ph 103c: the physics of ligo 27 may 1994 lecture...
TRANSCRIPT
-
Ph 103c: The Physics of LIGO 27 May 1994
LECTURE 18
The 40 Meter prototype Interferometer as an Example of Many of the Issues Studied in this Course
Lecture by Robert Spero
Assigned Reading:
XX. R. Weiss, Quart. Prog. Rep. Res. Lab. Electron. M.l. T. 105, 54 (1972). [The seminal paper presenting in detail how laser interferometers can be used for gravitational wave detection, including a comprehensive analysis of noise sources.]
YY. Robert L. Forward, "Wideband laser-interferometer gravitational-radiation experi-ment ," Phys. Rev. D 17(2) , 379-390 (1977). [A description of the first interferometric gravitational-wave detector to be built (a 2 m Michelson interferometer) and the first search for gravitational waves using such a detector (a coincidence run conducted in 1972 between the interferometer and several bar detectors).]
A Few Suggested Problems: Note: Your homework for Lectures 17 and 18 is to be turned in to Shirley Hampton in room 151 Bridge Annex before 1:00PM Friday June 3
1. In this course you have encountered all the significant noise sources for interferometric detectors that the LIGO team is now aware of. Which of these were unanticipated by Weiss in Ref. 1 above; and are they "fundamental" or are they "technical"?
2. The interferometer described in Weiss's paper has a different optical configuration from the 40 m interferometer, but the shot noise calculated by Weiss is similar to that achieved in the 40 m. Why? Compare the shot noise limited sensitivity calculated by Weiss with the sensitivity achieved by Forward, and account for the difference.
3. The thermal noise calculated by Weiss is based on viscous damping [4>(w) (w) independent of w]? cf. Lectures 13 and 14.
4. Weiss calculated noise from laser intensity fluctuations acting on the test masses via radiation pressure. Intensity fluctuations also result in noise (in a manner discussed in Spero's lecture) if the interferometer's operating point is offset from a "dark fringe" at the photodiode. Under what circumstances will this noise be larger than that due to radiation-pressure fluctuations.
1
-
Lecture 18 The 40 Meter Prototype Interferometer as an Example
of Many of the Issues Studied in this Course
by Robert Spero, 27 May 1994
Spero lectured from the following transparencies. Kip has annotated them a hit.
1
-
l E CTU1R.E 1 B
As E~fI,MPtE 0': Issvs S,,,,i>lEO //11 C() .. A~S£
!? SPERo :l? .MAt'" I qq'f
-
D.5iRI'BVi/OIll, AND ?~'Se CA"a~m-'~
r L flr~1tE 3J
V,E'" 1",,7'flFfnolfff r£~ , _~~~~MN~~~~
" ~ t~ ;,,.0 ANI!\t.y ~c. liS A -r~AIN t:)~ P(JLSlf t%
"",qYIN(, H~,6Hr "")((+)
G,Av$$/I'IN DlsrlYl BuTION~ wl,~~~
-
Co. VD voo.+'oo. '('4!
-
104
H
QJ
.0 1
000
6 10
0 ;:
l Z
10
0.6
1
o 1
His
toe:
ram
o
f P
uls
e
Hei
e:h
ts
'NOM
-e:,~uSSlIlW pul~
R f:)
TE 5
:
f'\t<
: i.
....,
ys~
, ~o
'/r'
(\41'1
"" Ie
"l.
-v
\ I""
'(' T
ape
3/2
/94
. S
ecti
on
1
. (4
6 m
inu
tes)
. ./ (
;/Jo
uJSI
/4N
y
N~/${! ./
"'~
-GA"~,~
k'
pI/
HE
2 3
Iv c:11 ~ "
"':) ~ ~
il .
1f4f
f1fS
SlD
/ ~L II
!WI'f
T Ib
v
~ P~5
4
-
m
co.
., , '.
am
~ , .
'm
z _
en
<0
• f ~'
"
.... • U ,
~
ON
.t' • •
MA
iUo
\EO
h
L 1'E
R
"'fO
'Nc.R~~~ s~
( A
Sl
I"IU
'A"l
/O~)
F'LT
En
INP
,,"-
, F
IL T
t-Ie
O
o.Jt
Pu-'-
o '5
I e
IS
20
25
30
3
5
"0
8 '5
Ie
15
2
8
25
30
35
ol
e
: :
I I
I I
; j
. --
I I
-: .
· ·-.1
. I
' i
. .
• .
, '
I
:.~
; I
': . j
· -
a,
_'._
:
m ..
co.:
":-. .
. I
.. __
...
. · .'"
cD
-:
-1 I
· .
pu
LS
l 11
r:It;
WT
-0>
~
· t·
.
I I
I :
: /t
IO
+-
E ",
ofH
" ()(
. S
, C# A
JI\L
.
~ . t
0..
