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Measurement of the polarization of the cosmic microwave background

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Measurement of the Polarization of the Cosmic
Microwave Background
T h e s is b y
B yron .J. P h ilh o u r
In P arrie d F u lfillm e n t o f th e R e q u ire m e n ts
fo r th e D egree o f
D o c to r o f P h ilo s o p h y
C a lifo r n ia I n s t it u t e o f T e c h n o lo g y
P asadena. C a lifo r n ia
2002
(S u b m itte d J a n u a ry 4. 2002)
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UMI Number: 3045006
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ii
©
2002
B y ro n .1. P liil lio u r
A ll R ig h ts R e se rved
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Acknowledgments
I w o u ld lik (' to th a n k Ravine lo r B h a tia . S a ra li C h u rc h . .Jason G le n n . B ill .Jones. B ria n
K e a tin g , a n d A n d re w Lange' fo r re a d in g a n d c o m m e n tin g
011
th e e-ontent a n d pre'sem-
ta tie m o f th is th e sis e>r th e assejciated p a p e r. T h is w o rk wemlcl n o t have be'em possible'
w it h o u t the1 e ffo rts o f A n d r e w Lange'. R a v in d e 'r B h a tia . a n d the- re>st o f the1 Pedatre n i te'ani in the1 O b s e rv a tie m a l C osm edogy la b e ira te a y a t C’alte'ch. the1 C h u rc h L a b a t
S ta n fo re l. a n d o u r ce dla b o ra te irs at O w ens V a lle y R a d46
i
servate>rv. in Pe'te'r Aeleds
la b o ra te )iy . anel in th e Caltee-h Mae-hine* Shejp. S p e 'ciiil th a n k s ge> to K a th y Demistem
anel S a ra h C h u rc h fe)r t h e ir em going su p p e irt. M y m a n M C’ R ’s ge>t a be*arel lik e a b illy
geiat. T h a n k s te> B ill. M edly. a n d C h e fo r th e co uch w h ile ' I visite'el Pasade'iia. T h a n k s
alse> to th e rest e)f th e F M C g an g , the' E ast T im e ir caelre1. D a b n e y House', a n d m y
frie n d s anel love'd earns.
"E a c h d iseove'iy. each advance1. e>ach increase' in the' su m o f h u m a n riche's,
owes its b e in g te> the* physie-al a n d m c 'iita l tr a v a il ed’ the' past a n d thepre'semt. B y w h a t r ig h t them can a n y enie1 whateweT appretpriate* the- lt'asr
nmrsed o f th is im m ense' whe)le> and say
T h is is m in e , neit yearns'.’"
P. K re ip e itk in . 77/e C'onqtu st o f D read
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Abstract
M e a s u re m e n t o f co sm ic m ic ro w a v e b a c k g ro u n d (C 'M B ) p o la r iz a tio n w il l p ro vide ' a
p o w e rfu l check on th e m o d e l th a t d e sc rib e s C’M B A T flu c tu a tio n s as a ris in g fro m
d e n s ity flu c tu a tio n s in th e e a r ly u n iv e rs e , b re a k degeneracies b e tw e e n c o s m o lo g ic a l
p a ra m e te rs th a t arise- in in t e r p r e t in g A T fh ic tu a tie m s . a n d m a y u ltim a te *ly allenv ele*fe c fie m o f th e stoe-hastic g ra v ity -w a v e backgrem nel preelicteel b y in fia tie n ia ry moele'ls.
W e elescribe* th e elevelopm e'iit a n d la b e ira te n y charae-te'rizatiem o f a bedenne'tric e*xpe*rim e n t designe-el to me-asure the- are-m inute-scale* petlarizariem e>f th e C’M B . T h e P olatrem
reeeive*r w ill be- m o u nte 'd a t th e C a s s e g ra in focu s ejf th e 5.5 m rc'le'se-e>pe* a t the' O w ens
V a lle y R a d io O b s e rv a to ry . T h e re c e iv e r w il l m easure Im th th e Q a n d i " Stoke's param ete-rs ewer a 20rA pass-banel centere*el n e a r 100 G H z . w it h th e in p u t pedarizatiem
s ig n a l m eK lulate'd a t ~
1 H z b y a re> tating. b ir e fr in g e n t. e p ia rrz half-wave* plate*.
In
s ix m e n ith s e>f edxservatiem we* [)la n te> obse*rve* ~ 400 2.5 are-minute* pixe-ls in a rin g
abem t the* X e irtli Ce*le*stial Pe)le* te> a pre*e-isiem e>f ~ 5 / / K pe*r p ixc'I ill e*ae4h o f Q anel
aele'cpiate* te> im a m b ig u e m s ly elete*e-t C 'M B pedarizatiem a t le*ve*ls pre*elie-te*el b y eurre*nt
me>de*ls.
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V
Contents
A c k n o w le d g m e n ts
iii
A b s tr a c t
iv
1
2
C o s m o lo g y a n d th e C o sm ic M icro w a v e B a ck g ro u n d
1
1.1
I n t r o d u c t i o n .....................................................................................
1
1.2
P o la r iz a tio n F o r m a lis m .............................................................
4
1.3
C 'M B P o la r iz a tio n T h e o r y ......................................................
G
1.4
C 'M B P o la r iz a tio n A n g u la r P o w e r S p e c t r u m ...............
10
1.5
M e a s u re m e n ts to D a t e .............................................................
14
1.(j
M e a s u re m e n ts P l a n n e d .............................................................
IG
1.7
O b s e rv in g S t r a t e g i e s .................................................................
17
P o la tr o n R e c e iv e r
19
2.1
I n t r o d u c t i o n ....................................................................................
10
2.2
T e le sco p e
........................................................................................
21
2.3
W a v e p l a t e ........................................................................................
24
2.4
F o cal P l a n e ....................................................................................
25
2.4.1
T h e r m a l M a ss a n d P r o f i l e ......................................
25
2.4.2
P o la r iz a tio n A n a l y s i s ..................................................
27
2.4.3
B e a m R e s p o n s e .............................................................
27
2.4.4
S p e c tra l R e s p o n s e .........................................................
2cN
2.4.5
R F I C o n t r o l .....................................................................
30
2.4.G
C o m m e rc ia l P a r t s .........................................................
30
2 .4 .7
D e te c to rs
.........................................................................
31
2.5
R e a d o u t E le c t r o n ic s .....................................................................
34
2.G
R F I C o n t r o l .....................................................................................
35
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vi
3
2.7
D a ta A c q u is itio n S y s t e m .............................................................................................
3G
2.8
In te g r a tio n o f R e c e iv e r w it h T elescope
39
P o la tr o n C r y o g e n ic S y s t e m
41
3.1
41
3.2
4
5
...............................................................
I n t r o d u c t i o n ........................................................................................................................
C o o lin g R e q u ire m e n ts
...............................................................................................
43
3.3
M e c h a n ic a l C’r v o c o o l e r .................................................................................................
4G
3.4
M u ltis ta g e S o r p tio n C o o le r .........................................................................................
49
3.5
I n t e g r a t i o n ...........................................................................................................................
52
3.G
M ie ro p h o n ie a n d R F I C o n t r o l ................................................................................
53
O b se r v in g S t r a te g y
57
4.1
I n t r o d u c t i o n .......................................................................................................................
57
4.2
A n tic ip a te d S e n s i t i v i t y ...............................................................................................
58
4.2.1
P h o to n X o i s e .....................................................................................................
5 ts
4 .2 .2
D e te c to r X o is e
.................................................................................................
G1
4 .2 .3
A m p lif ie r X o i s e .................................................................................................
G2
4.2.4
A tm o s p h e r ic X o i s e .........................................................................................
G2
4 .2 .5
F lu x S e n s i t i v i t y ................................................................................................
G4
4.3
C a lib r a tio n
......................................................................................................................
G5
4.4
S y s te m a tic P o l a r iz a t io n ...............................................................................................
GG
4.4.1
S y s te m a tic P o la riz e * 1 F l u x ..........................................................................
G8
4.4 .2
R e c e iv e r P o l a r i z a t i o n .....................................................................................
G9
4.5
A s tro p h y s ie a l F o r e g r o u n d s .......................................................................................
G9
4.G
Scan S t r a t e g y ..................................................................................................................
72
L a b o ra to ry C h a r a c te r iz a tio n
— O p tics
75
5.1
I n t r o d u c t i o n ......................................................................................................................
75
5.2
S p e c tra l B a n d s ..............................................................................................................
75
5.3
O p tic a l E f f i c i e n c y ..........................................................................................................
79
5.4
P o la r iz a tio n E f f i c i e n c y ...............................................................................................
80
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vii
6
5.5
D e te c to r P r o p e r t ie s .......................................................................................................
81
5.G
S e n s i t i v i t y ..........................................................................................................................
82
L a b o ra to ry C h a r a c te r iz a tio n — C ry o g en ics
83
G .l
I n t r o d u c t i o n .......................................................................................................................
83
6.2
M e c h a n ic a l C r y o c o o l e r ...............................................................................................
84
G.3
M u ltis ta g e S o r p tio n C o o le r ........................................................................................
85
7
F urther W ork a n d D is c u s s io n
88
A
H a lf W ave P la te s
91
A .l
W ave P late' C ro s s -p o la riz a tio n fo r /' ^ u{\ ...........................................................
92
A .2
W ave P la te C r o s s -p o la riz a tio n D ue to C o n v e rg in g B e a m
.........................
94
B ib lio g ra p h y
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96
v iii
List of Figures
1.1
C 'M B A T M a p O b ta in e d b y B O O M E R A N G ....................................................
2
1.2
M e a s u re m e n t o f S to k e s P a ra m e te rs Q a n d U
.....................................................
a
1.3
S c a tte rin g C ro ss S e c tio n fo r P o la riz e d L ig h t
....................................................
n
1.4
M o d e l C’M B P o la r iz a tio n M a p D ue to S c a la r P e r t u r b a t io n s .....................
!)
1.5
C’ M B A T P o w e r S p e c tru m O b ta in e d b y B O O M E R A N G ........................
12
LG
M o d e l C’ M B P o la r iz a tio n P ow er S p e c tru m a n d P u b lis h e d U p p e r L i m it
15
2.1
R e ce iver S c h e m a t ic ...........................................................................................................
20
2.2
P h o to : O V R O 5 .5 m T e le s c o p e ....................................................................................
22
2.3
P h o to s: S urface' S e ttin g C a m p a ig n
......................................................................
23
2.4
Surface* M a p s o f O V R O 5 .5 m T e le s c o p e ..............................................................
24
2.5
Feed S tr u c tu r e S c h e m a tic
............................................................................................
20
2 .0
P h o to : M ic ro m e s h B o l o m e t e r ....................................................................................
31
2 .7
B o lo m e te r S c h e m a t ic .......................................................................................................
32
2.8
B o lo m e te r R e a d o u t C ir c u it D ia g ra m
.....................................................................
34
2.0
P h o to : R F I F ilt e r A r r a y ...............................................................................................
37
2.10
P h o to : O V R O 5 .5 m T e le sco p e fro m R e a r
..........................................................
40
3.1
P h o to : M e c h a n ic a l C ry o c o o le r
................................................................................
47
3.2
M e c h a n ic a l C ry o c o o le r S c h e m a t ic .............................................................................
48
3.3
S im pU ' S o r p tio n F r i d g e S c h e m a t ic ............................................................................
50
3.4
M u ltis ta g e ' S o r p tio n C o o le r T h e rm a l C i r c u i t .....................................................
51
3.5
M u ltis ta g e S o r p tio n C o o le r S c h e m a tic .....................................................................
52
3.0
P h o to : P n e u m a tic V ib r a t io n I s o l a t o r .....................................................................
55
4.1
P o la riz e d G a la c tic F o re g ro u n d S p e c t r a .................................................................
71
4.2
P o la riz a tio n S e n s it iv it y as a F u n c tio n o f S can S tr a te g y P a ra m e te rs . .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
ix
5.1
P h o to : H D L - 8 T e st B e d
...........................................................................................
5 .2
M e a s u re d R e c e iv e r S p e c tra l P a ssb a n d a n d O V R O A tm o s p h e r ic S p e c tru m
78
5 .3
M e a s u re d R e c e iv e r P o la r iz a tio n E ffic ie n c y
.....................................................
81
6.1
M e c h a n ic a l C ry o c o o le r L o a d L in e s .......................................................................
N4
6 .2
M u ltis ta g e S o r p tio n C o o le r L o a d L i n o ................................................................
86
6 .3
M u ltis ta g e ' S o r p tio n C o o le r C y c lin g H is to r y
87
.................................................
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76
X
List of Tables
2.1
R e c e iv e r S p e c if ic a t io n s ...............................................................................................
21
2.2
B o lo m e te r S p e c if ic a t io n s ...........................................................................................
-13
2.3
R e le v a n t M o d u la tio n F r e q u e n c ie s ........................................................................
3«S
2.4
D a ta C h a n n e ls
..............................................................................................................
3iS
3.1
T h e r m o m e tr y C h a n n e ls ..............................................................................................
43
3.2
T h e r m o d y n a m ic P ro p e rtie s o f H e liu m jd ]
........................................................
50
4.1
A tm o s p h e r ic E m is s io n F lu c tu a tio n P a ra m e te rs
...........................................
04
4.2
A n t ic ip a t e d S e n s i t i v i t y ..............................................................................................
05
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1
Chapter 1
Cosmology and the Cosmic Microwave
Background
1.1
Introduction
T h e B ig B a il” m o d e l ( if c o s m o lo g ic a l e v o lu tio n has p ro v id e d a c o m p e llin g s o lu tio n
to th e p a ra d o x p o p u la riz e d a lm o s t tw o h u n d re d y e a rs ago b y a m a te u r a s tro n o m e r
H e in ric h O lb e rs :
" W a r u m is t es n a ch ts dunked?"
p a ra d o x rests o n tw o a s s u m p tio n s .
W 'liy is n ig h t- tim e d a rk ?
The
F ir s t, it assum es t h a t th e universe1 is in fin ite in
tim e a n d space, so t h a t e v e ry lin e o f s ig h t s h o u ld e v e n tu a lly in te rs e c t a lu m in o u s
o b je c t. S econd, it o bse rve s th a t th e n ig h t- tim e s k y is. in fa c t. d a rk .
T h e d is c o v e ry
b y E d w in H u b b le in 1929 [32] t h a t space is e x p a n d in g le d to a r e th in k in g o f th e firs t
a s s u m p tio n : i f g a la x ie s are m o v in g a p a rt, th e y w ere once m u c h clo s e r to g e th e r: hence,
th e u n iv e rs e has a f in it e age. a n d th e o b se rva b le u n iv e rs e a f in it e size. T h e d is c o v e ry
b y A r n o P enzias a n d R o b e rt W ils o n in 19G-1 o f co s m ic m ic ro w a v e ' b a c k g ro u n d (C 'M B )
r a d ia tio n [o7] led to a r e t h in k in g o f th e second a s s u m p tio n : tin * n ig h t sky is n o t d a rk !
E v e ry u n o b s tru c te d lin e o f s ig h t e v e n tu a lly docs in te rs e c t a lu m in o u s o b je c t, n a m e ly
th e p r im o r d ia l fir e b a ll th a t is th e universe1 in its e a rly, dense, h o t state1. E x p a n s io n o f
space1 m e re ly s h ifts th e ('m is s io n s p e c tru m o f th a t fire 'b a ll fro m v is u a l to m icro w a ve 1
w a v e le n g th s .
The1 C 'M B is a re m a rk a b le 1 to o l.
F o r exam ple1, th e p h y s ic a l d im e 'iis io n s o f d is ta n t
g a la x y c lu s te rs ca n be m easure'd b y in te 'rp re 'tiu g a rc m in u te -s c a le miHim e'teT-wave1 in ­
te n s ity d e cre m e n ts a t th e c lu s te r as u i> -s c a rte riiig o f C M B p h o to n s by a h o t in t r a ­
c lu s te r gas [71. 2iS]. T h e 1 observe'd d ip o le a n is o tro p y in th e C 'M B reveals t in 1 p e 'c u lia r
v e 'lo c iry o f the1 M ilk y W a y [70].
S lig h t te u u p e ra tu re a n is o tro p ie s ( A T / ’T ~
10- ’ )
o n large1 a n g u la r scale's r e w a l sca le -in va ria n ce 1 in the1 d e n s ity in h o m o g c 'n e itie s o f the1
e a rly univeTse1. a p r e d ic tio n o f in fla tio n mode'ls [70]. F u rth e rm o r e , re 'ccn tly o b ta in e d
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig u re 1.1: M a p o f C M B te m p e r a tu r e flu c tu a tio n s a b o u t th e m e a n C M B te m p e ra tu re .
2.728 K . as m e a s u re d b y th e B O O M E R A N G in s tru m e n t in its A n t a r c t ic b a llo o n flig h t
o f 1998. S om e s p a tia l f ilt e r in g has b e e n a p p lie d : see p a p e rs re fe re n c e d in te x t fo r
d e ta ils . B la c k d o t in lo w e r r ig h t- h a n d c o rn e r is th e a n g u la r size o f th e M o o n ( ~
F ig u re was o b ta in e d fro m th e B O O M E R A N G w e b site .
h ig h r e s o lu tio n m aps o f th e C M B . su ch as the* B O O M E R A N G
'/ ) .
m a p s h o w n in F ig ­
ure1 1.1. re ve a l a c o u s tic p e a ks in th e a n g u la r p o w e r s p e c tru m (F ig u r e 1.5). D a ta fro m
B O O M E R A N G . M A X I M A . D A S I. a n d o th e r e x p e rim e n ts h ave re c e n tly bee n used to
c o n s tra in a v a rie ty o f c o s m o lo g ic a l m o d e ls , as w e ll as p ro v id e a c c u ra te c o s m o lo g ic a l
p a ra m e te rs fo r c o ld d a r k m a t t e r ( C D M ) e v o lu tio n a r y m o d e ls
41. 13. 0 2. 73 . T h e
d e n s itv in h o m o g e n e itie s th e se m e a s u re m e n ts h ave u n v e ile d a re b e lie v e d to be th e
seeds o f th e g ra v ity -e n h a n c e d s tru c tu re 's w e sec1 in th e u n iv e rs e to d a y .
M e a s u re m e n t o f C M B p o la r iz a t io n is c o m p le m e n ta ry to . a n d an e x te n s io n o f. m ea­
s u re m e n ts o f C M B A T
flu c tu a tio n s .
T e m p e r a tu re a n is o tro p ie s in d u c e d b y d e n s ity
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3
fiu e rn a tio n s in rh o e a r ly u n iv e rs e s h o u ld th e m s e lv e s g e n e ra te m e a s u ra b le C M B p o ­
la riz a tio n [33. 30]. C o s m o lo g ic a l m o d e ls t h a t p re d ic t th e te m p e ra tu re a n g u la r p o w e r
s p e c tra p re d ic t c o rre s p o n d in g p o la r iz a tio n a n g u la r p o w e r s p e c tra .
A s d iscu sse d in
§1.3. m e a s u re m e n t o f th e p a tte rn a n d a m p lit u d e o f C M B p o la riz a tio n w il l e n a b le us
to do th e fo llo w in g :
• C h e c k th e c o n s is te n c y o f th e p a r a d ig m t h a t d e s c rib e s C M B A T flu c tu a tio n s as
a ris in g fr o m d e n s ity flu c tu a tio n s in tlit* e a r ly u n iv e rs t' (t ~ 3 00 .00 0 y r ) . U n lik e
te m p e r a tu r e flu c tu a tio n s , p o la r iz a tio n o f th e C M B ca n o n ly be g e n e ra te d o r
m o d ifie d b y s c a tte r in g (see §1.3).
•
B re a k d e g e n e ra cie s b e tw e e n c o s m o lo g ic a l p a ra m e te rs th a t arise in in t e r p r e t in g
A T flu c tu a tio n s .
F o r e x a m p le , it is d if f ic u lt to use A T in fo r m a tio n a lo n e to
d is tin g u is h b e tw e e n d ilu t io n o f s ig n a l a t la rg e a n g u la r scales d u e to r e io n iz a tio n
a n d an o v e r a ll ch a n g e in th e n o r m a liz a tio n o f th e p r im o r d ia l p o w e r s p e c tru m .
H o w e ve r, la te re io n iz a tio n s h o u ld p ro d u c e a re c o g n iz a b le s ig n a l
a t la rg e a n g u la r scales
r/io n
pow er
in p o la r iz a tio n [38],
• Test fo r th e presence o f th e s to c h a s tic g ra v ity -w a v e b a c k g ro u n d p re d ic te d b y
in f la tio n m o d e ls [GO. 35. G8. 3(J|.
S h o u ld th e y e x is t, p r im o r d ia l g r a v it y w aves
w o u ld c a r r y in fo r m a tio n fro m an in f la t io n a r y e ra n e v e r b efo re o p e n to in v e s tig a ­
tio n . a n d e n c o d e such in fo r m a tio n in a c u r l c o m p o n e n t to th e C M B p o la r iz a tio n
v e c to r p a tte r n .
C M B p o la r iz a tio n has n e ve r been d e te c te d . T h e s ta tu s o f th is d e v e lo p in g fie ld is
a n a lo g o u s to t h a t o f A T m e a s u re m e n ts te n t o fifte e n y e a rs ago. w it h e ven th e m o s t
s e n s itiv e u p p e r lim it s an o rd e r o f m a g n itu d e a b o v e th e th e o re tic a lly e x p e c te d s ig n a l
(§ 1 .5 ).
T h is s it u a tio n is set to ch ange so o n w it h th e o n g o in g d e p lo y m e n t o f a n e w
g e n e ra tio n o f e x p e rim e n ts s p e c ific a lly d e s ig n e d to m e a su re C M B p o la r iz a tio n ( § l. b ) .
T h e re m a in d e r o f C h a p te r 1 is d e v o te d to th e in t r o d u c t io n o f C M B p o la r iz a tio n
as a p ro b e o f c o s m o lo g ic a l p a ra m e te rs , a n d a fra m e w o rk fo r th e d e s c r ip tio n o f p o ­
la r iz a tio n is p ro v id e d .
A re v ie w o f th e s ta tu s a n d d ir e c tio n o f th e fie ld is in c lu d e d .
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4
C h a p to r 2 d e scrib e s o n e e x p e rim e n t u n d e r c o n s tr u c tio n , th e P o la tro n . w h ic h is d e ­
s ig n e d to m e a sure C M B p o la riz a tio n . In C h a p te r .'3. th e d e v e lo p m e n t o f th e c ry o g e n ic
s y s te m o f th e P o la tro n re ce ive r receives a clo se r lo o k : c o n s tru c tio n o f an a d e q u a te
c ry o g e n ic s y s te m has bee n th e fo cu s o f e n o rm o u s e ffo r t on th e p a rt o f th e P o la tro n
te a m .
C h a p te r 4 c o n ta in s a c a lc u la tio n o f th e e x p e c te d s e n s itiv ity o f th e P o la tro n
a n d d e scribe s th e o b s e rv in g s tra te g y we w ill e m p lo y to reduce* s y s te m a tic effe cts.
C h a p te rs 5 anel G are* d e v o te d to th e la b o ra to ry c h a r a c te riz a tio n o f the* in s tr u m e n t.
T h e fo rm e r d e s c rib e s th e o p tic a l syste m a n d p o la r iz a tio n c h a ra c te ris tic s : tin * la t te r
b r ie fly d e scrib e s th e c ry o g e n ic p e rfo rm a n c e o f th e s y s te m . In C h a p te r 7. we discu ss
these re s u lts a n d o u t lin e th e future* o f th e P o la tro n e x p e rim e n t. A te c h n ic a l a p p e n d ix
d e s c rib in g the* c a lc u la tio n o f th e p o la riz a tio n e ffic ie n c y o f half-wave* plate's is a lso
iiiedi icle*el.
1.2
Polarization Formalism
W e be'gin w it h a fo r m a l ele*scription o f the* p e d a riz a tio n ed" lig h t. A p h o to n t r a w lli n g
in the* c elire*e*tion w it h w a ve le u ig th A anel fre*e[ue*ne-y u ca n be* de*seribed b y an e*lc*e-rriefie'lel v e c to r
( l . D
The* ele'gre'e* te» w h ie 'li the* aelelitieinal phase* te*rms Ox { t ) a n d 0 ,, { f) are* e-orre*late>el is
the* ele'gre'e* to w hie’li tile* lig h t is polarize*el.
T im e '-a v e ra g in g em*r the* e*le*etric fie*le 1
ose-illatiems. we* e a n ek'se-ribe* the* p e d a riz a tio n w it h the* Stoke*s param e'te'rs
(
1. 2 )
(1..4)
(1 -4 )
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1. 0 )
Detector Aligned
with NE/SW
/
/
/
/
Detector Aligned
with East/West
/
Detector Aligned
with NW/SE
/
/
/
/
Detector Aligned
with North/South
Signals
Signals
I
F ig u re 1.2: Q a n d U as iiin a s u re tl b y iele'alized p o la riz a tio n ele'te'e-teas a lig n e 'd as sh ow n.
w h e re I re fe rs to th e in te n s ity . Q a n d U elescribe th e lin e a r p o la r iz a tio n a n d d e p e n d o n
th e d e f in it io n o f th e ( . r . ;/) c o o r d in a te s y s te m , a n d I ’ d escribe s th e c ir c u la r p o la r iz a tio n
o f th e p h o to n .
The' S to k e s p a ra m e te rs are o fte n c o n v e rte d fro m u n its o f in te n s ity to b rig h tn e s s
te m p e r a tu r e th r o u g h c ro s s -c a lib ra tio n w it h a n a s tro p h y s ic a l source' o f knenvn te'm p era tu re ' anel e u n is s iv ity .
E e [u iv a le n tlv . Q is ele'fine'd as th e te m p e ra tu re ' diffe're'ne-e* me>a-
sure’el b e tw e e n twe) sin g le '-p e jla riza t iem ele'te>e-te)rs. eme> aligne'd w it h the1 X o rth -S e n ith
(X -S ) elire'e-tiem. anel the' o th e 'f a lig lU 'e l w it h the1 E a s t-W e s t (E -W *) elire*e-tie>n.
wise'. f
Like1-
c a n 1)e> ele'fine'el as th e te 'n ip e 'ra tu re ' diffe're'ne-e' me-asure'd be'tw een ele'te'e to rs
aligne'el w it h the' X’ E -S W anel X W ’-S E dire'e-tiems as s lm w n in F ig u re ' 1.2. W e w ill use*
te n ip e 'fa tu re u n its te> ele'se ril>e> Steike-s p a ra in e te 'rs t hrem ghour t h is the'sis.
Q anel I ' are1 nett m ta tie m a lly in v a ria n t eibservabh's. b u t in s te 'a d tr a n s fb r m unele'r
reirariein b y angle1 0 frenn e-ejorelinates (./".//) te> (./• './/) . fe>lle>wing the* rule-
(}'
=
Q cos 2 0 + C s in 20
( l.U )
C
=
- Q sin 20 + r e-os 20.
(1 .7 )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
G
T h e fra c tio n a l p o la r iz a tio n p o f th e p h o to n c a n be d e fin e d as fo llo w s :
v T /- ’ + i " I
P = — ------- :--------------•
( 1-«S)
a n d th e p o la r iz a tio n a n g le 0p. d e fin e d fo r [() < 0p < ~ ], is
f)„ = i t a n - l ( C '/ g ) .
( l. h )
P o la r iz a tio n s k y m a p s p la ce a lin e w it h le n g th s ca le d b y p a t each p o in t ( f i . o ) o n the*
m a p . at an a n g le 0,, w it h re sp e ct to a chosen c o o rd in a te ' syste m .
F u rth e r u s e fu l d e fin itio n s in clu de '
I r = \ { I + Q ).
(1 .1 0 )
(
=
1. 1 1 )
a lth o u g h it is im p o r ta n t to re m e m b e r th a t these' a re nejt ve-ctor c o m p o n e n ts o f / .
Ir
a n d / v w o u ld be' the* in te n s irie 's me'asure'd b y "p e rfe 'c t" sin g le '-p e )la riza tie )ii <le*re>e-re»rs
en'ientc'd in theb y Ee|iis. 1.3 a n d
x - anely-elire'ctienis.
1.4.
.Note t h a t Q = I r — / 7 a n d C = 0.as
I f the1 (./. //) eoe>rdinate' syste'm is ro ta te 'd
b y 4o
antie-ipate'el
.Q =
0 anel
U = / r — I,r as antie-ipate'el b y Eeiu. l.G.
1.3
CMB Polarization Theory
P e d a riz a tio n arise's due' re) asym m e'trie- emiissiem. a bse)rptie)ii. o r se -a tte rin g o f p hotem s.
The're' are' se've'ral :'..-tTe>phvsieal semree's ejf p e d a riz a tio n . Fe>r instanee'. edemgate'el elust
g ra in s m s ta r - fo r m in g re'giems e 'tnit o r abse>rl) lig h t w it h pedarizatiem elire'e tie>n e>rthe>go u a l te> loe-al m agnetie- fiedd line's [21].
C M B p e)lari/.atie)u a rise s frenu the> asym m e'trie- T h o m s e m se-atte-ring in the* e'ra e>f h y elretge'u e -o m b ina tie )ii. S ig n ifie -a n t ped a riza tiem re'C[iiire's a suffie-ie>nr n u m b e 'r o f available*
seatte're'is. b u t a t the* same* tim e ' re'cpiire's a le)w e>ptie;il ele'pth. sine-e' n u m e ro u s se-atte*rs w ill sm e'ar o u t pre'terre’d pe>larizatie>n dire'e-tie>ns. C M B pedarizatiem is geme'rate'el
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d u r in g th e r e la tiv e ly s h o rt p e rio d o f tim e a fte r fre e -s tre a m in g has b e g u n , b u t b e fo re
c o m b in a tio n ends.
A s a re s u lt, a n o b s e rv e d in te n s ity d is t r ib u t io n a t th e s u rfa c e o f
la s t s c a tte rin g (as m e a sured b y a t y p ic a l C M B A T e x p e rim e n t) s h o u ld be a s s o c ia te d
w it h a p o la r iz a tio n p a tte rn .
T h e so u rce o f p o la riz a tio n is a s y m m e tric te m p e ra tu re
f lu c tu a tio n s o f a m p litu d e A T / T
~
10_>. T h e p o la r iz a tio n le ve l s h o u ld be s m a lle r
s t ill, w it h A Q / T < l ( ) - ,; [30].
C o n s id e r th e fin a l s c a tte r o f a C M B p h o to n o ff o f a fre e e le c tro n and in to th e :
d ir e c tio n , as s h o w n in F ig u re 1.3. T h e s c a tte rin g cross s e c tio n is
(l(T
-h(T-r _ ,
— = — -\p-p\~
(III
x c o s -ft.
(1 .1 2 )
w h e re n-y is th e u su a l T h o m s o n cross s e c tio n to s c a tte rin g , p ' is th e p o la riz a tio n
d ir e c tio n o f th e in c id e n t b ea m , p is th a t o f th e o u tg o in g b e a m , a n d f) is th e a n g le
fo rm e d b y th e tw o ve cto rs [8]. T h e eosJ fo rm o f th e cross s e c tio n re q u ire s th a t, in o rd e r
to o b se rve n o n z e ro lin e a r p o la r iz a tio n fro m a s m a ll so urce re g io n , th a t re g io n m u s t lie
w it h in an in te n s ity d is t r ib u t io n I ( O. o ) t h a t possesses a n o n z e ro q u a d ru p o le (I = 2.
m = 0. ± 1 . ± 2 ) m o m e n t [40]. T h is in te n s ity d is t r ib u t io n c a n a rise fro m D o p p le r s h ifts
a s s o c ia te d w it h m o tio n o f th e p h o to n -b a rv o n p la sm a o r w a v e le n g th s h ifts caused b y
th e passage' o f g r a v ita tio n a l wave's.
C M B te 'in p e 'ra tu re anise>tre>pie's are1 geueTate*el b y b e itli ''s c a la r" ( m = 0) p e -rtu rb a tio n s . e-ause'd b y va ria tie m s in ele-nsity. anel "ten.se>r" ( m = ± 2 ) p e 'rru rb a tie m s . eauseel
b y p rim e m lia l g ra v ita tie m a l wave's. The- inele'penelent c o n trib u tie ju etf e'ach ty p e o f [» 'rtu r b a tie n i ca n be- e lise u ta n g le d elue* tej t h e ir e liffe rin g e e e u trib u tio n s tee the1 re 's u lta n t
peelarizatie>n p a tte r n . 'Aee t o r " ( m = ± 1 ) p e rtu rb a tie m s are1 due' re> De>[)pler s h ifts assoc-iate'd w it h whirlpeeeel meitieen. a n d are1 ne>t asseee-iate'd w it h e le 'iisity iiihom eige'iie'irie's.
T h ere'fo re '. whate've’r p rim e tre lia l ve'cteir p e rtu rb a tie m s max- have' ewiste'd in the' e>arlv
unive-rse' weiulel neit greiw w it h the1 e xpansiem eif the- unive-rse'. anel are' neit e>xpee te'el to
be> eibse'rvable' [3 0 ]1.
