referred
to as the window function Wi. The result of this is
Cob3erved{9) = -L £ ( 2 / + 1)CtWi(9)
As a result, when an
(2.14)
observation shows some level of CM B anisotropy, th a t obser­
vation isover a set of angular scales, not ju st at one angular
scale. We will discuss
window functions in g reater detail in chapter five.
2.3
C o n tam in an ts
Due to the low levels of anisotropy in the CMB, any experim ent looking for
the anisotropy m ust be careful to consider possible contam ination from foreground
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16
sources. As th e photons from the last scattering surface travel towards us, they
travel by galactic clusters, which m ay cause gravitational lensing effects on very
sm all scales.
C ontinuing on into our galaxy, contam ination from galactic sources becomes
a p o tential problem . G alactic dust, synchrotron radiation and free-free emissions
can all produce photons in the microwave region. D ata analysis should evaluate the
d a ta for th e spectral characteristics of th e photons detected to be sure of a blackbody
source and not some other spectral function which would indicate a non-cosmological
origin of th e photons.
Synchrotron radiation is caused by charged particles (usually electrons) un­
dergoing acceleration as they travel through th e galaxy’s m agnetic field. It should
display a frequency dependence of
/ ( i/ ) oci/
(2.15)
where 0 is th e spectral index and lies betw een -0.5 and -1.1. Observations conducted
by Davies e t al (1987) in Tenerife are thought to have detected galactic synchrotron
radiation. However, at higher frequencies the intensity of this radiation is though
to die down to a level undetectable away from th e galactic plane (Readhead et al
1992).
G alactic free-free emission sources should also show a sim ilar power laws with
/? about 3.1. Again, levels are expected to be low, bu t this effect is much less well
understood th an synchrotron radiation.
G alactic dust is the contam ination due to the therm al emission of assorted
particles. It will also display a frequency dependence which will get larger as we go
to higher frequencies. M easurem ents by th e Cosmic Background Explorer (CO BE)
indicate a tem p eratu re of 23.3 K and a spectral index of 1.65 (Sm oot et al 1990,
W right et al 1991). We have selected our observing frequencies to minimize con­
tam ination from all galactic sources, so again, we expect this effect to be small.
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17
Last, as th e photons approach E arth, they can be contam inated by the
E a rth ’s atm osphere. T he Cosmic Background Explorer (C O B E) avoids this last
problem by being in orbit, and many balloon borne experim ents use high altitude
to significantly reduce this contam ination. Ground based experim ents m ust remove
atm ospheric noise by some means and m onitor th e spectral behavior of th e results.
One m ust also be careful to prevent contam ination from terrestrial sources of mi­
crowave radiation.
2.4
O b serv atio n s
At this tim e, observations of CMB anisotropy are sparse. Only a handful of
experim ents have detected any anisotropy, with very little overlap in angular scale.
W ith these observations, we work to gain b etter understanding of the origins of the
universe.
In 1964, Penzias and Wilson (1965) made th e first observations o f cosmic
microwave background radiation corresponding to a te m p e ratu re of 3K. Recently,
the FIRAS in strum ent on the COBE satellite has confirmed th a t th e radiation has
a Planck black body spectrum with a tem perature of 2.728 ± 0 .0 1 0 K (M ather et al
1994). This black body spectrum has shown a rem arkable degree of isotropy except
for the dipole anisotropy due to th e Doppler effect from th e m otion of th e earth
w ith respect to th e last scattering surface. T he best m easurem ents of th e dipole
yield a dipole m om ent of 3.343±0.016 m K towards (l,b) = (2 6 4 .4 ± 0 .3 °,4 8 .4 ± 0 .5 °)
(Sm oot et al 1991, 1992; Kogut et al 1993, Fixsen et al 1994).
D etection of anisotropy beyond the dipole has proven extrem ely difficult.
Theoretical work done through the m id 1980s indicated a value for A T /T of 10-5
and experim ental work had achieved an upper lim it on the anisotropy of 10-4 (Uson
and W ilkinson 1984). In 1992, the long sought after detection of anisotropy was
achieved by th e C O B E DM R experiment (Smoot et al 1992). T he C O BE observa­
tions were m ade w ith a set of six differential microwave radiom eters at three separate
frequencies. T he experim ent would m easure th e differential antenna tem p eratu re
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IS
betw een two 7 degree regions of the sky, 60 degrees apart.
The spin, o rb it and
orb ital precession allowed the entire sky to be covered in 6 m onths of observation.
T his rem ains the only orbital observation to date.
Since th a t tim e, a num ber of experim ents have reported detections of CMB
anisotropy a t a variety of angular scales. In 1991, Meyer et al, reported detection of
anisotropy w ith a 3.8 degree beam on a balloon flight. However, these results could
not be confirmed to be cosmic in origin. 1993 saw a flurry of reported results from
a diverse set of experiments. T he m illim eter wave anisotropy experim ent (M A X ),
reported detection of CMB anisotropy w ith a 0.5 degree beam on a balloon flight
(M einhold et al, 1993). Again, the possibility of foreground contam ination could
not be ruled out, but detection in m ore th a n one channel increased th e likelihood of
a cosmic origin. The Advanced Cosmic Microwave Explorer (ACME) also reported
detection of CMB anisotropy in 1993 (Schuster e t al, 1993). These observations were
carried out a t the Amundsen-Scott South Pole statio n using a set of high electron
m obility transistors (HEMT) in 4 channels. T h e use of 4 channels allowed th e exper­
im ent to alm ost distinguish between CMB and galactic sources, but the possibility of
contam ination remained. Further ground based observations in Saskatoon (W ollack
et al, 1993) using HEM T detectors in 3 channels was able to show th a t anisotropy
detected was more likely to be of cosmic origin th a n of any known foreground origin.
A nother balloon experim ent flown in Italy (A R G O ) (de Bernardis et al, 1993) using
bolom eters and operating with a 1 degree beam detected anisotropy. O nly two of
th e channels showed sufficient sensitivity to d etect the anisotropy. Spectral analysis
showed a cosmic origin to be likely, but could not rule out foreground sources.
In 1994, new detections were reported by the M edium Scale A nisotropy Mea­
surem ent (MSAM) (Cheng et al, 1994). This balloon borne experim ent had a 0.5
degree beam w idth making the sm allest scale detection to date. Difficulties in re­
solving foreground contam ination rem ained. T h e Python experim ent a t th e south
pole also reported detection at a scale of 1 degree. T he observations were m ade at
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19
90 GHz, which makes th e possibility of synchrotron contam ination unlikely. How­
ever, the possibility of free-free emission remains even though it is expected to be
at a much lower level th a n was detected. Observations were also m ade by a ground
based experim ent in Tenerife (Hancock et al, 1994). This experim ent uses 3 chan­
nels with a beam w idth o f 5.5 degrees. The three channels were able to exclude
galactic sources to a significant degree. MAX also reported on new observations
(Devlin et al, 1994; C lapp et al, 1994). ACME reported additional observations in
1995 (G undersen et al, 1995).
All CMB observations show uncertainty in the source of th e radiation to some
degree, however, the observations are becoming m ore able to elim inate sources of
foreground contam ination.
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Chapter 3
HARDWARE
In order to m ake observations of cosmic microwave background radiation
anisotropy, we need to be able to detect small fluctuations o f microwaves em itted
by the surface of last scattering. T he experim ent should have a well defined field
of view (the beam ) which will allow us to give a well defined window function and
thereby indicate th e scale of the fluctuations observed.
This experim ent used a set of 4 bolometers with ap p ro p riate filters to detect
microwave photons in 4 different bands. T he frequencies were chosen to minimize
contam ination from know n foreground sources and m axim ize sensitivity to a 2.7
K source (the Cosmic Microwave Background). The optics consist of an wobbling
parabolic prim ary m irro r and a hyperbolic secondary m irror which direct the pho­
tons to a W inston cone (W elford and W inston, 1989). T he p rim ary m irror wobbles
at a frequency of 4 Hz to allow us to make a differential m easurem ent of th e tem per­
ature. T he secondary m irro r directs th e incoming photons to th e w inston cone. The
W inston cone gives us excellent beam definition. In order to control th e pointing of
the telescope, the were arranged on an antenna with appropriate servocontrollers.
The entire arrangem ent was protected from local microwave sources by a set of alu­
minum radiation shields. A high, dry site w ith a stable atm osphere was selected to
minimize contam ination from atm ospheric noise. The bolom eters were set to collect
photons in different frequency bands to m onitor the spectral behavior of the signal
detected. This arrangem ent allowed us to look for contam ination from foreground
sources (CMB being behind everything else) such as the galaxy and the atm osphere.
20
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21
Liquid
Helium
F ig u r e 3.1: A ntenna and R adiation Shield
3.1
A n te n n a
The antenna consists of a ro tatin g support platform on six adjustable feet
(see figure 3.3). T he platform ’s azim uthal ro tatio n is driven by a DC m otor w ith two
optical encoders. The optical encoders provide position and speed inform ation to an
external servocontroller which directly controls th e m otors. T he platform supports
th e experim ent, the secondary m irror, and th e p rim ary m irror on an elevation track.
T he prim ary m irror is also driven on th e elevation track by a DC m otor w ith two
optical encoders. It is controlled by th e sam e external servocontroller.
The prim ary m irror is oscillated perpendicular to th e plane of th e elevation
track by a m otor and piston system which is set to oscillate at a frequency of 4
hertz. The prim ary m irror is an off axis parabolic m irror w ith a focal length of
1.330 m eters described by the equation
y = 4 / x 2.
(3.1)
T he secondary m irror is and off axis hyperbolic m irror described by th e equation
(;)'-(!)’ "
where a is 284 m m and b is 743 m m (see figure 3.2).
Together, these mirrors
reduce the field of view of the experim ent while effectively increasing th e aperture.
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22
S k y
Secondary
Mirror
/
Primary
Mirror
F ig u r e 3 .2 : Mirror System
This makes the experim ent m ore sensitive while reducing the angular scale of the
observations. In our case, we axe interested in features which axe a couple of degrees
on the sky, so the m irrors reduce our beam size to th e scale we axe in terested in.
T he entire system is surrounded by a set of radiation shields which prevent
local microwave sources from contam inating the data. T he shields consist of hinged
alum inum panels which can be raised and lowered to allow access to th e experim ent.
T hey are set up at a 45 degree angle to the ground to minimize retention of photons
entering the system .
We tested the beam response at the National Balloon Facility in Palestine
using a 90 GHz G unn source. T he beam shape was found to be roughly G aussian
w ith a beam w idth of 2.4 degrees FW HM . We found no significant sidelobes down
to -72dB.
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23
TTT
F ig u r e 3.3: A ntenna
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24
3.2
C old O ptics
After the photons are directed tow ards th e experim ent by the m irrors, they
enter th e cryogenic system where th e detectors axe through a polypropylene window
and th e cold optics diagram m ed in figure 3.5. This diagram is a two dim ensional
representation of a three dim ensional optics block.
First th e photons e n ter a w inston cone at 4.2 K, which is a high collection,
non-imaging optics piece.
Also known as a compound parabolic concentrator, a
winston cone is half of a parabola tilte d and th en rotated so th a t th e focus o f th e
sides is at the back of th e cone (see figure 3.4). All light from the cone’s field of
view is passed on. Photons from outside th e field of view are reflected back out of
the cone and do not e n ter th e system . T his gives us good beam definition. O ur
cone has an input ap ertu re diam eter o f 1.588 cm 2, and a half angle of 16.47 degrees,
giving us an Aft of 0.5 cm 2s tr where A is th e area of the input ap ertu re and ft is
the solid angle subtended by th e beam . A ft is directly proportional to th e n um ber
of photons received by th e experim ent.
T he photons then e n ter a reversed w inston cone to get the photons to travel
parallel to the optic axis. N ext th e photons pass through a high frequency blocking
filter consisting of black polyethylene an d flourogold.
Now the photons en ter th e optics block which is at 0.3 K. First th e photons
pass through a flourogold filter. This is another high frequency blocking filter. Since
we do not want the optics a t 4.2 K to touch the optics at 0.3 K, there is a gap betw een
them through which contam inating photons could enter. The filter elim inates m ost
of the undesired photons. A fter th e photons pass through the filter, th ey h it the
m ain splitter. The sp litter is essentially a high frequency pass alum inum th ick grill
filter set at a 45 degree angle to th e optic axis. Low frequency photons (C hannels
1 and 2) are reflected down a perpendicular optic tube. Each optic tu b e leads to
another beam splitter designed to pass th e appropriate frequencies, and reflect th e
others, resulting in 4 tubes with different frequency photons in each. T he 4 tubes
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25
Parabola
Concetrator Axis
Focus of
Parabola
F ig u r e 3.4: W inston Cone
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26
Channel 2
Optics Block
0.3 K
Channel 1
4.2 K
Photons
>
Channel 3
F ig u r e 3 .5 : Cold Optics
end w ith another winston cone which concentrates the photons onto th e individual
bolom eters.
All of this results in th e channel characteristics in table 3.1. T he actu al filter
functions (normalized to 1.0) axe shown in figure 3.6. These frequencies were chosen
to m inim ize contam ination from foreground sources.
T a b le 3 .1 : C haracteristics of Channels
Channel
1
2
3
4
W avelength(mm)
3.3
2.1
1.3
1.1
B andw idth(m m )
0.5
0.2
0.1
0.1
Noise (m K / \ / H z )
0.735
0.373
0.283
1.510
C M B /R J
1.288
1.66
3.66
4.82
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1.0
Filter Response
«
0.8
-
0.6
-
& 0.4 0.2
-
Ch4 Ch3
Ch2
Ch1
0.0
Wavelength (mm)
F ig u r e 3 .6 : F ilter Response
3 .3
B o lo m e te r s
Bolometers are, in essence, very sm all, very cold, light sensitive resistors. T he
bolom eter has essentially 4 parts which are an absorber, a resistor, a heat sink, and
a m echanical support.
T he absorber should be selected to absorb th e photons of interest, w ith ap­
propriate filters in front of it to prevent undesirable photons from being observed.
This absorber should have a low heat capacity and good therm al conductivity so
th a t when photons are absorbed, the absorber heats up and tran sm its the heat to
th e resistor. For convenience, we will consider an absorber w ith a heat capacity C,
and an input power response of
Pin = Po + Pie'"1
(3.3)
T = T0 + T ieiwt
(3.4)
and a tem p eratu re response of
T he resistor should have a high sensitivity to tem p eratu re change and a
low heat capacity. Thus, when the absorber heats up, so does th e resistor which
will cause a large change in resistance. The resistance is m easured by passing a
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28
Radiation
Absorber
Thermometer
H e a t
•Sink
Supporting
Substrate
Thermal
Link
F ig u r e 3 .7 : Bolometer
sm all current through the resistor and m easuring the voltage. T he wires carrying
the current should have a low resistance and a low therm al conductivity to keep
external heat from being tra n sm itte d to th e resistor. We will consider a resistor
w ith a resistance R and a tem p eratu re response
“ = 1 5 ?
(X 5 )
The heat sink should have a large heat capacity and a good th erm al contact
w ith the absorber and the resistor so th e energy absorbed from incom ing photons
does not remain in the resistor. T he quality of this contact will obviously effect the
response tim e of the bolometer. If we consider a heat sink w ith a sufficiently large
heat capacity, we can assume it has a constant tem perature Ta. We will fu rth er
assum e a therm al contact w ith a conductivity G.
Last, the m echanical support should have a low heat capacity and a low th er­
m al conductivity to minimized external influences on the system . If th e m echanical
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29
support connects the absorber, resistor and heat sink, th en it should have a high
th erm al conductivity to give a good response tim e for th e system .
If we apply conservation of energy to th e system , we get
Po + Pieiurt + I \ R + T ™ * * ) = G{T0 + T ie iuJt - T,) + i u C T velwt
al
(3.6)
which leads to
These give us
Po + I 2R = G(T0 - T3)
(3.7)
= G + i u C — I 2— .
(3.8)
the tem perature and the response characteristics of the bolom eter
respectively. Now we define the responsivity of the system
s = Vi = rrl§
Pi
Pi
iRa
G + iioC — I 2R a
1
]
As a practical m a tte r, real bolometers do not follow this theoretical response,
so the response of the system m ust be measured. We can define th e effective sensi­
tiv ity of the bolom eter as
aV
E ~ G -aP '
(3' 10)
If we consider a situation in which there is no power com ing in from photons, then
all of the incoming power is from the bias current. Now we can m easure th e voltage
on the bolom eter as a function of th e bias current an d use it in the equation
5* = 1 7 F
(X11)
where R is the resistance, I is the bias current, and Z is d V /d l.
In addition to noise from external contam ination of incom ing photons, th e de­
tecto r system itself can introduce noise. The m ain sources of noise in the bolom eter
system are photon noise (random fluctuations in th e blackbody radiation), phonon
noise in the heat sink, and Johnson noise in the bolom eter itself. We note th a t
other electronic com ponents not mentioned here can also produce noise from var­
ious sources. T he com ponents of prim ary concern are th e load resistor and th e
am plifier (see figure 3.10).
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30
W hen we consider the incom ing photons there will naturally be some random
fluctuations. In bolom eters, it is traditional to define the noise equivalent power,
which is the am ount of power which m ust be received to achieve a signal to noise
ratio of 1. If the noise is ju s t fluctuations in th e incom ing photons, we can apply
the well known formulas for th e signal and noise and get
(.N E P f =
T 5 A S I c t ( G 4 + <ltF<)
(
(3.12)
where
Gn = J
rxi*
F' = C
tn
^ dt
(3.13)
<3 1 4 »
and
hu
* - * ?
(X 15)
T he Johnson noise in the bolometer, of course, follows the form ula for John­
son noise in any resistor,
Vn = v 4 k T R d u
(3.16)
T he phonon noise in th e system will travel along the therm al link from the
heat sink to the bolom eter. If we treat this power transm ission in the standard
m anner, we arrive at
{ ( A P ) 2) = 4 K T 2Gdf.
(3.17)
T he noise in th e J F E T amplifier can generally be represented as a current
noise generator which represents th e shot noise in th e diode leakage current plus
Johnson noise.
Allof this isamplified by the gain of th e amplifier, resulting in
V 2 = g2( V 2 + I n
2 R 2)
(3.18)
where R is the resistance of the bolometer, and g is th e gain of th e amplifier.We note
th a t an appropriate choice of bolom eter and amplifier will result in the Johnson noise
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31
from th e bolom eter being much larger th an th e amplifier noise and of no concern.
In practice, this is almost always th e case.
All o f th e above sources are sum m ed in q u ad ratu re to give us th e to ta l noise.
As a practical m a tte r, the components were assembled and a set of d a ta was taken
w ith an alum inum shield covering th e input ap ertu re to prevent noise from external
sources entering. Since all of the channels have separate com ponents except for th e
heat sink, we expect the only noise correlations between channels to be from th erm al
fluctuations in the heat sink and vibration of the system . The actual m easurem ents
are shown in table 3.1.
3.4
C ryogenics
For optim al operation, our bolometers m ust be cooled to a te m p e ratu re of 0.3
Kelvin. In order to achieve this tem perature, we m ust minimize the am ount o f heat
entering th e system . The entire dewax is vacuum pum ped to minimize heat transfer
into the system .
T hat leaves ju st conduction through mechanical and electrical
contacts, an d radiation. Conduction through m echanical contact is m inim ized by
using a th in walled stainless steel tu b e for m echanical support. C onduction through
electrical contacts is minimized by using 0.001 inch wires carrying current on th e
order of 0.6\iA.
To m inim ize radiation transfer, th e cryogenic system consists of a 3 shell
dewar. T he outerm ost shell is in contact w ith th e atm osphere. T he first inner shell
is therm ally regulated by a liquid nitrogen bath to 77 kelvin. The innerm ost shell is
therm ally regulated to 4.2 kelvin by a liquid helium bath. Both shells are covered
in reflective alum inum which has a low emissivity. T he m ultiple shell system m eans
th a t m ost o f th e heat transferred into th e system is spent boiling com paratively
cheap liquid nitrogen, and most of th e rest is spent boiling liquid helium , resulting
in a stable and cool therm al environm ent for th e helium 3 refrigerator to o p erate in.