-~ l'
: .
'-.....
: ...
· D
I J ,
.",8
v TtO
l\l..S
t:
t
I .
: · : ·
-. ttt
; I
__
N.
_
....• .
e 5
18
15
2
0
25
3
0
35
4
0
SN
R··
Z
70e
12
8
7.48
76
8 79
8 9
99
0
28
8<
40
86
9
88
8
••• J
."-rl-'~" ii' iii
70
0
72
0
7.0
7
68
7
99
0
08
8
28
8
4.
86
e
88
8
••
O_
F •
P •• _
••
••••
'
TIM
e
f-
~
SE~I
I.s
• IN
.... •
i~:
tit t
··t--_.
: .
· \
• 5
II
15 ze
Z5
38
3
5
40
;! '
78
8
7Z
e
74
8
76
8
79
8 '.'
188
8
SH
A .. Z
82
. ..8
868
80
A
.L.I
._.l
J ,
I
• I ••• I
••• I
• ;
i
381
-
F • • 7
00
7
2ft
7
48
7f
ofl
70
0
AnC
l n
;>q
A
4A
AI,
R RA~
-
If1PEI?FfC7loN5 ltv PM5l /IIoD(;(.fTT/~ ~(flJ6 ?oc..c-f'-S C~ £"(.5
Pr;'AlrI"t6Jl IS ~"~",fj) "'/Til CHYJ7-'k. AY~ 50 p~$ C'(" Dt>fJ /VoIr A~ PC~"'''/iAT,oN
Vlt)
O/H.y cFr"fcr I!> S".,IJI.I.. I'1e>DClLIfTICW ~ INDex
~F Ri£FR~c?ICfV '(\, RES",r..,G- ,,,, A ~1I"N(i,e . /N c>?7ICAi.. Pl9rH ,-ef\lG-~1-I 0
-
,,-.
..
~
. III
N ~
.....
'--"
Ql
VI .... o I=! ..., o ;::: VI ""- ..., ~ p.
..., ~
o "0
Ql ..., III
...... ~
"0
o S Ql o.
• rr-
II -'--'-'-'-"'
4 2 o
-2
I I , , , , , , , ,
C. A
l.GO
Lr:.rr
IOtJ
0' e
ft fc
"I
TH
RE
E
PO
CK
ELS
C
ELL
S
-1'_
.....
. 5
o~
5f"\
PlLL
.. f\
\Sp'
L..I
&~nc
""
An
gle
s in
d
eg
rees:
lh
ela
1 =
.0 1
. lh
ela2
=.0
3.
lhela
3=
.0 1
alp
ha=
-.0
3 .
Qas
hed
li
ne:
, , , I , I , , , , I , , I I I , I , I I -'
P=I~ m
W
./'
L!'c
)C{,
oJ
• n
o d
riv
e lo
2n
d P
ock
ets
cell
, ,
, I I I , , I , I , , , I , , ,
, , , , , , , , , , , , , , , , I I
r,
I ,
, \
, \
, \ \ \
\ , , \ , , il , , , , \ , , , \ ,
I \
I ,
I ~,
I , , I , , , , , I , , , I I I ,
-"
4 II
I
I
-40
00
-3
00
0
-2
00
0
-10
00
0
10
00
2
00
0
30
00
4
00
0
Au
dio
vo
ltag
e
(vo
lls)
,
-
5 fRvo McIOf.t.. o~ toOc"t£S C EZL fr\ r,SA l..fC:,tlf"'l {tv'"
Jt\C.---I-"-T"-l
JI---..;..l
f~----I
fMC: Frequency of the light out of the mode cleaner
fl: Resonance frequency of the primary cavity
fo: Stabilized frequency
6fl: True frequency deviation (between fo and fl )
6fl ': Measurable frequency deviation (between fo and fl )
A: Open loop transfer function of the primary servo
fpc: Equivalent correction frequency to the PC
()1
-
6-· ~D
C "L
C{J
t..A
l'o
tv
of:
E
FF
EC
.'"
c::w
t:"I
?EQ
!JE
NC
y S
''''
S/L
lcA
TIo
tv 5p~vo
CM
Cfll
.#'A
:JM
()F
1£
".0
':a
RE
SP
/
~ I ~~lr
, .. or
M:
FR
E
80
.0 ,
~"
I I!I
! : ~ ~
~ ~ l
i1 ' ~
e-C I
(A
C(!
tJ/.
.... nc
ttIJI
"""'\
~ ,B
~
-'.~
V ~ (;
. 'M
"
tff'iu
.;:::"
J\j
.. 1
1f
't/~
A.,
f---
+-ij
I I, !
i I /
'.
11 i
f--+
I
. A
/ .
, :~
i-+-
~-++++t1
10
.0
/D1
v
'Nt
dB
0.0
Fx
d
Y ~
I I
~ I
! I!