Se-alar ( m
=
0 ) pe'rrurbatiem s arise- in the- ae-oustie- e'X{)ansiem a n d e-emi[)re’ssiem
1Hoxvevf'r. a n y C’M B p o la riz a tio n oxpe-riine'iit sensitive to Q and C eo nld . in p rin ciple, detect
veefor-m ode's o f p o la riz a tio n if th e y do e x is t.
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s
F i l l i n ' 1.3:
D u rin g T h o m s o n s c a tt e r in '’,, c e rta in o rie n ta tio n s o f in c e m iin g and o u t ­
g o in g p o la riz a tio n v e c to rs a re e x c lu d e d .
E ye g ra p h ic re p re se n ts d ir e c tio n in w h ic h
d if fe r e n t ia l s c a tte rin g cross s e c tio n is m e a su re d .
o f th e p r im o r d ia l p la sm a .
S uch processes have
110
s u c h , ca n o n ly p ro d u c e p o la r iz a tio n p a tte rn s w ith
p re fe rre d "h a n d e d n e s s " a nd . as
110
c u r l (F ig u re 1.4) [30].
D ire c t
m e a s u re m e n t o f th e a m p litu d e a n d d is t r ib u t io n o f sca la r p e r tu r b a tio n s w o u ld re p re ­
sent a m ile s to n e in th e s tu d y o f C M B a n is o tro p ie s because’ th e y w o id d ( 1 / v e rify th a t
te m p e r a tu r e a n is o tro p ie s in th e C M B were* g e n e ra te d in th e era o f c o m b in a tio n : a n y
p ro ce ss o th e r th a n re io n iz a tio n w h ic h a lte re d the’ C M B in te n s ity a fte r c o m b in a tio n
w o u ld n o t a lte r th e p o la riz a tio n , as there’ wemlel ne> lo n g e r l>e> su fficie m t num be’is e>f
e-hargeel se-atte’r in g beulie's: ( H i v e r ify th a t th e g ra v ita tie m a l in s t a b ilit y m o d e l o f c o l­
la p s in g p r im o r d ia l ele'iisity p e rtu rb a tie m s is c o rre v t at its e'arlie’St d ir e v t ly observable’
e’ p o c li: e-emibiuatiem: a n d ( l i i ) v e r ify t h a t th e p h o to n p m p a g a tio u ineiele’ ls whie-h le la te
the* e)l)se'rve>el in te n s ity e lis trilm tie m te> a set eif in it ia l eeismoleigie-al param e ’ te'rs are’ ae-e u ra te d y repre’s e n tin g th e se-atte’r in g e’ ve>nts whie-h eieeurre’el. In she>rt. a me'asure’ in e n t
e»f se-alar p e rtu rb a tie m s w em ld firm , a t w r y h ig h le e lsh ifr. the’ eib serva tie m a l fe>e>ting
011
whie-h fhe> g r a v ita tio n a l in s t a b ilit y p a ra e lig m re'sts.
Temseir {i n = ± 2 ) pe’rru rb a tie m s are* asseie-iateel w ith rlie' passage* e>f g r a v ita tio n a l
wave’s rh re m g h the' p rim e jrd ia l p la s m a . G ra v ita tie m a l wave’s are’ se d f-p re ip a g a tin g d is -
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9
F ig u re 1.4: S im u la te d p o la r iz a tio n G -m o d e p a t t e r n due to d e n s ity p e r tu r b a tio n s .
N o te th a t, o n th e se a n g u la r scales, p o la r iz a tio n p a tte r n is r a d ia l n e a r h o t (re d ) s p o ts
a n d ta n g e n tia l to c o ld (blue-) sp o ts. F ro m th e P h .D . the sis o f M . Z a ld a r ria g a
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SI
10
to r tio u s in th e s p a r e - tim e m e tr ic . Space in th e tw o d ire c tio n s p e rp e n d ic u la r to th e
d ire c tio n o f m o tio n o f a p a s s in g g r a v ita tio n a l w a v e e ith e r c o n tra c ts o r e x p a n d s , de ­
p e n d in g o n th e w a v e 's phase - th is e x p a n s io n a ffe c ts th e w a v e le n g th o f n e a rb y p h o ­
to n s a n d . th e re fo re ', t h e ir in te n s ity . T h e d ir e c t io n o f e x p a n s io n ro ta te s c lo c k w is e 1 o r
c o u n te r-c lo c k w is e as the* w a ve propagate's. a n d so g r a v it a t io n a l wave's have1 a wedlde'finc'd "lia n d e 'd n e s s ." A s g r a v it a t io n a l wave's pass t l u 1 s u rfa c e 'o f last se -a tte rin g . th e y
create1 b o th c u rl a n d riirl-fre 'e ' p a tte rn s in th e C M B p o la r iz a tio n fie'ld.
Dire*ct nie>a-
s u re m e n t e>f th e a m p litu d e ' a n d d is t r ib u t io n ejf te n se jr p e 'rru rb a tie m s w o u ld re'pre'se'iit
a b re a k th ro u g h in th e te 's tin g o f in fla tio n a r y m o d e ls o f c o s m o lo g ic a l e w o lu tio n prieer
te) th e e>ra o f c o m b iu a tie m . since* rhe'se m o d e ls p re 'clict p rim o re lia l g ra v ita tio n a l-w a v e 1
spe'ctra t h a t d e p e n d cm the* s p e c ific fo rm a n d a m p lit u d e o f the1 p o te n tia l th a t drive's
s u p e rlu m in a l e x p a n s io n [00]. M e a s u re m e n t o f a c u r l c o m p o n e n t to C’M B p e d a riz a tio n
m a y be1 c -o n ta m in a tc 'd . h o w e ve r, by w e a k g r a v it a t io n a l le n s in g o f the1 C M B
in the*
p e rio d s u b se q u e n t te> la s t s c a tte r in g [31].
1.4
CMB Polarization Angular Power Spectrum
Be'cause e>f its v e 'cto r n a tu re , the1 fo rm a lis m th re )u g h w h ic h we* e-ompare- m e'asure'inenr
anel the'eny is m ore1 e-omple'x fo r p e d a riz a tio n th a n it is fo r in te n s ity aniseuropie's. Siiie e'
a n is e u m p y e>f the1 C M B gene'rafe'.s pedarizatiem . it is n a tu r a l te) c>xte'lieI the1 fo r m a lis m
fo r a n a ly s is o f a n is e )tn )p ie s to p o la riz a tie jn .
M a p s fo r w h ic h the* C M B te 'in p e 'ra tu re '
T is k n o w n in evieh elire'e-rion h are* re m rin e ly a n a ly z e 'd v ia ew pansion ejf the* m a p in
spherie-al h a rm o n ic s
(1 .1 3 )
whe're1
( 1.14)
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11
a n d T,.rrlfj = 2.728 K is th e average te m p e ra tu re o f th e C M B [70]. T h e a u to - c o r r e la tio n
fu n c tio n C j . d e fin e d b y
(a hn 11I'm') ~ C f d l l ’ d,,,,,,'.
( 1-1-
is p re d ic te tl b y th e o ry . T in * C f ' * are exp<*cted t o ch'pend on s u c li c o s m o lo g ic a l p a r a m ­
e te rs as th e t o t a l m a ss-e n erg y d e n s ity {} o f th e C n ive rse . th e v a c u u m emergy d e n s ity
i l r . th e b a ry o n d e n s ity i l tl. H u b b le 's c o n s ta n t H t). and th e slope1 n o f th e [p rim o r­
d ia l p o w e r s p e c tru m , a m o n g o th e rs .
T h e m u lt ip o lc m o m e n ts <i[w are a re a liz a tio n
ot th e u n d e r ly in g s ta tis tic a l th e o ry th a t are s p e c ific to o u r universe1 a n d emr u n iq u e
v ie w p o in t w it h in it . T h e e x p e c te d variance1 in A T = T (n ) - T,.,„/, is
{(A T )-) = ^ = L ± i r / ' i r /
4 /t
d .iG )
where1 \ \ ) is a w in d o w fim c tie n i w h ic h take's inte> ae-e-ount the* / - spaee1 s e n s itiv ity epf the1
epbserving s tra te g y .
Fe)lle)wing Knepx [39]. we* e-emsieler a m a p maele1 epf th e em tire s k y w it h a G a u s s ia n
be'am.
The1 winelepw fune-tie>n
=
r ~ h,iT<. w h e re fy, is the1 G a u ssia n b e 'a m -w ie lth
[39]. T e m p e 'ra tu re flu ctuatiepns are1 me'asure'el w it h nepise1 pe>r [pixel rrT . The1 nepise* in a
m e'asurem ent epf the- tlie'epry jparame'te'rs C ] is
^
~ \i
{ l +
■
u
' 1 7 1
w ht're1 X,, is the1 n u m b e r epf inelepenele'nt jpixe'ls to r whie-h tem pe T a ture 1 me'asure'ine'nt.are maele1. Im jp o rta n tly . thcTe is a fu n d a m e n ta l U pw it lim it re> th e nepise1
C•
// nun
- i / —
fV 2 / + 1
a . i,i
w h ic h is in te r p r e te d as "cepsmie- variane-e1" anel is elite te> the1 fae-r th a t, at a n y a n g u la r
se-ale*. the're1 are1 a lim ite'el n u m b e r epf inele'peuiele'nf te m jp e 'ra tu re m t'a s u re m e n fs enie1 r a n
make* e>f the1 sky. whie-h is epf h n ite 1 sepliel are-a.
The1 m e a su re d te'in pe 'ra tu re 1 [pepwer s p e v fru in asseee-iated w ith the* B O O M E R A N G
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12
GOOO
w eak
DMR
396
■1000
0
.}
0
200
400
600
800
iOOO
I
F i^ m v 1.5: P o w e r s p e c tru m o f c o sm ic m ic ro w a v e b a c k g ro u n d flu c tu a tio n s o b ta in e d by
th e B O O M E R A N G in s tr u m e n t in an A n ta r c tic b a llo o n flig h t in W in t e r o f 1 9 9 9 /2 0 00 .
B O O M E R A N G p o in ts art* la b e lle d B 9 8 .’ L a rg e a n g le re s u lts o b ta in e d b y th e C O B E
D M R e x p e rim e n t a re la b e lle d D M R .' T h re e Q — 1 C D M m o d e ls a re in c lu d e d : s p e c ific
d e ta ils o f th o se m o d e ls c an be fo u n d in
41 .
m a p (F ig u re 1.1) is in c lu d e d as F ig u re ' 1.5.
K a m io n k o w s k i e t a l. 35 h ave d e ve lo p e d a fo rm a lis m v e ry s im ila r to t h a t d e s c rib e d
above' fo r th e a n a ly s is o f p o la r iz a tio n m aps.
( A s e p a ra te a n d e q u iv a le n t fo rm a lis m
has boon d e v e lo p e d b y Z a ld a r ria g a et al. 79 ). T h e y d e fin e a s y m m e tric , tra c e -fre e
te n s o r / ^ ( / t ) w h ic h d e s c rib e s th e lin e a r p o la riz a tio n o b s e rv e d in d ir e c tio n n — { O. o) .
I (
Q(n)
—( ' ( i i ) s in 0
\
-
~ y —( r{ n } s \ n O
(1 .1 9 )
—Q { n ) s i t r 0 J
B y a n a lo g y to (1 .1 3 ). I ’ . t A " ) is e x p a n d e d as a s u m o f a p p r o p r ia te o r th o n o r m a l basis
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13
fu n c tio n s o n th e sphere.
Ifinh
= YL H
Wlm } Urn
/ = I „ , = _/ -
(" ) +
,«/,( " >] •
( 1-~() >
w here
f
"in, = ^T—
(I ii P,lh ( / / ) } ' ( h) .
* fm/i ■’
(1 .2 1 )
<h„, = = r — I d h P.uA n )> a , / ' *( " )■
( 1.22)
a n d th e basis fu n c tio n s Yy(i\,nnh a n d Y ylm)fth a n* c o v a ria n t second d e r iv a tiv e s on th e
sphere ot th e u s u a l s p h e ric a l h a rm o n ic s V /,„. chosen because th e y a re a c o m p le te
o r th o n o r m a l b a sis sot fo r s y m m e tric tra c e -fre e te n so rs. T h e e x p a n s io n o f th e p o la r ­
iz a tio n te n s o r is b ro k e n in to tw o n a tu r a l sets o f b asis fu n c tio n s , la b e le d G a n d C .
since a s y m m e tr ic tra c e -fre e 2 x 2 te n s o r s u ch as P„i, can be w r it t e n as a s u m o f tw o
ten so rs, one w it h " e le c tric " o r " g r a d ie n t" p a r it y ( — l ) 7 and one w it h
" m a g n e tic " o r
" c u r l" p a r it y ( —
T h e m u lf ip o le m o m e n ts u[/ri. n(h n. a n d th e te m p e ra tu r e m u lt ip o lo m o m e n ts n /„ (
s h o u ld c o m p le te ly d e s c rib e a m a p o f th e C M B in b o th te m p e ra tu re a n d p o la r iz a tio n .
A n e x p a n d e d set o f p o w e r s p e c tra is needed t o f u lly c h a ra c te riz e th e te m p e r a tu r e a n d
p o la riz a tio n sta te ' o f th e C M B :
4m ')
=
C / Alt' (hnm' ■
(1 .2 3 )
"I'm ')
—
G,r<h),r
(1 .2 4 )
Ohm " I'',,, ■)
=
C 'O dif
4m ■)
=
C / ’r
Ohm " I'm ')
=
C '/
4m ')
=
C \ r Airh
04;
Ohm
Ohm
.
()ll'(\nm'■
hll'(\,im’■
( 1.20)
(1 .2 (i)
(1 .2 7 )
(1 .2 8 )
I f th e u n iv e rs e p re fe rs no o v e ra ll d ir e c tio n fo r C M B p o la riz a tio n . C 'f‘ ( a n d C'(, 1 are
zero b y s y m m e try . T h e re m a in in g C /'s e n c o d e fu n d a m e n ta l c o s m o lo g ic a l p a ra m e te rs .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14
G e n e ra tio n o f te m p e r a tu r e a n is o tro p ie s th r o u g h s c a la r processes such as g r a v it a t io n a l
c o lla p s e w ill p ro d u c e o n ly G '-ty p e p o la riz a tio n sin ce th e re is no p re fe rre d h a n d e d n e s s
o r c u r l d ir e c tio n fo r s u ch processes.
T e m p e ra tu re a n is o tro p ie s g e n e ra te d th r o u g h
te n s o r (a n d v e c to r) processes such as th e in flu e n c e o f p r im o r d ia l g r a v ity w aves w ill
p ro d u c e b o th G - a n d G '-ty p e p o la riz a tio n [35. 6 8],
T e m p e ra tu re a n d p o la r iz a tio n
p o w e r s p e c tra g e n e ra te d b y C M B F A S T [12] fo r a g iv e n c o s m o lo g ic a l m o d e l a re s h o w n
in F ig u re l.G.
T h e re a d e r is d ire c te d to K a m io n k o w s k i et a l. [35] fo r an e x te n s io n o f th is fo r­
m a lis m w h ic h a llo w s fo r th e c a lc u la tio n o f m u lt ip o le m o m e n ts and v a ria n c e s g iv e n
m e a s u re d p o la r iz a tio n tw o - p o in t c o rre la tio n fu n c tio n s .
In '(4.G. we w ill a p p ly th is
fo r m a lis m to an o b s e rv in g s tra te g y w h ic h m e a sures C M B p o la riz a tio n in a r in g a b o u t
th e n o r th c e le s tia l p o le .
In a n a lo g y to E q n . 1.1G. th e e x p e c te d v a ria n c e in t o t a l
p o la r iz a tio n Q~ + U~ is
<(/-’ +
C 1)
= 5 (y
w h e n 1 w e 've a ssum ed t h a t I F / ' = I F /
+ y
.
(i.a-ji
= IF /, th e w in d o w fu n c tio n c a lc u la te d fo r th e
e q u iv a le n t C M B A T e x p e rim e n t [35].
1.5
Measurements to Date
T w o re ce nt m e a s u re m e n ts p ro v id e th e m u st s trin g e n t u p p e r lim its o n th e p o la r iz a ­
t io n a n g u la r p o w e r s p e c tru m .
p la c e d lim it s on C'j' a n d C'j
A t m e d iu m a n g u la r scales. H o d m a n et al.
[24] have
w it h a g ro u n d -b a s e d c o r r e la tio n p o la rim e te r. P IQ U E .
T o s im p lify th e c o m p a ris o n o f one e x p e rim e n ta l re s u lt to a n o th e r, p o la r iz a tio n m e a ­
s u re m e n ts are o fte n e xp re sse d in te rm s o f ''H at b a n d p o w e r" te m p e ra tu re s , such th a t
/ ( / + I )G’/' / 2 ~ = T f w h e re X re fers to G - a n d G '-ty p e p o la riz a tio n . In th e m u lr ip o le
w in d o w s ( l ( ; ) = 2115/],', a n d (G-) = 2 1 2 lf.fr] th e y p la c e (Jb'/f co n fid e n c e lim it s o n th e
fia t b a n d p o w e r o f th e G - a n d G '-ty p e p o w e r s p e c tra o f 10 a n d !J //A ' re s p e c tiv e ly ,
a n d a lim it on th e G r'-type s p e c tru m o f 7 / / A ’ i f G /
is a ssum ed to be zero.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Those
re s u lts have been d iv id e d b y \J2 to a c c o u n t fo r th e d iffe re n c e b e tw e e n th e G A C'
lo r in a lis in fo r p o la riz a tio n p o w e r s p e c tra lis t'd here a n d th e E A
B fo rm a lis m used
b y H e c lin a n e t a l. T h is u p p e r lim it , a lo n g w it h p re d ic te d a n g u la r p o w e r s p e c tra fo r a
chosen c o s m o lo g ic a l m o d e l, a rt' p lo tt e d in F ig u re l.G.
A t la rg e a n g u la r scales. K e a tin g e t al. [37] have p la ce d lim it s
011
C'\' a n d C \
w it h
a g ro u n d -b a s e d c o rre la tio n p o la r im e te r . P O L A R . I 11 th e m u ltip o le w in d o w s 1 = 2
20 th e y p la c e Oo'X co n fid e n c e lim it s
p o w e r s p e c tra o f 7 f i K . a n d a lim it
011
011
th e fla t b a n d pow ers o f t i n 1 G - a n d C - ty p e
th e G’- ty p e s p e c tru m o f G //A * i f C j
is assum ed
to be zero. A g a in , these re s u lts have been d iv id e d b y \ / 2 to a c c o u n t fo r th e d iffe re n c e
b e tw e t'ii th e G A' C fo rm a lis m fo r p o la r iz a tio n p o w e r s p e c tra used h ere a n ti r lit' E A
B fo r m a lis m used b v K e a tin g et a l.
100.00
10.00-
1
S
. 0
0
f>0LAR
PIQG'E
-
0.10
0.01
10
100
M u ltip o lo
1000
M om ent
F ig u re l.G : M o d e l a n g u la r p o w e r s p e c tra g e n e ra te d by C M B F A S T [12] are p lo tte d fo r
a B O O M E R A X G - c o n s is te n t u n iv e rs e w it h p r im o r d ia l s c a la r s p e c tra l in d e x //>■ = 0.07.
H r = 1 — ns- a n ti r a tio o f c o n t r ib u t io n s to r li t ' 1 = 2 A T q u a d ru p o le fro m te n s o rs a n ti
sca la rs T / S
- 7( 1 —/ ; s ) - 0.21. S o lid lin e is G -fy p e p o la riz a tio n , d a s h e d lin e is C -ry p e
p o la r iz a tio n , a n d d o tte d lin e is best fit te m p e ra tu r e p o w e r s p e c tru m ft) B o o m e ra n g
d a ta . U p p e r lim it s a rt' fro m th e P IQ L ’ E a n ti P O L A R e x p e rim e n ts , a s s u m in g C’j = 0.
as d e s c rib e d a n d referenced in te x t.
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1G
The* S a s k a to o n e x p e rim e n t [52] p u t a (J 5 ‘/< c o n fid e n c e u p p e r l i m i t o f 1G f i K on
C M B p o la r iz a tio n in th e a n g u la r scale ra n g e c o rre s p o n d in g to 50 <
I <
100.
At
s m a lle r a n g u la r scales. 1' < H < .‘3'. P a r tr id g e e t a l. [55] p u t a 9 5 (T c o n fid e n c e u p p e r
lim it o f 100 f i K on p o la r iz a tio n .
(T h e s e d a ta h ave n o t been re a n a ly z e d to p ro v id e
m e a n in g fu l b a n d p o w e r lim it s fo r in c lu s io n in Figure* l.G .)
1.6
Measurements Planned
O n Ju n e .30. 2 0 0 1 . N A S A ’s M ic ro w a v e A n is o tr o p y Probe* ( M A P ) be*gan its t r i p te> the*
L2 E a rth -M e io n Lagrange* p o in t" . A lt h o u g h it is p r im a r ily inte*nele*d te> me*asure* te*mpcrature* a n is o tro p ie s , it also has s e n s it iv it y to p e d a riz a fio n . E S A ’ s P la n c k S u rv e y o r,
to be* la u nch e 'd in 2007. w il l cre*ate f u ll- s k y m a p s in ped a riza tiem a t m a n y fre*cpie*ne ie's'5.
T h e H ig h F re q u e n c y In s tr u m e n t ( H F I ) o n th e P la n c k S u rv e y o r s h o u ld la* sensitive*
enemgh to a llo w p e d a riza tie m a n g u la r penver sp ecfro sce jp y.
In advance* o f these o b s e rv a to rie s , m a n y p ro je c ts are planne*d o r alre*adv unde*rway.
E x p e rim e n ta l te c h n iq u e s v a ry g re a tly , w it h s ig n ific a n tly d iffe re n t cle*fe*e-ror systeuns
(in c e d ie re n t. ce diere n t corre*latie>n. a n d eedieremt D icke *-sw itche d p e d a rim e te rs ). pedariza tie m a n a ly z e rs (o rth o m e id e transchic-ers. w ir e g rid s , p o la riz a tio n -s c u is itiv e * bolemie*te*rs. anel wave* p la te 's), e ib serving freciuene-ies (b e tw e e n 15 a n d 400 G H z ) . te'le>sc-ope*s
( upw ard-le>e)king h o rn s , single* o n - a n d e iff-a x is dishe's. anel in te 'rfe re u n e te 'rs ). b ea m
size's (freun 7C t o 2 .5 ’ ). o b s e rv in g sire s (b a llo e u i- a n d sate'llife'-beirne* as we'll as g ro u n d base'd). anel sca n strate'gie's (sw itche'el. scanne'd. anel drift-se-anne'el: o b s e 'rv a rio n s o f
rin g s , patche's. eir the> emrire* s k y ).
Feir a re'vie'w o f senne* e airrent p o la riz a tie m e*.xpe'ri-
m e n ts . sea* S ta g g s e>t a l. [72].
In p a r tic u la r , the' L 'liiv e r s ify o f C liica g e j-b a se 'd De'gre>e A n g u la r Se-ale Inte'rfe'rome*teir ( D A S I ) 1. [)rom ise's h ig h s e n s itiv ity te» C M B p o la r iz a tio n fre)in its le>e*arie>n a t the*
S eaith Pole'.
D A S I re 'c e n fly e-omplete'el a s u rv e y o f inte'rm e’eliate' a n g u la r scale* C M B
_XT ffu e -tu a tio n s [G2. 22. 45] anel was re 'co n fig u re 'd fo r p o la riz a tie m e>bservations in
~http.'/'/rii n p. i/sff. rui.so. i/or
,f lift p:/ ' / astro, i s t r r . r s i i . n l / S A - i p n i r t i l / P rojret s ' P l a i n k
1l i t t p : / / astro, ur/iirat/o. i t i n/ i l nsi /
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17
W in t e r 0 0 /0 1 . O b s e rv a tio n s w ere m arie o v e r th e re ce n t a u s tra l w in te r , a n ti a n a ly s is
o f th e p o la r iz a tio n d a ta is o n g o in g . T h e c o m p le m e n ta ry C a lte c h -b a s e d C o s m ic B a c k ­
g ro u n d Im a g e r ( C 'B I ) :> m e a s u re d s m a ll a n g u la r scale A T flu c tu a tio n s [55], a n d has
been re c o n fig u re d fo r p o la r iz a t io n o b s e rv a tio n s fro m its s ite on the' A ta c a m a P la te a u
in C h ile [7].
1.7
Observing Strategies
F o r a n y C M B p o la r iz a tio n e x p e rim e n t, th e in s tr u m e n t d e s ig n a im s to u tiliz e a v a ila b le
e x p e rim e n ta l re so u rce s t o m a x im iz e th e p o la r iz a tio n s ig n a l o f in te re s t w h ile m in im iz ­
in g sources o f s t a t is t ic a l a n d s y s te m a tic e rro r.
C h o ic e o f o b s e rv in g fre q u e n c y is as c r it ic a l to C M B p o la r iz a tio n e x p e rim e n ts as it
is to C M B A T e x p e rim e n ts , w it h th e c o m p lic a tio n t h a t som e p o la r iz a tio n a n a ly z e rs
(su ch as h a lf-w a v e p la te s ) a n ' fu n d a m e n ta lly c h ro m a tic . G ro u n d -b a s e d o b s e rv a to rie s
m u s t c o n te n d w it h a tm o s p h e r ic ('m is s io n a n d a b s o rp tio n , w h ic h is a s tro n g fu n c t io n o f
w a v e le n g th . M o v in g t o lo n g e r w a v e le n g th s re d u ce s b a c k g ro u n d d e te c to r lo a d in g fro m
s k y te m p e ra tu re , b u t in cre ase s s e n s itiv ity to g a la c tic s y n c h r o tro n ('m is s io n , w h ic h
c a n be h ig h ly p o la riz e d .
D u e to th e u n k n o w n d is t r ib u t io n o f g a la c tic fo re g ro u n d
('m is s io n , e s p e c ia lly p o la r iz e d e m is s io n , m u lti- fr e q u e n c y e x p e rim e n ts a re p re fe ra b le .
H o w e ve r, m u lti-fre q u e n c y , m u lt i- p ix e l fo ca l p ia n o s re q u ire o ff-a x is p ix e ls . O ff- a x is re­
fle c tio n s w ill in tr o d u c e p o la r iz a tio n o ffsets w h ic h m a y v a ry w it h o b s e rv in g c o n d itio n s
o r p o in tin g d ir e c tio n . O b s e rv a tio n a l s tra te g ie s based o n s e q u e n tia l o b s e rv a tio n s w ith
d iffe re n t s p e c tra l b a n d s s u ffe r d u e to th e lo n g in te g r a tio n tim e s w h ic h w il l be re q u ire d
to obse rve p o la r iz a tio n s ig n a l a t a n y sin g le fre q u e n c y .
In s tr u m e n t b e a m -s iz e is d e te rm in e d p r im a r ily b y th e s c ie n tific g o a l o f th e e x p e r i­
m e n t. T h e m a c ro s c o p ic w a v e le n g th s o f C M B r a d ia t io n ( A
~
1 n u n ) m e a n t h a t re­
a lis tic a lly sized o p t ic a l s y s te m s p ro d u c e la rg e d if f r a c t io n - lim it e d b eam s (ti ~ A / D , , i ) .
e s p e c ia lly at lo n g w a v e le n g th s . S in ce p o la r iz a tio n s ig n a ls m u s t be c a u s a lly g e n e ra te d
a t th e su rfa c e o f la st s c a tte r in g , th e a n g u la r scale's o f in te re s t are at o r b e lo w th e
‘ht t p: / / i n n r . a s t r o . r a l t i <h.< rhi/ t j p / C D l ,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18
h o riz o n size a t th e tim e o f s c a tte rin g . L a rg e -a n g u la r scale p o la r iz a tio n (/ ~ 20). p o ­
te n tia lly g e n e ra te d a t a la te la st s c a tte rin g d u r in g re io u iz a tio n . ca n he o bse rve d w it h
large teed h o rn s d ir e c tly . S m a ll-a n g u la r scale p o la riz a tio n (/ ~ 5 0 0 ). g e n e ra te d in th e
era ot c o m b in a tio n , m u st be o b s e rv e d w it h telescopes w it h large' c o lle c tin g area.
R a d io -w a v e le n g th d e te c to rs h ave t r a d it io n a lly d e te c te d a s in g le - p o la riz a tio n b y
m a k in g use o f w a v e g u id e p o la r iz a tio n a n a ly z e rs such as o r th o m o d e tra n s d u c e rs to
se pa ra te th e tw o senses o f lin e a r p o la r iz a tio n .
H a lf-w a v e p la te s h ave been u tiliz e d
to m o d u la te th e in c o m in g p o la r iz a tio n p a tte rn .
A lte r n a tiv e p o la r iz a tio n a n a ly s is
schemes u tiliz e ’ w ir e g rid s o r p o la r iz a tio n se n s itiv e d e te c to rs to ana lyze 1 the’ pedarizariem e)f tw o se p a ra te 1 beam s.
F o r in s ta n c e . twet e o n e rm tra tin g feeds r a n illu m in a te 1 a
large’ w ir e g r id p o s itio n e r! a t a 45° a n g le w it h respect te> in c o m in g raeliarie>n.
The1
reje’ctiem ed’ c o m m o n m o d e s ig n a l in th a t case wemld d e p e n d em he»w we’ ll the1 twe> sej>arate’ beam s ca n be’ a lig n e d em th e sky. T h e q u a lify ed p e d a riz a tio n a n a ly s is prew iderl
b y siele’-b y-sid e ’ sin g le -p e d a riz a tie m d e te cte trs ed' v a ry in g e irie n ta f io n w ill de’penel em the1
s t a b ilit y o f th e d iffe r in g side-le)be a n d edf-axis etpfieal responses o f th e rwe> eh’te’e-teirs.
Pedarizatiem s e n s itiv e bedom eters w il l seton p ro v id e an a ttra e -tiv e w a y to me'asure1 b o th
se'nse’s o f liu e 'a r p e d a riz a tio n in a single' be’a m . u tiliz in g a e-emipact fee'd s tru e tu re 1 [54].
Chede-e o f eebserving p la tfo r m a n d dere’cten- system w ill u lt im a t e ly de'te'rm ine the'
a m o u n t o f in re g ra tie m tim e ’ necessary te> make’ a s ta t is t ic a lly s ig n ifie a n t ele'tevt iem
e>f p o la riz a tio n .
T h e S o u th Pede1. M a n n a K en. the’ A ta c a m a p la te m u in C h ile 1, anel
b a llo o n a ltitu e le s are’ a ttr a c tiv e ed>se'rving leecations elite* te> the1 lo w c o lu m n d e n s ity
e»f water- vapeir.
CMB
pedarizatiem memsurememts. he)we’ ve*r. are1 s u b je c t te> p o te n ­
tia l s y s te m a tic e’ffe c ts w h ic h have n e v e r before1 b e rn encemnte're'd. nett e'ven in ty p ic a l
n iillim e 'te r-w a v e ’le n g th m e a s u re m e n ts o f p o la riz e d e n iissio n frenn galae t ic anel e'xtragalactie- soure-es. Senne1 te n n is have1 chosen te> fo rg o p re m iu m edtse’r v in g cemelitiems in
exchange1 fo r the1 th o re m g h u n d e rs ta n d in g e>f p o la riz a tie m s y s te m a tie s t h a t in s tru m e n ­
ta l ae-e-e’.s s ib ility providc'.s.
G re m n d - a n d ballexm -benme m e n s u re m e n ts in the1 e m iiin g
yenrs w ill la y the1 grem nelwetrk fo r a deelie-aterl. spaee'craft-benme’ in s tru m e n t ca pa b le
e>f preddng the1 g ra v ita tie m a l-w a v e 1 e -o n trilm tie m te> C M B p o la riz a tie m .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
19
Chapter 2
Polatron Receiver
In th is e h a p te r. wo in tr o d u c e fin d d e s c rib e th e P o la tro n . a C M B p o la r im e te r . S p e c ific
e m p ha sis is pla ced
011
th e o p tic a l d e sig n o f th e telescope a n d re c e iv e r.
D e ta ile d
d is cu ssio n o f th e c ry o g e n ic s y s te m is d e fe rre d to th e n e x t c h a p te r.
2.1
Introduction
T h e P o la tro n is d e s ig n e d t o be used a t th e
0 .0
111
telescope a t th e O w e n s V a lle y
R a d io O b s e rv a to ry ( O Y R O ) to m easure C M B p o la r iz a tio n
011
a n g u la r scales w h e re
th e sig n a l is e x p e c te d to be h ig h e s t, a n d in a s p e c tra l b a n d w h e re g a la c tic fo re g ro u n d s
are e x p e c te d to be lo w e s t. T h e ra d io m e te r sh a re s m a n y e le m e n ts o f d e s ig n w it h th e
S u Z IE [29] a n d B o o m e ra n g [10] e x p e rim e n ts a n d w it h E S A 's P la n c k S u rv e y o r.