T he helium 3 refrigerator consists of a reservoir, a helium 3 pot, and a zeolite
pum p connected via a valve. To sta rt the cooling cycle, we purge the pum p of
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32
Pressure
He
Reservoir
Capillary
He Bath
77K Shield
m
Zeolite
Pump
Zeolite Valve
.4.2K Shield
F ig u re 3.8: Cryogenics
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33
4 -
3 -
2
Helium 4
-
Helium 3
0.01
100
0.1
Pressure (mm Hg)
F ig u re 3.9 : Helium T em perature vs Vapor Pressure
helium 3 by heating it (typically to 77K to minimize later cooling tim e) w ith a
current passing through a resistor. Then we isolate the pum p by closing th e valve,
(see figure 3.8)
T he next step is to condense liquid helium 3 into th e pot. Since the purging
of helium 3 has boiled off all of the helium 4 in the bath, we refill th a t b ath and
insert th e ‘cold finger’, a therm al contact between th e liquid helium bath and th e
pot. W hen this system is in equilibrium (about 3 to 4 hours) a t 4.2 K, th e cold
finger is removed since it is also a small therm al contact w ith the outside (300 K).
At this point we a tta c h a vacuum pum p to the liquid helium 4 b ath and lower
th e pressure (and therefore tem perature!). As th e tem p eratu re of th e helium 4 bath
decreases, helium 3 condenses in the tube between th e reservoir and pot where it is
in contact with the liquid helium 4 and gravity pulls the helium 3 down into the pot.
W hen the helium 3 finishes condensing (about 1.5 hours), we rem ove the vacuum
pum p and open th e valve to the zeolite pum p. The zeolite trap s th e helium 3 gas
particles, effectively keeping the vapor pressure low, which reduces th e tem p eratu re
of the helium 3 in the pot to 0.35 K. We use helium 3 instead of helium 4 because
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34
th e helium 3 has a much lower vapor pressure a t all tem peratures, which m eans th a t
as th e zeolite pum p reduces the pressure on th e helium 3 in the pot, th e helium 3
goes to a lower tem perature. Helium 4 has a lim it of about 1 K, whereas helium 3
will go down to 0.35 K.
A fter this, the liquid helium and nitrogen baths are refilled as needed. T he
helium 3 in th e pot was usually sufficient to m ain tain 0.35 kelvin for 60 hours, when
the cycle is repeated.
3.5
E lectro n ics
T he electronics systems can be broken down into three basic parts: th e de­
tector, the housekeeping electronics, and th e co m p u ter interface. The detector elec­
tronics system is the bolometer and signal am plifiers. T he housekeeping electronics
m onitor th e cryogenic and electronic support system s to ensure proper operation of
th e experim ent. T he com puter interface converts th e signals from the detector and
housekeeping system s to a digital form and stores it on disk for later d a ta analysis.
3.5.1
D e te c to r
T he detection system consists of a power source, a set of relays for turning th e
power on and off, the bolometers, and the am plifiers which amplify th e bolom eter
o u tp u t. As can be seen in the circuit diagram s, th e bolometers are each powered by
a 12V m ercury b a tte ry which is buffered by a low noise operational amplifier. T he
relays and op am ps are powered by 18V voltage regulators which in tu rn run off of
24V supplied from the outside. All internal electronics are shielded from external
R F noise and all external connections pass th ro u g h
it
filters to prevent R F noise
from entering th e system.
T he bolom eter is in series with a 10A/Q resistor to keep the power dissipation
in th e bolom eter low. Note th a t only th e 10AFQ resistor and the bolom eter are at
low tem peratures. All of the rest of th e electronics operate at ambient tem p eratu re
and are isolated from the low tem perature electronics by filters.
We do this to
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35
Buffered +12V
Typical Of 4 C hannels
Power On
lO kfl
lOkQ
2N 48677A 7726
>1000
>|
lOOkQ
rqrr
110pF
toon
tOOkQ
Coax
AD1170
Prog Gain Amp
60OLP-CE-6-1O.3K
1 LP RlterO-----10.3 kHz
R S-232
ADC
o(O O^
F ig u r e 3 .1 0 : D ata Acquisition C ircuit
m inim ize heat dissipation from electronic components in th e 0.3 K region and to
assure proper operation of th e electronic components which are designed to operate
a t room tem perature. T he signal from th e bolom eter is buffered from th e am plifier
by an F E T to insure th a t th e bolom eter gets a constant current. T h e signal is then
amplified and sent out through a BNC to the microcontroller electronics box.
Before being sent to th e microcontroller, the signal is am plified again by
program m able gain am plifiers, passed through a 10 Hz low pass filter, and finally
converted to a digital signal for the microcontroller.
3 .5 .2
H o u s e k e e p in g
T he housekeeping electronics consist of 2 therm om eters, a control system for
the m irror oscillation m otor, and th e antenna pointing system . T h e housekeeping
system also has an independent real tim e clock, and checks on th e external power
supply voltages and electronics box tem perature.
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36
© ->
+12V
Wobble Motor
4 Hz Clock
Phase
Compare
Therm om eter
Optical
Encoder
Counter
C ryostat
Therm om eter
+15V
A
+5V
A
-15V
A
R S -2 3 2
ADC
T herm om eter
Indep Clock
F ig u r e 3 .11: Housekeeping Electronics
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37
T he first therm om eter is a diode a ttach ed at to the helium 4 bath. It has a
known current passed through it and th e voltage is m easured to give the tem p er­
ature. T he second therm om eter is a G erm anium R esistor Therm om eter attach ed
to th e helium 3 refrigerator which is read by a lock-in circuit. The circuit switches
a current source on and off at a known frequency and operates a lock-in amplifier
which has th e voltage across the resistor as a signal input. This provides a good
reading of th e voltage while allowing us to keep a low current (and therefore low
power dissipation). The output voltages o f these two therm om eters are sent through
an ADC to th e microcontroller.
T he m irror oscillation is controlled by a phase com parator which evaluates
th e phase differential between a known oscillator and th e optical encoder m ounted
on the m otor. The phase com parator raises th e voltage th e m otor receives if it is
slower th a n 4 Hz and lowers the voltage if th e m otor is faster th an 4 Hz. The actual
wobbling frequency is sent to the micro controller by sending a 1 bit flag once per
revolution of the motor corresponding to th e sinusoidal m otion of the m irror.
T h e antenna pointing system is a DMC-720 two axis program m able servocontroller purchased from Galil M otion C ontrol. It receive com m ands from an RS-232
bus to run a set of 2 motors (azim uth and elevation). Positions of the m otors are
read by th e DMC-720 off of optical encoders m ounted on each motor.
3.5.3
C o m p u te r Interface
T h e com puter interface is a 68HC705C8 m icrocontroller which is program m ed
to send th e d a ta to the com puter down an RS-232 bus.
T he data are sent in
a m ajo r fram es and minor frames. A m ajo r fram e occurs once per m irror cycle,
triggered by the flag from the m otor controller. It consists of a 1 byte flag, a 3
byte fram e counter, 2 bytes from each channel, 4 bytes Real T im e Counter, 6 bytes
of housekeeping. A minor fram e occurs 19 tim es betw een each m ajor fram e and
consists of a 1 byte flag, 3 byte frame counter, and 2 bytes from each channel. T he
flag carries a 1 bit signal to differentiate between m ajor fram es and minor frames
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38
and also carries any relevant error codes. T he fram e counter is essentially a clock
tied to the m icrocontroller’s clock. The real tim e counter is th e reading from an
independent clock. The housekeeping data consists of 3 readings of power supply
voltages (+15V ,-15V ,+5V ) and 3 therm om eter readings from th e cry o stat pot, the
helium 4 bath, and the ex tern al electronics.
The fram es are sent to an Macintosh com puter running a Lab View program.
The program does a quick lock-in and writes both th e raw d a ta an d th e locked-in
data to disc. A lock-in is essentially a narrow band pass filter. It passes d a ta at
the frequency of the m irror wobble so we can evaluate the peak to peak differential
in the d a ta as th e m irror wobbles. We will discuss this in g reater d etail in our
discussion of th e d a ta analysis. T he lock-in inform ation is displayed on th e screen
along with some housekeeping inform ation for the experim ent o p erato r to m onitor.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 4
CALIBRATION
4.1
L ab o ra to ry
In order to ascertain a m agnitude for the m easured tem p eratu re differential,
we need to measure the bolom eter response as it switches between observing two
black body radiators of known tem p eratu re.
Ideally, these two radiators should
be close to the expected observing tem p eratu res, however, stable sources at 2.7 K
tem p eratu re axe difficult to find and m aintain. Instead, a source consisting of 2
tubs of liquid nitrogen (77 K) and 2 tubs of liquid oxygen (90 K) were placed on a
rotating table (see figure 4.1). All tubs had a microwave absorber lining th e bottom
to be certain of blackbody radiation.
T h e experiment was placed on an optics bench and mirrors were arranged to
focus th e beam onto one of the tubs. As th e table rotates, th e tub seen by the beam
changes. The bolometer response was m easured on an oscilloscope and norm alized
to account for amplifier gain.
If we observe a blackbody rad iato r w ith a detector, we will observe
t
PI n =
J fl
Channel
1
2
3
4
AV
0.0299
0.1646
0.3762
0.5560
r U o + A t/
dA
B ( v ,T ) d i
Juo—A v
CMB C alib r(^V /m K )
4.45
15.4
11.9
12.9
RJ Calibr(/zV /m K )
5.73
25.6
43.6
62.2
Error(% )
5.9
1.5
5.3
7.6
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
y
L
Mirror
LO & LN Baths
Motor
Side View
LN
LO
.LO
Reid of view
Tub
Top View
F ig u re 4.1: Laboratory Calibration Setup
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41
where B ( u , T ) is th e Planck radiation curve
4 hu3
1
(4-2 >
Since we are concerned w ith fluctuations in tem p eratu re in the cosmic microwave
background radiation, we are interested in th e change in th is radiation w ith changes
of tem perature.
If we take th e derivative of th e received power w ith respect to
tem p eratu re, we find th a t it is tem p eratu re dependent. However, if
hu
a
<K l '
(4' 3)
then
hu
i
eIq>fc T _
hu
ifcf’
A\
(4'4)
and
dB
Au2k
d T = ”
’
(
which displays no te m p e ratu re dependence a t all. This is known as th e RaleighJeans (R J) region of the blackbody spectrum . For all 4 channels of our experim ent,
both liquid nitrogen and liquid oxygen are well w ithin this region so we can consider
this tem p eratu re response to be accurate for all black body radiators in th e RaleighJeans region.
U nfortunately, cosmic microwave background radiation is not in the RaleighJeans region, so in order to get th e calibration for CMB we need to evaluate the
response to CMB versus th e response to RJ. Since CMB shows very little tem pera­
tu re fluctuation, we can m erely numerically evaluate
CMB
RJ
^ 1 t = 2.7A^- ^ \ t =2ok
(4.6)
for all 4 channels and divide by th e numerical evaluation for Raleigh-Jeans. Then
we can m ultiply the calibration measured in th e lab by th e appropriate conversion
factor to get the proper tem p eratu re response to CMB for th e each channel. The
conversion factors are shown in table 4.1.
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42
As a final note, this calibration is m ade for an expected CM B signal. As a
result, the spectral characteristics of th e Cosmic Microwave Background R adiation
(as seen by this experim ent) will be flat. Spectral characteristics of o th er sources
(such as the galaxy or atm osphere) will show a different frequency dependence in
our d a ta analysis th an th a t which would be observed in an absolute te m p e ratu re
m easurem ent.
4 .2
O b s e rv a tio n
In order to confirm o ur calibration, we conducted observations of a microwave
radiation source of well known intensity, th e full moon. We then conducted a com­
puter sim ulation of th e m oon passing through the experim ent’s field of view and
com pared the results.
The program P O IN T sim ulates the results of a uniform round source passing
through a Gaussian beam along th e direction of oscillation (i.e. th e m oon). T he
first thing the program does is to find the relative positions of th e beam center and
source center. This is a sim ple sinusoidal function (the oscillation) w ith a drift term
added (the source’s movem ent across the sky).
z = sinatf + vt
(4.7)
where z is the relative position of the source to the beam center, u> is th e wobbling
frequency of the m irror and v is th e o b ject’s m otion across th e sky.
T he program evaluates this position 16 times per sinusoidal cycle. A fter the
relative position is determ ined, the program evaluates the signal detected by th e
beam in a series of concentric circles centered on the beam center. Since th e signal
from a uniform source is th e sam e throughout any circle around th e beam center,
all we need to do is determ ine th e area taken up in each circle by th e source. The
program first checks to see if th e entire circle is covering the source. If it is, th en the
angle is obviously 2 n. If it isn’t, th e program uses the law of cosines to determ ine
the am ount of the circle th a t is covering th e source (see figure 4.2.
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43
B eam
C e n te r
S o u rc e
F ig u r e 4 .2 : A lgorithm used to evaluate response to th e moon.
/ r 2 _L _ r 2\
6 = 2 arccos ( —— -------- 1 I
\
2r bz
)
(4.8)
T he radius from beam center is rj, and th e radius o f th e source is r„. Thus,
the area taken up by the axe can be calculated
A = r/,0 A rj
(4.9)
where A r j is equal to th e distance between successive circles. E ach area is m ultiplied
by the beam sensitivity for th a t circle. All of th e signals for all of th e circles are
added up to get th e to ta l signal detected by the in stru m en t a t th a t point in tim e.
S(*) = £ A t-ex p ( ^ t )
(4 -10)
W hen a cycle is com pleted, with 16 d a ta points, th e d a ta is th e pu t through
a low pass filter. T h e low pass filter is sim ulated by p u ttin g th e d a ta through an
F F T , m ultiplying th e fourier signal by the freqency response characteristics of the
filter, and p u ttin g th e result through an inverse F F T . Now, th e signal is ready for
the lock in amplifier.
We evaluate bo th th e prim ary frequency response an d th e double frequency
response (the "tw o beam ” and ”three beam ” ). T he lock in functions are as follows:
L2=l
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(4-11)
44
600
Model
Data
400
200
200
400
Channel 1
600
18.4
18.6
18.8
19.0
RA (Hours)
Model
Data
500
500
1000
Channel 2
18.4
18.6
18.8
19.0
RA (Hours)
2000
Model
Data
1000
-1 0 0 0
2000
Channel 3
3000
18.4
18.6
18.8
19.0
RA (hours)
Model
Data
4000
2000
2000
4000
6000
Channel 4
18.4
18.6
18.8
19.0
RA (Hours)
F ig u re 4 .3 : Moon Observation
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45
T a b le 4 .1 : Observational C haracteristics o f th e Moon
Channel
(R J/C M B )
Moon Temp(K)
L ,=
1
1.288
196
2
1.66
240
3
3.66
216
4
4.82
229
1 16
y , S{ti) cos 2uti
16iV
(4.12)
where N is the beam coverage of the sky.
We conducted this analysis for a set of source sizes from 1 arc second to 5
degrees. The results were consistent with the dilution factor being th e only difference
between different source sizes.
In order to evaluate the effects of th e low pass filter on the signal, a lockin was executed on th e unfiltered signal for th e 0.5 degree source. There was no
discernible difference between the filtered and unfiltered results.
After this program was run, the d ata was m ultiplied by the m oon’s known
tem perature for each channel, the conversion factor from CM B to R J for each chan­
nel (since the lock-in program evaluates for CMB and th e moon is in the RaleighJeans region), and divided by 2 \/2 to norm alize the lock-in function.
Snut —
LTmoon( R J / C M B )
2y/2
(4.13)
The d a ta are assigned right ascension positions to m atch the observed moon
passage and com pared to the actual results. This com parison is seen in figure 4.3.
We find errors of less than 5 percent for channels 1 and 2, less than 10 percent for
channel 3 and a factor of 2.5 error for channel 4. However, since channel 4 is merely
an atm ospheric m onitor, having a correct calibration is no t necessary, we ju st need
it to be consistent in relation to the other channels.
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46
4.3
G a la c tic P la n e Crossing
Finally, in order to confirm the sensitivity of our experim ent, we evaluated
our d a ta in th e region of the galactic plane (right ascension 19-22 hours). If we are
going to claim to be able to observe CMB fluctuations on the order of 100 fiK we
should certainly be able to observe th e passage of th e galactic plane which will be a
large signal by comparison. Our spectral analysis should also be able to determ ine
th a t the galactic plane is not of cosmic origin.
As a basis for comparison, we constructed a com puter model of how o ur
experim ent should respond to the passing o f th e galactic plane. We assumed th a t
there are only three significant processes which contribute to galactic signal a t th e
frequencies we are interested in: free-free emission, synchrotron radiation, and d u st
emission.
Free-free emission and synchrotron rad iatio n are m odelled with a single pow er
law for b o th processes and extrapolated from m aps at 408 MHz and 1420MHz. D ust
estim ation is based on a map at 240 microns and a m odel which was taken from
Boulanger e t al (1996). The model is a grey body w ith em issivity 2 and te m p e ratu re
of 17.5 K.
A fter a m ap is m ade from these processes, we m erely sim ulate the passage
of our in strum ent through the galactic plane. T he results axe shown in figures 4.4
and 4.5 and are generally in good agreem ent.
We also subjected the d ata from th e galactic plane crossing to the sam e
spectral analysis which we conducted on th e rest of the d ata to verify th a t o u r
technique could correctly identify foreground contam ination. The results are shown
in figure 4.6. T he galaxy displays a spectral index of which is consistent w ith th e
value we expect for dust (1.5). CMB should have a spectral index of zero.
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47
1.0
0.5
0.0
•0.5
Channel 1 - 2 Beam
Galactic Plane Crossing
1.0
19.0
19.5
20.0
20.5
RA (Hours)
21.0
21.5
22.0
20.5
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F ig u r e 4.4: Galactic Plane Crossing - 2 Beam
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
1.0
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-0.5
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Galactic Plane Crossing
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•Galactic Plane Crossing
-1.0 -I
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F igure 4 .5 : Galactic Plane Crossing - 3 Beam
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
4Galactic Plane Analysis
2 Beam
2-
68%
‘95%
0-
-2 -
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100
Temperature (uK)
150
200
F ig u r e 4.6: Spectral Analysis of G alactic Plane
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 5
DATA ANALYSIS
In our d a ta analysis, we m ust be able to remove noise from atm ospheric
contam ination, determ ine if the signal we observe has a cosmological origin, and
calculate th e RM S fluctuations we observe if they axe cosmic in origin. We also
wish to elim inate noise from any nearby terrestrial source or noise introduced by
our electronics. We initially send the d a ta through a narrow band pass filter to
elim inate noise which does not correspond to th e m irror wobbling. T hen we use
d ata from channel 4 to remove atm ospheric noise, and finally conduct a correlation
analysis on the d a ta to find th e most probable source of th e photons and th e RMS
fluctuations.
5.1
L ock-In
T he first th in g we do is send the d a ta through a lock-in amplifier. T h e lock
in amplifier takes an input signal and m ultiplies by a known wave. The result is
then passed through a low pass filter (effectively an integrator) and th e o u tp u t is th e
RMS value of th e input signal a t the frequency of th e known wave, in accordance
with fourier transform s. In essence, the result is a very narrow band pass filter
(with phase inform ation!), th e band w idth determ ined by th e low pass filter. As th e
low pass filter passes lower and lower frequencies, th e integration tim e for accu rate
results increases, and the band w idth gets narrower.
In our case, we are concerned with th e fluctuations in sky te m p e ratu re as
an oscillating m irror changes its sky coverage. We know th e frequency of th e m ir­
ror oscillation, which corresponds to the changes of tem p eratu re as th e beam moves
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
July 29,1994
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F ig u r e 5.1: D ata From Good Observing Conditions A fter Lock-In
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52
Augusts, 1994
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F ig u re 5.3: D ata From T ypical Observing Conditions A fter Lock-In
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
T a b le 5 .1 : Lock-in Param eters
Channel
C alibration (f i V / K )
01
02
1
4.45
166.8
116.5
2
15.4
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across th e sky, so we use th a t as a reference wave, (w ith a phase shift em pirically de­
term ined). T hen we m ultiply the reference wave by th e digital signal, and integrate
over one cycle num erically instead of using a low pass filter. We divide each channel
by a calibration factor C which converts th e voltage measured at th e bolom eter into
a tem perature differential in the sky and m ultiply it by a norm alization factor N.