A
single1 entrance1 level is eouph'el te> an eirthem iexle1 tra n s e lu e v r ( O M T ) . w liie -h effie-iem tly
se'parate's the1 twe> s ta te s o f lin e v ir p o la r iz a tio n . Eae-h O M T e m tp u t is s p e v tr a lly filteTe>el
anel them te r m in a te d in a s ilie e m -n itrid e 1 m ierem ie'sh bedemie'ter. T h e 1 bedenne'teT s ig n a ls
are* e T v tre m ic a lly eliffereuievd. p re x lu c in g a s ig n a l t h a t is p re ip o rtio u a l te> the* eliffe're'iiev
in optie-al pe)we*r in the1 tw o a rm s e>f the1 O M T . A h alf-w ave 1 p la te 1 plaevel in fro n t o f
the1 iv e v iw r e-ontinuem sly m ta te 's the1 iiic e n n in g plane* e>f pedarizatiem . a llo w in g
11s
te>
a lte rn a te 1 be'tw evn m e'asurem e'iirs o f Q anel L ' a t a m n d u la tie m fre'epie'iie v we1 ehoose1.
T h is preivides a stre m g ehevk em s y s te m a tic erreirs. The1 eletevteirs are1 fe u d e d te> 0.25
K b y a c o m b in a tio n ed a edosed-e-ycle1 m e v h a iiic a l crveu-euder anel a clejsed-eycle1 tlir e v stage1 h e liu m seirptie^n e-oeder.
A syn o [)sis eif the* e 'xp e rim e m ta l s p e 'c ific a tio n s can be1
femnel in Table1 2.1. A scheunatie- e>f the* pedarim e'te'r is iiic lu d e 'd as F ig u re 1 2.1.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
WIRE
cao
WAVEPLATE
SPEED REDUCER
10 WAttNUMBER FITER
8 WAVENUM8ER FITER
FEEDHORN
SNOUT VACUUM SHROUO
WAVEPlATE MOTOR
SNOUT 80 K SHELD
SNOUT « K SHELD
RF BAFTU
orthom ooc transducer
VACUUM SHROUD EXTENSION
80 K RAOIADON SHELD EXTENSION
4 K RADIATION SHIELD
FIRST F4 CONCAL FEED
FEEDHORN SUPPORT
OPTICAL FITERS
SECONO F4 CONCAL FEED
BOLOMETER
SORPTION REFRIGERATOR
JFET BOX
250 mK TABLE
4 K R f FILTER BOX
VESPEL LEG
4 K BASEPLATE
ACCELEROtCTER
4 K TFCRMAl IN K
8 0 K BASEPLATE
4 K SUPPORT RING
SAPPHRE IN K
80 K THERMAL LNK
80 K SUPPORT RING
BO K BAFFLE
300 K BASEPLATE
ELECTRICAL CONNECTOR
OTrOCOOLER VACUUM CAN
CRYOCOOLER 80 K SHELD
4 K - 20 K HEAT EXCHANGER
POLYETHYLENE COUPlNC
CRYOCOOLER 20 K CM STAGE
20 K - 80 K HEAT EXCHANGER
PNEUMATIC CYUNOCR
BELLOWS
CRYOCOOLER 80 K GM STAGE
ISOLATOR ADAPTER PLATE
80 K - 300 x
h EAT
EXCHANGER
CRYOCOOLER 300 K FUNGE
JT VALVE MICROMETER
ty r
®F+1
—
JT HQJUM RETURN
GM HELIUM RETURN
GM HELIUM SUPPLY
&
Ww H L
& -
DtSPlACER electrical connector
CRYOCOOLER MOTOR HOUSING
F ig u re 2 .1 : P o la tro n G e n e ra l A s s e m b ly .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
21
Tele'scope:
5 .5 m C’assegrain Focus
P o la r iz a tio n A n a ly s is :
R e g a tin g Wave- P la te a n d
O r th o m o d e Transdue-eg-
P o la r iz a tio n Efficiene-y:
> 95M
S p c 'c tra l B a n d :
88
B e a m Size:
2 .5 a rc in in n te s F W H M
D e te c to rs :
S ilic o n - N it r id e M ie ro m e s h
B o lo m e te rs
S e n s itiv ity :
~ 5 0 0 / / K s 1 2 to Q a n d [
100 G H z
T a b le 2.1: R e e e ive r S p e c ific a tio n s
2.2
Telescope
T h e d e s ig n o f th e P o la tro n o p tic s a im s to m in im iz e b a c k g ro u n d lo a d in g a n d sys­
te m a tic p o la r iz a tio n e ffe c ts w h ile 1 e ffic ie n tly c o u p lin g the1 d e te c to rs to th e s k y w ith a
b e a m m a tc h e d to a n g u la r scales o f s c ie n tific in te r e s t. The1O V R O 5.5 m te le sco p e (F ig ­
u re 2 .2 ) is id e a lly s u ite d fo r such o b s e rv a tio n . F ro m 1992 to 1997. th is telescope1 was
eh'die-ate'd t o m e 'a su re m e n ts o f p r im a r y a n d seg-ondary C M B a n is o tro p ie 's as de'scribe'd
in Hen-big eg a l.. M y e rs eg ah. Legteh eg a l.. a n d M a so n eg al. [25. 51. 44. 48). A s p a rt
o f th is p ro g r a m , the1 te-k'se-ope1 was moelifie'el to m in im iz e the* w a rm g ro u n d egnission
th a t e-ouples in te i the1 ren-eiver b y s e a tte 'rin g fre m i th e sevonelary m ir r o r suppegg h'gs.
re 's u ltin g in a megisure'd g ro u n d spilloveg- te g u p e ra tu re 1 o f 9 I \ [42].
T h e 1 tedegse-ope1 has neve-r bedbre1 be'en use'd a t w ave'le'iigths <
1 em .
A lth o u g h
th e surfae-e1 is s u ffie d e n tly sm eioth em w a v e le n g th se-ales. large-se-ale1 d is h de'form itie's
m ig h t d is te irf and/eg- d ilu te 1 o u r begun. The1 elish eemsists o f 1G p an e ls, egich o f w h ic h
is eledbrm able1 a n d suppe>rte*d in nine1 plaee's w it h b o lts anel e-alibrate'el brass sh im s
(F ig u re 1 2 .3 ). B y altegdng the1 phase1 fre>nt d is t r ib u t io n o f the1 begun a t th e d is h surfaee1.
a g a u s s ia n d is t r ib u t io n o f surfae-e d e fo rm itie 's elescribeel b y an m i .s d e v ia tio n
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
fro m
22
F ig u re 2 .2 : A p h o to o f th e O Y R O 5 .5 m telescope.
p a r a b o lic s c a tte rs p o w e r o u t o f th e m a in b ea m .
T h e R u z e e q u a tio n
0 7 : re la te s th e
loss in p o in t so u rce g a in g fo r o b s e rv a tio n s at w a v e le n g th A fo r such p e r tu r b a tio n s .
g - r
f'-2'
A>'.
(2 .1 )
W h e n th e telescope* w as assem blerl at its o r ig in a l T a b le M o u n ta in site*, th e surface*
w as m e a su re d a n d se t to 0.20 m m
rrns a ccu ra cy.
W h e n th e telesco p e w a s la te r
d is a sse m b le d a n d m o v e d to tlu * O w ens V a lle y , th e s h im thickne sse s were* recordc*d
a n d re p ro d u c e d , b u t u p o n re a sse m b ly no ne*w s u rfa c e m e a su re m e n t was m a d e
In
F e b ru a ry . 1999. we m e*asured the* shape o f the* d is h w it h a n a rra y o f h ig h -r e s o lu tio n
A C -b ia s e d c a p a c itiv e semsors mounte*d on a r o t a t in g p a ra b o lic a rm .
d is c u s s io n o f th is c a m p a ig n can be* fo u n d in
09b
On >
A th o ro u g h
10 em le n g th scales, th e
m e a s u re d surface* rm.s a c c u ra c y w as 0 .2 4 ± 0 .0 2 m m o r ~ A /1 3 fo r A — 3 m m . Re*moval
anel a c ld itio n o f s h im s undc*r the* surfac e* allo\vc*d us t o rc'ducc* the* rm.s surfac e a c c u ra c y
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23
F ig u re 2.3: S u rfa c e s e ttin g c a m p a ig n . T o p le ft: p h o to t.aken d u r in g in s ta lla tio n o f a
p re v io u s ly u n u se d p a n e l. T o p r ig h t: re a tta c h m e n t o f p a n e l to te le sco p e s u p p o rt a fte r
s h im th ic k n e s s h a d bee n c h a n g e d . B o tto m : c lo s e -u p o f th e m e a su re m e n t a rm a n d
c a p a c itiv e sensors: p a n e l in p h o to was la te r re p la c e d .
to 0.15 ± 0 . 0 2 m m o r ~ A /2 0 ( F ig u r e 2.4).
U p o n re fle c tio n o ff a m e ta l s u rfa c e , u n p o la riz e d lig h t b e co m e s p a r tia lly p o la riz e d
in a d ir e c tio n a lo n g th e r e fle c tin g su rfa c e
234
F o r th e ty p e o f o ff-a x is te le s c o p e s
fa v o re d fo r lo w -b a c k g ro u n d C M B A T m e a su re m e n ts, la rg e p o la r iz a tio n o ffse ts a ris e
w h ic h m a y d e p e n d on p o in t in g d ir e c tio n a n d d is h te m p e ra tu r e . In o rd e r to m in im iz e ’
th e n u m b e r o f re fle c tio n s , p a r t ic u la r ly o ff-a x is re fle c tio n s , th e P o la tr o n re c e iv e r b e a m
w a is t w ill be p la c e d d ir e c t ly a t th e C a sse g ra in fo cu s o f th e te le s c o p e , w h ic h lie s 4 5 .7
c m above th e p a r a b o lic surface'. A s in g le e’titra n c e fevd illu m in a t e ’s the 1p r im a r y m ir r o r .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
24
H
I
9
1
M*
>
>1
Q.
0.5
A
”
|
-<>.5
S
&SQ
-1.5
. » v /
■'
•O
rg
w-v
m
A zim u th al B in
F ig a ro 2.4. S u rfa c e s o ttin g c a m p a ig n . T o p le ft: im a g o o f su rfa ce h e ig h t flu c tu a t io n s
m ack' b y m e a s u re m e n t a rm b e fo re im p ro v e m e n ts w ore m ade.
T o p r ig h t:
im a g e o f
sam e, a fte r im p ro v e m e n ts . B o tto m : p lo t o f s u rfa c e h e ig h t flu c tu a tio n s as a f u n c t io n
o f a z im u th a n g le at a fix e d ra d iu s : b lu e is b e fo re , ro d is a fte r im p ro v e m e n ts . A z im u t h a l
b in n u m b e r o n e c o rre s p o n d s to n o r th in th e p o la r m a p s.
2.3
W aveplate
In fro n t o f the* e n tra n c e feed is p la c e d a r o t a t in g , a m b ie n t te m p e ra tu re , b ir e fr in g e n t.
c r y s ta llin e q u a r t z h a lf-w a v e p la te 1 7.G c m in d ia m e te r a n d 3.2G c m th ic k .
T h e w a ve
p la te g e n e ra te s a ~ p h a se re ta r d a tio n b e tw e e n e le c tr ic fie ld v e c to rs w it h w a v e le n g th
~ 3 m m in c id e n t o n th e fast a n d s lo w r e fr a c tio n axes o f th e q u a rtz .
C o n s e q u e n tly .
the1 p o la r iz a t io n p a t t e r n fro m th e s k y is re fle c te d a b o u t the' o p tic a x is , r e s u lt in g in
m o d u la tio n o f th e p o la r iz a tio n s ig n a l a t fo u r tim e s th e p h y s ic a l r o t a t io n r a te o f th e
1V a lp e y -F is h e r C o r p o ra tio n . 75 S o u th S tre e t. H o p k in to n M A 0174s
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wavp p la te .
T h is m o d u la tio n te c h n iq u e is e m p lo y e d r o u tin e ly in m illim e te r-w a v e
p o la r im e tr y as it a llo w s b o th Stokes p a ra m e te rs Q a n d U to he m e asured w it h a
sin g le h o rn [21. 49].
T h e p o l a r i z a t i o n e f f i c i e n c y o f an o p tic a l e le m e n t is th e degree to w h ic h a lOO'/f
p o la riz e d s ig n a l w ill re m a in p o la riz e d o n passage th r o u g h th e elem ent. T w o e ffe c ts a re
e x p e c te d to re d u c e th e p o la riz a tio n e ffic ie n c y o f th e w ave p la te . F irs t, o b s e rv a tio n s
are m a d e o v e r a b ro a d s p e c tra l b an d , w h ile th e w a ve p la te is fu n d a m e n ta lly c h ro m a tic .
S econd, th e o p tic s o f th e telescope are m o d e r a te ly fa st, f / - i . 2 . D iffe re n t p a rts o f o u r
b ea m tra v e l d iffe re n t p a th le n g th s th r o u g h th e q u a r tz , so a phase' re ta r d a tio n o th e r
th a n 7T w ill re s u lt fo r those* p a rts o f th e b e a m . In o rd e r to m itig a te 1 th is see-emd e'ffe'ct.
the1 wave1 p la te is p la c e d in the* near fie ld o f th e e n tra n c e feed, where- the1b e a m is m o st
c o llim a te d . O n e c a n c a lc u la te 1 th e e x te n t to w h ic h an in p u t polarize'd sig n a l fro m the1
s k y w ill be d e p o la riz e d b y these* twe> e ffects. In th is s y s te m suedi a c a le u la tio n pn*die-ts
a p p r o x im a te ly 9 8 ‘X p e d a riz a tio n effie-iene-y (se*e A p p e n e lix A ) . T h is e*ffie-ie*ne-y e*ffe*e-r
e-an be me*asure*el anel e-eu-revfe'el fo r w ith g re a te r aee-uracy th a n o u r a n tic ip a te s ! ove*rall
e-alibratiem u n e *e rta in ty. anel is eliffe*re*nr fro m the* sourevs o f system atie- p o la riz a tie m
elise-ussesl Iate*r.
2.4
Focal Plane
The* fbe-al plane* fe*e*el s tru e -tu re we1 em plety is a m o e lifie a tie m o f a ele>sign [ l l j use-el b y
B O O M E R A N G . M A X I M A , anel AC’ B A R [90], anel base'line-d fo r use1 on the1 Plane-k
H F I. F ig u re 1 2.b is a e-artemn eliagram o f the1 P o la tro n fe*e*el s tru c tu re 1, illu s t r a t in g
the1 im p e trta n t wave'guide1 anel e-one-e'titrating co m p o n e m ts. The* de>sign was d riv e 'll b y
se've'ral e-eme-ems: in th e subse'e-tiems be'lenv. we> iteunize1 thecse* e-onee'rn.s anel elise tiss h o w
e'ae-h was aeldre'ssesl in the1 ele'sign.
2.4.1
Thermal Mass and Profile
De-sign o f lo c a l plane's fo r tede'se-ope's w it h Iim ite'el fiedels o f vie>w re*e|uires edose'-pae-king
o f seve'ral n a rro w -p m file 1 fevels.
A lth e m g h the1 Pedatrem is a s in g le -p ix e l ewpeudmcmt.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
26
Low-Pass
Metal-Mesh
Rlters
HDPE Vacuum
Window (300 K)
Orthomode
Transducer
Corrugated
Feedhom (4 K)
f/4 Conical
Homs
Bolometers
HDPE Lenses
0.25 K 4.2 K
Thermal Gap
1 cm
High-pass
Waveguide
Choke
Rectangular
to Circular
Waveguide
Transitions
Waveplate
Blocking
Rlters
(77 K and 4 K)
F i^ u n - 2.5: C a r to o n d ia g ra m o f th e P o la tro n o p tic a l feed s tr u c tu r e , b lo c k in g filte rs ,
a n d a m b ie n t te m p e ra tu r e h a lf-w a v e p la te .
t lit ' p o s itio n o f th e 5 .5 m telesco p e fo c u s a b o ve th e surface' o f th e telescope' lim its th e
g ir t h o f the* e x p e rim e n t as a whole'. T h e re is nej e'C|uivalent lim it to the* le n g th o f th e
fee'd. A d()c w a ve gu id e' benel in the' ” sich '-" e>r " o ff-" chaim ed a llo w s us to m a in ta in a
s lim pre>file' w it h o u t elegraeling th e o ff-c h a n n e l g a in . D u e te> the* / / 3 . 2 oprie-al de'sign
o f the' telt'se-ope'. th e e n tra n c e teed is epiite' la rg e : 4.1 emi in ape'rture* diam e'te'r anel
16.3 e-m in le 'iig th .
In orele'r to lim it the' raeliative' loael em o u r ele'teete>rs. a ll e-ennpenients in th e feeel
s tru c tu re ' m u s t be1 e-ooled to e rvoge'tiie- te in p e 'ra ru re s . The' lim ite 'd vending pow ers e»f
th e me'e-hanie a l e-ryoe-exder anel he'liu m seapfiem e-e)e>ler rc 'c p iin ' m in im iz a tie m o f the1 lie'at
e-apae-ity ed' the* e 'litire ' strue-ture'. T o t h a t e'liel. a ll e-emiponents are* u ia c h iu e e l o r e'le'e tre >fbrme'el fre m i o x y g e n i-fm * h ig h -e -o n e h ic tiv ity (O F H C ) C'u. In a e ld itio n . a ll e-emipone'iits
are> lig h t-w e 'ig h te 'd to the* e'.xtent th a t sue li e 'ffo rts elo ne)t e e)inprom ise' s tre n g th .
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2.4.2
Polarization Analysis
F lu c tu a tio n s in a tm o s p h e r ic e m issio n are a n im p o r t a n t fa c to r in th e d e g r a d a tio n o f
s e n s itiv ity o f g ro u n d -b a s e d m illim e te r-w a v e C M B e x p e rim e n ts . R e je c tio n o f c o m m o n m o d e s ig n a l b e tw e e n tw o p o la riz a tio n c h a n n e ls a llo w s g ro u n d -b a s e d p o la r im e te r s to
a chieve h ig h s e n s itiv ity .
O u r a tm o s p h e ric m o d e l d e ta ile d in j;4.2.4. su g g e sts t h a t a
c o m m o n -m o d e r e je c tio n r a t io (C 'M R R ) g re a te r th a n 100 sh o u ld e ffe c tiv e ly e lim in a te
th e c o n t r ib u t io n t o t o t a l re ce ive r noise fro m a tm o s p h e ric 1 /f noise. T h is c o rre s p o n d s
to a m a tc h in g b e tw e e n p o la riz a tio n s ta te s o f <
iz a tio n o f <
V Z . o r a s y s te m a tic re c e iv e r p o la r ­
VZ - T o a ch ie ve th is , a w a v e g u id e ch oke jo in s th e e n tra n c e ' fe t'd to an
o rth o -m o d e tra n s d u c e r . T h e o rth o -m o d e tra n s d u c e r ana lyze s th e p o la r iz a tio n w h ile 1 a
half-w ave 1 p la te 1 inem lulate's be)th sense's e)f in e c m iin g pedarizatiem w it h in a sin g le 1 Im a m
2.4.3
Beam Response
E x c e lle n t pre'elie-tive e-emtred ed th e Im a m rospemse1 g { i l ) in b o th p e d a riza tie m plane's is
re'ejuire'el. T h e 1 w a ve g u ie le e-heike1 se'ts th e n u m b e 'r o f memle's in th e G a u s s ia n devemipe)sitiem ed the1 b e a m re'spemse1 to u n ity . T h e e n tra n c e fee'd is e-orrugate'el. whie-h lim it s
the1 side'-lobe re'spemse1 anel im prove's th e p e d a riza tie m n u ite h in g . (Sem [5b. 18. 54] fo r
tlm re m g h elise-ussiems ed the1 a n g u la r anel p e d a riza tie m re'spemse1 ed single'-m oele1 een ru gate'el fe-e'els.) E x p re 's s in g the1 Im am re'spemse1 in rim e'-re've'rse as an e'ejuivalent broaeleast
be'am. the1 a m p lifu e le 1 o f the1 e'le'ctrie- hedel ve'e te ir is ed G au ssia n fo rm w it h Im a m w ie lth
ir( : ) sue-h th a t
wlie're1 the1 be'am w a is t
anel the1 a p e 'rtu re 1 w a is t i r „ = 0.b4.'15e/ fo r a e-eirrugate'el fee'd henm o f a p e 'rtu re 1 a anel
leuigth L (th e 1 e'epiivalemt ape'rture1 w a is t fo r a sm em rh-w alle'd feme I h o rn is ().7G8()e/).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
28
T h e beam w a is t is p la c e d a t th e focus o f th e te le s c o p e a n d is a t a d is ta n c e <7„ fro m
flu * h o rn a p e rtu re , w h e re
T h e s e e xp re ssio n s a llo w us to c a lc u la te th e re sp on se o f th e beam at th e e dg e o f th e
te le sco p e p rim a ry .
T h e h o rn a p e rtu re a a n d le n g th L . a lo n g w it h th e r h r o u g h p u t-
lim it in g w a v e g u id e c h o k e , c o m p le te ly d e te rm in e th e p r im a r y illu m in a tio n p a tte r n . B y
re d u c in g th e edge' re s p o n s e to -2 0 d B o f f m a x im u m , we can reduce e x p e c te d e m is s io n
fro m g ro u n d s p illo v e r to < 5 K . T h e c a lc u la te d b e a m w id t h in tin * fa r fie ld is 2.5
a rc m in u te s .
2.4.4
Spectral Response
B o lo m e te rs are s e n s itiv e to r a d ia tio n o v e r a b ro a d ra n g e o f fre qu e ncies. T h e P o la tro n
is a g ro u n d -b a s e d e x p e r im e n t, so d e te c to r re sp o n se m u s t be s t r ic t ly lim it e d t o w it h in
a v a ila b le w in d o w s in a tm o s p h e ric tra n s m is s io n . T o lim it o ff-a x is re fle c tio n s , w e chose
to use a s in g le o n -a x is feed. T h is , c o u p le d w it h th e d e c is io n to use a c h r o m a tic wave
p la te , m o tiv a te d o u r c h o ic e o f a s in g le o b s e rv in g fre q u e n c y n ear th e m in im u m in spec­
t r a l fo re g ro u n d s (f>4.5).
W e have' chosen a 2 0 '/ F W H M s p e c tra l b a n d p a s s c e n te re d
o n 9G G H z b e tw e e n th e GO a n d 118 G H z m o le c u la r o x y g e n line's (F ig u re 1 5 .2 ).
Due1
to the1 faintnc'ss o f the1 p o la r iz a tio n s ig n a l, h ig h efficieuie-y ( > 2()‘/ i ') in -b a n d s p e 'c tra l
f ilt e r in g is dc'sirable1.
T h e 88 G H z low-fre'ciueuie-y e'dge1 o f o u r b a n d is se*t b y a > 4A le n g th o f w ave'guide1
a t the1 e'xit a p e rtu re o f the* fee'd h o rn . It is d if f ic u lt te> m a tc h the1 c o rru g a te 'd th r o a t o f
th e c'lirrance1 fee'd te> siie-ll a s m a ll d ia m e te r. se> the1 e>xit a pe 'rtu re 1o f th e fee'd is s m o o th ly
rc’duce'd to th e c-lioke d ia m e tc 'r. T h e 10G G H z h ig h -frc'q u e n c-y e'dge1 o f o u r b a n d is se't
b y a m e tal-m e 'sh re'scmant g r id f ilt e r [4-‘3].
T he1 filte r s are1 more* e ffic ie n t in free spaee th a n in wave'guide1. see we1 e-ouple1 the1
e m rp u ts o f the1 O M T te) the1 g r id filte>rs v ia re c -ta n g u la r-te i-c irc -u la r wave'guide1 tr a n s i­
tio n s anel / / 4
c emic-al fe e 'd lio rn s. A re'c'ipreic-al / / 4
e-ouical fe'e'dhorn fo r eae-h channe'l
re'eonc-e'ut rate's the1 r a d ia t io n in to tu n e d in tc 'g ra tin g e-avitie's e e m ta in in g the1 b o lo m e ­
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20
te rs .
H ig h d e n s ity p o ly e th y le n e ( H D P E ) lenses at th e la rg e a p e rtu re o f each / / 4
feed c o llim a te th e r a d ia tio n fo r passage th ro u g h th e f ilt e r a t lo w in cid e n ce a n g le a n d
a ls o ensure th a t th e tw o feeds c o u p le e ffic ie n tly [ i l j .
T h e g a p b e tw e e n th e tw o / / 4
feeds also a llo w s us to c o o l th e m a jo r it y o f t i n 1 fo ca l p la n e to 4 K w h ile th e b o lo m e ­
t e r b a ck-e n d is co o le d to 0 .2 5 K : a s im ila r th e rm a l g a p in wave'guide1 w o u ld present
o p t ic a l a lig n m e n t d iffic u ltie s .
T h e' b u lk o f in c id e n t o u t- o f- b a n d o p tic a l p o w e r can
be in te rc e p te d at 4 K . w h e re m o re c o o lin g p o w e r is a v a ila b le th a n at s u l> -K e lv in
te m p e ra tu re s .
T h e m e ta l-m e s h filte r s w e re d e sign e d a n d fa b ric a te d a t P e te r A d e ’s la b o r a to r y
in Q M W C o lle g e in E n g la n d (the' la b has since m oved t o th e U n iv e rs ity a t C a r d iff.)
T h e m a n u fa c tu rin g process s a n d w ic h e s several layers o f in d u c tiv e o r c a p a c itiv e c o p p e r
m e sh e m b e d d e d in p o ly p ro p y le n e sheets [43]. T h e filte r s t y p ic a lly e x h ib it a <
20 d B
le a k a t tw ic e th e ir edge c u t - o f f fre q u e n c y , so an a d d itio n a l m e ta l-m e s h f ilt e r w it h an
edge a t 100 G H z is in c lu d e d . A f u r t h e r low -pass a lk a li-h a lid e f ilt e r co ate d w it h b la c k
p o ly p ro p y le n e b lo c k s r a d ia tio n above* 1050 G H z .
B o th o f these* filte 'rs are cemle'el to
4 .2 K . Large* e lia in e te r lenv-pass m e'tal-m e'sh filte rs w it h e*dges a t 240 anel 300 G H z are*
plaee*el in fro n t e)f the* fe*e*elhe)rn. a t 77 K and 4.2 K . in orde*r fe) lim it the* th e rm a l leiad
frenn the* emtrance* w indenv em th e b a n d -d e *fin in g filte*rs anel th e eryeigenie' stage's. The*
emtranee* winelenv its e lf is a pie*e-e* e)f H D P E w it h thie-kiie*ss tune*el to m in im iz e re'fievtive*
leiss in-banel.
The* e*dge* filte 'rs are* <*e)e»le*e1 te> 4 K anel 0.25 K in orele*r te> lim it the* raeliative* leiael
o n the* de*te*ctors.
A s a re 's u lt. one* possible* semre-e e>f s y s te m a tic e*rror is lemg time*-
e em stant lie*ating o r e-oeiling o f these* filte*rs. In eireleT fee avoiel s lo w e lrifts in ele*te*e-re»r
re 's p o n s iv ity . flu * filte*rs m u st be* we'll he*at-sunk a t 4 K anel 0.25 K . Tej th a t e*nel. we* use*
Cu-Be* wave* washe*rs te> press the* filte r s fir m ly a g a in s t the* fe*e*el stru ctu re * at eTvogemiete'tnp e ratu re 's.
Xeine* ejf th e spe*e-tral filte r s is expe'cte'd to preichlce* sig n ifie -a n t ( > 5 V i) ere>sspe>larizatiem o f iueem iing sig n a ls [ f ] , He>we*ve*r. the* p o la riz a tie m pre)pe*rtie*s o f the* b a n e l-e le fin in g
filte 'rs are im m a te *ria l. since* the* twe> pedarizatiem cennpem e'iits eif the* ine'em iing raeliatiem have* a h va e ly be*en se*parate*el b y the* O M T . S ystem a tie - pedarizatiem ineluee*el b y
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30
th e tw o b lo c k in g filte r s a n d w in d o w in fr o n t o f th e feed h o rn w il l re m a in fix e d w it h
respect to th e in s tr u m e n t w h ile th e p o la r iz a tio n p a tte r n fro m th e s k y ro ta te s w it h
th e w ave p la te . T h is e ffect is re m o v e d u p o n d e m o d u la tio n o f o u r s ig n a l a t fo u r rim e s
th e w ave p la te r o t a t io n fre q u e n cy.
2.4.5
RFI Control
In s tr u m e n ta l s e n s itiv it y can be d e g ra d e d b y d e te c to r re sp o n se t o ra d io -fre q u e n c y
in te rfe re n ce ' ( R F I ) . w h ic h m a y e n te r th r o u g h th e in s tru m e n t w in d o w o r be g e n e ra te d
w it h in th e e x p e rim e n t b y the' c ry o c o o le r m o to r .
T h e d e te c to rs c a n c o u p le to R F I
ra d ia fiv e ly . o r a lo n g th e le n g th o f h ig h -im p e d a n c e w ir in g b e tw e e n the' d e te c to r s a n d
th e ir c o ld a m p lifie rs . A F a ra d a y cage fo rm e d b y th e 4 K r a d ia tio n s h ie ld a n d a fire w a ll
b u ilt a t 4 K is o la te th e s u s c e p tib le c o m p o n e n ts fro m th e so urces o f R F I. A fu r th e r
a d v a n ta g e o f th e th e r m a l b re a k b e tw e e n th e 4 K a n d 0.25 K s e c tio n s o f the' feed
s tru c tu re is t h a t tlie* 4 K feed c a n be* in te g ra te d w it h th e s n o u t o f t in ' 4 K r a d ia tio n
s h ie ld . A n y r a d ia t io n w h ic h passes th r o u g h th e in s tru m e n t w in d o w m u s t pass th r o u g h
th e e n tra n ce ' feed - a n d th r o u g h c o ld f ilt e r in g
in o rd e r to co up le 1 r a d ia t iv e ly to th e
d e te c to rs a n d c o ld w ir in g .
2.4.6
Commercial Parts
A v a ila b ilit y a n d e xpe n se o f e x is tin g c o m m e rc ia l w aveguide1 p a rrs a re b a la n c e d a g a in s t
the1 e ffo rt a n d expense1 in v o lv e d in in -h o u s e de'sign a n d m a n u fa c tu r in g . T h e 1 O M T and
rc 'c ta n g u la r-to -c ir c u la r wave'guide1 t r a n s itio n s were1 purciiase'el fre m i G a n itn a - F Inc.-’ .
w h ic h s u p p lie d id e n tic a l 90 G H z O M T s fo r th e M A P obse-rvateny.
A n e-arlie>r. in -
house1 d e s ig n [9]. m a n u fa c tu re d b y H i-T e c h M icrenvave1*. was re'jevte-d a ft e r its in it ia l
p erfbrm anc-e w as deg ra e h'd b y u n c e m tre d la b le s lip p a g e ejf the1 t h in w a vc'g uieh 1 se'ptum
w h ic h s p lit th e tw o senses o f p o la riz a tie m .
T he1 wave-guiele- e-hoke w a s ele'sigue'el in -
hemse* anel m a n u fa e -ru ie e l b y Z en M a e h in in g 1. T h e 1 feeel henm w as ele'sigue'el in-hem se
JG a n n n a -F C o r p o ra tio n . 4111 F ijita S t.. Torrance-. C’A !)0a()a
■‘Hi-Tt-e-li M icrow ave-. In c .. T a l l Se-ars B lv d .. P ensacola. F L 42a 14
' Ze'ii M achine- .C Scie-ntific In strum c-n t. laUS S te-am boat Valle-v R o ad . P .O . B o x Id a s . Lyons. C O
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31
F ig u re - 2 .6 : P h o to o f a s ilic o n - n it r id e m ic ro m e s h b o lo m e te r.
a n d elect in fo r m e d b y H i-T e c h M ic ro w a v e . T h e b a c k e n d feed s tru c tu re 's we're el<-signed
in -h o u s e a n d fa b r ic a te d b y th e Calte-ch P h y s ie s D e p a rtm e n t M a c h in e S ho p .
2.4.7
Detectors
T he' P o la tre m uses tw o s ilic o n -n itrie le m ic ro m e s h ( "sp id c-r-w e -b ") b o lo m c -te rs ( F ig ­
ure- 2.6) s u p p lie d b y th e M ie ro -D e v ie c s Labeuateery at the- .Je-t P ro p u ls io n L a b o r a to r y .
Bolennete-rs c o n s is t o f an absorbe-r anel th e -rm is te jr p a ir suspe-ncle-el w it h th e -rm a l c o n ­
d u c t iv it y G fro m a e-edd b a th , as sh ow n in F ig u re - 2 .7
T h e impe-dance* o f th e absorbe-r
de-te'nnines th e o p tie a l efficiene-v. anel is c o n tro lle -d b y ele-positing a t h in golel h im u p o n
the- absorbe-r m e sh . A t th e c e n te r o f th e a b s o rb e r is a n X T D Ge- re-sistive- e-hip w it h
t e-mpe-rat u re -d e p e n d e n t re sist a nee
R (T ,WJ -
R„e \ / A / T h.,„
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( 2 _5)
Incoming Light (Popt)
Thermistor ( T ^ )
Conductivity (G)
Absorber
Heat Capacity (C)
Thermal Bath Ob^)
F i^ u n * 2 .7 : B o lo m e te r T h e r m a l S c h e m a tic .
w h e re A a n d R u are s e le c ta b le q u a n titie s , d e p e n d in g o n ly
011
c h ip m a te ria l a n d size.
T h e th e rm a l c o n d u c tiv it y is chosen so th a t
G
and T
i s
r«'ypt
( 2 . G)
Thnln - T,bath
n o t so h ig h t h a t th e b o lo m e te r s e n s itiv ity (§ 4 .2 ) a n d re s p o u s iv ity are
a d v e rs e ly a ffe cte d .
T h e re sp o n se tim e o f th e b o lo m e te r r to a flu c tu a tio n in in p u t
p o w e r is
- § ■
w h e re C’ is th e h ea t c a p a c ity o f th e b o lo m e te r, t y p ic a lly d o m in a te d b y th e th e rm is ­
to r .
T h e re s p o u s iv ity S o f th e s y s te m , m easured in V / \ Y . is th e change' in o u tp u t
v o lta g e w h ic h o c c u rs u p o n a ch a n g e in in p u t p o w e r.
T h e e le c tric a l re s p o u s iv ity is
m e a su re d by v a ry in g th e in p u t b ia s v o lta g e , so th a t p o w e r V;;o/o/ R /k,/„ *s d is s ip a te d in
th e d e te c to r, a n d m e a s u rin g the' e-hange in o u tp u t vedtage. T h e ' re s p e m s iv ity elepe'nels
em the' th e rm is te )r te m p e r a tu r e , anel hence1 th e d issip a te e l pe>wer. se> th e bedeune'te'r is
em ly lin e 'a r ove'r a s m a ll range1.
The* ejpen nie'sh ge'enne'trv e)f "sp ie le r-w e 1!
absen’be'rs ( / )
it y anel. the're'fore. the1 re'sjjejnse' t im e e»f th e detecte>r:
(//)
re'duce'S the1 h eat e a p a e reeluevs tile 1 p r o b a b ilit y
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E x p e c te d O p tic a l L o a d P „ pt :
.j j) \\* [)c>r c-hannel
S in k T e m p e ra tu re T,,,,* :
0 .2 5 K
O p e r a tin g T e m p e ra tu re 1
:
0 .4 5 K
T h c 'n n a l c c n ic h ic tiv iry G :
40 p \Y / K u 0.25 K
T h e r m is t o r H eat C a p a c ity C ':
1.5 p.I / K “
T im e 1 C o n s ta n t r :
25 ins
T h e r m is t o r R e sista nce /?/,„/„:
‘2 .0 M i l
N o ise E q u iv a le n t P o w e r:
2 .0 x lO -1, \ Y H z -1 '
E le c tr ic a l R c 's p o n s iv ity :
5 x 10s Y / \ Y
0.2 5 K
Tabic' 2.2: B o lo m e te r S p e c ific a tio n s
o f in te r a c tio n w it h co s m ic -ra y s : a nd ( / / / ) reducc’s th e d e te c to r m ass a n d hence its
s u s c e p tib ility to m ic ro p h o n ic s tim u la tio n .
F a b r ic a tio n te c h n o lo g y has im p ro v e d to the' p o in t th a t v e ry s p e c ific re q u e s ts c an be
m ade o f the* th e r m a l a n d e le c tric a l p e rfo rm a n c e o f th e d e te c to rs . S e le c tio n o f p ro p e r
b o lo m e te r s p e c ific a tio n s u n d e r a g iv e n o p tic a l hear load a m o u n ts to m a x im iz a tio n
o f th e a n tic ip a te d re s p o u s iv ity o f th e d e te c to rs , so th a t a ll source's o f p h o to n noise
sw a m p the' re a d o u t e le c tro n ic s noise', w h ile 1 m in im iz in g the1 a u tie -ip a te d eh'tee-tor noise
( b’4 .2 ). T h is is ac-hievc'd b y p ru d e n t selec-tiou o f a bso rb e 'r a n d th e r m is t o r m a te 'ria l anel
g e o m e try , as we'll as le'ad c-onduc-rivity. T h e 1 P o la tro n de'te'ctor sp c'cific-a tio n s an* liste*cI
in Table1 2.2.
The> 0.25 K o p e 'ra tiu g te m p e ra tu re o f the1 b o lo m e te rs is p ro v id e r 1 b y a t r ip le stage ’ He1,/’ He1/ {He s o rp tio n re frig e 'ra to r
T h e 1 ’ He stage1 co n e le 'iisa tio n p o in t
te m p e 'ta tu re is se't b y an HS-4 4.2 K e -ryocooler purc-hase'd fro m A P D C rv o g e m ic s ’ .
A s tu d y c a rrie 'd o u t b y B h a tia et al.
o f th e s u s c e p tib ility o f b o lo m e te 'r s y s te m s to
’A P D C ryo gen ics In c .. I0.40 E. D u an e A v e .. Suite1 I. Sunnyvale*. C’A
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34
V,drain
trim
bias
bias
Gain
Lock-In
x f 1boto A
V,diff
Filter
R bolo
source
j
F ig u re 2.8: D ia g r a m o f th e A C '-b ia s e d b o lo m e te r re a d o u t c ir c u it.
c ry o c o o le r m ic ro p h o u ie s s u g g e sts th a t c ry o c o o le rs a re a fe a s ib le a lte r n a tiv e to liq u id
Ho d e w a rs fo r re m o te o b s e rv a tio n s (C'i a n d [5 ]).
2.5
Readout Electronics
A s c h e m a tic o f th e re a d o u t c ir c u it is sh o w n in F ig u re 2.8. T h e b o lo m e te rs are p la c e d
in a n AC’- b rid g o a n d s in e -w a v e biased a t 200 H z [77].
T h e re la tiv e b ia s levels can
be a d ju s te d to t r im o u t g a in m is m a tc h b e tw e e n th e tw o c h a n n e ls [28]. The' o u tp u t
s ig n a ls are b u ffe re d b y a m a tc h e d . 120 K . lo w -n o is e .J F E T p a ir, th e n d iffe re n c e d a n d
d e m o d u la te d in a m b ie n t te m p e ra tu r e , lo w -n o is e a m p lif ie r e le c tro n ic s , p ro d u c in g a
s ig n a l 1’p q p p p r o p o r t io n a l to the* d iffe re n c e in o p t ic a l p o w e r in th e tw o p o la riz a tio n s :
1 P )[F F
S'f x
[ Q <os( 2<« x 4 J ii'p t ) ~\~
s iu (2 .i x 4 fu-p f ) j
1 no/s. .(2 .8 )
H e re . .S'-/-, m e a su re d in V / K . is th e d e te c to r r e s p o u s iv ity to th e rm a l fin er n a tio n s :
is th e b a n d -a v e ra g e d o p tic a l (p h o to n ) e ffic ie n c y o f th e in s tru m e n t: //,,„/ is tin *
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
p o la r iz a tio n e ffic ie n c y : Q a n d U a re m e a su re d in K . fix e d t o th e sky. a n d c o n v o lv e d
w it h o u r b e a m response: f u.p ~ O.G H z is th e p h y s ic a l r o t a t io n ra te o f th e w ave p la te :
a n d \ ,IOis, is th e s u m o f d e te c to r noise a n d noise fro m th e J F E T a m p lifie rs .
In a d d it io n to th e d if fe r e n t ia l m e a s u re m e n t, th e s ig n a l le v e l o f each in d e p e n d e n t
b o lo m e te r is s a m p le d a n d re c o rd e d .
T h e a b s o lu te s ig n a l levels are d e p e n d e n t
011
o p t ic a l lo a d in g , a n d so are e x p e c te d t o v a ry g re a tly w it h a tm o s p h e ric c o n d itio n s .
A s a re s u lt, th e s in g le -c h a n n e l m e a s u re m e n ts are A C -c o u p le d , w it h a h ig h -p a ss f ilt e r
c u t o f f a t 0.0G Hz. a fa c to r o f 10 b e lo w th e s ig n a l fre q u e n c y . T h e s in g le -c h a n n e l levels
m a y a lso a llo w us to c o n tin u o u s ly m o n it o r th e re s p o u s iv ity o f th e syste m : th e h a lf
w ave p la te s h o u ld p ro d u c e s lig h t d iffe r e n tia l ('m is s io n b e tw e e n its tw o re fra c tio n axes,
m o d u la te d a t 2
A n a d d itio n a l tw o b o lo m e te rs w it h th e same th e r m a l a n d e le c tric a l p ro p e rtie s
a n d a m p lif ie r c h a in , b u t w h ic h a re n o t e xposed to lig h t, a re in c lu d e d in th e s y s te m .
T h e s e d ia g n o s tic o r " d a r k " b o lo m e te rs are a useful to o l fo r in v e s tig a tio n o f a n u m b e r
o f s y s te m a tic e ffe cts th a t c o u ld im p a ir o u r m e a s u re m e n t, su ch as b o lo m e te r s in k
te m p e r a tu r e d r ifts a n d m ic r o p h o n ic response. A ll c h a n n e ls a re lo w -p a ss filte re d at G
H z. a fa c to r o f ~ ~ b e n e a th th e b o lo m e te r fre q u e n c y re sp o n se lim it .
A ll c o ld s ig n a ls in th e P o la tr o n a re c a rrie d by t w is te d - p a ir , s h ie ld e d , sta in le ss stee l
(T P S S ) w in '. S uch w ire is v e ry lo w c o n d u c tiv it y (G ~
I \ [2 0 ]). lim it in g th e p a r a s itic h e a t lo a d
011
l ( ) _1T u;,J \V c m -1 l \ _l at 4
th e m e c h a n ic a l c ry o c o o le r and m u ltis ta g e
c o o le r. T h e sh ie ld s p ro v id e p h y s ic a l p r o te c tio n as w e ll as p r o te c tio n fro m e le c tro m a g ­
n e tic p ic k u p . T h e tw o m a in d is a d v a n ta g e s o f T P S S wire* a re h ig h ca pa cita nce ' (
1
p F / c m ) a n d th e tim e a n d e x p e n s e in v o lv e d in a p p ly in g a c id fiu x a n d s o ld e rin g th e
s m a ll, lo w c o n d u c tiv it y leads.
2.6
RFI Control
E le c tr o m a g n e tic noise sources in c lu d e m o to rs , e le c tro n ic e q u ip m e n t, a n d ra d io a n d
r a d a r b ro a d c a s ts . T y p ic a l fre q u e n c ie s o f c o n ce rn arc' in th e ra d io p o r tio n o f th e spec­
tru m :
/' =
1(H) M H z
10 G H z (A = .4 c m
3
111).
L o w e r fre q u e n cie s are e x c lu d e d
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
:3G
b y th e p h y s ic a l size o f th e m e ta l e x te rio r o f o u r in s tru m e n t, w h ile h ig h e r fre q u e n c ie s
are " o p t ic a l" a n d c a n be c o n tro lle d b y s p e c tra l filte r s and b la c k e n e d a n d / o r re fle c ­
tiv e su rfa ce s. R a d io -fre q u e n c y in te rfe re n c e ( R F I) co u p le s to th e d e te c to rs p r im a r ily
th r o u g h th e h ig h -im p e d a n c e w ir in g b e tw e e n th e d e te c to rs a n d c o ld .IF E T a m p lifie rs .
A s d iscu sse d in ((2.4.5 above, th e 4 K r a d ia t io n s h ie ld a cts as a F a ra d a y cage w it h
a s in g le a p e r tu r e in th e e n tra n c e feed h o rn .
A l l w ire s ru n n in g to th e 4 K s ta g e are
filte re d a t a f in ' w a ll b u ilt in to th e 4 K cage.
A d e ta ile d d e s c r ip tio n o f th e d e v e lo p m e n t a n d te s tin g o f c o m p a c t c o ld f ilte r s fo r
th e P o la tr o n c a n bo fo u n d in [46]. C o m p a c t, s u rfa c e m o u n t E M I filte rs s u p p lie d b y
M u ra ta . In c .1’ . p ro v id e an a ttr a c tiv e <
a n d 200 M H z a n d <
20 d B o f s ig n a l a tte n u a tio n b e tw e e n 10 M H z
-40 d B b etw e e n 200 M H z a n d 1 G H z . a t ro o m te m p e ra tu r e .
H o w e ver, sin ce n u m e ro u s th e rm o m e try a n d s ig n a l lin e s ru n in to th e 4 K space, closep a c k in g o f th e se filte r s is re q u ire d (F ig u re 2 .9 ). S uch p a cka g in g led to a d e g ra d a tio n
in p e rfo rm a n c e d u e to c ro s s ta lk b e tw e e n a d ja c e n t f ilt e r lines, w h ic h c o m p lic a te d th e
tra n s m is s io n c ir c u it .
F u rth e r d e g ra d a tio n o c c u rre d u p o n c o o lin g o f th e f ilt e r s to 4
K . U ltim a te ly , th e h ire rs p e rfo rin best b e tw e e n 200 M H z a n d S G H z . w ith m e a s u re d
<
20 d B a tte n u a tio n across th a t b a n d , in th e P o la tro n c o n fig u ra tio n . F u r th e r R F I
re d u c tio n is a c c o m p lis h e d by [ lo tt in g o f th e e n tir e f ilt e r a n d a le n g th o f le a d w ire s in
E ccoso rb .
2.7
D ata Acquisition System
S ig n a l s a m p lin g is trig g e re d by an o p t o - in t e r r u p t e r w h ic h is s w itc h e d b y a 6 4 - to o th
w heel p h y s ic a lly a tta c h e d to th e wave p la te . A s a re s u lt, th e s a m p le d d a ta is s to re d
in a c o o r d in a te s y s te m fix e d to th e wave* p la te p o s itio n , ra th e r th a n as a tim e s tre a m ,
s im p lify in g d a ta a n a ly s is . For a p h y s ic a l w a ve p la te r o ta tio n ra te f , n , ~ O .lo H z. th is
a llo w s us to s a m p le th e b o lo m e te rs at ~ 2 0 Hz. w e ll above1 th e s ig n a l fre q u e n c y at
4
=
0 .6 H z a n d a fa c to r o f several above1 a d e te c to r b a n d w id th -d e fin in g lo w -p a s s
filte r a t 6 H z. T h e s ig n a l fre q u e n c y 0.6 H z a ls o lie's w e ll above th e ~ 30 m H z 1 / / knee
’’S up p lied by N e w a rk . !Hid() N o rw a lk B lv d .. S a n ta Fo S prin g s. C’A !)()(i7()-2!)32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig u r e 2.9: C lo se -p a cke d a r r a y o f R F I filte 'rs .
o f th e re a d o u t elec tr o n ic s (see T a b le 2.3 fo r a s y n o p s is o f th e v a rio u s re le va n t m o d u ­
la tio n fre q u e n c ie s ). 0 .6 H z is a s u b h a rm o n ic o f th e fu n d a m e n ta l v ib r a tio n fre q u e n c y
o f th e m e c h a n ic a l c ry o c o o le r. a llo w in g s e q u e n tia l m ic r o p h o n ic reponses to v ib r a t io n
to be d iffe re n c e d w hile* th e w ave p la te passes S to k e s p a ra m e te rs Q a n d —Q
A lte r ­
n a tiv e ly . sin ce th e w a ve p la te r o ta tio n ra te is c o n tr o lla b le , we c a n choose to set th e
s ig n a l fre q u e n c y at a n ir r a t io n a l s u b m u ltip le o f th e fu n d a m e n ta l v ib r a tio n fre q u e n c y .
T h e d a r k b o lo m e te rs a n d tw o th e rm is to r s used t o m o n it o r the- te m p e ra tu re o f th e
b o lo m e te r stage* arc* a ls o s a m p le d a t ~ 20 H z. Basic- c ry o g e n ic a n d o th e r h o u s e k e e p in g
d a ta arc* s a m p le d a t a lo w e r d a ta rate*. The* d a ta w ill b e s to re d lo c a lly on a ru g g e d iz e d
portable* c o m p u te r loc a te d on the* telesco p e, th e n tra n s fe r r e d v ia F T P to o u r d a ta
a n a ly s is c o m p u te r n ig h tly . A s y n o p s is o f th e s to re d d a ta a n d th e r m o m e tr y c h a n n e ls
are in c lu d e d as Table's 2 .4 a n d 3.1.
The* e x p e rim e n t is d e s ig n e d to ru n a u to n o m o u s ly fo r weeks a t a time*. I t w ill b e
c o n tro lle d b y U N IX - b a s e d s c h e d u lin g software* in s ta lle d on a P C in a slic'd n e a r the*
telescope.
C o m m a n d s w il l be se n t b y th e s c h e d u le r t o e ith e r th e telescope* c o n tr o l
c o m p u te r (a V A X s y s te m ) o r to th e p o rta b le * c o m p u te r.
The* portable* c o m p u te r
ru n s W in d o w s a n d L a b Y T E W . U p o n re c e ip t o f c o m m a n d s fr o m the s c h e d u le r, the*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
P a ra m e te r
Free[uency
A C D e te c to r B ia s
S am ple' R a te
B olen n ete r Re'spemse'
S ig n a l L o w -P a ss F ilt e r
C’rv o c o o le r F u n e la m e n ta l H arm onieS ig n a l Freepieney 4 f ir/)
S ystem atie- W a ve P la te ' E m is s io n 2
200 Hz
20 Hz
20 Hz
G Hz
2.4 H z
0.G Hz
0 .3 H z
W a ve P la te R o ta tio n
0 .1 5 Hz
S ig n a l H ig h -P a ss F ilt e r
0.0G Hz
T a b le 2.3: R e le v a n t M o d u la tio n F re q u e n cie s
C hannel
F u n c tio n
L D if f
L +
L ig h t B o lo m e re r D iffe 'n 'iice 1
DC
L ig h t B o lo m e te r # 1 Le've'l
AC
C o u p lin g
L
L ig h t B o le n n e te r # 2 Lewel
AC
L B ia s
L ig h t B o lo m e 'te rs B ia s Le'vel
DC
D D if f
D ia g n o s tic B o len n e'te r Differe'iu-e'
DC
D +
D ia g lio stie - B o lo m e 'te 'r # 1 Lenel
AC
D
D B ia s
D ia g no stie - Bolenne'ten- # 2 Levc'l
D ia g im stic- Berlome'te'rs B ias Le've'l
AC
TR1
T e m p e 'ra tu re ' C'e)iitre)l Diffe're>ne e
DC
T l
DC
TR2
T h e rn iis te )r # 1 Le've'l
T e m p e ra tu re ' M o n it o r Diffe'rence'
DC
T2
T h e r m is to r # 2 Le've'l
DC
DC
T a b ic' 2 .4 : D a ta C h a n n e ls
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
L a b V I E W s o ftw a re w ill c a n y o u t su ch ta s k s as c y c lin g th e m u ltis ta g e s o r p tio n c o o le r
fo r th e b o lo m e te r stage*, ta k in g a n d s to r in g d a ta , a n d s ta r tin g a n d s to p p in g th e wave*
p la te r o ta tio n . T h e L a b Y I E W s o ftw a re ' w il l a lso r e tu r n some1 d a ta t o th e se-hedule'r.
se> th a t the' schedule'!- c a n a u re m ia rie a lly c a r r y o u t tasks such as { jo in t in g , s k y d ip s . and
c a lib ra tie m .
2.8
Integration of Receiver with Telescope
The* P o la tre m re'ceiver a n d s u p p o r tin g th e r n u jin e 'tr y anel s ig n a l re a d o u t e*c{uipme*nt
a re lmuse'd in a re c ta n g u la r m e ta l e 'c iu ip m e u t b o x (the* " B B T " ) a p p n jx im a te 'ly 125 e in
lo n g a n d 75 c m o n a side'. The* b o x is d esigne'd to be* rolle'd alemg m e ta l tra c k s in to
the- tele'scope' frenn th e re a r, w h e n the' relese-ope is stejwed anel { jo in tin g a t tlie* lie)rizon
(F ig u re 2 .1 0 ). A lig n m e n t a n d s u p p o rt c o n n e 'c tio n s are made' at the* c e u itra l a{)e'rrure
o f th e relescej{)e'. fro m w h ic h th e B B T h a n g s. A t th e re'ar o f the' B B T is a bre'akour
pane'l c o n ta in in g c o n n e c tio n s fo r the' c ry o c o o le r h e liu m line's. e*thornet cejnne'crions fo r
tlie ' {je jrta b le ce jin p u te 'r. A C [leiw er cejune'ctiejns. B . \ C bre'akejiits fo r spex-ific s ig n a l anel
rh e 'n n e jm e rrv lin e s , a n d o th e r a u x ilia r y cemne'ctiems.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
F ig u re 2.10: O V R O 5 .5 m telescope fro m re a r in s to w e d p o s itio n .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
Chapter 3
Polatron Cryogenic System
In th is c h a p te r we discu ss th e tw o m a in e le m e n ts o f th e P o la tro n c ry o g e n ic s yste m : th e
4.2 K m e c h a n ic a l c ry o c o o le r a n d th e s u lj- K e lv in s e jrp tio n c o o k 'r. A f t e r m o tiv a tin g tin *
a p p lic a tio n o f the se te c h n o lo g ie s to t h is e x p e r im e n t, we d iscu ss t h e ir d e ra ile d d e sig n
a n d in t e g r a t io n .
A d is c u s s io n o f th e m ic r o p h o u ic and ra d io - fre q u e n c y p ro p e rtie s o f
th e s y s te m th e n fo llo w s .
3.1
Introduction
A ll m illim e te r - w a v e in s tru m e n ts d e s ig n e d fo r m e a s u re m e n t o f c o s m ic m ic ro w a v e h a c k g ro u n d s ig n a ls use c o o le d d e te c to rs a n d r a d ia t io n sh ie ld s to lo w e r th e in tr in s ic b a c k ­
g ro u n d n o ise o f th e e x p e rim e n t. D u e t o th e n a tu re ' o f the* d e te c to rs in v o lv e d , in c o h e r­
ent a n d c o h e re n t sy s te m s make' use> e>f r a e iic a lly d iffe re n t re frig e ra tie m technique's.
Incedie'rent-ele'te'e-tejr (fo r in s ta n c e . bolenne'trie-) in s tru m e n ts me'asure' the* te m p e ra tlire* increase* o f a rh e -rm a lly iso lateel d e te c to r axpe>se*el te» bremelbanel o p tic-a l raeliat iem.
Due' t o the* q u a n tiz a tie m ejf p h o n o n ene-rgy p ro p a g a tin g bc'twe'en the- h ea t s in k anel the'
eh'te'e-tor. bolen n e'te rs t y p ic a lly re 'q u ire s u l> -K e lv in elete'ctor reunpe-rature's to apprem ch
p ho ten i noise* lim ite 'e l pe'rtbrm ance' anel tei b r in g the* eh'te'e-tor inte) th e se -n iiconelucting
re'gime*. S u b - K e lv in te m p e ra tu re 's are- ty p ie -a lly aehh-ve’el th r o u g h e)iie* o f rlire'e* in e 'tlioels: s o r p tio n p u m p in g on licpiiel {He'. a d ia b a tic e k 'm a g tic 'tiz a tio n o f a p a ra m a g n e tic
s a lt, o r e lilu tie m e>f {He th re m g h 'He*. In m o s t o b s e rv a tio n a l applie-atiem s. w h ic h re'eiuire*
m n lt i- h o u r h o le l tim e 's, these' r e fr ig e r a tio n te'clm ic[u e s o p e ra te o ff a 1.4 K he-at s in k p ro vieh'el b y a b a t h o f punipe'el lie[uiel 'He*, w h ic h is in tu r n buffere’d b y a 77 K lieptieI
b a th . Cryoge-nie- he)ld rime's are* lim ite 'e l b y the' te )ta l penve-r absetrbe'el b y a give'ii stageand the* he-at e>f v a p o riz a tio n e>f th e r e fr ig e r a n t. A lth o u g h th e s o r p tio n re frig e -ra to rs are*
se-lf-cenitaine-el anel re-e-ye-le th e ir r e la t iv e ly s m a ll q u a n titie 'S o f crye tg e n ic gas. the- liighe-r
te-inpe-rature b a th s b o il eiff. w it h th e gase-ems p re id u e t e-ithe*r letst to the- arineisphe're
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42
o r re c o lle c te d fo r la te r c o n d e n s a tio n . D e p e n d in g
011
th e re m o te n e s s o r c o m p le x ity o f
th e o b s e rv in g p la tfo r m , r e f illin g these b a th s c a n be an e x p e n s iv e , tro u b le s o m e , and
s o m e tim e s d a n g e ro u s ta s k , p a r tic u la r ly d u r in g lo n g c a m p a ig n s . F u rth e rm o re , th e use
o f liq u id e ry o g e u s o fte n sets lim it s
011
th e o r ie n ta tio n o f in s tr u m e n t w it h respect to
g ra v ity .
C 'o h e re n t-d e te c to r in s tr u m e n ts such as P O L A R a n d P I Q U E (§ 1 .4 ) a m p lify th e
e le c tric fie ld o f C’M B r a d ia t io n d ire c tly .
T h e noise* in t r in s ic to su ch a m e a surem e n t
d e p e n d s o n th e te m p e r a tu r e o f th e a m p lify in g tr a n s is to r: o n ce th e fie ld has been a m ­
p lifie d . r o o m - te m p e r a tu r e e le c tro n ic s are a d e q u a te to a n a ly z e the* s ig n a l. A s a re s u lt,
ty p ic a l C 'M B in s tr u m e n ts o f th is ty p e re q u ire < 100 K o p e r a tin g te m p e ra tu re s . Such
te m p e ra tu re s a re e a s ily a c h ie v e d th ro u g h use o f c o m m e rc ia l s e lf-c o n ta in e d m e c h a n ic a l
c ry o c o o le rs w h ic h use ’ H e as a w o rk in g flu id . C a re m u s t be* ta k e n in the se e x p e rim e n ts
to lim it th e s y s te m a tic e ffe c ts d u e to v ib r a t io n a n d e le c tr ic a l in te rfe re n c e caused by
th e c ry o c o o le r m o to r .
T h e P o la tr o n e m p lo y s a clo se d -cye le c ry o g e n ic s y s te m t o a ch ie ve b o lo m e tric o p e r­
a tin g te m p e ra tu r e s o f ~ 0 .2 5 K . A s yn o p sis o f a ll c ry o g e n ic t h e r m o m e tr y a n d h e a te r
c h a n n e ls is in c lu d e d as T a b le 3.1.
A m e c h a n ic a l c ry o c o o le r p ro v id e s in te rm e d ia te -
te m p e ra tu r e h e a t s in k s a t 50 K a n d 4 K v ia re fr ig e r a tio n o f a 'He* w o rk in g flu id . A
c u s to m , m u lti- s ta g e ' H e / ’ H e / ’ H e s o rp tio n c o o le r, w h ic h w as in v e n te d fo r a p p lic a tio n
to th e P o la tro n . o p e ra te s o ff th e 4 K stage, a c h ie v in g n e a rly 40 h o u rs of h o ld rim e
b e n e a th 0 .2 5 K . T h e n * a re se ve ra l a d va n ta g e s to th is s y s te m : u o n e x p e n d itu re o f c ry o ­
g e n ic liq u id s , g r a v ity -in d e p e n d e n c e in m e c h a n ic a l d e sig n , a n d a u to n o m o u s o p e ra tio n .
T h e re are a lso s e ve ra l p o t e n t ia l d is a d v a n ta g e s :
noise d u e to m ic r o p h o u ic c o u p lin g
o f th e b o lo m e te r s ig n a ls t o c ry o c o o le r v ib r a t io n fre q u e n cie s, ra d io -fre q u e n c y in te r fe r­
ence g e n e ra te d b y th e c ry o c o o le r m o to r, a n d th e re d u ce d c o o lin g p o w e r a n d lim ite d
life tim e a n d r e lia b ilit y o f 4 K m e c h a n ic a l co o le rs.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
3.2
Cooling Requirements
B o lo m e te rs m u s t be in m e c h a n ic a l, e le c tric a l, a n d ra d ia tiv e c o n ta c t w it h a m b ie n t
tem pe ra ture* (3 0 0 K ) m a te ria ls . T h e lim ite d c o o lin g p o w e rs available* a t 0.25 K and
4
K
re q u ire s e ve ra l la ye rs o f h ea t in te rc e p tio n .
T h e a n tic ip a te d h ea t lo a d s o n each
o t these stages was c a lc u la te d a n d m in im iz e d u n d e r th e c o n s tra in ts th a t (/) th e 4 K
o p e ra tin g p o in t be* d e d ic a te d to s in k in g heat a ris in g in o p e ra tio n o f flu * m u ltis ta g e
s o rp tio n c o o le r: a n d (/’/’ ) the* 0.2 5 K o p e ra tin g p o in t be d e d ic a te d to s in k in g p ow er
in c id e n t cm th e b o lo m e te rs u n d e r seven* lo a d in g c o n d itio n s .
T h e rm a l p o w e r in p u t o n each stage* is c a lc u la te d as fo llo w s .
• R a d i a t i v e pot rcv. A l l
a tin g b la e k b o d ie s o f
c o m p o n e n ts o t th e re c e iv e r c a n be a p p ro x im a te d as ra d i­
k n o w n e m is s iv ity e. te m p e ra tu r e T . a n d surface* area .4.
The* p o w e r e m itte d is d e s c rib e d by the* S te fa n -B o ltz m a n n r e la tio n
Prad ~
X
A.
(3.1)
w hen* <r ~ (i p \ V / c m J/ A ’ 1. In fra re d ra d ia tive * lo a d s o n a give*n te m p e r a tu r e stage*
in the* P o la tro n ca n be* divid c*d in to th rc'o c a te g o rie s : ('m is s io n fro m the* h ig h are*a. Io w -e m is s iv ity v a c u u m ve*sse*l a n d r a d ia tio n shie*lels fo r highe*r tem pe'rature*
stage's: e m is s io n fro m the* cm viro n in e n r t r a n s n iit t e d b y the* ve*sse*l w in d o w anel
in fra re d b lo c k in g filte rs : anel e m issio n fro m th e h ig h - a b s o r p tiv ity (a n d henc-e*
h ig li- e 'in is s iv ir y ) filte r s theinse'lve*s. None* o f these* c o n tr ib u tio n s c a n be* t r iv ia ll y
ne'gle'cte'd.
In the* P o la tro n . radiative* powc*r in p u t is c-oucentrate*cl a t the* fro n t
e*nd o f the* re*ce'ive*r. while* c-ooling [>owe*r is co n ce n t ra t e*d at th e m e*chanical c ry oe-ooler i l l the* re a r. A s a rc'su lt. s u b s ta n tia l the *rm al powe*r is co n rlu e te 'd a lo n g
the* r a d ia tio n shie*lds b y e-opper b ra id .
•
C o n d u c t i n ' p o i r c r . C o n d u c -tiv e loads o n a g ive n te m p e -ra tu re stage* in the* P olatro n are* d o m in a te 'd b y w ir in g , ty p ie -a lly s m a ll-d ia m e 'te r stainle*ss o r m a n g a n in .
anel n u 'c h a n ic a l s u p p o rts . ty p ie -a lly fabricate*d fro m G -1 0 o r V c'spel. These* m ate*rials an* se'le'cte'fl fo r the*ir lo w th e rm a l c-cm d u ctivity.
C o n d u c te 'd powe*r is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
44
d e 'scrib e d bv
<" hi,,ih
y
(j(T )dT
(3-2)
r,.„.
w h o re y ( T ) is th e th e r m a l c o n d u c t iv it y o f th e c o n d u c tin g m a te r ia l as a f u n c tio n
o f te m p e ra tu re , m e a s u re d in W’/ K / c m : .4 is th e cross s e c tio n a l area o f th e
c o n d u c to r: and I is th e le n g th o f m a te r ia l b e tw e e n tw o b o d ie s at te m p e ra tu re s
Tin ,)h a n d Ti0,v.
A lt h o u g h th e n u m b e r o f science d e te c to rs in th e P o la tro n is
s m a ll, th e large n u m b e r o f t h e r m o m e tr y and d ia g n o s tic c h a n n e ls m ean t h a t th e
w ir in g c o n d u c tiv ity is u o n -u e g lig ib le . o f o rd e r 100 m \V a t 4 K a n d 0.1 / / \ V at
0 .2 5 K . L o n g e r w ire s re d u c e th e c o n d u c te d p o w e r, b u t in cre ase th e in te g ra te d
c a p a c ita n c e ' and hence th e s u s c e p tib ility to p ic k -u p . The* m e c h a n ic a l s u p p o rts
a n ' d e s ig n e d to c o n d u c t n o m o re th a n the w ire s a t a n y stage: th is can be
a c h ie v e d w it h no loss in m e c h a n ic a l s tre n g th d u e to th e c y lin d r ic a l s y m m e tr y
a n d o r ie n ta tio n o f th e re c e iv e r w it h respect to g ra v ity .
•
A p p l i e d h r a t t ' r p ow er , d e s c rib e d b y
Pi,.", = T P
w here' / is th e c u rre 'iit a p p lie 'd to a w ire' o r re 'sisto r o f impe'dance* /?.
(3 .3 )
A s w ill
be' de'seribe d . the' m u ltis ta g e ' s o rp tie m coole*r require's large* (0.5 \V ) he*at in p u ts
in t o the 1 4 I \ stage 1 d u r in g c y c lin g . T h is is the> d e n n in a n t source' o f loael o n th a t
stag e .
A s c a n be* seam in F ig u re 's 2.1 anel 3.4. the* m a in lo c a tio n s e>f he>at in tc 'rc c 'p tio n
ine-luek' the* 50 K stage- p ro v id e d b y the* m e-chanical c ry o c o o le r. a n d a 0.5 K stage*
pre)vidc'd b y the* so rp tie m in te rc o o le T .