W ith last scattering surface tem p eratu re fluctuations of much less th a n 1 percent,
we can easily consider the conversion to be linear.
N 20
L o = r Y , vi
° i=i
(5-1)
N 20
L i = — Y i VicosM ,- + <£i)
u .=i
(5 .2 )
N 20
L 2 = 7T ]C Vi cos(2wf«' + 02)
(5.3)
° i=i
T he results of the lock-in were then averaged into 1 second bins using program
R A V G l. We do th is because our d a ta are originally tim e coded to a resolution of 1
second at th e tim e of acquisition. W ith a m irror frequency of 4 Hz, we have 4 cycles
during each second which results in 4 d a ta points per second.
T hen th e files were subjected to a 3 sigma cut to remove spikes using C U T ­
OFFS. We present the results of this analysis for 3 different days, one (Ju ly 29)
was under excellent observing conditions, one (August 5) was under bad observing
conditions, and one (July 20) was under typical observing conditions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
5.2
A tm o sp h eric R ed u ctio n
To remove the atm ospheric noise from th e d ata, we applied the m ethod de­
scribed in Andreani et al. (1991). A tm ospheric subtraction is conducted by the
program ATM8. If our d a ta consists of ju s t CM BR, atm osphere, and a constant
offset due to a system atic error, then
A Ti = e ' a'A Tc + (1 - e~a' ) A T A + 0 ,
(5.4)
where T,- is the tem perature m easured by each channel, Tc is the CM BR tem p er­
ature, Ta is the atm osphere’s tem p eratu re, a,- is th e atm ospheric optical thickness
for each channel and 0,- is the offset in each channel. If a is sm all for all of th e
channels and they are linearly related by
Qt- = K.Q4
( 5 -5 )
A Ti = (1 — K,a4)A T c + k .c^A T a + 0,-.
(5.6)
then we can w rite the equation
If we take the sum and difference of each of th e first 3 channels w ith channel
4, we get
S{ = 2 — 0:4(1 + Ki)ATc + 0:4(1 + Ki ) A T A +
0 { + O4
Di = q 4(1 — k , ) A T c + a 4(Kt — l)ATyi + 0 , — 0 4
( 5 -7 )
(5.8)
We can proceed to solve for 5,- in term s of
Si =
K{ — 1
A + 2 A T C + 2 * i 0 i ~ ,0 4
«,• — 1
(5.9)
Since the atm osphere is not static, for individual d ata points we get different
results for Si and
However, if th e atm osphere is relatively stable, th e values for
Si and Di follow the given linear relation and we can calculate th e values of all of
th e param eters in the equation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
ATM8 calculates th e sum and difference between each of th e channels with
channel 4 over a user determ ined tim e interval. Em pirical testin g showed 112.5
seconds (32 per hour) to give good overall results. Too short a tim e interval would
not give enough points for a good linear fit, and too long a tim e interval would lose
accuracy due to changing atm ospheric conditions.
To illustrate th e effectiveness of the technique, we have done a fourier analysis
of the d a ta taken on July 20, a fairly typical day. We have also conducted, for
com parison, a fourier analysis of an instrum ent test in which th e lens cap was left
on to prevent any external signal from entering th e system . C asual analysis shows
th a t the two data sam ples exhibit the same behavior on tim e periods below 50
seconds. T he internal noise sam ple was taken early in th e cam paign and exhibits
slightly higher noise levels. This is due to minor changes to th e electronic filters
which were m ade la te r in the campaign. For tim e periods above 100 seconds, noise
due to external sources is dram atically larger. We expect th a t if our atm ospheric
subtraction technique is successful, the noise on large tim e scales (being prim arily
atm ospheric in origin) should reduce to the levels observed on sh o rter tim e scales
(which is detector noise and uncorrelated between channels). This is exactly w hat we
find in th e fourier analysis of the d a ta taken on July 20 after atm ospheric subtraction.
T he program calculates a best linear fit for each channel, and uses th a t result
to calculate A Tc for each channel over each interval. In general, th e atm osphere
subtraction routine was capable of reducing atm ospheric noise by 2 orders of mag­
nitude. T he program also calculates the average AT,- over th e sam e tim e interval.
We do this because, on some occasions, the observing conditions were good enough
th a t alm ost no atm ospheric contam ination appeared in some channels.
In these
cases, th e atm ospheric subtraction would a tte m p t to find correlation between the
atm ospheric noise seen in channel 4 and detector noise seen in th e o th er channel.
Upon finding this “correlation” th e program would su b tra ct it, effectively adding
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
July 20,1994
Channel 1
100nHz____________1mHz____________ 10mHz___________ 100mHz
1000
July 20,1994
Channel 2
100|iHz
1mHz
10mHz
100mHz
1mHz
10mHz
100mHz
July 20,1994
Channel 3
100pHz
July 20,1994
Channel 4
100nHz____________1mHz
10mHz___________ IQOmHz
F ig u r e 5.4: Fourier Analysis of Typical D ata
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•58
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F ig u r e 5.5: Fourier Analysis of Internal Noise
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
-16 -
July 29,1994
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
August 5,1994
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20 0-20 -40 -
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
62
-16
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July 20,1994
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-18
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July 20, 1994
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F ig u r e 5.9: D ata From Typical Observing A fter A tm osphere S ubtraction
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
atm ospheric noise from channel 4 to th e channel in question. Thus, we keep the
averaged raw d a ta for later com parison. Both results are w ritten to o u tp u t files
along w ith the corresponding errors.
We have included the results of this atm ospheric subtraction for th e three
days given as examples above to show th e response of the atm ospheric su b tractio n to
different situations. The d ata taken on July 29 for channel 1 illustrate in a striking
m anner the problem discussed in th e previous paragraph. The noise seen in the
locked-in data are less than th a t seen on July 20, bu t the noise seen in th e channel
1 after atm ospheric subtraction is larger. For the d a ta taken on July 20, th e results
essentially confirm our expectations. T he d a ta taken on August 5 readily show th a t
this d a ta has too much interference for th e assum ption of a thin atm osphere to be
valid. As a result, the data retains a large am ount of atm ospheric noise and little
to no CMB inform ation remains.
A fter atm ospheric subtraction th e d a ta is analyzed by the program SLIDER
which evaluates the fluctuations in th e d a ta in half hour blocks. H alf hour blocks
were chosen since they are larger th a n any individual feature our experim ent m ight
see w ith a 20 m inute (right ascension) peak to peak m irror oscillation.
T he program evaluates every half hour interval of the atm osphere su b tracted
d a ta and if the fluctuations in th a t half hour axe less th an an em pirically determ ined
am ount (see table 5.2), then all of th e d a ta in th at half hour interval axe passed to
the next step. Any d a ta th a t did not m eet the criterial for any half hour interval
containing it, were rejected. We also conducted the sam e analysis on th e averaged
locked in data. Due to concern ab o u t correlated residual atm osphere noise from
sunrise and sunset, we did not pass d a ta w ithin a half hour of those tim es on any
given day. Bad d a ta due to known haxdwaxe failures were also removed a t this tim e.
Again, we present results from d a ta taken on July 20, and Ju ly 29. D ata
taken on August 5 was all rejected for obvious reasons. Note th a t channel 1 was
com pletely rejected on July 29. T he corresponding averaged locked-in d a ta fared
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
T a b le 5 .2 : Noise thresholds for accepting d ata.
Harmonic
If
2f
C hannel 1 (mK)
0.40
0.30
Channel 2 (m K )
0.35
0.25
Channel 3 (m K )
0.50
0.50
b e tte r in this procedure due to the lack of additional noise from channel 4. Also,
note how th e spike in channel 3 from Ju ly 20 was removed. We d id n ’t want one
bad point to force the rejection of d a ta surrounding it, and this is a good exam ple
of how the program handles such a situation.
At this point, th e program O F F S E l is used to remove offset an d linear drifts
from the data. A m inim um of an hour of continuous d a ta was im posed for sub­
tracting a linear drift to prevent removing large scale features (such as th e galactic
plane) from the d a ta leaving an artificial signal.
Then the program STACKING does a weighted adding of all of th e rem ain­
ing d ata at each right ascension. If no d a ta was passed from atm osphere subtracted
d ata, the corresponding raw d a ta was included, having been sujected to the same
cut. The d a ta were also stacked in two seperate groups, and these groups were
evaluated for independent features (a jack-knife analysis). T he thresholds (see ta­
ble 5.2) for accepting and rejecting d a ta in the SLID ER program were em pirically
determ ined using this jack-knife analysis to prevent large, one tim e occurrances from
contam inating the data. Since the noise from the detectors is random and uncor­
related between days on which the d a ta is taken, adding together all of th e useful
d a ta taken from a p articu lar location in th e sky serves to reduce th is noise leaving
us w ith CMB and galactic signals. We note th at the error given by this procedure
is less than the RMS fluctuations of th e signal. Given our beam size, we do not
expect this uncorrelated signal between adjacent points, so we m ust conclude th at
other sources of error (i.e. vibration of th e system) are con trib u tin g to th e noise
levels and com pensate accordingly. To handle this situation, we set th e error to the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
-18
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July 20, 1994
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F ig u r e 5.11: D ata From Typical Observing A fter Rejection
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67
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RA (Hours)
22
1.0
O'
E
£3
3
s(D
0.5 -
24
26
t - 2 .0
Rnal Data
Channel 3
13 Beam
- 1.5
m
3—.
0.0 -
r
1 .0
Q.
E
£
-0.5 -
0.5
-1 .0 -I
0.0
18
20
22
RA (Hours)__________
F ig u r e 5.13: Final D ata: T hree Beam
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3
69
0.8
-
0.6
-
Correlation for 112.5 Second Bins
0.4 -
-
0.2
-
0.0
-
0.2
~
3 Beam
2 Beam
-0.4 -
0.6
~
Angle (Degrees)
F ig u r e 5.14: Theoretical Correlation Functions Normalized To 1
RMS fluctuations in th e signal as a reasonable approximation of all non-system atic
error. The final d ata axe shown in figures 5.12 and 5 . 13.
5 .3
C o r r e la tio n A n a ly s is
In order to put our results into a form which can be used in th e stu d y of
cosmology, we need to evaluate our d a ta for mean fluctuations in CMB and do a
spectral analysis to confirm the cosmic origin of our d a ta rath er th a n foreground
sources. We note th a t since our d a ta has been binned (by th e atm osphere noise
subtraction technique) into points of 112.5 seconds in right ascension, th ere will be
significant overlap in th e beam p a tte rn between adjacent d ata points. As such, the
d a ta points will not be independent, b u t will have a certain degree of correlation.
We can calculate the am ount of correlation we expect between d a ta points as a
function of th e ir seperation in right ascension with the formula
/
rbin/2
rbin/2+p
dQ /
d9i /
de2B { 9 1) B { e 2) T { e )
J —bin/2
J —btn/2+p
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( 5 . 10 )
70
0.03
O
□
A
—
0.02
0.01
0.00
Ch1 & Ch2
Ch2 & Ch3
Ch1 & Ch3
Theory
liiiliJl
iI []
0.01
•
0.02
3 Beam
•0.03
Separation (degrees)
F ig u r e 5 .15: C orrelated D a ta w ith Theory for x 2 Fit
where B is the beam response over the sky after lock-in, p is the separation betw een
points in right ascension and T is th e theoretical m odel of the tem p eratu re fluctua­
tions in th e sky. This integral is a tedious one, and we find it convenient to rew rite
th e function in term s of Legendre polynom ials in sim ilar fashion to calculating th e
window function.
C(p) = 2 >Wi(p)
( 5 . 11 )
I
w ith ai being th e multipole response of a p a rticu lar m odel of the CMB, and Wi(p)
being th e beam response. Note th a t if p is zero, Wi is ju s t the window function of
th e experim ent. This is done by the program C orrelation.
We can then conduct cross correlations on th e actual d ata and com pare it
w ith the theoretical values using a x 2 fit- We exclude d a ta from the galactic plane
and regions of the sky where insufficient d a ta was taken to overcome detector noise
since we cannot expect these d a ta to tell us anything about the cosmic microwave
background.
Since th e correlation peaks and shape depend on the am ount of actual fluctu­
ations observed and to what extent they were observed in each channel, we can vary
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
4 —I
2 Beam Correlation Analysis
RA 15-19, 22-24
i5%
2
-
0-
-2
.68%
-
-4 - I
50
100
Temperature (uK)
150
200
4 3 Beam Correlation Analysis
RA 15-19, 22-24
2
-
68%
095%
-2
-
-4 H
100
Temperature (uK)
150
200
F ig u re 5.16: x 2 Fit
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
72
th e theoretical values for the fluctuation and th e spectral characteristics. We can
th en take the values of the \ 2 fits and calculate th e best values of th e tem p eratu re
and spectral index, which gives us tem p eratu re fluctuations of 67l}°^K for our 2
beam analysis and 35t3g/zK for our 3 beam analysis. T he spectral index on the 2
b eam analysis is consistent with zero, which is w hat we expect for CM B.
5.4
W indow Function
Now th a t we have a value for th e fluctuations we have observed and found
th e m to be spectrally consistent w ith CMB we need to be able to m ake a statem en t
ab o u t the scale on which we observed the fluctuations.
Obviously, th e scale of
fluctuations observed cannot be larger than th e to ta l scale of the observations on
th e sky. It also cannot be smaller th an the resolution of the beam . A com plete
discussion of window functions is given in W hite e t al (1994) and is reconstructed
in b rief here.
If we recall from section 2.2 the window function represents th e m apping of
th e observing strategy over the fluctuations found on the sky and relates to th e
tem p eratu re fluctuation observed by
( 0 j U , = C(O) = i ^ o , 2»',.
(5.12)
In essence, the window function represents th e sensitivity of the experim ent to th e
various Legendre polynomials and therefore th e various angular scales.
W hile calculating the window function, we m ust be cognizant of th e beam
response of the experim ent and th e observing stra teg y used. The beam response
can be evaluated in term s of Legendre polynom ials according to
B = ^ - f ) ( 2 / + l)fl/P ,.
(5.13)
47r 1=0
If th e experim ent conducts observations over th e entire sky, then th e window func­
tion is merely
W, = B f P i .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(5.14)
73
O
6
Standard CDM
= 1
£2b = 0.05
h =0.5
£2
-
T|
2
-
Beam
2 Beam
0
-
100
1000
F ig u r e 5 .1 7 : Window Functions w ith CDM Model
O ur experim ent, like m ost others, has a gaussian beam profile,
-Q2
1
B = 2 ^ eXp (W
)
(5.15)
which can be expanded (in a sm all angle approxim ation) in term s of legendre poly­
nomials to yield
B[ = e x p ( - ^ /( / + l)<r2).
(5.16)
However, we are only conducting observations of a strip in th e sky a t +40 degrees
declination. O ur observing p a tte rn follows th e equations
0{t) =
e 0,
(f){t) = (f)o + vt + a sin(tuf)
(5.17)
(5.18)
where v is the speed of th e sky moving overhead, a is the am plitude of th e m irro r’s
oscillation across the sky and u> is th e speed of oscillation.
T he d a ta are th e n subject to a lock-in w ith an integration tim e equal
period of oscillation. If we assume a lock-in function of L(t) and th a t v «
to one
u we
can find th a t the m easured tem perature for one sweep is
N rt+St
T ( n ) = j t Jt
dtL(t) j d n B ( n ( t ) ) T ( n ( t ) ) .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(5.19)
74
where N is the a norm alization factor and St is th e period of oscillation. T h is is
th e function which describes the m apping of th e beam across th e sky. If we expand
this over a series of observations and expand in term s of Legendre polynom ials, we
arrive a t th e window function
A*r
WM ) =
+
i
•£ Y ^L lW S H A tfc o sim t)
(5.20)
1 m = —/
where
ij r
Lm( a ) = — / d tL ( t)e xp (i m as in (u jt) )
27r J
(5.21)
and
A 4> is the m otion of the the sky during one oscillation of th e beam . Please note
th a t all variables are defined as angles on th e sky. If we insert the values for our
experim ent we arrive at the window functions given in figure 5.17.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 6
CONCLUSIONS
We find tem p eratu re fluctuations in th e CMB of 67l[o/^K for m ultipoles of
I = 33lj3
311 upper lim it of 60 \i K for m ultipoles of / = 5 3 ^ 5 . We feel th a t
our spectral analysis indicates a cosmological origin for our observations.
These
results are consistent w ith cold dark m atter models of th e universe and w ith other
experim ents conducted on sim ilar angular scales as can be seen in figure 6.1.
T he technique of using a high sampling ra te during o u r observations and
conducting our d a ta analysis on different modes of oscillation (tw o beam and three
beam ) was successful in obtaining results for two different angular scales w ith the
sam e d ata. This m eans we axe able to report two distinct results w ith th e d a ta from
one experim ent. We feel th a t this is an advantage in conducting observations of
this sort and feel it will be advantageous to include as m any modes of oscillation as
possible during future observations. This will also have the advantage of being able
to construct a m ap of th e observing region based on th e ap p ro p riate sum m ation of
th e Fourier series.
W hile these results are encouraging, especially for ground based observations,
there is obviously a need for fu rth er observations at all angular scales to b e tte r define
the CMB anisotropy and thereby refine our understanding of stru c tu re developm ent
in th e universe.
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
7 •
6
O
o
r
M
O
-
□
o
V
M
5 4-
Bartol (This Experiment)
SP94
Tenerife
Saskatoon
Python II
MSAM95
I 3'
2
-
010
100
Figure 6.1: Observations with CDM Model
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Appendix
DATA ANALYSIS PROGRAMS
A.l
Calibration
PROGRAM POINT
REAL SIGNAL, POSITION, K, THETA, TEMP, ZERO
REAL SIGNALIN(32) , LOCK, L0CK2, HSQ, PZ, LOCKF, L0CKF2, THROW
REAL SIGSUMSQ, FILSUMSQ, SIGRMS, FILRMS, X, Y, M, V, B
REAL DEGREE(989), SENSE(989), BEAM, MB , SIGMA, SIGMASQ
INTEGER TIME, I, J
C INITIALIZE VARIABLES
SIGMA = 1 . 0 2
SIGMASQ = SIGMA*SIGMA
M=0.1
B=0.5
V=0.0000855031
THR0W=2.6
DO 30 1=1,32
SIGNALIN(I) = 0
30
CONTINUE
OPEN (14, FILE=»LOCKIN.DAT ’,STATUS='UNKNOWN')
WRITE (14,31) B,M
WRITE (14,32)
31
FORMAT (1X,'B=,,1X,F5.3,1X,,M=',1X,F5.3)
32
FORMAT (1X,'BEAM2
BEAM3*)
C MAIN LOOP - EACH CYCLE HAS 16 DATA POINTS, 4 CYCLES PER SECOND
C EACH TIME INCREMENT IS 1/64 SECOND
DO 100 TIME = -63999,64000
C FIND THE INPUT SIGNAL FOR THE SITUATION
SIGNAL = 0
C X=VT, Y=MX+B
X = V+TIME
77
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78
Y = M*X+B
X = THROW*SIN(0.392699*TIME)+X
ZER0=SQRT(X*X+Y*Y)
C
C
C
C
C
C
THIS SECTION FINDS THE SIGNAL BY SUMMING UP A SERIES
OF CONCENTRIC CIRCLE SEGMENTS WHICH ARE CENTERED ON
THE BEAM CENTER AND COVER THE MOON.
APPLY LAW OF COSINES TO FIND THE ANGLE OF EACH CIRCLE SEGMENT
IF THE BEAM IS WHOLLY WITHIN THE MOON, USE A SEMI CIRCLE
TO AVOID DOUBLE COUNTING.