In th e fo llo w in g se'ctiems. we- discuss the- tw o
m a in c o m p o n e n ts o f the* cryo g e n ic- s y s te m , a n d th c 'ir in te g r a tio n .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C hannel
L o c a tio n
C om ponent
Op<‘r a t in s P o w e r
o r T e m p e ra tu re
L
G M Sta»'e
1
D io d e T h e r m .
50 K
2
C M S ta g e
2
G M S ta g e 2
D io d e T h e rm .
H e a te r
20
4
4
. I T S tag e
0
• IT St a sc
C’o lr l L in k
C o ld P la te
G
t
10
IC 'H e C o n d e n s a tio n P o in t
1C' ‘ He P u m p
IC ‘ H e P u m p
11
IC
8
9
1 H i'
P u m p H e a ts w itc h
D io d e T h e r m .
H e a te r
D io d e T h e r m .
K
40 \V
0
4 K
0
1
\V
D io d e T h e rm .
4 K
5 K
D io d e T h e rm .
4 K
D io d e T h e r m .
H e a te r
4
50 K
0.5 \V
D io d e T h e r m .
4
50 K
12
IC 'H e P u m p H e a ts w itc h
H e a te r
0.5 W
13
14
IC {H e P u m p
D io d e T h e rm .
H e a re r
4
50 K
0.5 \V
15
IC ! H e P u m p H e a ts w itc h
1G
1C' ! H e P u m p H e a ts w itc h
D io d e T h e rm .
H e a te r
4
50 K
0.5 \V
17
IC S t ill
G R T T h e rm .
0.5
18
IC S t ill
0
10
4
50 K
IC 'H e P u m p
1.5 K
19
UC Pum p
H e a te r
D io d e T h e rm .
20
U C Pum p
H e a te r
0.5 W
21
L’ C P u m p H e a ts w itc h
H e a te r
G R T T h e rm
0.5 W
0.25 K
22
I 'C S t ill
24
D io d e T h e rm .
4 K
24
In n e r R a d ia tio n s h ie ld
O u t e r R a d ia tio n s h ie ld
D io d e T h e rm .
50 K
25
F o c a l P la n e
4 K
2G
•J F E T S tag e
.J F E T S tag e
D io d e T h e r m
D io d e T h e r m
H e a te r
10
27
K
120
m \V
Till)1<* 3 . 1 : T h e r m o m e tr y C h a n n e ls
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
m \V
4G
3.3
Mechanical Cryocooler
T h e 4 I \ h e a t s in k te m p e r a tu r e re q u ire d b y th e m u ltis ta g e s o rp tio n co o le r is p ro v id e d
b y a c o m m e rc ia l c ry o c o o le r s u p p lie d b y A P D C ry o g e n ic s ( M o d e l H S -4: F ig u re 3 .1 ).
T h e c ry o c o o le r c o n s is ts o f th re e stages o f re fr ig e r a tio n u s in g ‘ He w o rk in g flu id : tw o
G iffo rd -.M c M a h o n ( G M ) stage's, w h ic h p re c o o l the' f lu id : anel a Jemle'-Thennsem ( .IT )
e'Xpansiem stage', w h ic h p ro v id e r th e b ase-te'inpe'rature' e-oejling. The- e-ooler is ele'signe'el
to operate* in a n y em ientatiem . anel provide's a u o m in a l 1 \ V o f e e o lin g penve*r a t 4.2
K . A tlu tre ju g h ele'scriptiem o f G M / J T c-etolers can be fo u n d in [2]. A synopsis o f th a t
de'sc-ripfion fo llo w s , w it h s p e c ia l e m p ha sis o n th o se to p ic s whie-h a p p ly e lire e tlv to the*
e-rve)genic p e rfo rm a n c e e)f the' P o la tro n .
The- G iffo r d - M c M a h o n stag e s p reeool ro o m te m p e r a tu r e "‘ He bene*ath th e im e r sio n te m p e ra tu r e n e ce ssa ry fo r .Jem lc'-Thom son e x p a n s io n .
A se'parate'. c le c tric -a lly
pe)were*el. w a tor-c-o olc'd h e liu m co m p re sso r p ro vide 's a p re ssu re d iffe re n tia l P m / P <mt()pe'ratie>n o f r o t a r y in le t a n d o u tle ’t valve's in c o o r d in a tio n w it h sync-hronous motie>n
o f the' r e c ip ro c a tin g d is p la c e r provide's th e re frig e ra tie )n .
T h e gas a n d d is p la e e r d o
no w o rk em cmc* a n o th e r, sin ce th e pressure* e liffe re n tia l across the* d isp la e e r is s m a ll
a nd arise's la rg e ly due' to th e c e d in g o f the' gas. Inste'ael. the 1 gas Hows in to the- m a in
vejhune* o r in to a re 'g e n e 'ra to r. d e p e n d in g e)ii th e s ta tu s e»f th e in le t a n d o u tle t valve's
a n d the' p o s itio n o f th e d is p la e e r. T w o -s ta g e G M c e o le rs e jp e ra te s im ila rly , b u t allenv
fo r gre'ate'r e 'o o lin g pe>wer a t a le>we'r base te m p e ra tu re ' d u e to the 1 im p ro v e d pre-e-ooling
o f the' gas. The' lenv pressure' e liffe n 'iitia l ae-reiss the' d is p la e e r m enu th a t th e d e m a n d s
on the> s lid in g d is p la e e r seal are' lo w . ine re'asing r e lia b ilit y .
In the* e-ase' o f the' H S -4 . the' strejke* le n g th e>f the* d is p la c e rs has be-e'ii e u s to m re'ehieed to re'tnetve the' s lig h t im p a e 't the* d isp lae e 'r w o u le l u e jrm a lly m ake em the* c'nel
o f the- e vlinele'r. Sueh a m oelifie-atiem was in te n d t'd tej re'due-e1 v ib ra tie ju o f the 1 coe)le'r.
a lth o u g h ue) mc'asurc’iu e 'u t o f the' v ib r a tio n was m ade' be-tbre' the' me)eliHeatie)ns to o k
plaee.
The' .IT s y s te m ee>e)ls ‘ He* gas by a lle tw in g an isem thalpie- e x p a n s io n o f a liig h pre'ssurc' gas th r o u g h a s m a ll nozzle'.
A n ieloal gas \ve)tild expe'rie'iiee no e-hange' in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig u re ' 3.1: M o d e l HS--1 iiK 'c h a n ie a l c ry o c o o le r fro m A P D C ry o g e n ic s .
te m p e ra tu re ' u n d e r s u ch an e x p a n s io n . N o n -id e a l gases e x h ib it tw o m o le c u la r effects
w h ic h p ro d u c e o p p o s ite te m p e ra tu re ch anges u p o n .IT e x p a n s io n .
to th e in c re a s in g distance* b e tw e e n gas m o le cu le s u n d e r e x p a n s io n :
T h e firs t is due
the' lo w e r th e
pressure, th e lo w e r th e p o te n tia l e n e rg y o f in te r a c tio n a n d h e n ce th e lo w e r th e k in e tic
energy a n d te m p e r a tu r e .
The* second is d u e to tlie* in e o m p r e s s ib ility o f tlu * gas: at
th e h ig h p re ssu re s in th e nozzle s tre a m , re p u ls iv e e le c tric a l force's b e tw e e n th e gas
m olecules in c re a s e th e k in e tic e n e rg y a n d te m p e ra tu re .
T h e in v e rs io n te m p e ra tu re
b en e ath w h ic h th e f ir s t te rm d o m in a te s d ep e n d s on th e a to m ic p ro p e rtie s o f th e
gas: fo r h e liu m , t h a t te m p e ra tu r e is 40 K . C ry o g e n ic .IT stage's th e re fo re re q u ire
a p re -c o o lin g s ta g e in w h ic h th e gas te m p e ra tu r e is b ro u g h t b e n e a th th e in v e rs io n
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.x
GM displacers
Rotary valve
Regenerator
JT orifice
4.2 K
t
Compressors
F ig u re .4.2: M e c h a n ic a l C r y o c o o le r S c h e m a tic .
te m p e ra tu r e so t h a t e x p a n s io n cools it fu r th e r .
T h e H S -4 s y s te m in te g ra te s a tw o -s ta g e G M c o o le r w it h a J T stage* as s h o w n in
F ig u n * 4.2. T w o lin k e 'd . e)il-lu bricate 'e l. water-coe)le*el ( I S ' C ) h e liu m ee>mpre'sse>rs are'
re'quire'ri. Tlie'se* e-emipre'sseirs e-emsiime se've'ral k \ \ * ejf pe>we'r anel w ill be1 in s ta lle d ! em
the* a z im u th p la t f o r m o f the* ti'le ’smpe*. E ach is ra te n l fo r 10 . 0 0 0 h ours e>f p e'rfbrm ane-e
be'fore* se*rvie-ing. F o u r fk-xible* h e liu m line's 10 m in le n g th ru n fro m the* cemipre'.sseirs
to the> eTveiemole'r.
Tile* . I T re 'tu rn line' at the' cryoe-oeileT e-emtains eolel gas be'ne'ath
atm e)s[)he'ric pre'ssure'. se> care- m u st be* ta k e n te> m a in t a in the 1 p h y s ic a l in te 'g r ity e)f th is
line1. The> g r a v it a t io n a l pressure' elre>[> elite' te> the> lemg le n g th anel pejsiriem <»f the 1 e r y e>e-e»e)le>r abeive* tile* e-emiprt'sseirs is n e g lig ib le . A f ilt e r i l l the* .JT line1 prewemts e jo g g in g
o f rhe> e'xpansiem valve* b y im p u ritie 's in the* h e liu m line', b u t re'(|iiire's se>rvie-ing ewe'ry
1 0 .0 0 0
hemrs. Slie)iile 1 su ch a eJeig oe-cur. the 1 systeun m u s t be- warnie'el to a m b ie m t tem i-
p e'rature' anel rt'-e-e>e>le*ei
lie) elisassennbly is re'epiire'el. T h e ' .IT stage- prew ich's a stable*
4 K h e-atsiiik: in e e m tra s t. 4 K G M eemle'rs d is p la y in s t a b ilit y in base' re 'in p e 'ra flire *
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
w h ic h c o u ld g e n e ra te s y s te m a tic e rro rs in o u r m e a s u re m e n t [59].
T h e firs t G M s ta g e p ro v id e s a n o m in a l 50 \V o f c o o lin g p o w e r at 50 K . R a d ia tio n
s h ie ld s are h e a ts u n k a t th is te m p e ra tu re to p ro v id e a n in te rc e p t o f o p tic a l a n d c o n ­
d u c tiv e lo a d in g fro m 3 0 0 K o n to 4.2 K . T h e second G M stag e p ro vid e s a 20 K base
te m p e ra tu re , b u t th e c o o lin g p o w e r at th is s ta g e is used e n tir e ly fo r p re -c o o lin g o f
gas in th e .IT c ir c u it . T h e n * is no p ro v is io n in th e s y s te m fo r h e a ts in k in g o f r a d ia t io n
s h ie ld s o r th e r m a lly c o n d u c tiv e w ir in g a t th is te m p e r a tu r e . H ow ever, a ll c o m p o n e n ts
o f th e .IT s y s te m a re h e a ts u n k at th is te m p e ra tu r e .
3.4
M ultistage Sorption Cooler
D e te c to r te m p e ra tu re s o f 0.2 5 K a re achieved w it h a c u s to m , m u lti-s ta g e 1 'H e / 'H e / 'H e
s o rp tio n c o o le r t h a t w e d e s ig n e d in c o lla b o r a tio n w it h C ha se R esearch C r y o g e n ic s 1
fo r th e P o la tro n . W e b e g in w it h a re v ie w o f th e im p o r t a n t p ro p e rtie s o f s in g le -s ta g e
s o rp tio n re frig e ra to rs .
A s im p le s o rp tio n r e fr ig e r a to r c o n s is ts o f tw o c h a m b e rs :
a
I)u m i) c h a m b e r a b o ve a s t ill, c o n n e c te d b y a t h e r m a lly is o la tin g tu b e (F ig u re 3 .3 ). T i n 1
m id -p o in t o f th e c o n n e c tin g ru b e
the "c o n d e n s a tio n p o in t "
is a tta c h e d to a c o ld ,
e x te rn a l b a th . T in 1 p u m p is fille d w ith an a d s o rb a n t m a te r ia l, such as c h a rc o a l, a n d is
a tta c h e d v ia a lo w t h e r m a l c o n d u c tiv ity heat le a k to th e b a th . T h e e n tire r e fr ig e r a to r
is fille d w it h a w o r k in g f lu id w h ic h is a t a p re ssu re o f r o u g h ly 1 A tm o s p h e re w h e n
th e syste m is c o o le d t o n e a r th e c r itic a l te m p e r a tu r e T,.,.,, o f th e flu id , a b o v e w h ic h
te m p e ra tu re c o n d e n s a tio n c a n n o t o ccur.
S o rp tio n r e frig e ra to rs a rt 1 o p e ra te d as fo llo w s : f ir s t, a ll (d e m e nts o f th e r e f r ig e r a t o r
a re co o le d to w e ll b e n e a th T ,.ri/ th r o u g h c o n d u c tio n b e tw e e n th e w o rk in g f lu id a n d
th e c o n d e n s a tio n p o in t.
T h e n , hear is a p p lie d to th e p u m p to raise its te m p e r a tu r e
a bo ve th e a d s o rp tio n te m p e r a tu r e T ,„/s o f th e m a t e r ia l in th e p u m p fo r th e g iv e n
w o rk in g flu id
th is e n su re s th a t a ll gases have 1 been e x p e lle d fro m th e p u m p .
As
th e w o rk in g flu id liq u ifie s at t I n ' c o n d e n s a tio n p o in t , it d r ip s d o w n th e c o n n e c tin g
tu b e in to th e s t ill.
W h e n m o s t o f th e w o rk in g flu id has been liq u ifie d , h e a t to th e
'Chase* Research Cryogenics.
35
Wostenliolm Road. Sheffield S7 1LB. United Kingdom
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
Power in —
during cycling
Pump
Condensation Point
’ tubeS
Power in -------during operation
}
Still
'C P
leak
parasitic
\
\
\
\
V '\
Thermal Bath (Tbath)
Figure* 3.3: S c h e m a tic o f a s im p lifie d s o rp tio n frid g e .
F lu id
T,.r „
‘ He
‘ He
3.3
T „ f/> (c h a rc o a l)
T /w.s,
Q ,.„f, (l 1.5 K
15 K
1.1 K
22
15 K
0 .3 K
10 .J /g
J /g
T a b le 3.2: T h e rm o d y n a m ic - P ro p e rtie s o f H e liu m [4 j
p u m p is s h u t o ff. a n d it is a llo w e d to co ol. A s the' p u m p d ro p s b e lo w T,„/.s. th e v a p o r
pressure o f the' liq u id in th e s t i l l d ro p s , c o o lin g the' liq u id . G re a te r h e a t in p u t in to th e
liq u id raises b o th f l u 1 base1 te m p e ra tu r e T ,„.s, o f t lu ' liq u id a n d . to a g re a te r e x te n t,
its v a p o r pressure.
W h e n f lu ' liq u id is c o m p le te ly e x h a u s te d , th e e n tire procedure'
can be re p e a te d .
T h e c r it ic a l te m p e ra tu re , c h a rc o a l a d s o rp tio n te m p e ra tu re , p u m p e d base' te m p e r­
a tu re ’ . a n d la te n t heat o f v a p o riz a tio n o f ‘ He a n d ,{He a re s u m m a riz e d in T a b le 3.2. A
ty p ic a l s in g le -s ta g e '{ He frid g e o p e ra tin g o ff a large', p u m pe 'd L 'H e b a th m ig h t provide*
50 / / \V o f c o o lin g p o w e r a t 0 .3 K fo r l( i h o u rs [20].
Figure' 3.-1 is a d ia g ra m o f the' th e rm a l c ir c u it o f the* P o la tro n m u ltis ta g e so rp tio n coole'r. sc-paratc’d in to "in tc 'ro o o le r" (IC ) a n d " u ltr a c o o le r ” (U C ) substage's. A n
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51
INTERCOOLER
HePUMP
ULTRACOOLER
3 ,j
He PUMP
He PUMP
3
He HSW
IC He
HSW
3
\
UC He \
HSW
INTERMEDIATE b a s e p l a t e
rgj
He HEAT EXCHANGER UNK
He
CONDENSATION
PO IN T
LINK2
t il
LINK1
4He STILL
3 He CONDENSATION
POINT
TTT!
j:j 3He STILL
______________ La___________
He CONDENSATION
POINT
HeSTIU.
4 K BASEPLATE
/
LINK3
CRYOCOOLER
4 K HEATSINK
F ig u re 3.4:
C o o le r.
D ia g ra m o f the* T h e r m a l C ir c u it o f th e P o la tr o n M u ltis ta g e S o r p tio n
a s s e m b ly s c h e m a tic is in c lu d e d in F ig u re 3.5.
T h e IC o p e ra te s o ff a 4 K b a th a n d .
at tw o d iffe re n t tim e's, p ro v id e s in te r m e d ia te te m p e r a tu r e stage's o f 1.4 K anel 0 .5 K
th re m g h the* se 'q u e n tia l o p e ra tie m eif th e IC ‘ H e a n d I C ! He- se irp tio n e eeeile'rs. T h e 1 IC
'H e s t ill is solele're'd d ir e c t ly to th e IC 'H e s t ill: h o w e v e r, th e tw o flu id s ne-ve-r in te 'rm ix .
T h e 1 IC
1He*
stage 1 is c y d e e l fir s t. W h e 'ii the' IC s t i l l te m p e ra tu re ' reaehes 1.4 K . be>th
the* IC 'He- anel U C ! He' stage's are evek'ei.
C e m d en sa tiem e>f ’ He1 in the 1 IC anel U C
stage's e'xhausts the 1 'H e' liq u id in th e IC . T h e e 'o o lin g p o w e r eif the IC
use'd tei inte*re-e']jt a n d re-duce th e heat head on th e U C stage'
Tie* stage* is
as a re 's u lt. the' IC
! IIe
stage* is h e'avily leiaele'd.
The' IC stage- is ek'signe'el te) aehiewe' a base* te 'm p e 'ia tu re ' o f 0.50 K fo r 12 lu a irs
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52
SUPPORT LEG
IC 3He PUMP HEATSWITCH
IC 3 He PUMP
4He PUMP HEATSWITCH
UC He PUMP
UC 3He PUMP HEATSWITCH
4He PUMP
PUMP RADIATION SHIELD
UC 3He PUMP
* He PUMP
IC 3He PUMP
INTERMEDIATE BASEPLATE
IC He PUMP TUBE
4 He CONDENSATION LINK
IC 3He HEAT EXCHANGER LINK
4 He PUMP TUBE
U C 3He PUMP TUBE
cal
IC 3He HEAT EXCHANGER
UC 3He CONDENSATION POINT
SUPPORT LEG
UC STILL
SUPPORT LEG
IC STILL
±
4 K BASEPLATE
F ig u re 1 5.5: A s s e m b ly schem atic- o f th e P o la tro n M u ltis ta g e S o r p tio n C o o le r, p ro v id e d
b v Chase* R oseareh C'rvogenie-s.
u n d e r a 115 / / \ V lo a d , while* the* U C s ta g e is ele*signe*el to a ch ie ve base te*inpe*rature's o f
0 .25 K to r the* same* time* pe*riod. u iic Ic t a 5 / / \ V he*at lo a d . F u r th e r de*sign c o n s tra in ts
in c lu d e 'd (/) a d u t y cye-le > SO1/ : (/’/) in s ta n ta n e o u s p o w e r d is s ip a tio n c lu rin g e-yc-ling
A Q < 0.5 \V : a n d ( Hi ) ge*ome*trie- c o n s tra in ts a p p ro p ria te ' tee the* e*xpe*rim ent.
3.5
Integration
D c'sign o f th e inte'rface* b(*twee*n the* m e c h a n ic a l e-rvoe-ooler a n d the* m u ltis ta g e ' sorj>tie )ii c o o le r is a d e v e p tiv e ly s tr a ig h t fo rw a re l e*ngine*ering p ro je *e t.
\Vhe*n the* IC
'He*
stage* is c-yclc'el. the* e-ondemsatieni p o in t te*inpe*rature* rise's b y a m o u n t A T clue* te> gas
e-enidne-tiem e>f lie*at A Q fre)in the* p u m p . (H e re we* have* assume*d th a t a ll the* he*at etf
e le'sorption o f gas frenti the* p u m p make*s its w ay te) the* c-em densation p o in t : th is is a
eemse*rvative a s s u m p tie m .) The* me*e hauie-al eTveK-e>ole*r shem ld s in k th is he*at see t h a t
the* e-e)neleusatie)n p o in t te m p t'ra tu re * s ta y s we'll bene*ath the* e ritie -a l te*nipe*rarure* e>f
'He*. He'iie-e*. the* ee>nde*nsation p o in t o f the* IC 'He* stage* a n d the* e-e)ld t ip e>f tile* e-rv-
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o e o o le r m u s t be t h e r m a lly co u p le d w it h th e r m a l c o n d u c tiv ity G such t h a t th e penver
in p iit A Q cause's a te m p e ra tu r e rise A T < < T , ri< —
A s m e n tio n e d , th e c r it ic a l te m p e ra tu re o f 'H e is 5.2 K . so we re q u ire A T
K . T h e [to w e r in p u t d u r in g c y c lin g a s in g le r e fr ig e r a to r is ~
0 .5
<
1
\V . It fo llo w s th a t
we re q u ire G > 0 .5 \ V / K . A t 4.2 K . th e th e r m a l c o n d u c tiv ity o f O F H C C u is 2.5
W / e m / K . so wo re q u ire a le n g th o f O F H C c o p p e r w it h area to le n g th r a t io A / I >
0 .2
cm .
Id e a lly , th e m u ltis ta g e s o rp tio n c o o le r w o u ld be in te g ra te d d ir e c tly w it h th e c r y ­
o c o o le r. so t h a t th e c ry o c o o le r c o ld r ip w o u ld be in d ire c t c o n ta c t w it h th e IC
‘ He
c o n d e n s a tio n p o in t. M ild e r c o n s tra in ts o n th e th e r m a l c o n d u c tiv ity b e tw e e n th e L’ C
s t ill a n d th e d e te c to rs (o n th e o rd e r o f / A V / m K r a th e r th a n \ V / K ) c o u ld a llo w th e
th e rm a l lin k to be a c c o m p lis h e d at s u b - K e lv in te m p e ra tu re s . T h e P o la tro n c ry o g e n ic
s y s te m was im p le m e n te d w it h a L H e d e w a r- lik e c o ld [d a te o ff w h ic h th e m u ltis ta g e '
s o rp tio n c o o le r a n d b o lo m e te r stage 1 are1 su s p e n d e d .
T h u s the* th e 'rm a l lin k is f a ir ly
e-ennplie-ate'el. as s h o w n in F ig u re 1 3.4. A elire'c-t lin k ru n s be'tw evn the 1 erye>ee)oler eedcl
t ip anel th e IC 'H e 1 conde'nsatiem pednf. w h ile 1 a s e p a ra te , lenv-e-emelue-tivity lin k ru n s
frem i e)ther 4 K edeunents (su ch as the 1 feed s tru c tu re 1) tej a eedel plate 1 anel them to the 1
e-ryoe-oole'r t ip . F u rth e rm o re 1, the 1 heat e)f dese)rptie)ii etf gas e lu rin g e'aefi re n d e r ewe le> is
elumpe-el tei the 1 c*e>le1 plrite> v ia the 1 p u m p h e a t le'ak. In praetiee1. the- "4 K " eedel [>late 1
ru n s at ~ 5 K .
3.6
Microphonic and RFI Control
T he 1 me'e-hanieal e-ryea-emler is a s tro n g semre-e1 e)f v ib ra tie )n .
Micre)phe>nie- v ib r a t io n
ele'graele's s ig n a l q u a lit y th re m g h a v a rie ty o f m e c h a n is m s : ve)ltage> nedse* gemerate-el by
ra p id e-hange's in e-apae-itane-e1 elite1 te> redative 1 m o tio n be'twe'em sig n a l anel g re a m d line's:
inehie e'd vedtage 1 neiise1 gene'rate'fl by n m tie m e>f c u rre n t le>e>ps th re iu g h a m b ie n t magne'tiefiedels: h e 'a tin g etf the 1 beileime'ter clue te> ine-revise'el elissipate'e 1 ele'e-trie a l [)e)we>r: v a ry in g
e)[)tie-al s ig n a l elite1 te> meitiem anel subse'epicur m is a lig n m e n t e>f ei[)tie-al edemients: anel
an ineTe'ase* in beilem ie'ter s in k te m p e ra tu re 1 elite1 te> mie-rejphonie- lu 'a tin g etf the 1 e-e)IeI
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54
sta g o . A re v ie w o f these m e c h a n is m s , a n d h o w th e y d e g ra d e b o lo m e tric p e rfo rm a n c e
in p a r tic u la r , ca n be fo u n d in [4].
T h e m o st im p o r ta n t s te p in m it ig a t io n o f m ic ro p h o n ie response is use o f a lo w
o n tp u r-im p e d e n c e .J F E T s o u rc e -fo llo w e r at each b o lo m e te r o u tp u t (F igu re ' 2 .8 ). T h is
lim it s th e s u s c e p tib le w ir in g to th e h ig h -in ip e d a n c o le n g th b e tw e e n th e b o lo m e te r
a n d th e J F E T . T h is le n g th is m in im iz e d u n d e r th e c o n s tr a in t th a t th e .J F E T a n d
b o lo m e te r be s u ffic ie n tly t h e r m a lly is o la te d , as J F E T noise p e rfo rm a n c e is s e v e re ly
d e g ra d e d b e n e a th
110
K.
T he' P o la tro n e m p lo y s a
10
c m le n g th o f tw is te d p a ir, sh ie ld e d , stainless w ir e b e ­
tw e e n the' b o lo m e te r o u tp u t a n d J F E T in p u t. The* s h ie ld s arc' tie d to p h y s ic a l g ro u n d
a t th e b o lo m e te r in te g r a tin g c a v ity .
T w is te d - p a ir w ir in g m itig a te s tn ic ro p h o n ic c a ­
p a c itiv e a n d in d u c tiv e c o u p lin g b y fo rc in g b o th w ire s to move' in ta n d e m . T h e J F E T
a m p lifie rs are p la ce d on c ir c u it b o a rd w h ic h is s u s p e n d e d b y G - 1 0 s u p p o rts fro m r lie*
4 K c o ld p la te .
T he' te m p e r a tu r e o f th e c ir c u it b o a rd is ra ise d to
d is s ip a tio n in the' so u rce re s is to rs n e a r th e a m p lifie rs .
120
K by pow er
T h e su spe n sio n s y s te m has
b ee n s tiffe n e d to move* the' re s o n a n t fre q u e n c y o f th e s tru c tu re ' above th e b o lo m e tr ic
b ia s fre q u e n cy, a n d th e e n tir e s tr u c tu r e is p la ce d in a 4 K F a ra d a y cage. T h e b o lo m e ­
te rs th e m se lve s have re d u ce d m ass c o m p a re d to ty p ic a l c o m p o s ite ' b o lo m e te rs d u e t o
t h e ir o p e n -m e sh g e o m e try , a n d as such d is p la y re d u ce d s u s c e p tib ility to m ic ro p h o n ie
m o tio n [4].
In o rd e r to m itig a te s y s te m a tic e ffe cts due to v ib r a tio n - in d u c e d o p tic a l m is a lig n ­
m e n t. th e feed s tr u c tu r e is la t e r a lly s u p p o rte d at th e 4 K / 0.25 K th e rm a l g a p to
m a in ta in o p tic a l a lig n m e n t.
F u rth e r m itig a tio n o f m ic r o p h o n ie response is a c c o m p lis h e d th ro u g h th e m e c h a n ­
ic a l is o la tio n o f th e c ry o c o o le r fro m th e b o lo m e te r sta g e . T h is o ccu rs in th re e lo c a ­
tio n s : at th e 400 K p h y s ic a l s u p p o rt o f th e c ry o c o o le r. a t th e 80 K stage, a n d at t in '
4 I \ th e rm a l lin k b e tw e e n the' c o ld p la te a n d th e c ry o c o o le r r ip .
T h e c ry o c o o le r is
p h y s ic a lly su sp e n d e d fro m th e v a c u u m vessel b y s ta in le s s ste e l b ellow s s u p p lie d b y
N a tio n a l E le c tro s ta tic s C o r p o r a t io n -2
(F ig u re 1 2 .1 ). A tn m s p h e 'ric pressure 1 fore-e*s the 1
■ N a tio n a l E le c tro s ta tic s C o r p o ra tio n . 7")40 G ra h e r R oad . P .O . B ox (>20410. M id d le to n . \ V I Tittofit2-
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F ig u re 3.6: L o ft: p n e u m a tic v ib r a t io n is o la to r : R ig h t: m e c h a n ic a l c ry o c o o le r o p e ra t­
in g at a 4 5 c
v ib r a t io n is o la to r is d e s ig n e d to c o m p ly w it h t i l t in a s in g le d ire c tio n .
b e llo w s c lo s e d w h ile a leaked p n e u m a tic a ir-s u s p e n s io n s y s te m p ro v id e s a d is s ip a tiv e
re s to r in g fo rc e . T h e su spe n sio n s y s te m has tw o in d e p e n d e n t p re s s u re le v e ls a llo w in g
th e s y s te m t o re ta in m e ch a n ica l is o la tio n t h r o u g h a la rg e ra n g e o f t i l t a n g le s ( F ig ­
u re 3 .6 ). M e c h a n ic a l c o m p lia n c e a t th e 4 K th e r m a l lin k is a c c o m p lis h e d th r o u g h a
fle x ib le c o u p lin g m a n u fa c tu re d fro m O F H C C u b ra id .
V ib r a t io n a l e n e rg y can be d is s ip a te d in th e 0 .2 5 K b a th , in c re a s in g th e o p e ra tin g
te m p e r a tu r e a n d hence th e noise le v e l o f th e d e te c to rs .
E a ch d e te c to r is d ir e c tly
a tta c h e d to a c o p p e r rin g w h ic h is b o lte d to th e 0.25 K stag e .
B y p la c in g th e tw o
d e te c to rs in clo se th e rm a l p r o x im ity , s ig n a l due* t o v a ria tio n s in h e a ts in k te m p e ra tu re *
w ill be m a tc h e d b e tw e e n th e tw o d e te c to r s a n d re je c te d as c o m m o n -m o d e s ig n a l.
T h e re s p o n s e to in d u c e d v ib r a t io n o f a s ilic o n - n it r id e m ic ro m e s h b o lo m e tr ic svste m w it h s im ila r w ir in g and re a d o u t sch e m e w as m e a su re d b y B h a tia et a l
4 . The
b o lo m e te rs w e n * o p e ra te d at 0.3 a n d 0.1 K a n d s u b je c t to a c c e le ra tio n le ve ls ty p ic a l o f
v ib r a t io n c a u s e d b y space c ry o c o o le rs :
0
40 m g b e tw e e n
0
25 H z . T h e y c o n c lu d e
th a t s ta n d a r d m it ig a t io n te c h n iq u e s s u c h as th o s e d e s c rib e d above* a d e q u a te ly p ro ­
te c te d th e s y s te m fro m m ic ro p h o n ie s y s te m a tic * . w it h no noise above* th e cpuc'seent
X E P ~ 2 x 10 - I * \ V H z - 1 ' . It m u s t be strc'sse d th a t th e v a r ia t io n in e h 'te c to r type*,
reach>ut c ir c u it , anel ine'chanieal dc'sign be*twee*n e x p e rim e n ts m e a n s t h a t , a lth o u g h
0.410
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
these re s u lts e n c o u ra g e fu r th e r e x a m in a tio n o f c ry o c o o lc 'd b o lo m e tric s y s te m s , th e y
d o n o t in th e m s e lv e s g u a ra n te e su cce ssfu l o p e r a tio n .
Response* t o ra d io -fre q u e n c y in te rfe re n c e ( R F I ) is re la te d to m ic r o p h o n ie rc'sponse
in th a t th e s tro n g e s t so u rce o f R F I n e a r the* d e te c to rs is th e cryo co ol< *r m o t o r irse*lf.
F u rth e rm o re ', e lc 'c -tro m a g n e tic fie ld s generate*el in the' c ry o c o o le r m o t o r c a n in cro ase
in d u c tiv e ' m ic ro p h o n ie - re'sponse1. R F I c-cmples to the 1 h ig h -im p e 'd a n ce ' w ire's bc'twc'c'ii
the* b olom e 'te 'r a n d the 1 .J F E T s by d r iv in g c u rre n ts , a n d can cause' b o th v o lta g e 1 noise
anel b o lo m c 'te r h e a tin g .