DO 40 K=-0.25,0.25,0.01
POSITION = ZERO-K
HSQ = 0.0625-K*K
PZ=POSITION*ZERO
IF (CPZ.LE.O) .OR. ((4*PZ).LE.HSQ)) THEN
THETA = 3.1415926536
ELSE
TEMP * HSQ/2/PZ
IF (TEMP.LE.O) THEN
THETA=0
ELSE
THETA = 2*AC0S(1-TEMP)
END IF
END IF
C THE SIGNAL FOR EACH CIRCLE IS THE GAUSSIAN VALUE OF BEAM
C SENSITIVITY TIMES THE AREA OF THE CIRCLE SEGMENT
C AREA = RADIUS*ANGLE*THICKNESS
BEAM=EXP(-POSrnON*POSITION/2/SIGMASQ)
40
SIGNAL = ABS(POSITION) *THETA*0 .01+BEAM+SIGNAL
CONTINUE
C PROCESS EACH CYCLE
I = MOD(TIME,16)
IF (I.LE.O) THEN
1=1+16
END IF
SIGNALIN(2*1-1)=SIGNAL
SIGNALIN(2*I)=0
IF (I.EQ.16) THEN
C CALL FFT
CALL F0UR1(SIGNALIN, 16, 1)
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79
C DO FILTERING
SIGNALIN(7)=SIGNALIN(7)*0.38
SIGNALIN(8)=SIGNALIN(8)*0.38
SIGNAL IN(9)=SIGNALIN(9) *0.0027
SIGNALIN (10) =SIGNALIN (10) *0.0027
SIGNALIN (25)=SIGNALIN(25)*0.0027
SIGNALIN(26)=SIGNALIN(26) *0.0027
SIGNALIN(27)=SIGNALIN(27)*0.38
SIGNALIN(28)=SIGNALIN(28)*0.38
DO 60 J=ll, 24
SIGNALINC J)=SIGNALIN( J) *0.000071
60
CONTINUE
C CALL FFT(-l)
CALL F0UR1(SIGNALIN, 16, -1)
DO 70 J=1,32
SIGNALIN(J)=SIGNALIN(J)/16
70
CONTINUE
C DO THE LOCK IN
L0CKF=0
L0CKF2=0
DO 90 J=1,16
L0CKF=SIGNALIN(2* J-l) *SIN (0.392699* J) +LOCKF
L0CKF2=SIGNALIN(2*J-1)*C0S(0.785398* J)+L0CKF2
90
CONTINUE
L0CKF=0.013515*L0CKF
L0CKF2=0.013515*LOCKF2
WRITE (14,*) LOCKF, L0CKF2
END IF
100
CONTINUE
CLOSE (14)
END
A. 2
Lock-In
Program Lock_Save
j
implicit none
!
! Structures ---------
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
include 'TENERIFE_LOC_STRUCT.INC’
record /header_LOC/ header
record /data_frame.LOC/frame
Variables ---------------------------integer*4
Chi(20),
Ch2(20),
Ch3(20),
Ch4(20),
counter(20),
d_counter(20)
&
&
&
character*1024 buffer
character*512 block
character*80
in_dir,
out.dir,
log.dir
character*40
character*12
pass.buffer
character*4
time_a,
time_b
&
character*1
&
integer*!
integer*4
integer*4
&
file_name
flag.a,
flag_b,
file_format
! Either a (ASCII) or t (binary)
data_buffer(1024)
rcl, k, i, j, ib, ii, jj
counter_s,
counter_next,
Chl.s,
Ch2_s,
Ch3_s,
Ch4_s,
FT,
FTO,
Fast counter
Channel
Channel
Channel
Channel
Time of
Time of
1
2
3
4
frame
first frame
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
81
&
k
k
k
k
k
yy.
mo,
dd,
hh,
mm,
gain(4)
integer*2
LT,
VI,
*
CM
>
k
k
k
k
k
k
k
V3,
Tl,
T2,
flag.msn,
flag_lsn
k
k
k
k
k
k
k
k
k
a_l(4),
a_2(4),
b_l(4),
b_2(4),
Phi.1(4),
Phi_2(4),
f_r,
calib(4),
conv(4)
real*8
MJD,
f od,
ST,
LST,
H,
dec,
RA,
RAO,
long,
lat,
az,
el
k
k
k
k
k
k
k
k
k
k
k
logical
k
Local temperature
-15 Volts
+15 Volts
+5 Volts
Ex. ADC1
Ex. ADC2
/->
1
(d
o
real*4
Year
month
day
hours
minutes
amplifiers1 gains
Phases for the If lock in
Phases for the 2f lock in
Reference frequency
Calibration factors
Conversion from V(Qdas)
to mK(fflbolom)
Modified Julian Day
Fraction of Day
Sidereal Time
Local Sidereal Time
Hour angle
Declination
Right Ascension
Right Ascension at the start
Longitude
Latitude
Azimuth (decimal degrees)
Elevation (decimal degrees)
ex,
not.found,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
not.eof,
tab,
good_frame
&
Functions
double precision sla.GMST, ! These functions are from SlaLib
sla_DRANRM ! Coordinate conversion functions.
&
Parameters --------------------------------Set constants for the campaign
data
data
data
data
tab/9/
calib/4.45, 15.4, 11.9, 12.9/
Phi.l /166.8, 154.8, 149.1, 169.4/
Phi_2 /116.5, 106.2, 99.4, 122.6/
Tab character
Calibrations uV/K
If lock in phases
2f lock in phases
equivalence (data_buffer, buffer)
long = -16.5
lat = 28.3
! West
! North
in.dir = ’BRIAX4$DKA100:[USERS.CMB.DATA.94.DAT.FILES] ’
out.dir = ’BRIAX4$DKA100:[USERS.CMB.DATA_94.W0RK_FILES]
log.dir = ’BART0L$SCRATCH7:[LPICCIRI] ’
Inputs
Get the data file.
type 600
format(’ Enter input file(no extension)’,/,
'/.
’ Enter m for Moon
file’,/,
’ Enter t for short testfile: ’ $)
accept 601, file_name
601
format (A80)
600
if (file_name .eq. ’m ’ .or. file.name .eq. ’M ’) then
file.name = ’H9406240144’
else if (file.name .eq. ’t ’ .or. file.name .eq. ’T ’) then
file.name = ’H9408081953’
endif
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
S3
! Get the amplifier settings.
i
700
701
type 700
format(’ Enter amplifiers gains 4(11) no spaces: ' $)
accept 701, (gain(i), i=l,4)
format(4(11))
I
! Get the pointing location.
I
!
! 900
!
I
Disabled.
typ® 900
format(’ Enter azimuth and elevation (dec degrees): ' $)
accept *, az, el
do while(file_format .ne. ’a* .and. file.format .ne. 'A' .and.
&
file.format .ne. ’b ’ .and. file.format .ne. 'B')
type 800
800
format (' File format a=ASCII, b=binary: 1 ,$)
accept 801,file_format
801
format (Al)
enddo
j
! Initialize basic parameters ---------------------------------i
flag_a
not_found
not_eof
= char(,01'x)
= .true.
= .true.
;
! Set volt to millikelvin factors for all 4 channels.
j
do i=l,4
! Evaluate amplifiers
conv(i)=lE6/(calib(i)*2**float(gain(i))*4) ! & calculate
enddo
! conversion factors
! Find beginning right ascension and declination(in radians)
read(file_name, 301) yy, mo, dd, hh, mm ! Read date/time
format(lx,5(12))
hh = hh - 1
! Local Time to UT
call sla_CALDJ(yy, mo, dd, MJD, j )
! Calculate JD
call sla_DTF2D(hh, mm, dble(O.O), fod, j ) ! Fraction of day
MJD = MJD + fod
301
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
84
ST =
long=
lat =
LST =
LST =
sla.GMST(MJD)
long/57.2957795131
lat/57.2957795131
ST + long
sla_DRANRM(LST)
az = 0.dO
el = 78.5/57.2957795131
! ST is in radians
! long in radians
! LST=ST+longitude
! norm to 0-2pi
! az and el in radians
dec = asin(sin(el)*sin(lat)+cos(el)*cos(lat)*cos(az))
H
= ((sin(el)-sin(lat)*sin(dec))/(cos(lat)*cos(dec)))
if (H .gt. 1.0 .and. H .It. 1.0001) then
H = 1.0
endif
H = acos(H)
if (sin(az) .gt. 0.0) then
H = 6.28318530718 - H
endif
RAO = LST - H
Open .DAT file (raw data file) -----------------------------open(unit=10, file=in_dir//file.name//’.DAT',
k
readonly,
k
status=’old’,
k
form=’unformatted’,
&
organization^ sequential’)
Open lock-in output file
&
&
k
k
if (file_format .eq. 'a' .or. file.format .eq. 'A') then
open(unit=ll, file=out_dir//file.name//’.L0C’,
status=,new',
recl=512)
else
open(unit=ll, file=out_dir//file.name//’.LOB’3
status=’new’,
form=’unformatted’)
endif
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
So
Write ouput file header —
501
k
k
k
k
k
k
k
k
if (file.format .eq. 'a' .or. file.format .eq. ’A ’) then
write(ll, 501]
501) (tab, i=l 20 )
format(’RA’ al,
’Chl_a_0 ,al,’Chl_a_l ,al,’Chl.b.l’,al,
’Chl_a_2 ,al,’Chl_b_2 ,al,
’Ch2_a_0 ,al,’Ch2.a_l ,al, ’Ch2_b_l’,al,
’Ch2_a_2 ,al,’Ch2_b_2 ,al,
’Ch3_a_0 ,al,’Ch3_a_l ,al, ’Ch3_b_l’,al,
’Ch3_a_2 ,al,’Ch3_b_2 ,al,
’Ch4_a_0 ,al,’Ch4_a_l ,al, ’Ch4_b_l’,al,
’Ch4_a_2 ,al,’Ch4_b_2 )
else
do j=l,4
header.calib(j) = calib(j)
header.gain(j) = gain(j)
header.phi_l(j) = phi_l(j)
header.phi_2(j) = phi_2(j)
enddo
write(11) header
endif
Open error log file
open(unit=12, file=log_dir//file.name//’.log’,
status=’new’)
Program’s body
read(10) block
buffer = block
read(10) block
buffer(513:) = block
! Load two 512 bytes blocks into
! string named buffer. We use buffer
! to find the beginning data block
! flag 01 and sync the reading
ib = 1024
do while (not.found)
if (ib .It. 512) then
read(10) block
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
buffer(ib+1:) = block
ib = ib + 512
endif
k = index(buffer,flag_a)
time_a = buffer(k+12:k+15)
flag_b = buffer(k+250:k+250)
time_b = buffer(k+262:k+265)
if (flag_b .eq. flag_a .and.
&
(time.a .eq. time_b .or. time_b .eq. time_a)) then
buffer = buffer(k:)
ib = ib - k + 1
not_found = .false,
else
buffer=buffer(k+1:)
ib = ib - (k+1) + 1
endif
enddo
At this point the buffer should contain a string which
starts with the 01 flag.
The programs reads out the first long frame which is actually the
last frame of the prevoius incomplete set of sample over a period.
&
&
call extr_lf(buffer(1:22),
Counter.s, Chl_s, Ch2_s, Ch3_s, Ch4_s,
FT, LT, VI, V2, V3, Tl, T2)
FTO = FT
! Set the time of the 1st frame
buffer = buffer(23:)
ib = ib - 22
At this point the buffer should have the first frame (flag 00)
of the next complete period. The program can now start looping.
j
=
1
! Set s-frames* counter to one
do while (not_eof)
if (ib .It. 512) then
! Check to see that there are at
read(10,err=999)block !
least 512 bytes in buffer, if
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
buffer(ib+l:) = block
ib = ib + 512
end if
k
! not read another block,
call extr_flag(buffer(l:12),
! Examine the frame's flag
flag.msn, flag_lsn)
if (flag_msn .eq. 0 .and. flag_lsn .eq. 0) then
k
call extr.sf(buffer(1:12),
counter.s, Chl.s, Ch2_s, Ch3_s, Ch4_s)
counter(j) = counter.s
Chl(j) = Chl.s
Ch2(j) = Ch2_s
Ch3(j) = Ch3_s
Ch4(j) = Ch4_s
j = j + 1
buffer = buffer(13:)
ib = ib - 12
else if(flag_msn .eq. 0 .and. flag.lsn .eq. 1) then
k
k
call extr.lf(buffer(1:22),
Counter.s, Chl_s, Ch2_s, Ch3_s, Ch4_s,
FT, LT, VI, V2, V3, Tl, T2)
if (j .eq. 20) then
counter(20) = counter_s
Chi(20) = Chl.s
Ch2(20) = Ch2_s
Ch3(20) = Ch3_s
Ch4(20) = Ch4_s
buffer = buffer(23:)
ib = ib -22
j = 1
! Reset s-frames’ counter
call extr.ct(buffer(l:12), counter.next)
call timing(counter, counter.next,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
&
d_counter, f_r, good.frame)
if (good.frame) then
&
call lck_in(d_counter, f_r, Chi, Ch2, Ch3, Ch4,
Phi.l, Phi_2,a_0, a_l, a_2, b_l, b_2)
RA = RAO + (FT - FTO)* 7 .29195426E-5 ! Convert DeltaT
RA = sla_DRANRM(RA)
! to DeltaRA
RA = RA * 3.81971863
! norm to 0-2p
! 0-24h
if (file.format.eq. 'a' .or. file_format.eq. ’A') then
do i=l, 4
a_0(i) = a_0(i)*conv(i)
a_l(i) = a_l(i)*conv(i)
a_2(i) = a_2(i)*conv(i)
b_l(i) = b_l(i)*conv(i)
b_2(i) = b_2(i)*conv(i)
enddo
&
&
&
&
201
write(ll, 201) RA, (tab, a_0(i) ,
tab, a_l(i),
tab, b_l(i) ,
tab, a_2(i) ,
tab, b_2(i) , i=l,4)
format (lx,F9.5,20 (A1,elO.3) )
else
frame.RA = sngl(RA)
do i=l,4
fraune.Lck.Of (i) = sngl(a_0(i)*conv(i))
fraune.Lck.lf (i) = sngl(a_l(i)*conv(i))
frame.Lck_2f(i) = sngl(a_2(i)*conv(i))
enddo
write(11) frame
endif
else
call error_manager(4, flag_msn, flag.lsn, FT)
endif
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
89
else
buffer = buffer(23:)
ib = ib - 22
j = 1
! Reset s-frames' counter
endif
else if(flag.msn .ne. 0 .and. flag_lsn .eq. 0) then
call extr.lf(buffer(l:22),
Counter.s, Chl.s, Ch2_s, Ch3_s, Ch4_s,
FT, LT, VI, V2, V3, Tl, T2)
&
&
type 100, (data_buffer(jj), jj=l,22)
buffer = buffer(23:)
ib = ib - 22
call error_manager(l, flag.msn, flag.lsn, FT)
else if (flag.msn .ne. 0 .and. flag.lsn .eq. 1) then
call extr.lf (buffer(1:22) ,
Counter.s, Chl.s, Ch2_s, Ch3_s, Ch4_s,
FT, LT, VI, V2, V3, Tl, T2)
&
&
type 100, (data_buffer(jj), jj=l,22)
buffer = buffer(23:)
ib = ib - 22
j = 1
! Reset s-frames1 counter
call err or .manager (2, flag.msn, flag.lsn, FT)
else
call error.manager(3, flag.msn, flag.lsn, FT)
endif
enddo
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
90
I
999
not_eof = .false.
i
stop
end
Include files
include
include
include
include
include
include
include
'extr.sf.for'
'extr.lf.for'
'extr.ct.for'
'extr.flag.for'
'lck.in.for'
'error.manager.for’
'timing.for'
subrout ine extr_ct(frame,
&
counter.s)
implicit none
character*12 frame
!Input frame
character*4
counter_$
!Fast counter (character buffer)
integer*4
counter.s
!Fast counter
integer*4
counter
!Fast counter
equivalence (counter, counter_$)
Breaking the frame into pieces
counter_$(l:1) = frame( 4: 4)
counter_$(2:2) = frame( 3: 3)
counter_$(3:3) = frame( 2: 2)
counter.s = counter
end
subroutine extr.flag(frame,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
&
I.flag.msn, I.flag.lsn)
implicit none
character*1
frame
! Input frame
character*2
flag_$
! short/long frame flag
integer*2
I_flag_msn, ! Frame flag most signif nibble
I_flag_lsn, ! Frame flag least signif nibble
flag
! Frame flag
&
&
equivalence (flag, flag_$)
I.flag.msn : 0
I_flag_lsn = 0
Breaking the frame into pieces
flag_$(l:l) = frame( 1: 1)
call mvbits(flag, 4, 4, I.flag.msn, 0)
call mvbits(flag, 0, 4, I.flag.lsn, 0)
end
subroutine extr.lf(frame,
k
I.counter, I.Chl, I.Ch2, I_Ch3, I_Ch4,
&
I.RA, I_LT, I_V1, I_V2, I.V3, I_T1, I_T2)
implicit none
character*12 frame
Input frame
character*4
counter_$,
Chl_$,
Ch2_$,
Ch3_$,
Ch4_$,
RA_$
Fast counter (character buffer)
Channel 1 (character buffer)
Channel 2 (character buffer)
Channel 3 (character buffer)
Channel 4 (character buffer)
Time (Right Ascension)
character*2
LT_$,
Local T (character buffer)
k
k
k
k
k
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
92
ft
Vl_$,
V2_$,
V3_$,
Tl_$,
T2_$
ft
ft
ft
ft
! -15
! +15
! +5
! Ex.
! Ex.
Volts (character buffer)
Volts (character buffer)
Volts (character buffer)
ADC1 (character buffer)
ADC2 (character buffer)
integer*4
I_counter,
I.Chl,
I.Ch2,
I_Ch3,
I_Ch4,
I_RA
Fast counter
Channel 1
Channel 2
Channel 3
Channel 4
Time (Right Ascension)
integer*2
I.LT,
I.V1,
I.V2,
I.V3,
I.T1,
I_T2
Local temperature
-15 Volts
+15 Volts
+5 Volts
Ex. ADC1
Ex. ADC2
integer*4
counter,
Chi,
Ch2,
Ch3,
Ch4,
RA
Fast counter
Channel 1
Channel 2
Channel 3
Channel 4
Time (Right Ascension)
integer*2
LT,
VI,
V2,
V3,
Tl,
T2
Local temperature
-15 Volts
+15 Volts
+5 Volts
Ex. ADC1
Ex. ADC2
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
equivalence
equivalence
equivalence
equivalence
equivalence
equivalence
equivalence
equivalence
(counter, counter_$)
(Chi, Chl_$)
(Ch2, Ch2.$)
(Ch3, Ch3.$)
(Ch4, Ch4_$)
(RA, RA_$)
(LT, LT_$)
(VI, Vl_$)
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
93
equivalence
equivalence
equivalence
equivalence
(V2,
(V3,
(Tl,
(T2,
V2_$)
V3_$)
Tl_$)
T2_$)
Breaking the frame into pieces
counter_$(l:1) = frame( 4: 4)
counter_$(2:2) = frame( 3: 3)
counter_$(3:3) = frame( 2: 2)
Chl_$(l:1)
Chl_$(2:2)
= frame( 6: 6)
= frame( 5: 5)
Ch2_$(l:l)
Ch2_$(2:2)
= frame( 8: 8)
= frame(7: 7)
Ch3_$(l:l) = frame(10:10)
Ch3_$(2:2) = frame( 9: 9)
Ch4_$(l:1) = frame(12:12)
Ch4_$(2:2) = frame(ll:ll)
HA_$(1:1)
RA_$(2:2)
RA_$(3:3)
RA_$(4:4)
=
=
=
=
frame(16:16)
frame(15:15)
frame(14:14)
frame(13:13)
LT_$(1:1)
Vl_$(l:1)
V2_$(l:l)
V3_$(l:1)
Tl_$(l:l)
T2_$(l:1)
=
=
=
=
=
=
frame(17:17)
frame(18:18)
frame(19:19)
frame(20:20)
frame(21:21)
frame(22:22)
I_counter = counter
I.Chl = Chi
I_Ch2 = Ch2
I_Ch3 = Ch3
I_Ch4 = Ch4
I.RA = RA
I.LT = LT
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94
I.V1
I.V2
I.V3
I.Tl
I.T2
=
=
=
=
=
VI
V2
V3
Tl
T2
end
subroutine extr.sf(frame,
&
counter.s, Chl.s, Ch2_s, Ch3_s, Ch4_s)
implicit none
character*12 frame
Input frame
character*4
counter_$,
Chl.S,
Ch2_$,
Ch3_$,
Ch4_$
Fast counter (character buffer)
Channel 1 (character buffer)
Channel 2 (character buffer)
Channel 3 (character buffer)
Channel 4 (character buffer)
integer*4
counter.s,
Chl.s,
Ch2_s,
Ch3_s,
Ch4_s
Fast counter
Channel 1
Channel 2
Channel 3
Channel 4
integer*4
counter,
Chi,
Ch2,
Ch3,
Ch4
Fast counter
Channel 1
Channel 2
Channel 3
Channel 4
&
&
equivalence
equivalence
equivalence
equivalence
equivalence
(counter, counter_$)
(Chi, Chl_$)
(Ch2, Ch2_$)
(Ch3, Ch3_$)
(Ch4, Ch4_$)
Breaking the frame into pieces
counter_$ (1:1) = frame( 4: 4)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
95
counter_$(2:2) = frame( 3: 3)
counter_$(3:3) = frameC 2: 2)
j
Chl_$(l:l)
Chl_$(2:2)
= frame(6: 6)
= frame(5: 5)
Ch2_$(l:l)
Ch2_$(2:2)
= frame(8: 8)
= frame(7: 7)
I
I
Ch3_$(l:l) = frame(10:10)
Ch3_$(2:2) = frameC 9: 9)
I
Ch4_$(l:1) = frame(12:12)
Ch4_$(2:2) = frame(ll:ll)
I
counter.s = counter
Chl.s = Chi
Ch2_s = Ch2
Ch3_s = Ch3
Ch4_s = Ch4
i
end
This subroutine does a 1st and 2nd harmonic deconvolution
of 4 data channels.