T lir e e d e s ig n te c h n iq u e 's were aime*d a t re 'd u c in g R F I s u s e -e p tib ility o f the 1 P o la tro n :
firs t, the* b o lc n n t'te r stage 1 is e 'lectrie-ally is o la te d fro m the* rest o f the 1 sy s te 'in v ia a
K a p ro n th e r m a l lin k betw c'c'ti th e m u ltis ta g e ' s o r p tio n c o o le r a n d the* stage*: se'cond.
as discusse-'d. th e 4 K stage* a cts as a F a ra d a y cage* w it h a single* ape'rture* a t the* fee'd
h o rn t h r o a t: t h ir d , a lso disc-ussrd p re v io u s ly , a ll line's c'nre'ring the* 4 K space* are* R F I
filte re d
[40].
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Chapter 4
Observing Strategy
In th is c h a p te r. we* in tro d u c e ' the* basic o b s e rv in g s tra te g y o f th e P o la tro n e x p e r i­
m e n t.
A c a lc u la tio n o f th e a n tic ip a te d s e n s itiv ity fo llo w s , in c lu d in g a d is c u s s io n o f
c a lib r a tio n m e th o d s .
C 'M B p o la r iz a tio n e x p e rim e n ts a re p a r tic u la r ly susce,55‘ i 1
1
* to
s y s te m a tic effe cts, so we d is c u s s th e a n tic ip a te d p o la riz a tio n s y s te m a tic s in th is e x p e r ­
im e n t a n d th e a n tic ip a te d c o n tu s io n fro m p o la riz e d a s tro p h y s ie a l fo re g ro u n d s . T h e
c h a p te r ends w it h d is c u s s io n o f a p ro p o se d scan s tra te g y .
4.1
Introduction
B e fo re m a k in g a d e ra ile d c a lc u la tio n o f in s tru m e n ta l s e n s itiv ity , it is u seful to m a k e
a n o rd e r-o f-m a g n itu d e c a lc u la tio n ot th e s e n s itiv ity levels re q u ire d to d ete ct C’M B p o ­
la riz a tio n . C o n s id e r an id e a liz e d p o la rim e te r w ith in s ta n ta n e o u s s e n s itiv ity to S to k e s
p a ra m e te r Q (o r U ) o f I m K v/-s w h ic h m aps A ’ , = 900 p ix e ls (1 square degree) in a
rin g a b o u t th e n o r th c e le s tia l p o le w it h fy, = 2 ' re s o lu tio n fo r (j m o n th s a n d 50/<' o b ­
s e rv in g e ffic ie n c y . E ach p ix e l is o b se rve d to s e n s itiv ity rrT — 15 / / K in each o f Q a n d L ".
T h e /-space' w in d o w fo r such a n e x p e rim e n t rim s fro m a p p r o x im a te ly
o> l „ „ tx ~ ( 1 8 0 -/2 '). o r / ~ 180
(1 8 0 / 1 " )
5000. A s s u m in g th a t th e m e a su re m e n t is not s a m p le
variance' lim ite -d . the 1 e 'xp e rim e 'u t is se'tisifive* te> r-rns p e n a liz a tio n fin e -tu a tio n s at the'
le've'l o f 15 / / K / yOOO o r ~ 0 .5 / / K in fia t banel powe>r. A lth e m g h the' n n s p o la riz a t iem
le've'l se'e'n b y sue-h an e'xpe'rim e'nt w ill v a ry w it h m eidel. meide'ls whie-li are' e -o m p atible> w it h the> A T
p o w e r s p e 'c tru m me'asureel by B O O M E R A N G
p re 'd ict r o u g h ly 2
4 ( i K e>f p e ila riza tie m penver em these a n g u la r se-ale's (sev F ig u re ' 1.0).
The're'tbrev
o u r m ode'l peilarim e'te'r w em ld C'irhe'r make* a eemfielent eletee tio n ejf p eila riza tie m . e>r it
wem ld preivide* a e-halle'tiging n u ll re 'su lt.
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4.2
Anticipated Sensitivity
F iv e m a in so u rce s o f noise lim it th e u lt im a t e s e n s itiv ity o f th e P o la tro n :
p h o to n
noise, d e te c to r noise, a m p lifie r noise, flu c tu a tio n s in a tm o s p h e ric e m is s io n , a n d n on a tm o s p h e rie 1 / / noise. We w ill e s tim a te th e c o n tr ib u tio n s fro m th e fir s t fo u r o f these
b e lo w .
T h e c p ia n tita tiv e re s u lts are s u m m a riz e d in T a b le 4.2.
I t is c o n v e n tio n a l to
express th e n o ise in te rm s o f a X oise E q u iv a le n t P ow er ( X E P ) . m e a s u re d in u n its o f
W H z-1
E x p e r im e n ta l
s y s te m a tic e rro rs d u e to
4.2.1
1/
1/
/
noise is d iffic u lt to p re d ic t in a d v a n c e : m it ig a t io n o f
/ noise is a d d re sse d b y o u r scan s tra te g y .
Photon Noise
P h o to n noise a rise s fro m q u a n tu m flu c tu a tio n s in b a c k g ro u n d e m is s io n fro m th e a t­
m o sp h e re . te le s c o p e , a n d re ce ive r e n v iro n m e n t. C a lc u la tio n o f tin * p h o to n noise p ro ­
ceeds as fo llo w s .
F ir s t, the e m is s iv ity a n d te m p e ra tu re o f th e lo a d in g e n v iro n m e n t
are d e te rm in e d in o rd e r to c a lc u la te th e th e r m a l m ode o c c u p a n c y o f f lu ' b a c k g ro u n d
p h o to n s . T h e n , th e s ta tis tic a l v a ria n c e in th e m o d e o c c u p a n c y is c a lc u la te d . F in a lly ,
th a t v a ria n c e is c o n v e rte d in to a n o ise p o w e r.
A t rim es, c a lc u la tio n o f th e p h o to n
noise fo r th e P o la tr o n w ill p ro ce e d s o m e w h a t h e u ris rie a lly . p r e fe r r in g b a n d -a v e ra g e d
q u a n titie s (.4 x A / ') to d iffe re n tia l s p e c tr a l q u a n tifie s (.4,,<•//')• T h is is a re a s o n a b le
a p p r o x im a tio n t o m a ke fo r a s p e c tra l b a n d w id th o f ~
2O
/ f : th e a ve ra g e d is c re p a n c y
b etw e e n p re d ic te d a n d a c tu a l s e n s itiv it y fo r a n ensem ble o f C’ .M B e x p e rim e n ts is lik e ly
> > 2 0 /i'. T h is c a lc u la tio n is based on a m o re rig o ro u s th e o re tic a l tre a tm e n t o f p h o to n
noise fo u n d in [63].
F o r th e P o la tro n . r lu 1 o p tic a l p o w e r is d o m in a te d by in - a n d o u t- o f- b a n d e m is s io n
fro m th e 118 G H z ()■_> lin e , th e s tre n g th o f w h ic h re m a in s f a ir ly c o n s ta n t o v e r c h a n g in g
w e a th e r c o n d itio n s . The* m ost v a ria b le c o m p o n e n t is th e fa r w in g s o f H_.C) lin e ('m is ­
sion a t h ig h e r fre q u e n c ie s , w h ic h is q u a n tifie d b y th e p r e c ip ita b le w a te r v a p o r c o lu m n
d e n s ity
b e tw e e n 3 a n d
B e tw e e n S e p te m b e r a n d M a y . p i r r fo r th e O V R O s ite t y p ic a lly ranges
8
m m (see w i r t f . o r r o . c a l t c c h . <tin fo r a s n a p s h o t o f t lu ' c u rre n t and
3 0 -d a y w e a th e r c o n d itio n s ). M e a s u re m e n ts c a rrie d out b y a d e d ic a te d ra d io m e te r o f
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•59
th e z e n ith a tm o sp h e ric- s p e c tr a l tra n s m is s io n t . ( u ) a t O V R O (see F ig u re 5 .2 ) a llo w
us to co m p u te ' a b a n d -a v e ra g e d a tm o s p h e ric e m is s iv iry
f
J i)
r/ ( / ' ) ( 1 - t . ( v ) ) d i
(4 .1 )
T h e a tm o s p h e ric tra n s m is s io n w ill v a ry w it h th ic k n e s s , a n d hence the- a lt it u d e angle'
o f a g iv e n o b s e rv a tio n .
f =
0 .2
u nd c'r
0
In the' d im -tie m ot' th e _\e)rth C e lc'stia l Pole'. we> e'stiniate*
n u n o f p ier.
The' average' n u m b e 'r o f p h o to n s a r r iv in g a t a single* detee-tejr [)e*r se>c-e>neI pe>r H z <>f
spc'c-tral b a n d w id th p e r p o la r iz a t io n state' ( # / s / H z / p e ) l) is give'ii b y P lane-k's ewpre'ssiem
whe're*
is the' s p c 'c tra l e ffic ie n c y o f th e e»ptie-al c h a in l)etwe'e'ii tlu * elete'e t o r a n d the 1
sourc-c'. n o t c o u n tin g th e p o la r iz a t io n a n a ly s is . The* variane-e* in n. w h ic h is the* source'
o f p h o to n noise, is g iv e n b y
(4 .5 )
( ( A n f ) = ( ( / / - /“/ ) “ ) = n + r r .
a c-onseciuc'nce' o f b o so n e -o n n tin g s ta tis tic s .
The' fir s t tc 'rm is inte'rpre’te'el as ty p ic a l
G a u s s ia n statistie -s. while* the* se con d te>nn ca n be in te rp re 'te 'd as " b u n c h in g " in p ho tem
a r r iv a l tim e'.
Fe>r n ~
1. b o t h the* n anel n te 'n n s are* im p o r ta n t.
It is im p o r t a n t te>
re 'ine'inber th a t th is th c 'n n a l m ode' n u m b e r is separate* fro m th e n u m b e 'r o f s p a tia l
m ode's rn in the* be'am d c'c -o m p o s itio n . g ive 'ii b y the* th r o u g h p u t n 'la t io n
fo r ra d io
telc'se-o[)e>s A i l = n i \ 2. where* A is. te> take' eme1 ape'rture*. the* ilh n n in a tc 'd are'a o f the*
p r im a r y m ir r o r , anel i l is the* bc'am se)liel angle-.
in =
A s m e'iirione'd. fo r the' P o la tro n .
1.
A s s u m in g an a tm o sp h c'rie - te 'tn p e ra tu re o f 280 K . e 'm is s iv ity r ~
c'ffic-iene-y //„,,, ~
0 .2
0 .2
. a n d o p tic a l
. we' e -a lcu la te
(4 .4 )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
T h u s , we o a n n o r t r iv ia ll y n e g le ct e it h e r te r m in th e o c c u p a tio n v a ria n c e . 1
T o c a lc u la te th e o p tic a l p o w e r in c id e n t o n a sin g le d e te c to r , we w e ig h t n by e n e rg y
h u a n d in te g ra te o v e r rlie sp<*ctral b a n d :
P,,,t
=
[
(4 .5 )
X (hl')du
J it
n x (hu) A u
'
•
-
(4 .6)
(s) H ¥ )
W e n o w c a lc u la te th e p h o to n n o ise . E q u . 4.6 can be r e w r it t e n
Pr/it
"
-
M
M
so t h a t E t[ii. 4.5 fo r th e v a ria n c e n o w reads
((A //)-) -
P" p' (1 + /7).
(hu)Au
(4 .9)
T h e [jo w c r variance* in one secon d is th e b a n d -in te g ra te d tn o d e -o e c u p a n e y variance*.
we*ighte*d b y p h o to n e n e rg y:
(Pnpt)
x U S(,('] =
f{)
{ ( A n ) 2) ( hu) ' 2d u
(4 .1 0 )
~~
{ ( A n ) 2) ( h u ) 2A u
(4 .11 )
~
P , pi •'< ( hu) (
(4 .1 2 )
1
+ n ).
w h e re it has been a ssum ed t h a t u p o n in te g ra tio n o ver in f in it e s im a l fre q u e n c y b a n d s
d u the* c o n tr ib u tio n to th e p o w e r variance* is s q u a re '-a d d itiv e .
p h o to n X E P , i s
X E P /,/,..s
The* single* ele*te*eteir
the* rrns variance*
=
\ / 2 x y P„,,t h u (1 + n )
( 4. 15)
' I t lias I >t »<*11 argue'd. ho\ve*ve*r. rlia t tlie* it2 te*rni lias b<>i*ii ne>itlii*r fu lly justifie*<I n o r ex|>c*riuie*nrally
m easu red ill a lio lo u ii'tn c systinn. Since* its ilie-lusiou can he inorivate'el by n o li-e iu a lirm il eonsidera tio n s . it is argued flu* "bunching" ti'n n is inre*grated clown ove*r the* b o lo m e te r rc'sponsc [lerioel
r ~~ 2-ri ms > > i ' ~ l . W e include the* te*nii as a pre*e-aution against o\-e*r-e*sriinating o u r se-nsitivity.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
01
~
2.0 x
10
'' \Y H z
5.f> x
10
11
n \ j / A v /i' \
s ) (irr)
- x (1 + n
u'141
W Hz
(4.15)
w h e n ’ the* e x tr a fa c to r ot \ / 2 arises in t lie c o n v e rs io n fro m p h o to n s p e r second to Hz
b a n d w id th .
A n a d d itio n a l fa c to r of v/2 rakes in t o a c c o u n t th e fact th a t tin * n o ise in a m easure­
m e n t o f S to ke s p a ra m e te r Q o r i
is t in ’ noise' in th e sig n a l d iffe re n c e ta k e n betw een
tw o u n c o rre la te d d e te c to rs :
X E P ,,/, ~ 5.4 x
4.2.2
10
' \\
Hz
( 4 . 1C>)
Detector Noise
T h e second source' ejf neiise is fu n d a m e 'n ta l the’rm a l fiiie-tuatiem s in the' ele'te'e-teirs. De>te'cteir neiise a rise's as pliemem sheit uoise> in th e lenv c o n e lu c tiv ity ( G ) th e r m a l lin k
be'twe'en the' the'rm isten- anel the' b a th o r as J o h n s o n neiise- in the 1 rh e 'rin is te ir [05]. For
o u r e ip e ra tin g e -o n fig u ra tio n a t bedenne'ter te'inpe'rature' T . the' p h o u o ii uense* is
XEP
photi
(4.17)
~
1.0 x
10
1' \ \
Hz
T
- x
C.
h o lt i
( 4 . IS)
0.45 K J V»() p \ Y / K
wliere* k f i is rhe> B e d tz m a n n e-onstant. Xeite* th a t the> th e rm a l e-emelue-tiviry G is its e jf
te'inpe'rature'-de'iie'iiele'nt.
The' e'xpe'cte'el J o h n s o n lie/ise'
v/ 4A/jT|,„/0R h t > fo
XEP John
(4.10)
S
~
2.5 x
10
W Hz
- x
T,h o l o
(VO.45
KJ
R h o lt t \
\2 M i l )
h i x UP A l \
W
(.4.20)
s
/
wlie're' S is a n e'stim ate' eif the* e'le*c*trie-a 1 re 'sp e m sivity uildeT th e F in d in g e-onelitions
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
G2
e x p e c te d a t th e telescope’ ( 3 0 . 0 ). and R
is
a f u n c t io n o f te m p e ra tu re (o 2 .4 .7 ).
A s above, th e t o t a l d iffe r e n tia l d e te c to r n o ise is in cre a se d b y v 2 d u e t o d iffe re n c ­
in g :
X E P .,,,
4.2.3
=
C 2 x V X E P ^ „ „ + X E P ;,„ „ ,
14.21)
~
2,'J x l ( ) - ‘ : W H z '^
(4 .2 2 )
Amplifier Noise
T h e t h ir d c o m p o n e n t o f noise' is a m p lifie r imise* in th e e-old m atehe'd .J F E T s .
nie'asnred d iffe 'r e n tia l uehse1 pe*rformane-e e»f ~ 4
11V
The*
H z - 1 J is e-emverte*d t o e>stiinate'rl
X E P by d iv id in g b y a n e 's tim a te o f the' e*Ie'ctrical re s p e m s iv ity X:
X E P ,,,,,,, -
4.2.4
1.3 x l ( r
17
W H z- ^ x
^
U j
(4 .2 3 )
Atmospheric Noise
T h e fin a l co m p e m e 'iit o f noise* is 1 / / flu c tu a tio n s in artneisphe'rie- w a te 'r v a p o r r o n te 'iit.
D iffe re ne -in g the' twe) eh'te'e-tor sig n a ls re'je'c-ts e -o inino n -in o de ' H u c tu a tie )u s . T h is
re'chnic[Ue is id e n tie -a l to t h a t use'd ill the 1 Sunyae'V-Ze*rdovie-h Ilifrare>d E x p e 'rim e 'n t
( S ilZ IE ) . e'xe-e'pt t h a t S tlZ IE eliffere'tie-e'S the’ pow e'r i l l tw o s p a tia l pixe'ls. whe’re'as the'
P o la tro n diHere'ne-c's the* pe)\ve*r in tw o se'iises o f lin e a r p o la r iz a tio n w it h in rhe> same'
s p a tia l pixe*l. Sinee 1 the> a tm e isp lie re ' is ne>t s ig n ifie -a n tly pe)larize>d [3i>]. a tm osp h e'rie - 1 /
noise' is lim ite'el o n ly b y the' c o m m o n m ode' re'je*criem r a t io (C’M R R ) e>f the ' re'ce’ ive>r.
G ro m u l-b a s e 'd ine'asure’m e'nts o f C M B p e ila riz a tie m w o u lel n o t be feasible 1 w it h o u t c a n e-e'llat io n o f a fm eisph o ric- fh ic tu a tie n is in th is m a n n e 'r.
The* le've'l o f re 's id u a l atm eisphcrie- e'missiem flu c tu a tio n s a t o u r s ig n a l fre'epicne-v can
be> e'stim ate'd u s in g the 1 m e 'th o d s e>f Clm re-h [l( ) j. S ince 1 S tlZ IE a n d the- P o la tr o n have
s im ila r be'am size's, the* atm osphe'rie- H u c tu a tio n s obse'rve'd b y S tlZ IE a t 2 1 7 G H z fro m
M a n ila Ke*a are* scale'el to o b t a in an e'stim ate 1 o f a tm e is p h o ric Hue tu a tio n s th a t w ill bese'e-n b y the 1 P o la tre m a t 100 G H z frenn O V R O . T h is s c a lin g ivlie's o n th e 1 fo llo w in g
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G.'i
a s s u m p tio n s : th a t re s id u a l a tm o sp h e ric- noise is d o m in a te d b y g a in m is m a tc h e s a n d
n o t b ea m m is m a tc h e s : t h a t Z e e m a n s p lit t in g o f ()•_> lin e s b y th e E a r th 's m a g n e tic h e ld
is n e g lig ib le [-18]: t h a t th e g a in s o f th e tw o
a
re g u la r basis to
p o la r iz a tio n c h a n n e ls
ca n be m a tc h e d o n
V A :t h a t H u c tu a tio n s arc1 d u e to v a r ia tio n s in w a fe r v a p o r
c o n te n t:
a n d th a t th e O V R O a tm o s p h e r ic e m issio n flu c tu a tio n s c a n be e s tim a te d b y fre q u e n c y
s c a lin g M a n n a K e a e m is s io n h u c tu a tio n s . as m e a s u re d b y S u Z IE .
The 1 d iffe re n c e in a tm o s p h e ric o p a c itie s a t th e tw o site's is e nco d ed in th e r a t io
Ri
=
(
%
2.0
" " " < / (
■-""/■■
w h e re ty p ic a l m e a s u re d 225 G H z z e n ith o p a c itie s r s- =
(4.24)
(4.20)
0 .0 7 at M a n ila
K ea a n d
Tp ~ O.o at O V R O . a n d th e assum ed a ltitu d e ' angle's are* ftg ~ GO a n d Op ~ 4 0 : . A
se'coud r a tio . R._> = 0 .1 8 . is a s c a lin g fae-tor w h ic h take's in t o aee-emnt the 1 eliffe're'iie-e'
in the 1 e -o n trib u tio n to the' t o t a l atm osphorie- opae-iry due' t o wate>r v a p o r at //p = 08
G H z a n d ug = 2 17 G H z (se'e> Dane-se- et al. [1 5 ]).
F o llo w in g C h u rc h [ 1 0 ], we' e-ale-ulate
The> s u b s c rip t P re fe rs te> the' P o la tro n a n d S re'fers t o S u Z IE . The- q u a n tity X E P g =
1 .0
x l ( ) -1 -’ \ \ * H z - 1 ~ w as me'asure'd b y S u Z IE a t M a n n a K e a in a single' ehanne-l a t
the- P olatre m s ig n a l fre'c|iic'ncv 4 f , n , = O.G H z. A fae-tor o f 1 /2 is in c lu d e d to conveT t
the 1 S u Z IE elata to a sin g le' p o la riz a tio n . The- elepe-nele-nee' em spe'e-fral fre't[ue'uc-y a n d
b a n d w id th arise 1 in the* th e r m a l n a tu re ' o f the* eunission. A side’-b y-sid e ' e-om parison e>f
the- eiuantitie'S re'Ie'vant t o a c a lc u la tio n o f atm eisphe'rie- Hue-tuatiem s at the 1 tw o site's
ca n lie 1 fo il tie 1 in Table- 4 .1 . The- antie-ipafc'd neiise- ean be- re -w ritte n
X E P „ , , „ ~ 4.G x 1 0 - |!' W H z -3 x
(^5)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-
(4 .2 7 )
64
Q u a n t it y
S u Z IE
P o la tro n
1
100
60
40
CMRR
A lt it u d e A n g le
Z e n ith O p a c ity r ( c‘ 225 G H z )
0.07
0.5
O b s e rv in g O p a c ity <
0.92
0.46
T h r o u g h p u t .4 0 ( i n n r )
F re q u e n c y u (G H z )
14.0
9.N
96
217
0.07
B a n d w id th A e / V
O p tic a l E ffic ie n c y
0 .2
0.4
o
# o f P o la riz a tio n s
0 .2
I
T a b le 4.1: C o m p a ris o n o f q u a n tifie s used to e a le u la fe e xp e cte d a tm o s p h e ric fh ie tu a rio n s fo r S u Z IE a n d P o la tro n
4.2.5
Flux Sensitivity
T h e t o t a l d iffe r e n tia l noise p e rfo rm a n c e o f th e s y s te m is p re d ic te d b y a d d in g th e X E P
fro m each so urce in q u a d ra tu re :
X E P L ,/
=
X E P;, + XEP’-),, + XEP;,,,,, + XEP;,,,,.
(4.2S)
T h e X E P is c o n v e rte d to X o ise E q u iv a le n t P o la riz e d C’ M B T e m p e ra tu re . X EP T,.,,,/,.
m e a su re d in //K .s 1 2. as fo llo w s .
F ir s t, we e a le u la fe th e X oise E q u iv a le n t P o la riz e d
F lu x D e n s ity ( X E P F D ) . m e a su re d in J y s 1
w h ic h is tlie s e n s itiv ity o f th e re c e iv e r
t o p o la riz e d lig h t in a s in g le second o f in te g r a tio n tim e :
XEPFD
w Ik 'iv
~
----------- N— r " " - ------ -=
Ae x
x A x \/2
~
10.cS m.Jv s
, >
(4 .2 9 )
X E P „ „ ,,/
x --------------------------—
[ n r 1, w Hz
A ~ 16.4 n r is th e illm n iu a t e d area
of
-]
(
x (
0 .2
\ ( 0 .2 \
\ Av / i ' J
I
)
)
( 4. 40)
th e telescope p rim a ry , a n d the 1 fa c to r o f
\ / 2 arises in th e c o n v e rs io n fro m H z - 1 2 to s 1 J: th e b a n d w id th o f a "b o x c a r" f ilt e r on
d a ta sa m p le d fo r rim e r is l /
2
r . T h e t o t a l C’M B Hux d e n s ity in b o th p o la riz a tio n s .
F r„,/,. m e a sured in Jy. is
2 Ins x n
A*
x O
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(4 .4 1 )
p irr
(m m )
X E P ,,/,
X E P /,„/„
X EP ,,,,,,,
X E P „ ,,„
X E P /,,/
XEPFD
(m .Iy y /s )
XEPT
( / / K v/7 )
3
4 .9
2.9
1.3
.03
5.8
02
435
0
5 .4
2.9
1.3
.04
G. 2
07
470
8
5 .9
2.9
1.3
.05
0.7
73
512
T a b le 4.2:
A n tic ip a t e d
1 ()-17\V H z ' 1 -.
S e n s itiv ity .
D iffe r e n tia l
~
N'EPs
an*
g iv e n
in
184.8 .Jy.
u n its
of
(4 .4 2 )
H(>re H ~ O x 1 0 ~ ‘ s r is rlie beam s o lid a n g le . a n d n ~ 0.2 has been e v a lu a te d fo r T ,.,„/,
= 2 .7 K . C o n v e r tin g fro m in te n s ity t o CME3 p o la r iz a tio n te m p e ra tu re , th e X E P T,.,,,/,
is th e n
X EP T,.,,,/,
( ' - I
— ----- ' ^ = — r
1nnh
w lie re ./• = h u / f >T,.,„/, ~
XEPFD
x —
.
J
l
(4 .3 3 )
ftnl,
1.7. Here, th e X 'E P T is re fe rrin g to tin * s e n s itiv ity to S toke s
p a ra m e te r Q ( / / K ) in a second o f o b s e rv in g tim e . C a lc u la te d X E P F D a n d X E P T,.,,,/,
fo r d iffe re n t a tm o s p h e r ic c o n d itio n s a re in c lu d e d in T a b le 4.2.
Q u o tin g a n tic ip a te d o r re a lize d s e n s itiv itie s fo r C M B p o la riz a tio n e x p e rim e n ts is
m ade d if fic u lt b y th e va rio u s fa c to rs o f 2 w h ic h m a y e n te r c a lc u la tio n s .
O ne con­
v e n ie n t m e th o d fo r re s tin g w h a t one m e a ns b y a p o la riz a tio n X E T (o r X E P T ) is
to c o n s id e r th e ease* th a t th e tw o c o m p o n e n ts o f lin e a r p o la riz a tio n are s u m m e d
ra th e r th a n d iffe re n c e d , in w h ic h case a c o n v e n tio n a l C M B A T m e a su re m e n t w o u ld
re s u lt.
O m it t in g th e (m u c h ) in cre a se d noise a ris in g in c o m m o n -m o d e a tm o s p h e ric
H u c tu a tio n s . th e e q u iv a le n t e x p e rim e n ta l X E T s h o u ld be th e lis te d X E P T . S uch an
e x p e rim e n t, o f course*, loses a fa c to r o f V - in s e n s itiv ity b y s p lit t in g th e p o la riz a tio n
and th e n a d d in g the* tw o u n c o rre la te d d e te c to rs .
4.3
Calibration
C a lib r a tio n o f th e a b s o lu te rc s p o n s iv ity o f th e in s tr u m e n t w ill be a c c o m p lis h e d th r o u g h
s in g le - p o la riz a tio n o b s e rv a tio n o f la rg e ly u n p o la riz e d sources, such as p la n e ts . E ach
s in g le -c h a n n e l s ig n a l w ill be d o m in a te d b y th e a tm o s p h e ric H u c tu a tio n s d e s c rib e d
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(j(i
above.
A s b e fo re , th e le v e l o f such flu c tu a tio n s o b s e rv e d w ith th e S u Z IE re c e iv e r
c a n be scaled t o p re d ic t n o ise levels fo r th e P o la tr o n . a lb e it w it h
re je c tio n a n d
110
110
c o m m o n -m o d e
a d v a n ta g e d u e to tin* p o la r iz a tio n m o d u la tio n a t 4
A ty p ic a l
d r if t scan o v e r a c a lib r a to r o c c u rs o ve r a rim e p e rio d o f ~ .*30 seconds. W e e x p e c t a
s in g le -c h a n n e l N E F D
011
th o se rim e scales o f ~
a ty p ic a l c a lib r a to r ( M a rs , fo r in s ta n c e ) is
011
70 .Jy y/». T h e a n tic ip a te d f lu x fro m
th e o rd e r o f several h u n d re d J y . so sev­
e ra l d r if t s o v e r th e sam e so u rc e m a y be re q u ir e d in p o o r w e a th e r. H ence, c a lib r a tio n
u n c e r ta in ty w il l be d o m in a te d , as it is in th e S u Z IE e x p e rim e n t, b y th e u n c e r ta in ty
in th e b rig h tn e s s o f th e c a lib r a to r s th e m s e lv e s .
W e e x p e c t to flu x c a lib ra te ' to th e
o - l 0 ‘/( a c c u ra c y t y p ic a lly a ch ie ve d fo r C M B o b s e rv a tio n s .
4.4
System atic Polarization
U n t il re c e n tly , m illim e te r - w a v e p o la r iin e tr y has c o n s is te d m a in ly o f the' s tu d y o f m a g ­
n e tic fie ld s th r o u g h th e m e a s u re m e n t o f th e p o la r iz a tio n p a tte rn s o f m o le c u la r c lo u d s
a n d c o m p a c t d u s ty source's. T h e q u a n tity o f se-ieuitihe- inte're'st fo r rhe'se- s tu d ie 's has
be'eui th e r/rr/rre
o f polarization
(o r. s im p ly , p o l a r i z a t i o n ) o f a semrce'. a ve'e-tor-like
q u a n tity w h ic h has an a lig n m e 'iit dire*ctiem ft>tmrr, . m odule) r o ta tio n b y ISO"', a n d peesitive> fra c tio n a l m a g n itu d e
0
< p s,mrr, <
1
fo r ew ery obseuve'd positiem (ft. o )
011
the' sky.
T h is q u a n tity is ofteui deneUe'd p stmrr., (ft. o ) : m a p s o f th is pseuidesve'c-tor fie'lel are* o fte n
oveuiaiel on e'missiem in t e n s it y cemtemrs so th a t t h e re la tie m s h ip be'tw evn file* magne'tiefie'le 1 a n d the> e'tnissive* s tru e -tu re o f th e source' is d cu n o n stra te 'd .
T y p ic a l elust so urces are1 p o la rize 'd at the'
1
— 10(/( le've'l. so a ele*an nie'asure'tne'nr
e>f sueJi shemlel be' a ce u ra te ' re) < V X . A u s e fu l e p iiiilt it y te) define' is the' fra c tie )iia l sys­
t e m a t i c p o l a r i z a t i o n . 7U,/S-
a system i. w h ic h is the' peTc-euitage* p o la riz a tio n me’asure'el
w lie 'ti an in t r in s ic a lly im p e d a rize e l source* is obse rve 'd . B y d e 'fin itio n th is e p ia n tiry eloe's
ne)t v a ry w it h seiurce' b rig h tn e 's s .
It is u s u a lly cause'd by. a n d fixe'el w it h re*spe'ct to .
the 1 te'le'se-e>pe' a n d re'ce'iver. One* c-an d e te 'rm in e the* e xte'nt o f s y s te 'in a tic p o la r iz a tio n
b y m e'a sn rin g the 1 e)bse>rved pe)larizatie>n fre>ni seiurce' w h ie h is k n o w n to be> n n p o la r ize'el. I t ca n ;ilse> be* me'asure'el th ro u g h o b s e rv a tio n ejf a knetw n pe)larize*el se)ure e* ove*r
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67
a p e r io d o f tim e such th a t th e p a ra lla c tic - angle 1 o f th e source 1 ro ta te s w it h respect
to th e te le s c o p e . The 1 p o la r iz a tio n as a fu n c tio n o f tim e m e a s u re d in th e telescope's
c o o r d in a te fra m e s h o u ld d escribe' a c irc le 1 w it h ra d iu s Psoum n iic l c e n te r ejffset b y />
tro m the> o r ig in . O nee Ji
is m e a s u re d in th is w a v it c a n be s im p ly s u b tra e te 'd pixe*l
b y [)ixe'l fr o m m a p s o f o b se rve d p o la r iz a t io n PnhJft- o):
P s „u rc ,\ti. o )
- P o iJ V - o ) - p , „ , -
(4.3-4)
In th e lo w s ig n a l-to -u o is e 1 regim e1, p o la r iz a tio n pc're-entage 1 c a n lie1 a e liffie u lt c|iiaut i t y te> a n a ly z e 1, sine-e it is n o t G a u s s ia n -e lis trib u te 'd a b o u t a n ie 'an o f ze ro . T o remeely
t liis . re d u ce 'd ( frae-riemal) S trike s p a ra m e te rs e/ = Q / I anel ti = U / 1 are1 introelucc'd.
w it h Q a n d L' the 1 m easured S to k e s p aram e'te'rs a n d / the 1 m easureel soure-e1 in te n s ity .
T h e e p ia n titie 's e/ a n d n e-an be p e is itiv e eir n e g a tiv e . T h e syste u n a f ie- p o la riz a tio n adels
ill the 1 sam e 1 w a y as before:
<l„,urn (0- o )
"snurrr ( ft. O )
=
(ft. o ) -
( 4 .3 o )
(/„/,.s ( ft. O ) ~ U,,,,.
T he 1 p o la r iz a t io n p a tte rn ca n s t ill be1 revejvered sinc-e p „ mrr, -
( 4.G6 )
y <i;l)urr, + "i,,,,-,-, a ll( l
ft,nun; = :j t a i l " 1 ( T V Q ).