The data, 20 samples per channel, are acquired while the mirror
is moving the beam sinussoidally across the sky.
The phases are set to have all the signal on the cosine
components (a.l and a_2), the sine components (quadrature
(b.l and b_2)) should have virtually zero signal in it.
If you want to speed up this routine you can comment out
all the calculation involving the quad components.
subroutine lck_in(d_counter, f.r, Chi, Ch2, Ch3, Ch4,
&
Phi.l, Phi_2, a_0, a.l, a_2, b.l, b_2)
implicit none
integer*4
&
&
Chi(20),
Ch2(20),
Ch3(20),
! Channel 1 data
! Channel 2 data
! Channel 3 data
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
ft
Ch4(20),
d_counter(20),
ft
ft
! Channel 4 data
! Times tags of the samples
! Loop indices
i> j
real*4
Ch_V(20,4),
a_0(4),
a.l(4),
b.l(4),
a.2(4),
b_2(4),
Phi.1(4),
Phi_2(4),
sin2PifrDt(20,4),
cos2PifrDt(20,4),
sin4PifrDt(20,4),
cos4PifrDt(20,4),
norm,
f-r,
frDt,
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft
ft •
ft
ft
ft
ft
ft
ft
Pi,
TwPi,
FoPi
Data channels (Volts)
DC components
If components
If components (quadrature)
2f componets
2f components (quadrature)
Phases for If computation
Phases for 2f computation
Precalculated sine
and cosine arrays
They speed up the
calculations
Normalization sqrt(2)/20
Reference frequency
fr*Dt
Pi = 3.14159265359
2Pi = 6.28318530718
4Pi = 12.5663706144
Constants
data Pi
/3.14159265359/
data TwPi /6.28318530718/
data FoPi /12.5663706144/
data norm /7.07106781185e-2/
! Pi
! 2*Pi
! 4*Pi
! sqrt(2)/20
Reset variable to zero
do j = 1 , 4
i
a_0(j)
a_l(j)
b.l (j )
a_2(j)
b_2(j)
=
=
=
=
=
0.
0.
o.
0.
0.
j
enddo
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
! Transform du to Volts at DAS
I
do i = 1,20
I
Ch_V(i,l)
Ch_V(i,2)
Ch_V(i,3)
Ch_V(i,4)
=
=
=
=
float(Chi(i)*10)/65535
float(Ch2(i)*10)/65535
float(Ch3(i)*10)/65535
float(Ch4(i)*10)/65535
-5
-5
-5
-5
I
enddo
j
! Calculate sine and cosine arrays
I
do i = 1,20
j
frDt = float(d_counter(i))*f_r
j
do j = 1,4
I
sin2PifrDt(i,j)
cos2PifrDt(i,j)
sin4PifrDt(i,j)
cos4PifrDt(i,j)
=
=
=
=
sin(TwPi*frDt
cos(TwPi*frDt
sin(FoPi*frDt
cos(FoPi*frDt
+
+
+
+
Phi_l(j)/180.*Pi)
Phi_l(j)/180.*Pi)
Phi_2(j)/180.*Pi)
Phi_2(j)/180.*Pi)
i
enddo
enddo
! Calculates lock-in components
do i = 1,20
do j= 1,4
i
a_0(j) = a_0(j) + Ch_V(i,j)
! DC
a_l(j) = a_l(j) + Ch_V(i,j) * cos2PifrDt(i,j) ! Cos If
a_2(j) = a_2(j) + Ch_V(i,j) * cos4PifrDt(i,j) ! Cos 2f
b_l(j) = b_l(j) + Ch_V(i,j) * sin2PifrDt(i,j) ! Sin If
b_2(j ) = b_2(j) + Ch_V(i,j) * sin4PifrDt(i,j) ! Sin 2f
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
enddo
enddo
I
! Normalize components
I
do i=l,4
a_0(i)
a_l(i)
a_2(i)
b_l(i)
b_2(i)
enddo
=
=
=
=
=
a_0(i)/20
a_l(i)*norm
a_2(i)*norm
b_l(i)*norm
b_2(i)*norm
j
end
A .3
B in n in g
program ravgl
! Program fits a straight line to data set in .25 hours
j
implicit none
I
!
i
Structures ------------------------------------include 'TENERIFE.LOC.STRUCT.INC'
include ‘TENERIFE.RVG.STRUCT.INC'
i
record
record
record
record
/header.loc/ in_stat
/data_frame_loc/ in.frame
/header.rvg/ out_stat
/data_frame_rvg/ out_frame
Variables --------------------------------------------integer*4
&
nch,
Inch is the number of channels
no_pts,j
real*8 ra_old,epsilon,
& diff_lf_avg(4),diff_2f_avg(4)
character*40
locamp
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
c h a r a c te r *80
in_dir,
out.dir
logical
not_eof,
tab
k
k
! Initialize variables
data tab/9/ [spacing tab character
in.dir = ’BRIAX4$DKA100:[USERS.CMB.DATA_94.WORK.FILES]'
out_dir=’BRIAX4$DKA100:[USERS.CMB.DATA_94.WORK.FILES]'
type 600
600 format(' Enter input file name (no extension):’$)
accept 601, locamp
601 format (a80)
Open .lob file----------------open(unit=10, file=in_dir//locamp//'.lob',
k
status='old',
k
form='unformatted',
k
recl=2048)
Open .ATM file (data after averaging the ra’s)-----open(unit=12, file=out_dir//locamp//'.rvg',
k
status='new',
k
form=’unformatted',
k
recl=4096)
not_eof =.true.
! Parameters Input
! reading the header and writing to the output file
read(10) in.stat
do j = 1,4
out.stat.gain(j) =
in_stat.gain(j)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
out.stat .calib(j) = in.stat.calib(j)
out.stat.phi.l(j) = in.stat.phi_l(j)
out.stat .phi_2(j) = in.stat.phi_2(j)
enddo
write(12) out_stat
Initialize basic parameters----------------------------no_pts = 1 ! is the counter indicating how many points
! have the same ra
read(10) in_frame
ra_old = in_frame.ra
do nch = 1 , 4
out_frame.diff_avg_lf (nch) = in_frame.Lck_lf (nch)
out .frame, diff_avg_2f (nch) = in.frame.Lck_2f(nch)
enddo
100 do while (not_eof)
101
read(10, err=999) in.frame
epsilon = dabs(in_frame.ra - ra.old)
if (epsilon .It. l.e-6) then
no_pts = no.pts + 1
ra_old = in_frame.ra
do nch =1,4
out .frame.diff_avg_lf (nch) = in_frame.Lck.lf(nch) +
&
out .frame, diff_avg_ If (nch)
out .frame.diff_avg_2f (nch) = in.frame.Lck_2f(nch) +
&
out .frame, diff_avg_2f (nch)
enddo
go to 101
else
do nch =1,4
out .frame.diff.avg.lf (nch) = out.frame.diff_avg_lf(nch)/
&
no.pts
out .frame.diff_avg_2f (nch) = out.frame.diff_avg_2f(nch)/
k
no.pts
enddo
out_frame.ra.avg = ra.old
write(12) out.frame
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
101
do nch = 1 , 4
out_frame.diff.avg_If(nch) = in_frame.Lck_lf(nch)
out.frame.diff_avg_2f(nch) = in.frame.Lck_2f(nch)
enddo
!
no.pts = 1
ra.old = in.frame.ra
I
endif
I
enddo
999 not.eof = .false,
stop
end
program cutoff1
! PROGRAM CALCULATES AVG AND STD DEV FOR 3 SIGMA CUT
I
implicit none
i
Structures -------------------------------------------
!
I
include 'TENERIFE.RVG.STRUCT.INC»
include 'TENERIFE.cut.STRUCT.INC'
I
record
record
record
record
record
record
record
/header.rvg/ in.stat
/data.frame.rvg/ In.frame
/header.cut/ out.stat
/data.frame.cutl/ out.frame1
/data_frame_cut2/ out_frame2
/data_frame_cut/ out.frame
/data_frame_cut3/ out_frame3
Variables -------------------------------------------integer*4 nch,i, Inch is the number of charnels
& no.data,
&
no_good.pts
j
real*8
&
eta,
diff.If(4),
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
102
k
k
k
k
k
k
k
k
k
diff_2f(4),
diff_lf_avg(4),
diff_2f_avg(4),
diff_avg_lf(4),
diff_avg_2f(4),
diff_lf_sqsum(4),
diff_2f_sqsum(4),
diff_lf_sig(4),
diff_2f_sig(4)
character*40 locamp
character*15 total_no_data
character*20 points_after_cutoff
character*80
in_dir,
k
out_dir
logical
k tab
not_eof,
data tab/9/ (spacing tab character
Initialize variables
in.dir = 1BRIAX4$DKA100:[USERS.CMB.DATA.94.WQRK_FILES] 1
out_dir='BRIAX4$DKA100:[USERS.CMB.DATA.94.H0RK_FILES] ’
I
type 600
600 format(J Enter input file name (no extension):’$)
accept 601, locamp
601 format (a80)
i
type 700
700 format(' Enter the cutoff level (a number format fl0.1):’$)
accept 701, eta
701 format (F10.1)
j
k
k
k
open(unit=10, file=in_dir//locamp//'.rvg',
status=’old',
form55'unformatted’,
readonly)
j
! Open .VLK file (data after lock-in statistics)----------
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
103
open(unit=12, file=out_dir//locamp//'.cut',
&
status='new’,
&
form=’unformatted',
&
recl=2048)
Read and write the header of the file--------read(10) in.stat
do nch = 1,4
out.stat.gain(nch)
out.stat.calib(nch)
out.stat.phi.1(nch)
out.stat.phi_2(nch)
out.stat.bin.size
enddo
out.stat.eta
write (12) out.stat
=
=
=
=
=
in.stat.gain(nch)
in.stat.calib(nch)
in.stat .phi.1(nch)
in.stat .phi_2(nch)
in.stat.bin.size
= eta
Initialize basic parameters---do nch =1,4
diff.lf.avg(nch) = O.dO
diff_2f_avg(nch) = O.dO
diff_lf_sqsum(nch) = O.dO
diff_2f_sqsum(nch) = O.dO
enddo
!average value in a bin
!sum of the squares in a
!bin
no.data = 0
!counter for the number of points
!in a file
no.good.pts = 0 '.counter for pts lying below eta*sig
not.eof = .true.
read the value of right ascension, the vax lock in files
for the four ----------------------------------------do while (not.eof)
read(10, err=888) in.frame
no.data = no.data + 1
do nch = 1,4
diff.lf(nch) = in_frame.diff_avg.lf(nch)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
104
dif f _2f (nch) = in.frame.diff_avg_2f(nch)
diff.lf.avg(nch) =
diff_2f_avg(nch) =
diff_lf_avg(nch) + diff_lf(nch)
diff_2f_avg(nch) + diff_2f(nch)
diff.lf.sqsum(nch) = diff_lf_sqsum(nch) +
diff.lf(nch)**2
diff_2f_sqsum(nch) = diff_2f.sqsum(nch) +
&
diff_2f(nch)**2
enddo
enddo
&
888 out_framel.no.data = no.data
WRITE(12) OUT.FRAME1
to calculate the average of the vax diff files
do nch =1,4
diff.lf.avg(nch)
diff_2f_avg(nch)
= diff.lf.avg(nch) /no.data
= diff_2f.avg(nch) /no.data
to calculate the std dev of the vax diff fliesdiff.lf.sig(nch) = DSQRT((DABS((diff_lf_sqsum(nch)
&
no_data*diff_lf_avg(nch)**2)/(no_data-l))))
diff_2f_sig(nch) = DSQRT((DABS((diff_2f_sqsum(nch) &
no_data*diff_2f.avg(nch)**2)/(no.data-1))))
enddo
closing the file .csp so that it can be opened again for checking
spikes
close(lO)
Write to the new file the averages and sigmas of the channels
to be used in a later program----------------------------------do nch = 1 , 4
out_frame2.diff_lf_avg(nch)
out_frame2.diff_2f_avg(nch)
out_frame2.diff_lf_sig(nch)
out_frame2.diff_2f_sig(nch)
=
=
=
=
diff .lf.avg(nch)
diff_2f_avg(nch)
diff.lf.sig(nch)
diff _2f_sig(nch)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105
enddo
write(12) out_frame2
to check whether the data lie outside the eta*sigma cutoff—
open(unit=10, file=in_dir//locamp//’.rvg’,
k
status=’old *,
k
form55'unformatted’,
k
readonly)
read(10) in.stat
do while (not.eof)
777
read(10, err=999) in.frame
out .frame, cut _ra = in.frame.ra.avg
if (dabs(in.frame.diff.avg.If(4) - diff_lf_avg(4)) .It.
k
eta*diff_lf_sig(4)) then
if (dabs(in.frame.diff.avg.lf(3) - diff.lf_avg(3)) .It.
k
eta*diff_lf_sig(3)) then
if (dabs(in.frame.diff.avg.lf(2) - diff_lf_avg(2)) .It.
k
eta*diff_lf_sig(2)) then
if (dabs(in.frame.diff.avg.lf(1) - diff.lf.avg(l)) .It.
k
eta*diff_lf.sig(l)) then
if (dabs(in.frame.diff_avg_2f(4) - diff_2f_avg(4)) .It.
k
eta*diff_2f_sig(4)) then
if (dabs(in.frame.diff_avg_2f(3) - diff_2f_avg(3)) .It.
k
eta*diff_2f_sig(3)) then
if (dabs(in.frame.diff_avg_2f(2) - diff_2f_avg(2)) .It.
k
eta*diff.2f_sig(2)) then
if (dabs(in.frame.diff_avg_2f(l) - diff_2f_avg(l)) .It.
k
eta*diff_2f_sig(l)) then
do nch = 1 , 4
out.frame.diff.If(nch) = in.frame.diff.avg.If(nch)
out.frame.diff_2f(nch) = in.frame.diff_avg_2f(nch)
enddo
write(12) out.frame
no_good_pts = no.good.pts + 1
else
go to 777
endif
endif
endif
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
106
endif
endif
endif
endif
endif
enddo
j
999 not.eof = .false.
out_frame3.no_good.pts = no_good_pts
write(12) out_frame3
stop
end
A.4
Atmosphere Subtraction
program atm8
! Program fits a straight line to the sum and difference of
! 2 channels (1&4,2&4,3&4) and uses the slope and zero intercept
! as a basis for atmospheric noise subtraction. The results are
! saved in the .atm files. The program also finds the average
! value of the data points and sends the results to the .nar
! files for later comparison to judge the success of the
! atmospheric subtraction. Last modified 12-1-95.
j
implicit none
j
!
I
Structures --------------------------------------------include ’TENERIFE.CUT.STRUCT.INC»
include 'TENERIFE.ATM5.STRUCT.INC ’
i
record
record
record
record
record
record
record
record
record
record
/header.cut/ in.stat
/data.frame.cutl/ in.framel
/data_frame_cut2/ in_frame2
/data.frame.cut/ in.frame
/data_frame_cut3/ in_frame3
/header.atm/ out.stat
/data.frame.atml/ out.framel
/data_frame_atm2/ out_frame2
/data.frame.atm/ out.frame
/data_frame_atm3/ out_frame3
I
!
Variables ----------------------------------------------
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
107
integer*4
4
k
nch,
j,n,counter,
begin.counter
Inch is the number of channels
Icounts points in each bin
real*8 bw,ra,
k
ra.start, ra_end,
4
ra_atm(2000),
4 atm.If(2000,4),atm_2f(2000,4),
4 cut_lf_avg(4),cut_2f_avg(4),
4 cut_lf_sig(4),cut_2f_sig(4),
4
hsum.lf(2000),hsum_2f(2000),
4
hdiff _lf (2000), hdiff_2f (2000),
4 hsig_If(2000),hsig_2f(2000),
4 msig.lf(2000),msig_2f(2000),
4 lsig_lf(2000),lsig_2f(2000),
4 hint.lf,hslope_lf,
4
hint.sig.lf ,hslope_sig_lf,
4 hmwt.lf,hchi2_lf,hq_lf,
4 hint_2f,hslope_2f,
4
hint_sig_2f,hslope_sig_2f,
4 hmwt_2f,hchi2_2f,hq_2f,
4
hatt.lf, hatt_2f,
4
hsky.lf, hsky_2f,
4
msum.lf(2000),msum_2f(2000) ,
4
mdiff _ If (2000 ),mdiff.2f (2000),
4 mint.lf,mslope_lf,
4
mint_sig_lf,mslope_sig_lf,
4 mmwt.lf,mchi2_lf,mq_lf,
4 mint_2f,mslope_2f,
4
mint_sig_2f,mslope_sig_2f,
4 mmwt_2f,mchi2_2f ,mq_2f,
4
matt.If, matt_2f,
4
msky.lf, msky_2f,
4
lsum.lf(2000),lsum_2f(2000) ,
4
ldiff.lf (2000) ,ldiff_2f (2000) ,
4 lint.lf,lslope_lf,
4
lint.sig.lf,lslope_sig_lf,
4 lmwt.lf,lchi2_lf,lq_lf,
4 lint_2f,lslope_2f,
4
lint_sig_2f,lslope_sig_2f,
4 lmwt_2f,lchi2_2f,lq_2f,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
108
k
k
k
k
k
k
k
k
k
k
latt.lf, latt_2f,
lsky.lf, lsky_2f,
hsky_sig_lf,hsky_sig_2f,
msky_sig_lf,msky_sig_2f,
lsky_sig_lf,lsky_sig_2f,
hatt_sig_lf,hatt_sig_2f,
matt_sig_lf,matt_sig_2f,
latt_sig_lf,latt_sig_2f,
Avg.lf(4),Avg_2f(4) ,
Sig.lf(4),Sig_2f(4)
character*40
character*20
character*25
character*80
k
locamp
atmosphere.removal
bin.width_for_lineax.fit
in.dir,
out.dir
i
logical
k
not.eof,
tab
i
data tab/9/
Initialize variables
in.dir =' BRIAX4$DKA100:[USERS.CMB.DATA.94.WORK.FILES] »
out_dir=1BRIAX4$DKA100:[USERS.CMB.DATA.94.WORK.FILES] J
I
counter = 0
begin.counter = 0
not.eof =.true.
do nch=l,4
Avg.lf(nch)=0.