F o r liie ’a su re 'm e n ts o f b r ig h t . p o la riz e 'd so lire-es sue-li as d u s t anel m o le c u la r e-loiids.
th is e -h a ra e 'te 'riza tio n o f system atie - e 'rro rs re la tin g to p o la r iz a tio n is aele'eiuate. C M B
p o la r iz a tio n m o a sureniients. how ew er. are 1 d iffe re n t.
It is the 1 n o n -u o rm a liz.e 'd Sroke>s
p aram e'te'rs Q anel U th a t are1 o f in te rc 's t. neit the 1 fr a c tio n a l p o la r iz a tio n p o r th e
re'clnced p a ra m e 'te 'rs e/ anel u.
T h e u n d e r ly in g in te n s ity e lis tr ib u tio n is b r ig h t, w ith
te n n p e ra tu re 1 2.72S K . and c 'x tre m c 'ly u n ifo r m , b u t v a ry in g ae-re)ss the 1 s k y w ith some 1
lik e ly u n k n o w n a m p litu e le 1 A T / T >
10
" ’ . Hene-e\ givem a m e 'asurem e'iit o f syste-matie-
p o la riz a tie m e/s(/s fro m o b s e rv a tio n o f an unpedarize'el soure-e1. the 1 re 's u lta n t s y s te m a tic
Q,ns{ft. O) = (p,/sT ( f t . o) c a n n o t be1 s im p ly eale-ulate'el anel su h tra cte 'e l fro m the 1 d a ta .
sine-e1 T ( f t . o ) is. as yc't. u n k iie n v ii. Sine-e1 we1 are1 leteiking fo r H u e -tu a tio n s A Q / T ~ lO -1’.
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68
wo re q u ire
and
0 .0 1
to e n s u re t lia r we a re not s y s te m a tie a lly p o la r iz in g A T
fin e r n a tio n s . A n o b s e rv in g s tra re g y w h ic h m easures th e p o la r iz a tio n o f a s in g le p ix e l
at d iffe re n t p a r a lla c tic angles a llo w s t h is s y s te m a tic p o la riz a tio n to bo s u b tra c te d to
< VA even i f th e u n d e rly in g in te n s ity d is t r ib u t io n is u n k n o w n .
S ig n a l p ic k - u p in th e fa r sid e lo b e s o f th e m a in beam can a ffe c t fa in t-b a c k g r o u n d
m e a s u re m e n ts i f the' source in th e s id e lo b e s is b rig h t e n o u g h .
th e g a la x y , a n d th e h o riz o n are e x a m p le s o f such sources.
T h e su n. t lu ' m o o n ,
In a d d itio n , fo r p o la r­
iz a tio n m e a s u re m e n ts , tlit* tw o c o m p o n e n ts o f lin e a r p o la riz a tio n w ill have d iffe re n t
b e a m sh ap e s, since* th e p o la riz a tio n a n a ly z e r (in o u r case* th e O M T ) d efin e s a set o f
c o o rd in a te s w it h respect to th e re c e iv e r, te le sco p e , and telesco p e s u rro u n d in g s . T h e
d iffe r e n tia l p ic k -u p fro m the* so u rce in th e tw o beam s s h o u ld n o t be g re a te r th a n th e
e x p e c te d C’ M B p o la riz a tio n s ig n a l.
T h e o b s e rv a tio n s tra re g y . th e n , is s u b je c t to a
c e rta in set o f re s tric tio n s on th e a n g le b e tw e e n th e observed re g io n o f s k y a n d these
v a rio u s so u rce s.
O b s e rv a tio n n e a r the* N o r th C e le s tia l Pole m itig a te s a ll o f these*
e ffects.
4.4.1
Systematic Polarized Flux
In c o n tra s t t o th e s y s te m a tic p o la r iz a tio n d e s c rib e d above*, whie-li am em nrs to a p< rccntafp
p e d a riz a tio u ae-quire*el b y an obse*rve*d unpe>larize*d semre-e. the* P o la tro n w ill
obse*rve* a varie*ty e>f s y s te m a tic pedarize'el flu x e s w h ie h are* inde'pe'iidc'U f <)f the* b r ig h tue'ss e>f an eibserve'd soure-e*.
F o r instance*. rhe*rm al ra d ia tio n fro m the* s u rre m n d in g
e*iivironine*nr w ill scatte*r fro m the* re*le*se-e>pe* fe*e*el le*gs in to o u r system i. p ic k in g u p
some* p o la riz a tie m e lu rin g the* se-attewing. T h is type* and m ost type's e>f polarize*d H ux
w ill v a ry slenvly. a n d w ill be* remieived fre jm the* elata as a DC-le*ve*l while* d r ift- s c a n n in g .
W hile* a e tive d y s e a n n ilig the* te*Ie*se-(>pe*. s p u rio u s signals ra n lie* remieive'ei b y re'teremein g tlie 'in to the* te'le'se-ope' s s u rro u n d in g e>iiviremme'iir. while* astre>pliysie-al semre-c's w ill
rotate* abem t the* N o r th Ce*le*stial Peile*.
The* wave* plate* its e lf is a semrce* o f s y s te m a tic peilarize'd Hux. A s a conseque*ne-e* o f
the* n u 'th o e l use*el te> proehice* b ire 'frin g e n c e . the* tw o c ry s ta l axe*s e>f the* wave* plate* ine u r
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09
d iffe r in g loss ta n g e n ts a n d re H e e tiv itie s .
p la te w ill
at
2
Ik *
L’ n p o la riz e d s k y r a d ia t io n in e id e n t on th e
c o n v e rte d to a s y s te m a tic flu x . T h is s ig n a l, h o w e v e r, w il l be m o d u la te d
/ „ 7, and w ill n o t c o n tr ib u te to th e s ig n a l a fte r lo c k -in a t 4
4.4.2
Receiver Polarization
G a in m ism a tch e s b e tw e e n th e tw o b o lo m e te r ch a n n e ls g e n e ra te a f r a c t io n a l s y s te m a tic
p o la riz a tio n such th a t an u n p o la riz e d so u rce o f in te n s ity 1( f ) in c id e n t o n th e re c e iv e r
w ill p ro d u c e a s ig n a l Q'r ,,.(t) — <l'r, r I ( t ) w h ic h is not m o d u la te d b y th e w a ve p la te
a t fre q u e n c y 4
T h e m a g n itu d e o f th e re c e iv e r p o la r iz a tio n is in v e rs e ly re la te d to
th e c o m m o n m o d e re je c tio n r a tio o f th e in s tr u m e n t:
in p u t in te n s ity I ( t ) va rie s o n rim e scales t ~
f u p " " ill in c lu d e c o m p o n e n ts o f 1( f ) .
|e/.,,.( /) ] =
1J C M R R .
I f th e
1 /4 /,,.,,. th e n th e d e m o d u la te d s ig n a l at
A n e x a m p le o f th is e ffe c t was tre a te d e a rlie r
d j2 .o ) fo r th e case o f u n p o la riz e d s k y H u c tu a tio n s . A s d is c u s s e d in <j4.2.4. we e x p e c t
C’ M R R p e rfo rm a n c e fo r the 1 P o la tro n a t o r a b o v e a fa c to r o f
th e in d iv id u a l d e te c to r re s p o n s iv itie s .
100
d u e to b ia s t r im o f
In o th e r w o rd s, the' re c e iv e r p o la r iz a tio n can
be re d u ce d to b e n e a th 1(Z b y a d ju s tm e n t o f th e re la tiv e g a in s o f th e tw o p o la r iz a tio n
ch a n n e ls.
A n o th e r source' e>f cemime)n-me>ele' s ig n a l is v a ria tie m in the' teunpeTature 1 o f the*
bedemu'feT stage'. V a ria tie m s a t fre>que*ne-y 4 f „ . v w ill be1 re'e-e>rele>el as s ig n a l. Be'e-ause the*
g a in eliflers to r eeptieal s ig n a ls ine-idemt o n rhe> re'e-e*iver as opi)e)sed te> rh e 'rm a l s ig n a ls
a t the' bolom e'te'rs the'inse'lve's. a spe'cifie- re 'la tiv e g a in a e lju s tm e 'iit w h ic h t r im s o u t
e emiinem-moele 1 e>ptieal s ig n a ls is n o t likedy to alse> t r im o u t e-emnnem-nioele te'm ite 'ra ture'
H u e tu a tie jiis.
F o r th is reasejn the 1 bejlejniete'r stage 1 w ill be1 te u n p e 'ta tlire ' eontre>lle'< 1 to
~ 100 n K H z - 1
4.5
s t a b ilit y u s in g m e theids ele'se-ribe>el in H e d zap fel e t a l. [29].
Astrophysical Foregrounds
T h e 1 P o la tro n sp e 'ctra l banel is e lejse1 te> the 1 m in im u m
fee arise 1 fro m eebserving rh re tu g h e»ur o w n g a la x y .
e>f e e tn ta m in a tie u i e'stimate'el
Peelarize'el fo re 'g ro u n e l preeee'sse's
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70
in c lu d e ' s y n c h ro tro n e m is s io n , fre e -fre e e m issio n , t h e r m a l d u s t e m issio n , a n d . p e rh a p s ,
e m is s io n fro m s p in n in g d u s t g ra in s .
G a la c tic s y n c h r o tro n e m is s io n is lik e ly to he h ig h ly p o la riz e d .
B o u e h e t et al.
[0 ] p o in t o u t th a t s p e c tra l in d e x a n d p o la riz a tio n in fo r m a tio n o b ta in e d fro m lo n g w a v e le n g th o b s e rv a tio n s o f g a la c tic s y n c h ro tro n m ig h t n o t e x te n d to m illim e t e r w ave­
le n g th s . N e ve rth e le ss, b y m a k in g th e a s s u m p tio n s t h a t th e ('m is s io n is 4 4 <A p o la riz e d
a n d has th e sam e s p a tia l d is t r ib u t io n as tin ' u n p o la riz e d ('m is s io n at lo n g w a v e le n g th s ,
th e y p re d ic t a t
100
G H z th e fo llo w in g a n g u la r [to w e r s p e c tra b e tw e e n g a la c tic la t i­
tu d e s 30° a n d 7 5 ':
C , 7" '7'
=
0.9 r
=
() y
' fih '2
(4 .3 7 )
//A -j
(4
;,(S)
O b s e rv a tio n s o f g a la c tic d u s t re g io n s a t 100 fi .m in d ic a te th a t w h o re d u s t ('m is s io n
is b r ig h t, th e le ve l o f p o la r iz a t io n is o f o rd e r 2'X [2 0 ] a p a rt fro m a le w s m a ll re g io n s
in w h ic h th e p o la r iz a tio n rise s to
1 0 * /.
H o w e ve r, th e d egree o f p o la r iz a tio n o f h ig h
la t it u d e c irru s ('m is s io n is u n k n o w n . A m o d e l fo r h ig h - la t ir u d e g a la c tic d u s t p o la riz e d
('m is s io n has been c re a te d b y P ru n e t et al.
[G lj. T h is m o d e l assum es t h a t c irr u s is
tra c e d b y o b se rve d H I ('m is s io n a n d th a t th e d u s t g ra in s are s im ila r in s h a p e to
th o s e o bse rve d b y H ild e b r a n d et a l. [2G]. A 17.5 K P la n c k s p e c tru m w it h e m is s iv ity
p r o p o r tio n a l to u 2 is a ssu m e d . T h e d u s t g ra in s a re e x p e c te d to a lig n w it h th e g a la c tic
m a g n e tic h e ld : in o rd e r t o m a ke a c o n s e rv a tiv e e s tim a te , a n u n fa v o ra b le o r ie n ta tio n
fo r th e m a g n e tic fie ld is u sed.
T h e assum ed in tr in s ic d u s t p o la riz e d e m is s iv ity o f
~ 3 0 ‘A is re d u ce d d u e to p r o je c tio n effects. A t
p re d ic te d b y
Free-free
100
G H z . th e a n g u la r p o w e r s p e c tra
B o u c h e r et a l. b e tw e e n g a la c tic la titu d e s 3 l) : a n d
C " / ! 1' 1
=
C ‘(l!,s'
=
S .‘J x
1 0 .0
10“ 1 l~ l 3
x 1 0 -1 / “ ‘
1
75 a rc
f/I\2
(4 .3 b )
/ / A 'J.
(4 .4 0 )
('m is s io n in H I I re g io n s , lik e th e C M B . c a n p ic k
up som e s m a ll p o la r ­
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71
iz a tio n th r o u g h T h o m s o n s c a tte rin g . T h is is lik e ly to g e n e ra te a le ve l o f p o la riz a tio n
m uch lo w e r th a n t h a t o f s y n c h r o tr o n ra d ia tio n .
p ro po se d b y D ra in e et a l.
L ik e w is e , th e s p in n in g d u s t g ra in s
[19] s h o u ld not be p o la riz e d a t o r n e a r th e level o f s y n ­
c h ro tro n (‘m is s io n . N e ith e r o f these is lik e ly to c o n ta m in a te o u r m e a su re m e n ts. T h e
g a la c tic s y n c h r o tro n a n d d u s t p o la riz e d (‘m issio n a t
100
G H z is th u s e s tim a te d to be
m ore th a n a n o rd e r o f m a g n itu d e b e lo w th e C M B s ig n a l o v e r th e /-ra n g e to w h ic h
th e P o la tro n is s e n s itiv e (see F ig u re 4 .1 ).
1 0 . 0 0
:
L'
=
£
=
100
GHz
.
—
:
I =
_
1000
1. 0 0 :
0.10
N
0.01
.
100
1000
M ultipole M om ent
______
100
F r e q u e n c y (GHz)
10 0 0
F ig u re 4.1: P o la r iz a tio n G a la c tic F o re g ro u n d S p e c tra . L e ft p a n e l: p re d ic te d p o la riz a ­
tio n Hat b a n d p o w e r a t
100
G H z as a fu n c tio n o f m u lr ip o le m o m e n t / fo r m o d el C M B
G -ty p e H u c tu a tio n s (s o lid lin e ) , g a la c tic s y n c h ro tro n (d a s h e d lin e ), a n d g a la c tic d u s t
(d a s h -d o tte d lin e ). T h e d o t t e d lin e in d ic a te s a g e n e ric P o la tr o n w in d o w fu n c tio n in
a r b it r a r y u n its (see o4 .G.) R ig h t p a n e l: p re d ic te d p o la r iz a tio n Hat b a n d p ow er a t / =
1000
as a fu n c tio n o f s p e c tra l fre q u e n c y , same lin o ty p e key. w it h d o tte d lin e in d ic a tin g
th e chosen P o la tro n s p e c tra l p a ssb a n d in a r b it r a r y u n its . T e m p e ra tu re s are s ta te d in
R ayleigh-.Joans u n its . C M B G - ty p e a n g u la r s p e c tru m w as g e n e ra te d b y C M B F A S T
[12] fo r a B O O M E R A X G - e o u s is te u t C’ D M u niverse .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.6
Scan Strategy
In d e p e n d e n t m e a s u re m e n ts o f S tokes p a ra m e te rs Q a n d U at s e v e ra l s e p a ra te loe a tio n s on tlie* s k y a re necessary in o rd e r to d e te rm in e th e p o la r iz a tio n m u lrip o le
m o m e n ts d e s c rib e d in E q n . 1.21.
I f to o fe w in d e p e n d e n t m e a s u re m e n ts are m ade,
th e n th e s a m p le size is to o s m a ll to d e te rm in e a n a c c u ra te v a ria n c e in th e S toke s pa­
ra m e te rs. I f to o m a n y in d e p e n d e n t m e a s u re m e n ts are m ade, th e n each m e a su re m e n t
w ill su ffe r fro m n o ise d u e to s h o rt in te g r a tio n rim e . T h e s a m p le size* is fu n d a m e n ta lly
lim ite d b y th e n u m b e r o f in d e p e n d e n t m e a s u re m e n ts one ca n m ake o n th e sphere.
D esign o f a n o p t im u m scan s tra te g y is n o t o n ly in flu e n c e d b y s a m p le size co n ­
s id e ra tio n s . E n v ir o n m e n ta l a n d s c ie n tific c o n s id e ra tio n s also p la y a ro le . S e v e ra l en­
v iro n m e n ta l c o n s id e ra tio n s led us to c o n s id e r o b s e rv a tio n s o f re g io n s n e a r th e n o r th
c e le s tia l p o le ( X C P ) : w h e n o b s e rv in g n e a r th e X C P . d iu r n a l m o tio n re q u ire s o n ly
s lig h t m o tio n o f flu * te le sco p e w ith re sp e ct t o its p h y s ic a l e n v iro n m e n t, re d u c in g sidelo b e m o d u la tio n : th e X C P is > 07c n o r th o f th e e c lip tic p la n e in s u m m e r, so th e
S un. M o o n , a n d p la n e ts arc 4 lo c a te d w e ll b e h in d th e telescope: fu r th e r m o r e , e n o u g h
C M B e x p e rim e n ts h ave o b se rve d n e a r th e X C P t h a t th e n ' is m o re
b u t s t ill scant
kn o w le d g e a b o u t g a la c tic fo re g ro u n d s in t h a t re g io n [44].
I n itia lly , th e s c ie n tific g o a l o f th e e x p e rim e n t w ill be to d e te c t s ig n ific a n t n n s
p o la riz a tio n on a ll a n g u la r scales to w h ic h th e e x p e rim e n t is s e n s itiv e . T h is a m o u n ts
to g e n e ra tin g a b ro a d w in d o w in /-sp ace a n d o b s e rv in g few er p ix e ls , so t h a t th e noise
p e r p ix e l is lo w e r. A f t e r a d e te c tio n has bee n m a d e , a n d it is c le a r t h a t tin * d e te c tio n
is not lim ite d b y s y s te m a tic effects, th e P o la tr o n b ea m size1 is w e ll-s u ite d fo r s p a tia l
s p e ctro s c o p y o f C M B p o la riz a tio n .
A g re a te r n u m b e r o f p ix e ls w ill b e o b s e rv e d in
a given a m o u n t o f rim e , a n d th e d a ta w il l be* b in n e d in m u ltip le /-s p a c e w in d o w s in
o rd e r to search fo r a c o u s tic peaks.
Since C M B te m p e r a tu r e a n is o tro p y g e n e ra te s p o la riz a tio n , one* c o u ld use a m ea­
su re d A T
m a p to lo c a te re g ion s w it h la rg e te m p e ra tu r e g ra d ie n ts .
in te n d e d to d e te c t p o la r iz a tio n sig n a l m ig h t fo cu s o n these re g ion s.
o f h ig h -re s o lu rio n . h ig h s ig n a l-to -n o is e A T
O b s e rv a tio n s
In th e absence
m a p s, how ever, a scan s tr a te g y ca n be
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
d e s ig n e d w h ic h rakes a d v a n ta g e o f th e s ta tis tic a l r e la tio n s h ip b etw een te m p e r a tu r e
a n d p o la r iz a tio n p o w e r s p e c tra .
In th e presence o f I f f
noise, s im p le d r if t scan m e a s u re m e n ts on rin g s a b o u t th e
X C P are d e g ra d e d b y lo n g rim e -s c a le c o rre la tio n s .
T h e R in g 5 m /4 0 m e x p e rim e n t,
w h ic h used the' O Y R O 5 .5 m te le sco p e to m e a sure A T flu c tu a t io n s in X C 'P rin g s , h e ld
th e telesco p e a t a fix e d e le v a tio n a n d p e rfo rm e d r e g u la r b h n o d s in rig h t a s c e n s io n
[44], d iffe re n c in g th e m e a s u re d va lu e s to re m o ve lo n g -tim e s c a le d rifts .
In P h ilh o u r et al.
[5 8 ]. th e s e n s itiv ity o f th e P o la tr o n to C M B p o la r iz a tio n is
e s tim a te d as a fu n c tio n o f r in g o p e n in g a n g le Hru,,r
I n p u t s to th e s e n s itiv ity m o d e l
in c lu d e th e a n tic ip a te d b e a m size*, in s ta n ta n e o u s s e n s it iv it y to S tokes p a ra m e te rs Q
a n d U . a n d p o la r iz a tio n p o w e r s p e c tra C'f' a n d C'f
g e n e ra te d by C’M B F A S T
[12]
fo r a range* o f m o d e ls c o n s is te 'iit w it h th e te m p e ra tu r e p o w e r s p e c tru m m e a s u re d b y
B O O M E R A X G . M o d e l w in d o w fu n c tio n s are g e n e ra te d w it h response p<*aked a t the*
C M B p o la r iz a tio n p o w e r s p e c tr u m peaks.
F ig u re 4.2 p lo ts de'te'ction s ig n a l-to -n o is c *
as a fu n c tio n o f r in g o p e n in g angle* fo r thre*e> d iffe re n t t o t a l inte*gratie)ii rim e's. Re*sults
fo r a syste’ tn w ith e )u t l / f
noise, w it h
l/f
neuse*. a n d w it h
iff
s tra te 'g y dise-usse*el abewe* are* include*d.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
noise* a n d the* n o d
74
N u m b e r o f P i x e ls
10
s
5£
iz:
10
:
8
r
6
r
100
N u m b e r o f P i x e ls
N u m b e r o f P i x e ls
1000
10
3 W eek s
100
1000
10
100
1000
24 W eeks
12 Weeks
4
.0
0.01
0 .1 0
1.00
1 0 .0 0
R in g O p e n i n g A n g le 0
0 .1 0
1.00
R in g O p e n i n g A n g le 0
0.01
0 10
1.00
10.00
R in g O p e n i n g A n g le 0
F i l l i n ' 4.2: P o la r iz a tio n S e n s it iv it y as a F u n c tio n o f R in g O p e n in g ; A n g le . S ho w n arc*
th re e d iffe re n t t o t a l in te g r a tio n rim e s fo r an in s tru m e n t w h ic h m easures b o th S toke s
P a ra m e te rs Q a n d C w it h th e a n tic ip a te d P o la tro n in s ta n ta n e o u s s e n s itiv ity . D o tte d
curve's re p re sen t a n tic ip a te d s ig n a l-fo -n o is e r a tio u n d e r id e a l in s tru m e n t p e rfo rm a n c e '
(n o l / f
n oise).
D a sh e d cu rve's rc'prc'sc'iit the- same' m casurc’ tn e n r in the 1 prc'semce e>f
1/ J noise1. The- s o lid curve's repre-’sc'iit pe-rform ance' in the> pre'semc-c* of l / f noise*, b u t
p a irs o f Q a n d C are* d iffe rr'iic c 'd in p a irs se'parate'd b y bh in R ig h t A s c v n s io n a b o u t
the' X C P . A n g u la r p o w e r s p e 'c tra c o n s is te n t w it h B O O M E R A N G
assum e'd. as discusseel in the 1 te*xt.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
m e a s u re 'iiie n fs is
Chapter 5
Laboratory Characterization — Optics
P o la riz a tio n a n a ly s is c a p a b ility a dds a n ew d im e n s io n to th e o p tic a l c h a ra c te riz a tio n
o f m illim e te r - w a v e in s tru m e n ts . T h is c h a p te r d e ta ils th e la b o r a to r y c h a ra c te riz a tio n
o f th e P o la tro n o p tic s in a s e p a ra te o p t ic a l te s tb e d .
5.1
Introduction
In o rd e r to *;a in f a m ilia r it y w it h th e fo c a l p la n e w ith o u t th e a d d itio n a l c o m p lic a tio n
o f th (' m e c h a n ic a l e ry o e o o le r a n d its a s s o c ia te d h a rd w a re , we p e rfo rm e d e xtensive 1
te s tin '; on th e P o la tro n fo ca l p la n e in a se pa ra te 1 eiptie-al te stb e ^l. A n Infrare-el L a b s 1
H D L -ts liq u id He1 d e w a r e m tfitte 'd w it h a Chase 1 Labejrateiries ! He> s o r p tio n e-e>e)le>r presvieled a ()..‘1() K e ijie 'ra tin g p o in t fo r r l u 1 bolenne'ters (Figure* o . l ) .
M e 'a su re m e n ts o f
the- s p e c tra l pass-banel. o p tic a l e ffic ie n c y , pedarizatiem effie-ieuiew. s e u is itiv irv . a n d de>te'eteir p re ip e 'rtie s fo r the 1 emtire 1 systeun. ine-hieling the1 wave1 plate*, we're1 perform e'el.
The 1 d iffe re u itia l noise 1 pe'rform ance 1 e>f the 1 te'st re'eeive'r is ade'quate 1 feir e ip tie a l te'sting
piLrj)e)se>s. b u t lacke-el the 1 1 / / s t a b ilit y n e vd e d fo r C M B eibseuwatiems at the 1 tede'sertpe1.
Fe>r th is re'ce'ivc'r. the 1 bedemieUeTs were* DC’-b ia se'd. anel net e*ffe>rts we're* niaele 1 to m it ­
igate 1 radiee-fre'que'ne-y pie'kup e>r m icre)[)he)nic [d c k n p .
Furrheuuiien-e1. no t r im
e irc u it
was available* te> balance* the 1 re sp e m sivit ie*s o f the 1 deue'e-tors. m e 'a n in g the 1 systeun was
eweui nieire* su sce'ptib le 1 to fiue*tuatienis i l l tile 1 bolome'teu' stage 1 te u n p e ra tlire 1 anel o 111e1r
leiw-fre'queuicy c o in m o ii inoele1 s ig n a l.
5.2
Spectral Bands
S p e c tra l b a n d s //( / ') weu’e* ineuisure'el iiie le p e u ie le n fly fo r the 1 twee p o la r iz a tio n e-hanneds
u s in g a Fourieu- T ra n s fo rm Spe'e-trom e'ter ( F T S ) . The 1 F T S eemsists o f a o()() K / 77 K
'in fra re d L a b o ra to rie s , hie-.. ISOs East 1Tr 1i StreH't, Tucson. A Z S n T H M io O u
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76
F ig u re 5.1: A p h o to o f th e P o la tro n fo c a l p la n e w it h in th e H D L - 8 te st b e d .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
c h o p p e d so urce, a m y la r b e a m - s p litte r, a n d a c o m p u te r - c o n tr o lle d fla t m ir r o r w h ic h
m o d u la te s th e in te r fo r o n ie tr ie phase d iffe re n c e a lo n g its tw o a rm s .
T w o p a r a b o lic
c o llim a tin g m ir r o r s in c re a s e th e s ig n a l th r o u g h p u t o f the 1 s y s te m : th e so urce is p la c e d
a t th e fo cu s o f th e fir s t m ir r o r , th e e ntrance' feed o f th e in s tr u m e n t u n d e r m e a s u re m e n t
is p la ce d at th e fo c u s o f th e se con d m ir r o r . T h e fre q u e n c y re s o lu tio n o f the 1 F T S is
d e te rm in e d b y th e t h r o w o f the 1 p o s irio n a b le Hat m ir r o r .
F o r a fix e d m ir r o r s te p ,
h ig h e r-re 's o lu tio n m e a s u re m e n ts re q u ire lo n g e r scans o f th e p o s irio n a b le m ir r o r , a n d
hence b e tte r lo w -fre q u e n c y s t a b ilit y in flu * in s tr u m e n t.
scans lo n g e r th a n
20
F o r th e P o la tro n te s t-b e d .
m in u te s w e re useless flu e to d r if t s , a n d so th e s p e c tra l re s o lu tio n
was lim it e d to 2 G H z . a d e q u a te fo r o u r p urp o se s.
T h e m e a s u re d b a n d s , [d o tte d in F ig u re o.2. a re id e n tic a l w it h in th e 2 G H z s p e c tra l
re s o lu tio n o f th e F T S m e a s u re m e n t.
T h e c e n te r fre q u e n c y (/,, o f th e b a n d w h e n
o b s e rv in g a so u rce o f in t e n s it y I „ is d e fin e d as
ul) = —
I
---- —
, _ tl
.
( o . l)
< l v r i ( i ' )
T h e m e a su re d b a n d c e n te rs a n d w id th s fo r b o th c lm n n e ls an* /zn = !Ji< ± 2 G H z a n d
A /z = 17 ± 2 G H z f u ll w id t h at h a lf m a x im u m (F W ’ H M ) .
W e se arche d fo r s p e c tr a l le a ks a t fre q u e n cie s above 1 o u r b a n d w it h brass th ic k g r ill
H irers.
T h ic k g r ill H ire rs an* m e ta l p la te s w it h d r ille d holes t h a t act as w a v e g u id e
chokes a t w a v e le n g th s a b o v e 1.7 tim e s th e h ole d ia m e te r [70].
H ig h -fre q u e n c y r a d i­
a tio n passes th r o u g h , t h o u g h w it h re d uce d e ffic ie n c y d u e t o the 1 e ffe c tiv e area o f th e
holes.
A c h o p p e d •}()() K / 77 K b la e k b o d y lo a d was p la c e d in fro n t ot the 1 re c e iv e r
a n d th e s ig n a l w as d e m o d u la te d a t th e ch o p fre q u e n c y . A th ic k g r ill f ilt e r w it h c a l­
c u la te d lo w -fre q u e n c y c u t o f f at loO G H z was used. A m e a s u re d u p p e r lim it o f
1 .0
G
w as p la ce d o n o u t- o f- b a n d p o w e r c o m p a re d to in -b a n d p o w e r fo r each ch a n n e l.
T h ese m e a s u re m e n ts c a n be tra n s la te d in to an u p p e r lim it o n rlit* o u t-o f-b a n d
c o n t r ib u t io n fro m d u s t t o th e b rig h tn e s s te m p e ra tu r e t h a t w o u ld bo m e a sured b y t i n 1
ra d io m e te r. S in ce th e d e ta ile d s p e c tru m o f a n y le a k w o u ld be u n k n o w n , a w o rs t-c a s e
s c e n a rio is assum ed .
W e re p re s e n t h ig h - la titu d e d u s t e m is s io n b y a R a y le ig h -.le a n s
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig u re 5.2:
A tm o s p h e r ic S p e c tru m a n d P o la tro n Pass b a n d .
S o lid lin o :
a m odal
a tm o sp h e ric- tra n s m is s io n s p e c tru m fo r th e O w ens V a lle y a s s u m in g G 111111 c o lu m n
d e n s ity o f p re e ip ita b le w a te r v a p o r. D o tte d line: f lu ' P o la tr o n p a ssb a n d . in u n its
re la tiv e ' to p e a k tra n s m is s io n , as m e a su re d
011
a F o u rie r T ra n s fo rm
S p e c tro m e te r
( F T S ) . T h e fre q u e n c y re s o lu tio n o f th e F T S is 2 G H z . T h e s p e c tra l b an d s fo r the*
tw o o r th o g o n a l p o la r iz a tio n c h a n n e ls a re id e n tic a l w it h in th is re s o lu tio n .
s p e c tru m w it h a n is o tro p y te m p e r a tu r e 70 / / K (fo llo w in g R u lil [Go]) and 1()'T p o la r­
iz a tio n . an a p p r o x im a tio n w h ic h o v e re s tim a te s the e x p e c te d p o w e r at a ll frequencies.
I f th e e m is s io n fro m th e 77 K a n d .200 K lo a d s is also a ssu m e d to be R a yle ig h -.le a n s
at a ll fre q u e n c ie s , we ca n use th e t h ic k - g r ill m e a su re m e n t to set an u p p e r lim it o f T
= 0 .0 7 / / K t o th e a n tic ip a te d o u t- o f- b a n d c o n tr ib u tio n fro m d u s t.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
5.3
Optical Efficiency
T h e s p e c tra l banel-ave*raged o p tic a l (p h o to n ) e ffic ie n c y i]„p, o f th e re c e iv e r is m e a sured
b y f illin g th e b e a m w it h 300 K a n d 77 K b la c k b o d y lo a ds, m e a s u rin g the* p o w e r on
each d e te c to r fo r each lo a f I. and c o m p a r in g th e m e a su re d p o w e r d iffe re n c e to the
e x p e c te d [to w e r d iffe re n c e .
A P „ pl ~ A i ' ~ - ( A Q ) [ D uj : m K ) -
£ ,,,(7 7 /0 ].
(.72)
T h e fa c to r o f 1 /2 a c c o u n ts fo r th e s p lit in p o la r iz a tio n . A i l = A~ is th e th r o u g h p u t
o f th e s yste m , a n d B t, { T ) is th e P la n c k b la c k b o d y s p e c tru m .
T h e m e a su re d o p tic a l [to w e r P„pt is d e te rm in e d as fo llo w s . T h e s y s te m is exposed
to b e a m - fillin g r a d ia t io n fro m
= 300 K a n d T/,,,. = 77 K " b la c k b o d y ” m a te ria ls ,
in th is cast' E c c o s o rb f o a n r .
For th e 77 K m e a s u re m e n t th e fo a m is im m e rs e d in
liq u id n itro g e n .
In each m e a s u re m e n t, th e b o lo m e te r im p e d a n c e /?/„,/„ is m e a sured
as a fu n c tio n o f a p p lie d e le c tric a l b ia s [to w e r D „„.s =
I
Pb„i,,-
T in * b o lo m e te r
resistance* d e [te n d s a lm o s t e m tire ly on b o lo m e te r te m p e ra tu re , a n d h e n ce o n to ta l
a p p lie d p o w e r Popl -t- Pina*'- A t f'fp ia l b ftlo m e te r resistance*, tin * t o t a l a p p lie 'd [to w e r is
th e sam e, a n d so tin * d iffe re n c e in o p tic a l [to w e r AT*,,,,/ is th e m e a su re d difference* in
e le c tric a l [to w e r A Pi,llt*- T lu * me'asurem e'nr is repe'ate*d fo r a range* o f applie>e[ jtetwe'rs.