Avg_2f(nch)=0
Sig.lf(nch)=0
Sig_2f(nch)=0
enddo
type 600
600 format(' Enter input file name (no extension):^)
accept 601, locamp
601 format (a80)
I
! Open .cut file (data after 3 sigma c u t ) -----------------
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
109
open(unit=10, file=in_dir//locamp//’.cut’,
&
status='old’,
Sc
form=’unformatted’,
Sc
recl=2048)
Open .ATM file (data after removal of atmospheric drift)open(unit=12, file=out_dir//locamp//’.atm’,
Sc
status=’new’,
Sc
form='unformatted’,
Sc
recl=4096)
Open .nar file (data in bins with no atmosphere removal)
open(unit=14, file=out_dir//locamp//’.nar’,
Sc
status=’new’,
&
form=’unformatted’,
Sc
recl=4096)
Get bin size
700
type 700
format (' Enter the value of the bin width in hours: ’,$)
accept *, bw
reading the header and writing to the output files---------read(10) in.stat
out.stat.bin.size = bw
write(12) out.stat
write(14) out.stat
read(10) in.framel
out.framel.no.data = in.framel.no.data
write(12) out.framel
write(14) out.framel
Reading the offsets and standard deviations for all channels
and writing them to the output files
read(10) in_frame2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
110
do nch = 1,4
cut_lf_avg(nch) = in.frame2.diff.If_avg(nch)
cut_2f_avg(nch) = in.frame2.diff_2f_avg(nch)
cut.lf.sig(nch) = in.frame2.diff.If_sig(nch)
cut_2f_sig(nch) = in.frame2.diff_2f_sig(nch)
out_frame2.cut.lf_avg(nch) = cut.lf .avg(nch)
out_frame2.cut_2f_avg(nch) = cut_2f_avg(nch)
out_frame2.cut.lf_sig(nch) = cut.lf.sig(nch)
out_frame2.cut_2f_sig(nch) = cut_2f_sig(nch)
enddo
write(12) out_frame2
write(14) out_frame2
Begin Main Loop
100 do while (not.eof)
If this is the first loop then set the start to be an integer
multiple of the bin width
if (begin.counter .eq. 0) then
read(10, err=999) in.frame
n
= jidint(in.frame.cut_ra/bw)
ra.start = n * bw
ra.end
= ra.start + bw
begin.counter = 1
end if
Advance to the beginning of the first loop
do while (in.frame.cut.ra.le.ra.start)
read(10, err=999) in.frame
enddo
Read the bin in
do while (in.frame.cut_ra .le. (ra.end) .and.
&
in.f rame.cut.ra .gt. ra.start)
counter = counter + 1
ra.atm(counter) = in.frame.cut.ra
do nch =1,4
atm.If(counter,nch) = in.frame.diff_If(nch)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ill
atm_2f (counter,nch) = in.frame.diff_2f(nch)
Avg.lf(nch)
= Avg_lf(nch) + atm.If(counter,nch)
Avg_2f(nch)
= Avg_2f(nch) + atm_2f(counter,nch)
Sig.lf(nch)
= Sig.lf(nch) + atm.lf(counter,nch)**2
Sig_2f(nch)
=Sig_2f(nch) + atm_2f(counter,nch)**2
enddo
read (10,err=999) in_frame
enddo
i
!
!
!
!
i
If a bin has more than nine points then evaluate the
atmospheric subtraction,
Calculating the sum and difference of the high(h) ch4+/-ch3,
medium(m) ch4 +/-ch2 and low(l) ch4 +/- chi channels
if (counter.gt.5) then
do j = 1, counter
h s u m .lf ( j ) = a tm . I f (
h d i f f . l f ( j ) = a tm . I f (;
h su m _ 2 f(j) = atm _2f (;
h d i f f _ 2 f (j ) = atm _2 f (;
msum_If( j ) s a tm . I f (;
m d i f f . l f ( j ) = a tm . I f (;
msum_2f( j ) = atm _2f (,
m d i f f _ 2 f (j ) = atm _2f (;
1s u m . I f ( j ) = a tm . I f (,
l d i f f . l f ( j ) = a tm . I f (;
l s u m _ 2 f ( j) = atm _2f (;
l d i f f _ 2 f (j ) = atm _2f (,
enddo
222
,4)
,4)
,4)
,4)
,4)
,4)
,4)
,4)
,4)
,4)
,4)
,4)
+ a tm .If(
a tm . I f (;
+ atm_2f (;
- a tm _ 2 f(
+ a tm . I f (;
- a tm . I f (;
+ atm_2f (.
atm _2f (;
+ a tm .If(
a tm . I f (;
+ atm_2f (;
atm_2f (;
,3 )
,3 )
,3 )
,3)
,2 )
,2 )
,2)
,2 )
,1)
,1 )
,1)
,1 )
Find a linear fit for each sum and difference
&
k
CALL FITl(hdiff_lf, hsum_lf, counter,
hint.lf, hslope.lf, hint_sig_lf, hslope_sig_lf,
hchi2.1f)
k
k
CALL FITl(hdiff_2f, hsum_2f, counter,
hint_2f, hslope_2f, hint_sig_2f, hslope_sig_2f,
hchi2_2f)
k
CALL FITl(mdiff_lf, msum_lf, counter,
mint.lf, mslope.lf, mint_sig_lf, mslope_sig_lf,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
&
mchi2_lf)
&
&
CALL FIT1(mdiff_2f, msum_2f, counter,
mint_2f, mslope_2f, mint_sig_2f, mslope_sig_2f,
mchi2_2f)
&
&
CALL FITl(ldiff_lf, lsum.lf, counter,
lint.lf, lslope_lf, lint_sig_lf, lslope_sig_lf,
lchi2_lf)
&
&
CALL FITl(ldiff_2f, lsum_2f, counter,
lint_2f, lslope_2f, lint_sig_2f, lslope_sig_2f,
lchi2_2f)
Find the atmospheric attenuation factor from the linear fits
hatt.lf =
hatt_2f =
(1 + hslope_lf)/(hslope_lf - 1)
(1 + hslope_2f)/(hslope_2f - 1)
matt.lf =
matt_2f =
(1 + mslope_lf)/(mslope_lf - 1)
(1 + mslope_2f)/(mslope_2f - 1)
latt.lf =
latt_2f =
(1 +
(1 +
lslope_lf)/(lslope_lf - 1)
lslope_2f)/(lslope_2f - 1)
Find the result of the atmospheric subtraction
&
&
&
&
&
&
lsky.lf = (lint_lf/2) C(latt_lf*cut_lf_avg(l)-cut_lf_avg(4))/(latt_lf - 1
lsky_2f = (lint_2f/2) ((latt_2f*cut_2f_avg(l)-cut_2f_avg(4))/(latt_2f - 1
msky.lf = (mint_lf/2) ((matt_lf*cut_lf_avg(2)-cut_lf_avg(4))/(matt_lf
msky_2f = (mint_2f/2) ((matt_2f*cut_2f_avg(2)-cut_2f_avg(4))/(matt_2f
-1
-1
hsky.lf = (hint_If/2) ((hatt_lf*cut_lf_avg(3)-cut_lf_avg(4))/(hatt_lf - 1
hsky_2f = (hint_2f/2) ((hatt_2f*cut_2f_avg(3)-cut_2f_avg(4))/(hatt_2f - 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
! Find the atmospheric attenuation error bars
I
hatt_sig_lf = 2*hslope_sig_lf/((hslope_lf-l)**2)
hatt_sig_2f = 2*hslope_sig_2f/((hslope_2f-l)**2)
I
matt_sig_lf = 2*mslope_sig_lf/((mslope_lf-l)**2)
matt_sig_2f = 2*mslope_sig_2f/((mslope_2f-l)**2)
i
latt.sig.lf = 2*lslope_sig_lf/((lslope_lf-l)**2)
latt_sig_2f = 2*lslope_sig_2f/((lslope_2f-l)**2)
Find the error bars on the data after atmospheric subtraction
k
k
k
k
hsky_sig_lf = dsqrt((hint_sig_lf**2/4.d0) +
((cut_lf_avg(3) - cut_lf_avg(4))*hatt_sig_lf
/(hatt_lf-l)**2)**2)
hsky_sig_2f = dsqrt((hint _sig_2f**2/4.dO) +
((cut_2f_avg(3) - cut_2f_avg(4))*hatt_sig_2f
/(hatt_2f-l)**2)**2)
i
k
k
k
k
k
k
k
k
msky_sig_lf = dsqrt((mint_sig_lf**2/4.d0) +
(Ccut_lf_avg(2) - cut_lf_avg(4))*matt_sig_lf
/(matt_lf-l)**2)**2)
msky_sig_2f = dsqrt( (mint _sig_2f**2/4. dO) +
((cut_2f_avg(2) - cut_2f_avg(4))*matt_sig_2f
/(matt_2f-l)**2)**2)
lsky_sig_lf = dsqrt((lint_sig_lf**2/4.d0) +
((cut_lf_avg(l) - cut_lf_avg(4))*latt_sig_lf
/(latt_lf-l)**2)**2)
lsky_sig_2f = dsqrt( (lint _sig_2f**2/4. dO) +
((cut_2f_avg(l) - cut_2f_avg(4))*latt_sig_2f
/(latt_2f-l)**2)**2)
Put all results into the output format for .atm files.
out_frame.hsky_lf = hsky.lf
out_frame.hsky_2f = hsky_2f
out_frame.hatt_lf = hatt.lf
out_frame.hatt_2f = hatt_2f
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
out_frame.hsky_sig_2f = hsky_sig_2f
out_frame.hsky_sig.lf = hsky_sig_lf
i
out_frame.hatt_sig_lf = hatt_sig_lf
out_frame.hatt_sig_2f = hatt_sig_2f
I
out.frame.msky.if = msky.lf
out_frame.msky_2f = msky_2f
I
out.frame.msky_sig_lf = msky_sig_lf
out_frame.msky_sig_2f = msky_sig_2f
j
out.frame.matt.If = matt.lf
out.frame.matt_2f = matt_2f
I
out_frame.matt_sig_lf = matt_sig_lf
out_frame.matt_sig_2f = matt_sig_2f
j
out.frame.lsky.lf = lsky.lf
out.frame.lsky_2f = lsky_2f
I
out_frame.lsky_sig.lf = lsky_sig_lf
out_frame.lsky_sig_2f = lsky_sig_2f
j
out.frame.latt.lf = latt.lf
out_frame.latt_2f = latt_2f
j
out_frame.latt_sig_lf = latt_sig_lf
out.frame.latt_sig_2f = latt_sig_2f
I
ra = (ra_start + ra_end)/2.d0
out.frame.ra = ra
i
write(12) out.frame
! Find the averages and the error bars for the data without the
! atmospheric subtraction
do nch = 1,4
Avg.lf(nch) = Avg_lf(nch)/counter
Avg_2f(nch) = Avg_2f(nch)/counter
Sig.lf(nch) = dsqrt((Sig_lf(nch)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
115
&
&
-counter*Avg_lf(nch)**2)/(counter-1))
Sig_2f(nch) = dsqrt((Sig_2f(nch)
-counter*Avg_2f(nch)**2)/(counter-1))
enddo
Put the output into appropriate format. The format is identical
to the format for the .atm files to facilitate later comparison.
Channel 4 is written to all of the attenuation variables since
it is used to do the atmospheric subtraction.
out.frame.lsky.lf = Avg_lf(l)
out_frame.lsky_2f * Avg_2f(l)
out.frame.msky.lf = Avg_lf(2)
out_frame.msky_2f = Avg_2f(2)
out_frame.hsky.lf = Avg_lf(3)
out_frame.hsky_2f = Avg_2f(3)
out.frame.latt.lf = Avg_lf(4)
out_frame.latt_2f = Avg_2f(4)
out.frame.matt.If = Avg_lf(4)
out.frame.matt_2f = Avg_2f(4)
out.frame.hatt.If = Avg_lf(4)
out_frame.hatt_2f = Avg_2f(4)
out.frame.lsky_sig_lf = Sig.lf(l)
out_frame.lsky_sig_2f = Sig_2f(l)
out_frame.msky_sig_lf = Sig_lf(2)
out_frame.msky_sig_2f = Sig_2f(2)
out_frame.hsky_sig_lf = Sig_lf(3)
out_frame.hsky_sig_2f = Sig_2f(3)
out_frame.latt_sig_lf = Sig_lf(4)
out_frame.latt_sig_2f = Sig_2f(4)
out_frame.matt_sig_lf = Sig_lf(4)
out_frame.matt_sig_2f = Sig_2f(4)
out_frame.hatt.sig_If = Sig_lf(4)
out .frame, hatt _sig_2f = Sig_2f(4)
write(14) out.frame
endif
Reset all of the variables to do the next bin.
Remember the first point has already been read.
counter = 1
ra.atm(counter) = in.frame.cut.ra
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
do nch =1,4
atm.lf(counter,nch) = in_frame.diff_lf(nch)
atm_2f(counter,nch) = in_frame.diff_2f(nch)
Avg.lf(nch) = atm_If (counter,nch)
Avg_2f(nch) = atm_2f(counter,nch)
Sig_lf(nch) = atm_lf(counter,nch)**2
Sig_2f(nch) = atm_2f(counter,nch)**2
enddo
write (5,*) in_frame.cut_ra,ra_start ,ra_end
ra_start = ra_end
ra_end = ra_start + bw
if (ra.end .gt. 24.dO) then
ra_start = O.dO
ra_end
= bw
endif
enddo
j
! End of main loop
I
999 not_eof = .false.
close(lO)
close(12)
close(14)
stop
end
j
! Include files---------------------------------------------i
include 'fitl.for'
A .5
!
!
!
!
!
!
!
!
!
!
D a ta R e je ctio n
Program Slider
This program looks at the fluctuations in a user determined
block of data. It looks at the data with the atmosphere
subtraction. The program compares that to a preset expected
level of noise which is comparable in magnatude to detector
noise. If the selected bit is less than the expected noise
then that data is written out to the output file (.acc).
If it is not, a zero is written to that portion
of the output file. A log file is kept at .acl which
writes the RA and the number of positive readings as the
block slides over the data point. The data output file is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
recorded in the same format as the .atm files. A zero
written to any data in the file indicates that data is
unacceptable or irrelavent. The program accepts a data file
of files to be processed. The program also removes data
known to be bad due to hardware failures, i.e. bolometers
warming up. The block of data slides through the data 1
data point at a time.
Jon Nicholas. February 20, 1996
Program changed to get data from .nar files and output to
.nac files.
Jon Nicholas. February 26, 1996
implicit none
Structures ----------------------------------------------include 'TENERIFE.ATM5.STRUCT.INC'
record /header.ATM/ in.stat
record /header.atm/ out_stat
record /data_frame_atm/ atmdat
record /data_frame_atm/ nardat
record /data_frame_atm/ output
Variables ---------------------------------------------character*80
character*40
real*8
k
k
k
k
k
k
in.dir, out_dir
in.file, rfile,
dum
RA(500,2),
S(500,3,2,2),E(500,3,2,2), ! Signal and Error
KA(500,3,2),EK(500,3,2),
! Attenuation and Error
noise(3,2),sigma,
! Expected Max Noise
division,ra_start,ra_end,
sigatm(3,2,2), avgatm(3,2,2),
rise,set,date,rra,sra
i
logical
not_eof,
tab
integer*4
nch,i,j,k,f,counter, accept(500,3,2,2),
begin,n,filen,numfil,size,1,
yy,ml,dd,hh,m2,time
k
i
k
k
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
! Parameters ----------------------------------------------I
data tab/9/
! Spacing Tab character
i
! Initialize basic parameters ----------------------------I
not.eof
= .true.