In th is way. we m e a sure band-ave*rage*el e tp ric a l e*fficie*ncie*s o f 2().()’/
b o th ch an n els.
±
2
. 't/i’ for
W e assume* th a t ne*arly a ll o f th e loss in o u r fe*e*el s tru c tu re ' takes
plaee* in the* c o ld f ilt e r in g a n d at the* d e te c to r itsedf. The* wave* plate* is a n t i- n ’fie c rio n
coate'd to m in im iz e letss. a c h ie v in g a m easure'd in se *rtion lttss o f <
1
. T in * tee*el h o rn .
O M T . a n d associate*d w a ve g u id e eeimpetne'iits w ere se*[iarate*ly me*asure*el w a rm o n a
h ig h -frt'e ju e n c y n e tw o rk analyze*!' a n d fo u n d ret gene'rate* < l'7i re*turu letss ae retss the*
sp e 'ctra l banel.
JE V Robe*rts. S")0() Ste>llar D riv e . P.O . B ox x(>N. C u lv e r C ity . C'A !)2(td2
’The'ri* is all a d d itio n a l. sm alleT dependi'lice* o f re'sistaiice on bias voltage1 (the* "elect lie tii’ld
effec t") w hich m ust be* accounted for (id .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
5.4
Polarization Efficiency
T o measure* th e p o la r iz a t io n e ffic ie n c y . we* c o n s tru c te d a p o la riz e d so u rc e by p la c in g a
10 cm diam eteu- c ir c u la r a p e r tu r e g r id o f 0.05 n u n d ia m e te r g o ld -p la te d tu n g s te n w ire
w it h 0.19 m m g r id s p a c in g in fr o n t o f a c h o p p e d 500 K / 77 K b la c k b o d y lo a d .
A
piece o f a b s o rb in g m a t e r ia l w as p la c e d in fro n t o f th e g r id t o lim it th e a p e rtu re to ~ 5
c m c irc u la r d ia m e te r. T h e s o u rc e w as placed o n th e o p t ic a x is , a p p ro x im a te ly
fro m th e e n tra n c e o f th e re c e iv e r.
10
cm
L o c k in g -in to th e c h o p p e d s ig n a l, th e wave p la te
w as ro ta te d in 128 s te p s t h r o u g h 300° (see F ig u re 5 .3 ). S in c e > 99.5'/<' p o la riz a tio n
is p ro d u c e d b y th e w ir e g r id [47]. th e degree to w h ic h th e lo c k - in s ig n a l does n o t fa ll
to zero is th e m e a s u re d c ro s s -p o la r iz a tio n \ =
la b o r a to r y p o la r iz a tio n e ffic ie n c y o f
1
—
In th is w a y we m easure a
= 9 7 .8 /f ± 0 . 7 '/ . in g o o d a g re e m e n t w it h an
h e u ris tic c a lc u la tio n (see A p p e n d ix A ) .
T h e p o la r iz a tio n e ffic ie n c y o f th e re ce iver o p tic s w as m e a s u re d in a s im ila r m a n ­
n e r. w ith th e w a ve p la te re m o v e d a n d th e w ire g r id s o u rc e r o ta te d th r o u g h 3 0 0 5 T h e
m e a su re d p o la r iz a tio n e ffic ie n c y was t]f,„i = 9 9 .5 'A ± 0 . 7 ' / . c o n fir m in g th a t tin* d o m i­
n a n t source o f c r o s s - p o la r iz a tio n in o u r re ce ive r is th e passage o f s ig n a l th ro u g h th e
w ave p la te . T h e O M T a n d a s s o c ia te d w a ve gu id e c o m p o n e n ts w o re s e p a ra te ly m ea­
su re d w a rm o n a h ig h -fr e q u e n c y n e tw o rk a n a ly z e r a n d fo u n d to g e n e ra te < 0.03V7
c ro s s -p o la riz a tio n a cro ss th e s p e c tra l baud.
B o lo m e te r r e s p o n s iv ity d e p e n d s o n the le ve l o f o p t ic a l lo a d in g . F o r a large* w ir e ­
g r id source*, re»ratiou o f the* g r id th r o u g h 3 0 0 ' cemlel m e td u la te the* a m o u n t o f petwer
e>u the* be>lonie*ter. since* th e b e )lo m o to rs can elete*ct th e ir 4 K o p tic s in rc'ffe'ction. T h is
wemlel uiule'f-e'sriinate* tile* p e d a riza tie m e'fficie'ticy since* the* bedenne'ters wemlel be* metre*
re'sponsive d u r in g th e m e a s u re m e n t ejf h ighest c ro s s -p o la r iz a tio n . B y lim it in g the* size*
e»f the* source* anel m e a s u r in g the* DC-le*ve*l o f the* bedomete*rs ( in orde*r te> trae-k the*
re 's p e tn s iv iry ). we* cenild be* sure* t h a t the* b ed om otor re *s p o n s iv ity re*maine*el the* same*
th ro u g h e n it th e me‘a sure*m o n t.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SI
F i l l i n ' o .3 :
P o la r iz a tio n E ffic ie n c y M e a s u re m e n t.
D e p ic te d is th e re s u lt o f the po ­
la r iz a tio n e ffic ie n c y m e a s u re m e n t d e s c rib e d in th e te x t.
E r r o r b a rs a re 2-rr.
Best
fir fu n c tio n is O.S + 3 4 . 4 s in ( 4 / ) — 0 . 2 s in ( 2 / — 5.G~) + ( ) . l s i n ( / ) m \ ': th e m easured
p o la r iz a tio n e ffic ie n c y is (9 7 .8 ± 0 .7 )V
A.
5.5
D etector Properties
T h e P o la tr o n b o lo u u 'te rs possess th e r m a l a n d e le c tric a l p ro p e rtie s chosen to p ro ­
v id e h ig h s e n s itiv it y u n d e r th e o p t ic a l lo a d in g c o n d itio n s a n d o p e r a tin g te m p e ra tu re s
s p e c ific to t in ' e x p e rim e n t.
T h e y w e n ’ p re v io u s ly flo w n as scie n ce d e te c to rs a b o a rd
th e B O O M E R A N G p a y lo a d in 1998. T h e d e te c to rs have a m e a s u re d response rim e
r = 25 m s. w h ic h p u ts an u p p e r lim it o n th e a llo w a b le fre q u e n c y o f m o d u la tio n o f
th e s ig n a l at /
~ f 2 t t r )—1 ~ G H z. T h e m e a sured th e rm a l c o n d u c tiv itie s G are
p \ V / K a t 0 .4 K . a n d th e p ea k e le c tr ic a l re s p o n s iv itie s S a n ' ~ 3 x
10"
lo a d in g c o n d itio n s s im ila r to those’ e x p e c te d a t th e tele sco p e .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
V / \ V [13] u n d e r
5.6
Sensitivity
A lth o u g h th e H D L -S d e w a r a n d re a d o u t ('leetronie-s w ere n o t d e s ig n e d to he used
fo r a c tu a l o b s e rv a tio n s , w e m e asured a ra w d e te c to r s e n s itiv ity fo r th is s y s te m as a
base lin e fo r fu tu r e im p ro v e m e n ts .
B o lo m e te r n o ise sp e c tra w ere m e a s u re d lo o k in g
in to a 77 K b la c k b o d y lo a d , w h ic h is a fa ir a p p r o x im a tio n to th e ~
bO K lo a d in g
te m p e ra tu re e x p e c te d a t th e telescope. T h e lo w -fre q u e n c y sig n a l is d o m in a te d b y l / f
noise w ith a knee a t ~
I H z.
T h is noise a rise s in tlu * .J F E T s o u rc e -fo llo w e r, as the
d e te c to rs are n o t p la c e d in an AC’-b rid g e . T h e m e a s u re d b o lo m e te r X E P at
O.G H z is ~ 30 x 10-1 , \ V H z - 1
=
As c a lc u la te d in 112.5. and u n d e r s im ila r o b s e rv in g
c o n d itio n s , th is w o u ld a m o u n t to an XET,.,,,/, ~ 3 .2 m K s 1
I f we w e re o b s e rv in g
w it h th is test re c e iv e r, w o w o u ld choose' a h ig h e r w ave p la te r o t a t io n fre q u e n c y , o ut
o f th e l / f noise b u r b e n e a th th e low -pass c u t o f f d u e to th e b o lo m e te r response' tim e'.
S uch a m in im u m in th e n o is e s p e c tru m e x is ts a t 4 H z. T h e n ' we m easure' a bolenncte'r
XEP of ~
10
x
10
—1 ‘ \ Y H z _ 1 J . whie-h wemlel a m o u n t to an XET,.,,,/, ~
e e n n p a ra b k' to the' ide'alize'd p o la riin e ro r o f lj4 .1 .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 m K s 1 -.
s:j
Chapter 6
Laboratory Characterization —
Cryogenics
S u b s ta n tia l e-rye > -enginee'ring c 'ffb rt has bevn inve ste e l in r liis in s tru m e n t to re*cenr a n d
sue-ce'ssful end. T h e e-ryergenic s y s te m weuit th r o u g h s e v e ra l in c a rn a tio n s : th is c h a p te r
a n d th e sis d e s c rib e th e c u r r e n t in c a rn a tio n a n d tlu * re s u lts a chieve d fo r t h a t s y s te m
a lo n e .
W e d e s c rib e h e re th e p e rfo rm a n c e o f th e c ry o c o o le r a n d m u ltis ta g e s o r p tio n
c o o le rs.
6.1
Introduction
W e have in te g ra te d a c o m m e rc ia l 4 K m e c h a n ic a l c ry o c o o le r w ith a c u s to m s t i l >K e lv in m u ltis ta g e s o r p tio n c o o le r to achieve t u r n k e y c o o lin g fro m 400 K to 0 .2 5 K .
P e rfo rm a n c e m e a s u re m e n ts o f th e syste m w ere h a m p e re d b y n u m e ro u s fa c to rs :
•
Turn-around f i rm.
T h e tim e betw een in d e p e n d e n t m e a su re m e n ts d e p e n d s on
th e w a rm -u p a n d c o o l-d o w n tim e o f th e in s tr u m e n t. T h e se in tu r n d e p e n d o n the*
heat c a p a c ity o f. a n d th e r m a l c o n d u c tiv ity to . v a rio u s su spended te m p e r a tu r e
stages, as w e ll as th e c o o lin g p ow er a v a ila b le a t each stage. T o ta l tu r n - a r o u n d
tim e fo r th e P o la tr o n is a b o u t one week.
•
M i a.surt ttu n t e r r o r . L o a d cu rve s an* g e n e ra te d b y a p p ly in g p ow er to a h e a te r re ­
s is to r a tta c h e d to a te m p e r a tu r e stage, th e n m e a s u rin g tlu * te m p e ra tu re ( u s u a lly
w ith d io d e o r re s is ta n c e th e rm o m e te rs ) a t a ffe c te d stages.
H e a te rs a n d t h e r ­
m o m e te rs . as w e ll as t h e ir lead w ires, m u s t be p r o p e r ly h e a ts u n k . H e a ts in k in g
becom es in c re a s in g ly d if fic u lt a t low te m p e ra tu r e s due' to the 1 increase in t h e r m a l
b o u n d a ry ( K a p itz a ) re s is ta n c e .
•
C't'i/oi/in/c a n d r a r u i i m leaks. S m a ll leaks in th e m e c h a n ic a l c ry o c o o le r o r m u l­
tistage' s o rp tio n e-e>e>lcr w ill ne>t e>nly e 'v e 'n fu a llv e x h a u s t th e 'ir h e liu m s u p p lie ’s.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
6 .0 0
GM2 Load
—ow
(O 4.00
• - 10W
20W
2 .0 0
0 .0 0
------------------------------------------0 .5 0
1.00
1.50
2.00
JT Load (W)
F ig u re G .l: M e a s u re d lo a d lin e s o n th e .IT stage o f th e m e c h a n ic a l c ry o c o o le r. T h e
.JT a p e rtu re w as t h r o t t le d fo r p e a k p e rfo rm a n c e at e v e ry lo a d p o in t. L in e s fo r v a ry in g
h e a t loads on th e 50 K l ‘s t G M s ta g e a rc show n.
b u t w ill a lso in tro d u c e t h e r m a lly c o n d u c tin g p a r tic le s in t o th e v a c u u m space.
6.2
Mechanical Cryocooler
T h e A P D H S -4 m e c h a n ic a l c ry o c o o le r a d v e rtis e d 1 XV c o o lin g p e rfo rm a n c e at 4 K . A s
a n tic ip a te d , c o o lin g p e rfo rm a n c e d e p e n d s on th e ( c o n tr o lla b le ) a p e r tu r e size o f th e
•IT nozzle. U n d e r c o n d itio n s o f h ig h e r lo a d , g re a te r c o o lin g c a n be a ch ie ve d th r o u g h
a la rg e r .JT a p e rtu re *.
T h e c o o lin g p o w e r also d e p e n d s o n th e te m p e ra tu r e o f th e
p re c o o lin g G M stag e s, w h ic h in t u r n d e p e n d on t h e ir a p p lie d h e a t lo a d .
M e a s u re d
•JT stage* lo a d line's fo r a se*ries o f G M -s ta g e heat lo a d s a re ple>tte*d in F ig u re G .l.
In th e three* y e a rs o f re 'g u la r use o f th is cryo co olcT . we w a rm e d u p th e syste m th re e
tim e's due* to w h a t we* belic*ve*d t o be a c lo g in th e .JT n o z z le cause*d lw im p u r itie s in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tlu * .JT h e liu m s y s te m . In eaeli o f these in s ta n c e s , th e s y m p to m was a n in a b ilit y o f tlu*
s y ste m to a c h ie v e 4 K te m p e ra tu re s d e s p ite s ta n d a r d t h r o t t lin g o f th e .JT a p e rtu re
011
c o o ld o w n . I n each instance*, su b se q u e n t c o o ld o w n s were w ith o u t in c id e n t.
6.3
M ultistage Sorption Cooler
T h e m u ltis ta g e s o r p tio n c o o le r was s u c c e s s fu lly o p e ra te d o ff o f th e
4
K base* te m p e ra ­
tu re p ro v id e d b y th e m e c h a n ic a l c ry o c o o le r. T h e L’ C s t ill a tta in e d a base* te m p e ra tu re
o f 0.24 K a n d a te m p e ra tu r e o f 0.25 K a t the* a n tic ip a te d O.o / / \ V lo a d . T lu * d u t y cycle*
o f th e c o o le r is d'-i'X. w it h a to t a l h o ld rim e o f the* re frig e ra to r b e n e a th 0.2G K o f 47
h ou rs. L o a d line's
011
the* LTC s t ill are sh o w n in Figure* G.2. Figure* G..4 is a rim c '-h is to ry
o f a typie-al c y c lin g procedure* fo r the* c o o le r.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
300
290 •
(5 270
,0> 260
250
240
230 ---------------------------------------------------0
2
4
6
8
10
Applied Power (j^W)
F ig u re 6.2: L o a d lin t' o n L’ C s t ill o f m u ltis ta g e s o r p tio n co o le r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
100
He-3 H S W s
He-4 H S W
10
C H e-3 P U M P
H e-4 P U M P
in
oc
UC H e-3 P U M P
JT
H e-4 C P
<
oc
UJ
Q.
HX
1
C STILL
UC STILL
0.1
20
40
60
80
100
120
140
T I M E (MIN)
F ig u re 6 .3 : T im e - h is t o r y o f a c o m p le te m u ltis ta g e s o r p tio n c o o le r c y c lin g p ro c e d u re .
A base te m p e r a tu r e o f 0.2 5 K is o b ta in e d a fte r
110
m in u te s .
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8S
Chapter 7
Further Work and Discussion
T h is th e s is has a im e d to m o tiv a te th e v a r ie t y o f e x p e rim e n ta l e ffo rts b e in g m a d e to
d e te c t a n d c h a ra c te riz e th e p o la r iz a tio n o f th e c o s m ic m ic ro w a v e b a c k g ro u n d , and
d e m o n s tra te th e a b ilitie s o f tin * P o la tr o n e x p e rim e n t to c a rry o u t o n e s u c h e ffo rt.
A lth o u g h im p ro v e m e n ts in d e te c to r te c h n o lo g y h ave re v o lu tio n iz e d th e fie ld o f C’ M B
research, m e a s u re m e n t o f C 'M B p o la r iz a tio n w il l re q u ire s u b s ta n tia l in t e g r a t io n rim e .
T h e P o la tro n has c o m b in e d an a m b itio u s s c ie n tific goal w ith a d if f ic u lt e n g in e e rin g
ta s k : fa b r ic a tio n o f a c ry o g e n ic s y s te m w h ic h a llo w s a u to n o m o u s o b s e rv a tio n o f C 'M B
p o la r iz a tio n o v e r v e ry lo n g p e rio d s o f rim e .
T h e m o s t s ig n ific a n t re s u lts p re s e n te d in t h is th e s is are as fo llo w s :
• W e h ave d e s ig n e d a n d b u ilt a b o lo m e tr ic m illim e te r-w a v e le n g th p o la r im e te r
w it h d e m o n s tra te d ~
1
m K yCe s e n s itiv ity , h ig h ( > 9 5 '/ ) p o la r iz a tio n e ffic ie n c y ,
a n d a p o w e rfu l p o la riz a tio n m o d u la tio n te c h n iq u e w h ic h e m p lo y s a h a lf-w a v e
p la te to re je c t s y s te m a tic p o la r iz a tio n e ffe cts.
• W e h ave in te g r a te d a m e c h a n ic a l c r y o c o o le r w it h a m u ltis ta g e ' h e liu m s o rp tio n
r e fr ig e r a to r to p ro v id e a u to n o m o u s , e lo s e d -c y c le c o o lin g fro m 300 K to 0.25 K .
w it h a d e q u a te c o o lin g p o w e r a t a ll sta g e s.
• W e have' p re pa re e l the 1 O V R O 5.5 m fede'sceepe* lo r obse'rvariem s a t m m -w a v e d e n g th s
b y m e 'a s u rin g a n d a d ju s tin g th e su rface ' ae-euraev threm gh the> use o f a e apae irive'
se'iiseir a rra y .
• We* have* d e s ig n e d a n o b se 'rvin g sch e m e w h ic h a im s to ae-hiewe m a x im u m p o la riza tie m s ig n a l b y m a te fiin g the* /-space* winelenv fu n e tio n e)f the' ('x p e rim e n r to
the' pre-'clie-te*eI p e a k s e>f the* p e )la riza tie )n penveT spee tru in .
• We* have* m ade' a ea re 'fu l caleailatiem ejf the* preclie-te'el semrces ejf ne>ise' fo r a gremnelbase'el bedome'trie- pedarime'teT. d e 'in e )n s tra filig th a t bae-kgrenmel phe)te)n-lie)ise'
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
xy
lim ite d p e rfo rm a n c e c an . iu p rin c ip le , he a c h ie v e d .
T h is c a lc u la tio n s tr e n g t h ­
ens th e case fo r n e w g ro u n d -b a s e d p o la rim e te rs w h ic h re ly 011 c o m m o n -m o d e
re je c tio n o f a tm o s p h e ric flu c tu a tio n s .
•
W e have (in th e A p p e n d ix ) m ad e h e u ris tic c a lc u la tio n s (if half-wave* plate* crossp o la r iz a tio n d u e to c h ro m a tic ity a n d o ff-a n g le response*. The*se> e-alculatiem s la y
a g ro u n d w e irk fo r more* eh'tailed e-alculatiem s whie-h m a y he* re*quire*el fo r the*
de*sign anel fabrie-atiem o f achrennatic plate's fo r in u ltifro q u o n c y e*xp erim enrs.
The* follejw ing w eirk re*mains before the* Pedarrem ca n be fieldeel:
• C harae-te'rizatiem o f th e nehse performane-e* o f the* bedemiete'rs unele*r th e v ib r a t io n
e-e>nelitiejns cause*el b y th e m echanie-al eTyoce)ede*r.
P re 'lim in a rv w eirk s u g g e sts
th a t the* v ib ra tie m -in d u c e d dete’e ten- nedse is toe) h ig h fo r the* eibse'rving s tra te *g y
we* propose*.
A n inve*srigatiem is u n d e rw a y te> e *x i)e rim e n ta lly dete'rm ine* anel
m itig a te * the* v ib ra tie m p a th fro m the* eTyoceioler e-old r ip to the* bedemie'ter stage*.
•
C h a ra c te riz a rie )ii e>f the* p(*rfonnane-e e)f e-edel e)[jrie-al e*e)iiipe)iie*iits unde*r v ib r a ­
tiem. M e'asureine'iits are* b e in g made* at a v a r ie ty e>f t ilt angle's tej inve*sfigate* the*
influe'ne-e* e>f the* g r a v ity ve*e to r 011 the* stiffne*ss e>f a ll structure's. V a r y in g e>ptical
in is a lig n m e u t due* te> v ib r a tio n w ill be* a n a ly z e d a n d m itig a te 'd .
Ill tile* lem g-te*rm . the* P o la tro n pm vide's a eryeigonic anel data-ae-quisitiem p la tfe irm
to r w h ich the* Id eal plane* can be* nie>elifie*e[ emee* th e in it ia l seieuiee* gemls o f the* e*xperime'ut are* ine*t. Feir in s ta n c e , if the* r('e-e>ive*r were* plae-ed in an u p w a rd -lo e ik in g po siriem
a t a elry leicatiem. it cem ld e a rry o u t an inve'stigatieni o f p o la riz a tie m at large* a n g u la r
se-ale's w it h little* h u m a n inte'rve’iitiem .
L’lrim a te 'lv . niulri-freque*ne-y ejbservations o f C’M B peiiarizatiem w ill be* re*c[iiire>d to
rule* ou t e o n r a m in a tio n o f sig n al b y galae tie- fore'grounds.
T h e re*ee*ive*r irse*1f e-an be*
mexlitie'd te> etbse'rve* in m a n y fre*e[ue*ne-y bands, u tiliz in g a n achremiatie- half-w ave* pUite*
to re'tain the* strem g re*je*e tiejii e)f system atie- e*tfe*e-ts su cli plate's a llo w . It is unlikedy th a t
t lie* 0 o 111 te'le'sceipe* wemlel be* use'ful a t higheT fre'([iie'ne-ie*s elue* te» the* surface* inae-curae-y.
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90
H o w e ver, th e p h y s ic a l size o f rh e re c e iv e r floes n o t p re c lu d e its in s ta llm e n t a t a lte r n a te
sites.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
Appendix A
Half Wave Plates
In t iiis A p p e n d ix w e re v ie w th e o p tie a l p ro p e rrie s o f h a lf-w a v e p la te s a n d e a lru la te
th e e xp e e re d p o la r iz a tio n e ffic ie n c y o f o u r p la te .
T h e h a lf-w a v e p la re is a c y lin d e r o f b ire frin g c ’iit . ./-c u t c r y s ta llin e ’ q u a rtz .
The
p la te g e n e ra te s a rr phase r e ta r d a tio n b e tw e e n e le c tr ic fie ld v e c to rs o f fre q u e n c y
-~
!JG G H z (w a v e le n g th A ~ .3 n u n ) in c id e n t o n the* fa st a n d s lo w r e f r a c tio n axes o f th e
q u a rtz .
T h e m e a s u re d d iffe re n c e in in d e x o f r e fr a c tio n a lo n g t h e tw o axes a t these
w a ve le n g th s is A n
- 0.048. where’ n ~ 2 .0 8 . T h e d iffe r e n tia l p h a s e s h ift A o g e n e ra te d
betwec’ii o r th o g o n a lly p o la riz e d ra y s a lig n e d w it h th e fast a n d s lo w axes o f th e p la te
is
Ao =
2 —i s x
A n x /.
( A . l)
r
w here / re fers to the 1 p h y s ic a l p a th le n g th th e ra ys tr a v e l th r o u g h th e p la te . F o r plane
wave’s o n th e o ptic- a xis. I is th e rh ic k n c ’ss o f the’ p la te t = .'32.0 m m . anel a phasere’tarelatie m o f ~ is ae-hie’ veel fo r u =
the* c-enter o f o u r b a n d .
C o n s id e r a lin e -a rly p olarize ’d plane’ wave- trave’ llin g in the> c d ire e -tio n in a ceiordinatc’ syste-m ( x . y ) fixe-el te> o u r p o la rim e ’teu- w it h e-lc’ctrie- fie-le 1
E (./-.//. c. / ) = [C h j-x -f- E,,(/y ] s i n ( o . ,).
whe-re- o zt =
2
tr( ^ — n f ) is flu - k in e u n a tic com pem c’n t o f the- phase-.
The*in te n s ity o f sue-h a be-am is / = E ^ r + E f t . a n d
the- Stoke-s param e-te-rs me-asure’d
by an iele’al p o la riin e te ’r aligne’d w it h th is c e /o rd in a te sys te m are’
f (i =
(A .2)
= E {~h.— E fhl anel
2Eur E{),r
The- wave’ is in cid c-n t em a half-w ave- plate- w it h p o la r iz a tio n angle- H = t a n " 1 ( E nil E ()J.)
w ith re-spen t te> the’ fast axis. i9 is re’Strie-tc’d te> the- range- [(). —]. A se’conel eetorelinatesystem , ( i . j ) . is fixe-el te» the- plate-'s fa s t anel s lo w axe’s, respe’c-tive-ly.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In the- pbite-
92
c o o rd in a te s , th e e le c tr ic fie ld v e c to r o f th e in c o m in g w ave is
E ( i . j . z . t ) = {[E h j- c o s (d ) - r E Ul, -sin(<9)]i + [E „,y c o s (^ ) -
E i)s s in ( d ) ] j} s in ( o ; .f ).
I A . 3)
U p o n passage t h r o u g h th e p la te , th e phase o f th e j c o m p o n e n t is d e la y e d b y A o =
i c o m p o n e n t. F o r / ' = ut). A o = rr a n d so th e j te rm
^ ^ A n x t w it h re s p e c t to th e
s im p ly flip s sig n .
I n o th e r w o rd s , tin* p o la riz a tio n v e c to r has been re fle c te d a b o u t
th e fast a xis, w h ic h is e q u iv a le n t to a r o ta tio n b y A d = —2 d. C o n v e rtin g b a c k to th e
p o la rim e te r c o o r d in a te s y s te m .
E ' ( . r . tj. z . t ) = { [ E t)j. cos( 2d)
E ()U s in (2 d )]x + [ E {),, cos( 2d) -
E 0r s in (2 d )]y }- s in ( o - . , ).
(A .4 )
T h e S tokes p a ra m e te rs a re r o ta te d b y 4d:
Q’
=
[E (U. c o s ( 2 d) + E,,,/ s in (2 d )]J -
=
Qi) cos( 4 d ) -t- [ (, sin( 4 d ).
[£*,,„ e o s (2d) -
E Uj. sin( 2 d ) ] J
(A .5 )
(A .G )
and
C
A .l
= f o cos(4d ) — Q ,,s in ( 4 d ).
( A . 7)
Wave P la te Cross-polarization for u ^ u()
C o n s id e r a p o la riz e d b e a m o f in te n s ity /,, in c id e n t o n th e w a ve p la te w it h p o la r iz a tio n
v e c to r y a lig iu 'd at a 4o
a n g le to tlie* fast ( i ) a n d s lo w (j ) axes o f th e p la te .
fre q u e n c y //,, th e p o la r iz a tio n
For
w ill be ro ta te d b y 9 0 : . in to th e x c lire c tio n . a n d a
p o la riz a tio n d e te c to r a lig n e d w it h y w ill m e a sure n o s ig n a l.
F o r fre q u e n c ie s // == ;/(l
th e wave p la te is less e ffic ie n t, a n d some c ro s s -p o la r s ig n a l w ill be d e te c te d .
The
e le c tric fie ld in c id e n t o n th e p la te is
E(i.j.z.t) =
s in ( o ZJ )
[i + j ] .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( A .is )
93
T h e phase r e ta r d a tio n fo r th e p o la riz a tio n c o m p o n e n t a lig n e d w it h th e slo w a x is is
Ao =
^ t ^ A // x t = - - { - d o . w h e re d o = - ( ( u / u , , ) —
1
).
I 'p o n passage th r o u g h th e
p la te .
£
E (i . j . z.t)
=
=
—A js in (
E{
)i + sin( o ; ., ± rr -+- d o I j ] .
|s in ( o c./) i — s in iO ;./ ± d o ) j j
.
( A .O )
(A . 10)
T h e p r o je c tio n o f th is v e c to r a lo n g th e d e te c to r ( y ) d ir e c tio n is
£■
E ■y
=
=
T h e d e te c to r
- A [ s in lo - . /) - s in ( o ; ., + eio)]
E, i
(A .l
[s iit ( o z_t ) — s in ( o ; ./) cos(r)'o) — c o s fo - . , ) s in (e io )].
1
)
( A . 12)
is se nsitive' to t i n ' rim e average' o f th e se pta n' o f tlie* e'h'ctrie- tiedel.
(| E • y | J) = / „ x i [ l - c o s (d o ) \ .
(A . 13)
The' to ta l fra c tie m a l e-m ss-pedarizatiem se*e'ii b y a e h'te 'cto r w it h s p e v tra l re'spouse* r / ( r )
aligue'd a lo n g the 1 y e lire ctie m is tlie 'll
rhs ! / ( / / ) / „ ( / / ) x i [ l -c o s (e V ;;)j
\ = --------------- 7yT~i--------- ~r---------------------- •
tii'i/i
(A . 14)
/z)/,,(//)
W it h the' m easitre'd s p e v tra l re'spemse- o f the' Pedatrem re'ce'ive'f. Eept. # A .1 4 pre'elicts
a eTe)ss-[)olarizatie»n \ =
0 .0
/f i O . 1 '4 (//,,„/ =
1
—\ =
0 0 .1
'/ ±
0
. 1 ' / ) . whe>re' rhe* e>rre>r
is d o m in a te 'cl b y th e a c c u ra c y o t the' uie*asurt'uie'ut o f th e s p e v tra l b a n d near the* banel
e'clgevs. The- same' cale-ulatiem w it h a moele'l G a u ssia n s p e 'c tra l banel w ith banel c e 'iite r
anel w ie lth e'([ital tej the' m e a stire el P oIatre)ti value's p re d ic ts \ =
0
.S1/
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(ij,,,,/ = 0 0 .2 '/ ).
94
A.2
Wave Plate Cross-polarization Due to Con­
verging Beam
Plae-eine'iit o f th e wave' p la te in a e e n iv e rg in g b ea m geuieTate's c ro s s -p o la riz a tio n since
d iffe re n t p a r ts o f th e beam tra v e l t h r o u g h d iffe re n t th ic k n e s s e s o f q u a r tz , and e x p e ­
rience d iffe re n t p ha se s h ifts .
M o d e llin g th is effect ca n be q u ite in v o lv e d , since th e
wave p la te is in th e n ea r h e ld o f a s in g le -m o d e g a u ssia n b e a m w it h a c h a n g in g phase
p ro file .
S in c e th e e x p e c te d c r o s s - p o la r iz a tio n is f a ir ly lo w . a s im p le c a lc u la tio n can
help us to u n d e rs ta n d th e basic p e rfo rm a n c e .
C o n s id e r a p o la riz e d b e a m o f in t e n s it y /,, in c id e n t on th e w ave p la te at a ng le H
w ith re s p e c t to n o r m a l, and w it h p o la r iz a t io n v e c to r y a lig n e d a t a 4 5 ' angle to th e
fast ( i) a n d s lo w ( j ) axes o f th e p la te .
T h e phase s h ift u p o n passage th ro u g h th e
p la te is A o = = ^ A / / x /s e c ( fl) = tt 4- d o . where' d o = ~ (se e (d ) —
1
). T he' response' o f
a p ed a riza tiem e le te x to r a lig n e d w it h y is as s h e w n in e'quatiem ( A i d ) .
The* a n g u la r respemse* (j {6) o f the' fee'd h o rn at a e lista n ce c f n m i the 1 h o rn phase'
cente'f ( lo c u s ) c a n be> estim ate'el as i l l Wylele* e>t al. [78]:
X
e
" ''- " A
where 1
( A . 15)
i
i r { z ) — er,
1
+
j
Ac
(A . Lb)
■tin
f/'n = 0.G4 a. anel a is the' apeTture* r a d iu s ed the* fe*e*el he>rn.
The' t o t a l fr a c tio n a l e re is s -p o la riz a tie m sea'ii b y the' ele'te'e-tor is rlie 'ii
J,,~
x 4 [ i — <-()S(/)o )]
^^
J'n <IV2~6<i(H)
T h is pre'eliets \ ~ 0 .5 '/ (//,,„/ — 9 9 . 5 '/ ) fo r the* Pedatrem re'e-edve'r. In c o m b in a tio n
w ith the' e-ale u la tie m e>f e ro ss-p e d a riza rie n i due' te» the 1 P edatrem s p e 'c tra l ban e lw ie lth .
a to ta l p e d a riz a tie m efficie'iie-y fo r the' ree-eive'r ed’
~
9 8 . 5 '/
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is pre'elicte'el.
The*
m e a sured e ffic ie n c y is 97.S1/
± 0.7'X (tjo .-t).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
OG
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