noise(l,1) = 0.40
noise(2,l) = 0.35
noise(3,1) = 0.50
noise(l,2) = 0.30
noise(2,2) = 0.25
noise(3,2) =0.50
I
! Inputs ------------------------------------------------j
600
601
type 600
format (' Enter input file (no extension): ',$)
accept 601, in_file
format (A40)
I
602
type 602
format (' Enter division size (hours): ',$)
accept *, division
I
in_dir = 'BRIAX4$dkal00: [users.cmb.data_94.work_files.all_32] ’
out_dir='BRIAX4$dkal00: [users.cmb.data_94.work_files.all_32] '
;
! Open 1/0 files -------------------------------------------i
k
k
603
open(unit=14, file =in_dir//in_file//'.mrg',
status = ’old',
form = Jformatted')
read(14,603) numfil
format (i4)
do filen=l,numfil
counter = 0
begin = 0
do nch=l,3
do f=l ,2
do n=l,2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
119
604
&
&
&
avgatm(nch,f,n) = 0 . 0
sigatm(nch,f,n) = 0 . 0
enddo
enddo
enddo
read (14,601) rfile
write ( 6 , * ) rfile
read (rfile,604) dum,yy,ml,dd,hh,m2
format (al,5(i2))
date = 6*ml+dd
rise = 482-52*cos(0.0174532*(date-201))
set = 1210+56*cos(0.0174532*(date-201))
time = hh.*60+m2
open(unit=10, file =in_dir//rfile//’.nar’,
status = ’old’,
form
='unformatted’,
reel
= 2048)
j
open(unit=ll, file
=in_dir//rfile//’.atm',
&
status ='old’,
&
form
= ’unformatted’,
&
reel
= 2048)
i
&
&
&
open(unit=12, file
= out_dir//rfile//’.ace’,
status ='new’,
form
= ’unformatted’ ,
reel
= 2048)
I
open(unit=13, file
= out_dir//rfile//’.acl’,
&
status = ’new’,
&
form
= ’formatted’,
&
reel
= 2048)
j
&
&
&
open(unit=15, file = out_dir//rfile//’.ncr’,
status = ’new’,
form
= ’unformatted',
reel
= 2048)
Read/write HEADER
read(10), in.stat
out_stat = in_stat
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
120
read(ll), out.stat
write(12) out_stat
write(15) out_stat
write(13,100) ’R A ’,tab,'chl.lf',tab,'chl_2f',
&
tab,'ch2_lf’ ,tab,'ch2_2f',
&
tab,1ch3_lf’,tab,*ch3_2f'
100 format(a3,6(al,a6))
Main loop
do while (not.eof)
read(10,err=999) nardat
read(ll,err=999) atmdat
counter=counter+l
! Store the data
RA(counter,l) = atmdat.ra
! Shift low RA data to 24+ hours
if (RA(counter,1).It.6.0) then
RA(counter,1)=RA(counter,1)+24.0
endif
S(counter,1,1,1 = atmdat.lsky.lf
S(counter,2,1,1 = atmdat .msky_If
S(counter,3,1,1 = atmdat.hsky_If
S(counter,1,2,1 = atmdat.lsky_2f
S(counter,2,2,1 = atmdat .msky_2f
S(counter,3,2,1 = atmdat .hsky_2f
E(counter,1,1,1 = atmdat.lsky.sig.If
E(counter,2,1,1 = atmdat.msky.sig.If
E(counter,3,1,1 = atmdat.hsky_sig_If
E(counter,1,2,1 = atmdat .lsky_sig_2f
E(counter,2,2,1 = atmdat.msky_sig_2f
E(counter,3,2,1 = atmdat.hsky_sig_2f
KA(counter,1,1) : atmdat.latt_If
KA(counter,2,1) = atmdat.matt.If
KA(counter,3,1) s atmdat.hatt.If
KA(counter,1,2) : atmdat.latt_2f
KA(counter,2,2) = atmdat.matt_2f
KA(counter,3,2) = atmdat.hatt_2f
EK(counter,1,1) = atmdat.latt.sig.lf
EK(counter,2,1) = atmdat.matt.sig.If
EK(counter,3,1) = atmdat.hatt.sig.lf
EK(counter,1,2) = atmdat.latt_sig_2f
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
121
EK(counter,2,2) = atmdat.matt_sig_2f
EK(counter,3,2) = atmdat.hatt_sig_2f
! Clear the accept counters
do nch=l,3
do f=l,2
do n=l,2
accept(counter,nch,f ,n) = 0
enddo
enddo
enddo
RA(counter,2) = nardat.ra
if (RA(counter,2) .It.6.0) then
RA (counter,2) = RA(counter,2)+6.0
endif
S(counter,1,1,2 = nardat.lsky.lf
S(counter,2,1,2 = nardat.msky_If
S(counter,3,1,2 = nardat.hsky_If
S(counter,1,2,2 = nardat.lsky_2f
S(counter,2,2,2 = nardat.msky_2f
S(counter,3,2,2 = nardat.hsky_2f
E(counter,1,1,2 = nardat.lsky_sig_lf
E(counter,2,1,2 = nardat.msky_sig_lf
E(counter,3,1,2 = nardat.hsky_sig_If
E(counter,1,2,2 = nardat.lsky_sig_2f
E(counter,2,2,2 = nardat.msky_sig_2f
E(counter,3,2,2 = nardat.hskv_sie_2f
enddo
999 continue
j
! Analyze the data
i
ra_start=RA(l,1)
ra_end=ra_start+division
do i=l,counter
! Do the first block
if (begin.eq.O) then
do nch=l,3
do f=1,2
do n=l,2
avgat m (nch,f ,n)=avgatm (nch,f,n)+S(i,nch,f,n)
sigatm(nch,f ,n)=sigatm(nch,f ,n) +
&
S(i,nch,f,n)*S(i,nch,f,n)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122
&
&
&
&
&
enddo
enddo
enddo
if (RA(i,l).ge.ra.end) then
rra=rise-time+ra_start*60
if (rra.lt.360.0) then
rra=rra+1440.0
endif
if (rra.gt.1800.0) then
rra=rra-1440.0
endif
sra=set—time+ra_start*60
if (sra.lt.360.0) then
sra=sra+1440.0
endif
if (sra.gt.1800.0) then
sra=sra-1440.0
endif
begin = 1
size = i-1
do nch=l,3
do f=1,2
do n=l,2
avgatm(nch,f ,n) =avgatm (nch,f ,n)-S(i ,nch,f ,n)
sigatm(nch,f ,n)=sigatm(nch,f ,n) S(i,nch,f,n)*S(i,nch,f,n)
sigma= (sigatm(nch,f ,n) -avgatm(nch,f ,n) *
avgatm(nch,f,n)/size)/(size-l)
sigma=dsqrt (sigma)
if (sigma.le.noise(nch,f)) then
do 1=1,size
accept(1,nch,f ,n)=accept(1,nch,f ,n)+1
enddo
endif
avgatm (nch,f ,n) =avgatm (nch,f ,n) -S (1, nch,f ,n)
+S(i,nch,f,n)
sigatm(nch,f ,n) =sigatm (nch,f ,n) -S (1 ,nch,f ,n) *
S(l,nch,f ,n)+S(i,nch,f ,n)*S(i ,nch,f ,n)
sigma=dsqrt ((sigatm (nch,f ,n) -avgatm (nch,f ,n) *
avgatm(nch,f,n)/size)/ (size-1))
if (sigma.le.noise(nch,f)) then
do 1=2,i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
123
accept(1,nch,f ,n)=accept(1,nch,f ,n)+1
enddo
endif
enddo
enddo
enddo
endif
else
do nch=l,3
do f=l,2
do n=l,2
avgatm (nch,f ,n) =avgatm (nch,f ,n)-S((i-size),nch,f ,n)
k
+S(i,nch,f,n)
sigatm(nch,f ,n)=sigatm(nch,f ,n) -S ((i-size),nch,f ,n) *
k
S((i-size) ,nch,f,n)+S(i,nch,f,n)*S(i,nch,f,n)
sigma=dsqrt ((sigatm (nch,f ,n) -avgatm (nch,f ,n)*
k
avgatm(nch,f ,n)/s ize)/(size-1))
if (sigma.le.noise(nch.f)) then
do l=(i-size+l),i
accept (1, nch,f ,n) =accept (1, nch,f ,n)+1
enddo
endif
enddo
enddo
enddo
endif
enddo
Temporary section to write out data without atmospheric subtraction
for all data selected. January 12, 1996
else
do i=l,counter
S(i,j,k,l) = S(i,j,k,2)
E(i,j,k,1) = E(i,j,k,2)
KA(i,j,k) * 0.0
EK(i,j ,k) = 0.0
enddo
End of temporary section
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
! Remove data when bolometers warmed up.
i
if (rfile.eq.»H9406111829') then
do i=l,counter
if ((RA(i,l) .gt.19.0).or.(RA(i,l).It.6.0)) then
do nch=l,3
do f=l ,2
do n=l,2
S(i,nch,f,n) = 0.0
E(i,nch,f,n) = 0.0
enddo
enddo
enddo
endif
enddo
endif
if (rfile.eq. 'H9406142143') then
do i=l,counter
if ((RA(i,l) .gt.17.25).or.(RA(i,l).It.6.0)) then
do nch=l,3
do f=l,2
do n=l,2
S(i,nch,f,n) =0.0
E(i,nch,f,n) = 0.0
enddo
enddo
enddo
endif
enddo
endif
if (rfile.eq.’H9406222042') then
do i=l,counter
if ((RA(i, 1) .gt.25.75).or.(RA(i,1).lt.6.0)) then
do nch=l,3
do f=l,2
do n=l,2
S(i,nch,f,n) =0. 0
E(i,nch,f,n) = 0.0
enddo
enddo
enddo
endif
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
enddo
endif
if (rfile.eq.’H9406252025’) then
do i=l,counter
if ((RA(i,l).gt.16.75).or.(RA(i,l)-lt.6.0)) then
do nch=l,3
do f=1,2
do n=l,2
S(i,nch,f,n) = 0 . 0
E(i,nch,f,n) = 0.0
enddo
enddo
enddo
endif
enddo
endif
if (rfile.eq.’H9406290151') then
do i=l,counter
if ((RA(i,l) .gt.20.5) .or. (RA(i,l) .lt.6.0)) then
do nch=l,3
do f=l,2
do n=l,2
S(i,nch,f,n) = 0.0
E(i,nch,f,n) = 0.0
enddo
enddo
enddo
endif
enddo
endif
if (rfile.eq.'H9407162229') then
do i=l,counter
if ((RA(i,l) -gt.23.5) .or. (RA(i,l) .lt.6.0)) then
do nch=l,3
do f=l,2
do n=l,2
S(i,nch,f,n) = 0.0
E(i,nch,f,n) = 0.0
enddo
enddo
enddo
endif
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
126
enddo
endif
Remove known bad data from channel 2.
&
if ((rfile.eq.’H9406262040’).or.(rfile.eq. 'H9406272233') .or.
(rfile.eq.'H9406282017').or.(rfile.eq.,H9406290151’))then
do i=l,counter
do f=l,2
do n=l,2
S(i,2,f,n) = 0.0
E(i,2,f,n) = 0.0
enddo
enddo
enddo
endif
if (rfile.eq.’H9406242103’) then
do i=l,counter
if ((RA(i,1).gt.14.5).and.(RA(i,1).It.18.7)) then
do f=l,2
do n=l,2
S(i,2,f,n) = 0.0
E(i,2,f,n) = 0.0
enddo
enddo
endif
enddo
endif
Remove data above the threshold
do i=l,counter
do nch=l,3
do f - 1 , 2
do n=l,2
if (accept(i,nch,f,n).eq.0) then
S(i,nch,f,n) = 0.0
E(i,nch,f,n) = 0.0
endif
enddo
enddo
enddo
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
127
! Remove sunrise and sunset
if ((((RA(i,l)*60-rra).It.60.0).and.
&
((RA(i,l)*60-rra) .gt.-30.0))
&
.or.(((RA(i,l)*60-sra).It.60.0)
&
.and.((RA(i,l)*60-sra).gt.-30.0)))
do nch=l,3
do f=1,2
do n=l,2
S(i,nch,f,n)=0.0
E(i,nch,f,n)=0.0
enddo
enddo
enddo
endif
enddo
then
;
! Write to file
i
do i=l,counter
output.ra = RA(i,l)
output.lsky.lf = S(i,1,1,1)
output.msky_If = S(i,2,l,l)
output.hsky_If = S(i,3,l,l)
output.lsky_2f = S(i,1,2,1)
output.msky_2f = S(i,2,2,l)
output.hsky_2f = S(i,3,2,l)
output,lsky_sig_lf = E(i,1,1,1)
output.msky_sig_If = E(i,2,l,l)
output.hsky_sig_If = E(i,3,l,l)
output.lsky_sig_2f = E(i,1,2,1)
output.msky_sig_2f = E(i,2,2,l)
output.hsky_sig_2f = E(i,3,2,l)
output.latt_If = KA(i,l,l)
output.matt.If = KA(i,2,l)
output.hatt.If = KA(i,3,l)
output.latt_2f = KA(i,l,2)
output.matt_2f = KA(i,2,2)
output.hatt_2f = KA(i,3,2)
output.latt.sig.lf = EK(i,l,l)
output.matt.sig.If = EK(i,2,l)
output.hatt.sig.lf = EK(i,3,l)
output.latt.sig.2f = EK(i,l,2)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
128
k
k
k
output.matt_sig_2f * EK(i,2,2)
output.hatt_sig_2f = EK(i,3,2)
write(12) output
output.ra = RA(i,2)
output.lsky.lf = S(i,1,1,2)
output.msky.If = S(i,2,l,2)
output.hsky.If = S(i,3,l,2)
output.lsky_2f = S(i,1,2,2)
output.msky_2f = S(i,2,2,2)
output.hsky.2f = S(i,3,2,2)
output.lsky.sig.lf = E(i,l,l,2)
output.msky.sig.If = E(i,2,l,2)
output.hsky.sig.If = E(i,3,l,2)
output.lsky_sig_2f = E(i,l,2,2)
output.msky_sig_2f = E(i,2,2,2)
output.hsky_sig_2f = E(i,3,2,2)
write(15) output
write(13,200) ra(i,l),
tab,accept(i, 1,1,1),tab,accept(i, 1,2,1) ,
tab,accept(i,2,1,1) ,tab,accept(i,2,2,1) ,
tab,accept(i,3,l,l),tab,accept(i,3,2,1)
enddo
I
200
format(f9.4,6(al,i4))
i
! End of main loop
!
!
A.6
close(lO)
close(ll)
close(12)
close(13)
close(15)
enddo
close(14)
stop
end
Stacking
Program Offsel
! Changed to new program. February 13, 1996. Jon Nicholas.
! This Program does an offset subtraction from the data
! selected as good by either the reject or slider programs.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
129
! It writes the results to .aco files. February 22, 1996.
! Program now reads in .ncr files and will use that data if there is
! no data from the .acc files. Jon Nicholas. February 26, 1996.
implicit none
! Structures ------------------------------------------include 'TENERIFE_ATM5_STRUCT.INC'
record /header_ATM/ in.stat
record/header_atm/ out_stat
record /data_frame.atm/ atmdat
record /data_frame_atm/ nardat
record /data.frame.atm/ output
Variables
character*80
character*40
real*8
&
in.dir, out.dir
in_file, rfile
RA(500,2),
S (500,3,2,2) ,E(500,3,2,2) , ! Signal and Error
KA(500,3,2),EK(500,3,2),
! Attenuation & Error
x(7,3,2,2), y(4,3,2,2),
! Fit components
slope,intercept,denom,length,
intsig,slpsig
logical
not.eof,
tab
integer*4
nch,i,f.counter,
n ,filen,numfil,last(3,2,2)
&
Parameters
data tab/9/
! Tab character
Inputs
600
601
type 600
format (’ Enter input file (no extension): ’,$)
accept 601, in_file
format (A40)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
130
in.dir = 'BRIAX4$dkalOO:[users.cmb .data.94.work_f iles .all_32]
out_dir= ’BRIAX4$dkal00:[users.cmb.data.94. work.files.all_32]
Open I/O files
&
k
603
k
k
k
open(unit=14, file =in_dir//in_file//’.mrg’,
status ='old’,
form ='formatted’)
read(14,603) numfil
format (i4)
do filen=l,numfil
counter = 0
not.eof = .true,
read (14,601) rfile
write (6,*) rfile
open(unit=10, file
=in_dir//rfile//’.acc’,
status = ’old’,
form
= ’unformatted ’,
reel
= 2048)
i
k
k
k
open(unit=ll, file
status
form
reel
= in_dir//rfile//’.ncr’,
= ’old’,
='unformatted',
= 2048)
k
k
k
open(unit=13, file
= out_dir//rfile//’.aco',
status = ’new’,
form
= ’unformatted’,
reel
= 2048)
j
Initialize variables
do nch=l,3
do f=l,2
do n=l,2
last(nch,f,n) = 0
do i=l,3
x(i,nch,f,n) = 0.0
y(i,nch,f,n) = 0.0
enddo
do i=4,7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
131
x(i,nch,f,n) = 0.0
enddo
enddo
enddo
enddo
Read/write HEADER
read(10), in_stat
out.stat = in_stat
read(ll), in_stat
write(13) out_stat
Main loop
do while (not_eof)
read(10,err=999) atmdat
read(ll,err=999) nardat
counter = counter+1
RA(counter,1) = atmdat.ra
S(counter,1,1,1) = atmdat.lsky.lf
S(counter,2,1,1) = atmdat.msky.If
S(counter,3,1,1) = atmdat.hsky.If
S(counter,1,2,1) = atmdat.1sky.2f
S(counter,2,2,1) = atmdat.msky_2f
S(counter,3,2,1) = atmdat.hsky.2f
E(counter,1,1,1) = atmdat.lsky.sig.If
E(counter,2,1,1) = atmdat.msky.sig.lf
E(counter,3,1,1) = atmdat.hsky.sig.If
E(counter,1,2,1) = atmdat.lsky_sig.2f
E(counter,2,2,l) = atmdat.msky.sig.2f
E(counter,3,2,l) = atmdat.hsky.sig.2f
KA(counter,1,1) = atmdat.latt.If
KA (counter,2,1) = atmdat.matt.If
KA(counter,3,1) = atmdat.hatt.If
KA(counter,1,2) = atmdat.latt_2f
KA (counter,2,2) = atmdat.matt_2f
KA(counter,3,2) = atmdat.hatt_2f
EK(counter,1,1) = atmdat.latt.sig.If
EK(counter,2,1) = atmdat.matt_sig_If
EK(counter,3,1) = atmdat.hatt.sig.If
EK (counter,1,2) = atmdat.latt_sig_2f
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
132
EK(counter,2,2) = atmdat.matt_sig_2f
EK(counter,3,2) = atmdat.hatt_sig_2f
RA(counter,2) = nardat.ra
S(counter,1,1,2 = nardat.lsky.lf
S(counter,2,1,2 = nardat.msky_If
S(counter,3,1,2 = nardat.hsky.If
S(counter,1,2,2 = nardat.lsky_2f
S(counter,2,2,2 = nardat.msky.2f
S(counter,3,2,2 = nardat.hsky_2f
E(counter,1,1,2 = nardat.lsky.sig.lf
E(counter,2,l,2 = nardat.msky.sig.If
E(counter,3,1,2 = nardat.hsky.sig.lf
E(counter,1,2,2 = nardat.lsky_sig_2f
E(counter,2,2,2 = nardat.msky_sig_2f
E(counter,3,2,2 = nardat.hsky.sig.2f
Add to averages
k
k
k
k
k
do f=l ,2
do nch=l,3
do n=l ,2
if (E(counter,nch,f,n).ne.(0.0)) then
y(l,nch,f,n)=y(1,nch,f,n)+S(counter,nch,f,n)
/ (E(counter,nch,f,n)*E(counter,nch,f,n))
x(l,nch,f,n)=x(l,nch,f,n)+l
/ (E(counter,nch,f,n)*E(counter,nch,f,n))
x(2,nch,f ,n)=x(2,nch,f ,n)+RA(counter,n)
/(E(counter,nch,f,n)*E(counter,nch,f,n))
x (3,nch,f ,n)=x(3,nch,f ,n)+RA(counter,n)*RA(counter,n)
/ (E(counter,nch,f,n)*E(counter,nch,f,n))
y(2,nch,f,n)=y(2,nch,f,n)+S(counter,nch,f,n)*
RA(counter,n)/(E(counter,nch,f,n)*E(counter,nch,f,n))
if (last(nch,f,n).eq.O) then
last(nch,f,n) = counter
endif
else
if (last(nch,f,n).ne.O) then
1ength=RA(count er-l,n)-RA(last(nch,f,n),n)
if (length.lt.(1.0)) then
denom=x(1,nch,f ,n)
intercept=y(1,nch,f ,n)/denom
slope=0.0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
133
&
&
&
&
999
intsig=l/denom
slpsig=0.0
else
denom=x(1,nch,f ,n)*x(3,nch,f ,n) x(2,nch,f,n)*x(2,nch,f,n)
intercepts(x(3,nch,f ,n) *y (1,nch,f ,n) x(2,nch,f ,n)*y(2,nch,f ,n))/denom
slope=(x(l,nch,f,n)*y(2,nch,f,n) x(2,nch,f,n)*y(1,nch,f,n))/denom
int sig=x(1,nch,f ,n)/denom
slpsig=x(3,nch,f ,n)/denom
endif
do i=last(nch,f,n),(counter-1)
S (i,nch,f ,n)=S(i ,nch,f ,n)-RA (i,n)*slope-intercept
E(i,nch,f,n)=dsqrt(E(i,nch,f,n)*E(i,nch,f,n) +
RA(i,n)*slpsig + intsig)
enddo
last(nch,f,n) = 0
do i=l,2
x(i,nch,f,n) = 0.0
y(i,nch,f,n) = 0.0
enddo
x(3,nch,f,n) = 0.0
endif
endif
enddo
enddo
enddo
enddo
continue
do f=l,2
do nch=l,3
do n=l,2
if (last(nch,f,n).ne.0) then
length=RA(counter,n)-RA(last(nch,f ,n),n)
if (length.lt.(1.0)) then
denom=x(1,nch,f ,n)
int ercept=y(1,nch,f ,n)/denom
slope=0.0
intsig=l/denom
slpsig=0.0
else
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
134
&
&
k
k
denom=x(1,nch,f ,n) *x (3,nch,f ,n) x(2,nch,f,n)*x(2,nch,f,n)
intercepts(x(3,nch,f,n)*y(l,nch,f,n) x(2,nch,f,n)*y(2,nch,f,n))/denom
slope=(x(l,nch,f,n)*y(2,nch,f,n) x(2,nch,f,n)*y(1,nch,f,n))/denom
int sig=x(1,nch,f ,n) /denom
sips ig=x(3,nch,f ,n)/denom
endif
do i=last(nch,f,n).counter
S(i,nch,f,n)=S(i,nch,f,n)-RA(i,n)*slope-intercept
E(i,nch,f,n)=dsqrt(E(i,nch,f,n)*E(i,nch,f,n) +
RA(i,n)*slpsig + intsig)
enddo
endif
enddo
enddo
enddo
Enter .nar data if .atm data unacceptable.
do i=l,counter
do nch=l,3
do f=l,2
if (E(i,nch,f,1).eq.0.0) then
S(i,nch,f,l) = S(i,nch,f,2)
E(i,nch,f,l) = E(i,nch,f,2)
endif
enddo
enddo
output.ra = RA(i,l)
output.lsky.lf = S(i,1,1,1)
output.msky.If = S(i,2,l,l)
output.hsky.If = S(i,3,l,l)
output.lsky_2f = S(i,1,2,1)
output.msky.2f = S(i,2,2,l)
output.hsky.2f = S(i,3,2,l)
output.lsky.sig.lf = E(i,1,1,1)
output.msky.sig.lf = E(i,2,l,l)
output.hsky.sig.If = E(i,3,l,l)
output.lsky_sig_2f = E(i,1,2,1)
output.msky_sig_2f = E(i,2,2,l)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
135
output.hsky_sig_2f = E(i,3,2,l)
output.latt_If = KA(i,l,l)
output.matt.If = KA(i,2,l)
output.hatt.If = KA(i,3,l)
output.latt_2f = KA(i,l,2)
output.matt_2f = KA(i,2,2)
output.hatt_2f = KA(i,3,2)
output.latt.sig.lf = EK(i,l,l)
output.matt.sig.If = EK(i,2,l)
output.hatt.sig.If = EK(i,3,l)
output .latt_sig_2f = EK(i,l,2)
output.matt.sig.2f = EK(i,2,2)
output.hatt_sig_2f = EK(i,3,2)
write(13) output
enddo
j
! End of main loop
j
!
close(lO)
close(ll)
close(13)
enddo
close(14)
close(l5)
stop
end
program Stacking
PROGRAM MERGES FILES ACCORDING TO THEIR R.A. AFTER LOCK-IN,
BINNING, 3-SIG CUTOFF AND ATMOSPHERE REMOVAL. Uses a weighted
average based on the standard deviation. Read Data Reduction and
Error Analysis by Bevington & Robinson. 2nd Ed. p.59.
Written by Jon Nicholas. January 11, 1996.
implicit none
Structures ---------------------------------------------include 'TENERIFE.ATM.CUT.STRUCT.INC'
include »TENERIFE.ATM5.STRUCT.INC'
record /header.atm/
record /data.frame.atm/
header
input
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
136
Variables
integer*4
k
ch,nch,f,
Inch is the number of channels
n,i,j,k,bin,
numfil,filen
counts(768,3,2)
real*8
k
character*80
logical*!
avg(768,3,2),sig(768,3,2),
tmpsky(3,2) ,tmpsig(3,2) ,ra
in_dir, out.dir, mfile, hfile
tab, not.eof
! Parameters
data tab/9/ !Spacing tab charachter
! Initialize basic parameters
do bin=l,768
do nch=l,3
do f=l ,2
avg(bin,nch,f) = 0 . 0
sig(bin,nch,f) = 0 . 0
counts(bin,nch,f) = 0
enddo
enddo
enddo
not_eof = .true.
Inputs
type 600
600 formatC’ Enter merge file selection (no extension):' $)
accept 601, mfile
601
FORMAT(A80)
in.dir = ’BRIAX4$DKA100:[USERS.CMB.DATA.94.WORK.FILES.all_32] ’
out_dir='BRIAX4$DKA100:[USERS.CMB.DATA.94.H0RK_FILES.all_32] ’
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
137
! Open the merge file which designates which files to merge
I
open(unit=10,file
= in_dir//mfile//'.mrg’,
k
status = ’old',
k
form
= 'formatted')
read (10,602) numfil
602 format (i4)
do filen = 1,numfil
Open .acc files (data after atmospheric cut analysis)read (10,601) hfile
write (6,*) hfile
open(unit=ll, file
k
status
k
form
k
reel
= in_dir//hfile//’.aco',
= ’old',
= ’unformatted',
= 2048)
Read file header ------------------------read(11) header
Read in the data and store it
do while (not.eof)
read(ll, err=800) input
Assign bin based on RA
bin = jidnnt((64*(input.ra-6.0)+l)/2)
tmpsky(l,1
input.lsky.lf
tmpsky(l,2
input.lsky_2f
tmpsky(2,1
input.msky.lf
tmpsky(2,2
input.msky_2f
tmpsky(3,1
input.hsky_If
tmpsky(3,2
input.hsky_2f
tmpsig(l,l
input.lsky_sig_lf
tmpsig(l,2
input.lsky_sig_2f
tmpsig(2,l
input.msky_sig_lf
tmpsig(2,2
input.msky_sig_2f
tmpsig(3,1
input.hsky_sig_lf
tmpsig(3,2
input.hsky_sig_2f
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
138
do nch = 1,3
do f = 1,2
if (tmpsig(nch,f) .ne.O.dO) then
avg(bin,nch,f) = avg(bin,nch,f) + tmpsky(nch,f)/
ft
(tmpsig(nch,f)*tmpsig(nch,f))
sig(bin,nch,f) = sig(bin,nch,f) + 1/
ft
(tmpsig(nch,f)*tmpsig(nch,f))
counts(bin,nch,f) = counts(bin,nch,f) + 1
endif
enddo
enddo
enddo
i
! Close the file and get the next one
I
800
continue
close (11)
enddo
close (10)
I
! Finalize data analysis and write to file.
i
open(unit=10,file
= out_dir//mfile//’.mgd',
ft
status = 'new',
ft
form
= 'formatted',
ft
reel
= 4096)
! Header
write (10,603) 'RA',
ft tab,'avgl.lf',tab,'sigl.lf',tab,'nol_lf’,
ft tab,’avgl_2f’,tab,’sigl_2f',tab,'nol_2f',
ft
tab,'avg2_lf',tab,'sig2_lf',tab,'no2_lf',
ft tab,'avg2_2f',tab,’sig2_2f’,tab,’no2_2f’,
ft
tab,'avg3_lf’,tab,'sig3_lf',tab,'no3_lf',
ft
tab,'avg3_2f',tab,’sig3_2f',tab,'no3_2f'
603 format (a4,18(al,a7))
do bin=l,768
do nch=l,3
do f=l,2
ra = dble(2*bin-l)/64+6.0
if (sig(bin,nch,f).ne.O.dO) then
avg(bin,nch,f) = avg(bin,nch,f)/sig(bin,nch,f)
sig(bin,nch,f) = l/dsqrt(sig(bin,nch,f))
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
139
endif
enddo
enddo
write (10,604) ra,
k
tab,avg(bin,l,l),tab,sig(bin,l,l),tab,counts(bin,1,1),
k
tab,avg(bin,l,2),tab,sig(bin,1,2),tab,counts(bin,1,2),
k
tab,avg(bin,2,l) ,tab,sig(bin,2,1),tab,counts(bin,2,1),
k
tab,avg(bin,2,2),tab,sig(bin,2,2),tab,counts(bin,2,2),
k
tab,avg(bin,3,l),tab,sig(bin,3,1),tab,counts(bin,3,1),
k
tab,avg(bin,3,2),tab,sig(bin,3,2),tab,counts(bin,3,2)
enddo
604 format (f9.5,6(al,f9.5,al,f9.5,al,i4))
close (10)
stop
end
A.7 Correlation Analysis
PROGRAM Correlation
C+
C
C Program finds The rms level of signal in a smaller scale CMB
C anisotropy measurement, based on a given window function.
C FUNCTIONAL DESCRIPTION:
C
C
Program reads in 1 files:
multipole predictions
C
or else generates a flat spectrum
C
Program then generates the window functions
C
C Then program sums the product of multipole moments X
C
window functions
C Correlation function is then the ratio of the rms at zero
C
lag to the rms at angle phi
C
C AUTHOR(S):
C
C
Bob Schaefer
C
C CREATION DATE:
C
C
July 30, 1996
C
C [common blocks]
Reproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
140
C [design]
C
C MODIFICATION HISTORY:
C
C Date
I Name I Description
C --------------- +------ ----------------------------------------C [change.entry]
CC Variables Wl(il,i2,i3)
window functions
C
il = 1, (legendre polynomial 1)
C
i2 = lock in harmonic (1 = 2beam, 2=3beam)
C
i3 = lag angle coefficient
C
Al(i)
CMB anisotropy multipole moments
C
SUM
rms temp, anisotropy flue, at each lag phi
C
RMS2 rms temp. flue, at each lag phi
C
RAt
ratios of rms(angle phi_i)/rms(angle=0)
C
BP
I[W_1] of Bond, 1995 - normaizes band power
C
avel Average 1 of each window function
C
bandp band power
C
DIMENSION W1(300,6,20), Al(1000)
DIMENSION SUM(20), RMS2(20), RAT(20)
DIMENSION BP(20), AVEL(20), BANDP(20)
C
C
initialize window functions
data wl/ 36000*0.0/
write(6,*)’ At what declination are you observing?’
read(5,*)dec
write(6,*)' how many minutes (R.A.) per data bin?’
read(5,*)binmin
C
lets not go crazy here
lmax = 200
C
C
generate the window functions
CALL GETwl(binmin,dec,lmax.wl)
write(6,*)’ What Spectrum? l=(Flat), 2=(0m_b=0.05 CDM,n=l)’
read(5,*)ispect
Reproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
141
if(ispect.n e .1. and.ispect.ne.2.)then
write(6,*)' Spectrum must be 1 or 2, not’,ispect
write(6,*)’ Defaulting to flat spectrum’
ispect = 1
endif
CALL READal(al,lmax,ispect)
write(6,*)’ which harmonic? 1 = 2beam, 2 = 3
read(5,*)ih
C
C
C
C
C
beam, ...,6’
Do j=l,20
sum(j) = 0 . 0
Enddo
lupper = lmax
DO 1=2, lupper
DO j= 1,20
sum(j) = sum(j) + al(I)*wl(I,ih,j)
ENDDO
Enddo
using cobe four year normalization Q_rms-PS = 18 mico-K
Q=18.
print file headers
Write(6,*)’
degrees RA
degrees
rms delta T ’,
>
’
correlation’
Write(21,*)’ degrees RA
degrees
rms delta T',
>
’
correlation’
Do j=l,20
SUM(j) = (Q/20.)**2*SUM(j)
RMS2(j) = Sum(j) * 2.726E6**2
if(j.eq.l)write(6,*)' rms2 norm is = ’,rms2(l)
rat(j) = rms2(j) /rms2(l)
for correlation coefficients
RA = float(j-l)*binmin
reald = RA*cosd(dec)
Write(6,*)RA,reald,rms2(j) ,rat(j)
Write(21,*)RA,reald,rms2(j) ,rat(j)
Enddo
write to for021.dat
Band power
do j=l,20
bp(j) = 0 . 0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
142
avel(j) = 0 . 0
enddo
do I = 2, lupper
do j=l,20
bp(j) = bp(j) + float(2*1+1)*wl(i,ih,j)/float( 2*1 *(1+1))
avel(j) = avel(j) + float((2*I+l)*i)*wl(i,ih,j)
>
/float(2*1 *(1+1))
enddo
enddo
do j=l,20
bandp(j) = rms2(j)/bp(j)
write (6,*) j ,' bin band power''2=' ,bandp(j) ,' I[W] = ',bp(j)
avel(j) = avel(j)/bp(j)
write(6,*)' average 1 =
avel(j),' j=',j
enddo
STOP 'finished!'
END
SUBROUTINE readal(al,lmax,ispect)
C
C
C
C
C
reads in
multipolemomentcoefficients or generates flat
harrsion - zeldovich spectrum multipoles.
theseare
normalizedtoQ=20 micro-K
DIMENSION al(1500),alplot(1500)
go to (1,2) ispect
2
continue
OPEN (
1 UNIT=11,
1 ERR = 98,
C
de Laix and Schaefer multipoles
1 FILE = 'cl_cdm_norm.dat',
C
Sugiyama's multipoles
C 1 FILE = 'cl_sugiyama.dat',
1 STATUS = 'old')
C
forget the dipole + monopole terms
Al(l) = 0.0
DO i=2,1400
READ (ll,*,end=99)l, alplot(i)
if(i.ne.l)write(6,*)' do index=',i,’ but 1=',1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
143
C
C
C
C
C
END DO
99
continue
CLOSE(unit=ll,disp=’keep’)
sugiyama normalizes to sigma(l(T\circ) or Q_rms-PS=14.8!
adj = (20./14.8)**2
do 1=2,lmax
el=l
for sugiyama curves
al(l)=(el+0.5)/(el+l.)/el *alplot(l)*adj
for schaefer and delaix curves
al(1) = (2.*el+l.) /(el+1.)/el *alplot (1) / 1 .084e+10
enddo
write(6,*)al(2)
return
98
continue
write(6,*)’ somethings wrong with the multipole file...’
return
generating H-Z flat spectrum
1
continue
a2_20 = 6.*5.38E-11/5.
do 1=2,lmax
el=l
al(l)=(2.*el+l.)/(el+l.)/el *a2_20
enddo
write(6,*)al(2)
RETURN
END
SUBROUTINE GETwl (binmin,decl,lmax,wl)
C
C
C
C
C
C
This routine calculates the window functions between 20
adjacent bins of data using the window function formulas
of Srednicki and White, 1995, ApJ 443, 6.
dimension plm(300,301)
dimension Wl(300,6,20), eloc(301,6), escan(301)
dimension enorms(12)
common pi
inital values for Legendre Functions
data plm/ 90300*0.0/
Experimental parameters
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
144
C
>
C
C
data sigma/ 1.02/
2.57 degree throw nomralizations
data enorms/ 1.217,3.228,10.387, 37.956, 157.67, 738.67,
3882.6, 22502., 1.4396E5, 1.0059E6, 7.6324e6, 6.25246e7 /
Numerical constants
pi =acos(-l.)
pi4 =4.*pi
d2r = pi/180,
sigma = sigma*d2r
C
C
C
CC
value of alpha = 2.57 old Bartol Tenerife Experiment
alpha = 2.57 * d2r
drift frequency in degrees/min
omegs =0.25
taking binmin minute angularbinning inright ascension
dphi = omegs * binmin *d2r
C
C
C
C
C
C
C
C
dec = decl * d2r
limiting case dphi -> 0; dec = 0 degrees
dphi = 1./300000.
dec = 0 . 0
alpha = alpha/cos(dec)
angular steps of correlation function indegrees
If you want coefficients for correlations dphic = dphi
if you want a smooth correlationfunction use dphic«dphi
dphic = dphi
C
c
C
C
C
calculate all Pirn then spherical harmonics can be easily
generated later by multiplying plm * cos(ra + phi_rand)
c
C
C
C
C
LegendreP calculates Plm(cos(theta)) where theta is the
polar angle and goes from 0 to pi, but the declination
goes from -pi/2 to +pi/2, so we add pi/2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
145
C
C
Pl-m = (-l)**m Plm
note our index is not m but m+1, so that P10 is Plm(l,l)
Call LegendreP(dec +pi/2.,lmax,Plm)
C
C
C
C
C
C
Calculate the scan and lock-in functions
ib = nbeams - 1
do ib = 1,6
eloc(l, ib) = 0.0
enddo
escan(l) = 0.0
do i = 2,301
em = i-1
eloc(i,l) = ( pi* bessjl( em*alpha) )**2
do ib= 2,6
eloc(i,ib) = ( pi* bessj(ib, em*alpha) )**2
enddo
escan(i) = ( Sin(em*dphi/2.)/(em*dphi/2.) )**2
enddo
calculate the window functions
do 1 * 1, 300
el * 1
do ib=l,6
do m= 1,1
em = m
do j=l,20
ej = j-1
wlmterm = (Plm(l,m+l))**2*eloc(m+l,ib)*escan(m+l)
Wl(l,ib,j) = Wl(l,ib,j) + wlmterm * cos(ej*dphic*em)
enddo
enddo
normalize the window functions
bl2 = 0.0
if(el*sigma.It.8.)bl2 = exp(-el*(el+l)*sigma**2)
wlterm = enorms(ib)*2.*bl2* pi4/(2.*el+l.)
do j=l,20
Wl(l,ib,j) = Wl(l,ib,j) *wlterm
enddo
enddo
enddo
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
146
return
end
SUBROUTINE legendreP(theta4,lmax,Plm4)
C+
C
C ABSTRACT:
C
C
Based on numerical recipes algorithms, this routine calculates
C
all of the Legendre functions with spehrical harmonic
C
normalizations, to convert to Ylm, then you just need to
C
multiply by e~(i m \phi)
C
C FUNCTIONAL DESCRIPTION:
C
C
Finds the all of the Legendre Functions P_l~m [cos(theta)] for
C
1 = 2, lmax, m=0, 1. Note that the P_l"{-m} = (-1)"m P_l~m,
C
so to save space we calculate only the positive m values.
C
C FORMAL PARAMETERS:
C
C
lmax:
the maximum 1 desired, all Plm for m=0, 1 and 1=2,lmax
C
C [common blocks]
C DESIGN:
C
C
1. All P_l~l are calculated.
C
2. Then P_l~m, m \neq 1 are generated with am 1 recursion
C
relation
C
CIMPLICIT Real*16 (A-H.O-Z)
REAL*4 PLM4(300,301)
REAL*4 Theta4
dimension plm(301,302)
data icall/ -1/
C
intialize value of pi
if(icall.eq.-1)then
pi = qacos(-l.qO)
fourpi = 4.q0*pi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
147
icall = 0
endif
if (lmax.gt.300)then.
write(6,*)’ cannot do ’,lmax,' Pirns, doing lmax=300 instead’
lmax = 300
endif
C
C
C
C
C
C
>
10
theta = qext(theta4)
x = Cos(theta)
calculate all p“l_l first
em2fac = 1.00
calculate all plm except dipole and monopole terms
which are calculated first
Plm(l.l) = x
Plm(l,2) = - (l.-x**2)**0.5
Plm(2,3) = 3.*(1. - x**2)
Plm(2,2) = -3.*x*(l. - x**2)**0.5
Plm(2,l) = 0.5*(3.*x**2 - 1.)
do 1 = 2, lmax
el = Qfloat(l)
em2fac = em2fac*(2.q0*el-l.q0)
Plm(l,l+1) = em2fac*(l.q0-x**2)**(el/2.q0)
if(mod(l,2).ne.0)Plm(l,l+l) = - Plm(l,l+1)
plm(l+l,l+l) = x*(2.q0*el+l.qO)*Plm(l,1+1)
write(6,*)l
enddo
get all other plm
do m=l,lmax-l
do l=m+l,lmax
el = qfloat(l)
em = qfloat(m-l)
if(l.eq.2)go to 10
plm(l,m)= x*(2.q0*el-l.q0)*plm(l-l,m)/(el-em)
-(el+em -1.qO)*Plm(l-2,m)/(el-em)
continue
enddo
enddo
thetad = theta*180.q0/pi
write(6,*)’ generated plm for dec = ’.thetad
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
148
C normalize spherical harmonics
do 1=2,lmax
do m= 1, 1+1
el = qfloat(l)
em = qfloat(m-l)
summ = qfloat(l-m+2)
sump = qfloat(1+m)
C
write(6,*)’ l-m+l=',summ
glmm = gammlnl6(summ)
C
write(6,*)’ l+m+l=’,sump
glpm = gammlnl6(sump)
plm(l,m) = sqrt((2.*el+l.)/fourpi)*exp( 0.5*(glmm-glpm) )
>
* plm(l,m)
enddo
enddo
C
Write(6,*)' normalized plm '
C
if Plm’s are ridiculously small, ignore them,
C
if Pirn's are ridiculously large, something is bad
C
so we write both cases to Spher_wopr.dat
open(unit=21,f ile=’spher.wopr.dat',status®'new')
C
do 1=2, lmax
do m= 1, 1+1
if(QABS(Plm(l,m)) .g t .1.q+30.or .QABS(Plm(l,m)).It.1.q-30)then
if(QABS(Plm(l,m)) .gt.l.q+30)
>
write(21,*)’ 1=’,1,' m=',m,Plm(l,m)
Plm(l,m) =0 . 0
else
Plm4(l,m) = Plm(l,m)
endif
enddo
enddo
close(unit=21)
return
END
*
real*16 function gammlnl6(xx)
real*16 cof(6),stp,half,one,fpf,x,tmp,ser,xx
data cof,stp/76.18009173Q0,-86.50532033Q0,24.01409822QO,
-1.231739516q0,.120858003q-2,-.536382q-5,2.50662827465q0/
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
149
C
C
11
data half,one,fpf /0. 5q0,1. OqO,5. 5q0/
write(6,*)’ but inside gammlnl6 it becomes*',xx
if (xx.lt. l.q0)xx=1.0Q0
x=xx-one
tmp=x+fpf
tmp= (x+half )*log(tmp)-tmp
ser=one
do 11 j=l,6
x=x+one
ser=ser+cof(j)/x
continue
gammlnl6=tmp+log(stp*ser)
return
end
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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