: :
I ! "\
~ !
~-~~
'~~+'
I~,l
I" ~
10
0
Lo
g
Hz
10~
~i3-
. 1
F~~ .
. e"<
)' SU
fr.-e
ssio
l'\
of th
e rl
-;~7
' ~\
I;tl
se
l-\l
o.
A:
t
-
M\~OR HEAT,PC. A!J L.''''')T 1'0 OPTICAL PO",e~
J;o IIEI"ftV6 fFrE. c:V i) ,4t ECHIWIC'''' DI57'C:'1n'c.v VIA 7HUirr1U. Es9AJv~JV (pt)
'4) OPTiCAL DI frotnltW vll4 ;th~1W9(' D(PF-,,~NCE CF I(II'OE7I. O~ RHRReT~,v r4'f'1/~1)
j~ ffF.$",,-r IN LEIV"SIItI(; AWD 8~A- DUrtNt""'o~ "THAT MG D/~FIc:.VLT "'7C> a:...T~L IF THt: A1J,.Jccp!*/) floweR 15 -0 ~ \ W 'Aas"" .
\
\
\
\
\
\
\
\
\
\
-
i) R e OVC:;'IUr. ~vrlON //11 CoA"'~Cir
~&So>~" ~ fe-S
Sf'I'W .. d. SMJlU A" £.AIR" 7~~~ C~CTIIJ/'IY .,.J ) --- ) . lSI
1..(r l. ~_'" t e.-y:. • ) 2A-$ J. ""
01.. 0"" .>. MAI'Cf?IA/,. -('o-fo!'lCl AT (I,v/"'-~ ) (,,,-to/Ie 1 ;rt a.p1' ......... Id.- .. -t F"'Scl) 5/L1'fJ O.SCI ''''
,. , CilQ.;' ;~B \.., ..... b ;~ w~ 11 ~ I~:, ,., d~ , ;"....be ov~
Bk-' .,., . 0.6 S"''''J,~ .. k \"'e .. ;;;~ . 5APpI'l tRE ,.&t
" '3S
, .) ? Ie:> IIV ,Ht Sk.'(
~ A () vAIIIC(D 0 prKHL A1?OFVvGF 1"P{..,r~
SuCH R!> Ot.-Al. f?ECr't:'-/~G.
bJ ADA9711/f ()P7JC..5
10
-
~~T/- NOISE Flt.7Cf?S ~D
5fR\IO B.RN!)Iu/I)'tH
[l'CT~r ,.)
VNCo",7fioLUJ) 7T'.sr /'f~.$ I~ 6l~1~"" /1" 77,75 -S 1~/v~1.. TJA/VD {:, /00 1-1.1 8", IIAJ ~,4;p6c
- I l'1o,,~ "'fAle r: , tH .. OPT1~A~ i.E ~ER 51!,.,SlIOJ~ $r.ru....,· /.1 .AD~(fClIt.,f&( .. 'T YAIJ(,I5 ~ I HI B .. r /W>ISI' Ft:tI? f ~ be> H~ (/;"'~7"'- &r-
)
-
11i19c7tCAt.. ul'1nA 71Ott1S it:> COIv R9~~ ":-I£;~
V(>oIT -V,I'\
i') PII1Jt fA,,.,. A''''Ec'O .:%19\1- ~~""A4C{ ~) ,c1t.7~R cwrp.., (\'o/.J~
\ "-' ... \ -Rc:. -
c::o.1y) bee: ~"- 1:.W :s"'
-
] - '-:"-\J~ ':' 4AT 6/? - ,- I \I (.f):- I/~,"~
FJeq(;'t/Q9(. C"N.se~"E"C£ : IVodf AT F/(.7((f 0Jr~'t
t!PN Se: SlGtvfF"~7, EfPt!C/~("" Ar f:WQCbwCfU
"" JI ERE U;oP C. R Jill IS s", A t £
J~$CW ~Cu.( (tv
X~IO~ R~.,c.. ~ 'l. St
,...., .. /0 V J V(.()-::.2 , /o ( VH~)
l E: "Oh:.:p \ ~ 0 ~ 1::-\..0 k...~ a{' -t-\.., ' ~.s ~~ ",,~"1 w~'rrJ a. \0 0 ",-i.
-
S Tf4 R TING, c,...p PI E Q::;"./Tfi!oL S'r'S 7l:i't : LoCI
-
((EQ"'nfl1l£IV-n- Ft:VP ~ /1c'f""S"'~
-
SUPPORT FRAME
___ +-t-r250l'm DIAMETER .." STEEL WIRE
~".I> ..... ·/6 0.'. "" PIEZO TRANSLATOR -1--1-1-"1:"1
~~I~NE TIC CONTROL BLOCK WITH RARE EARTt~ PERMANENT MAGNETS
TENSION SPRING 80 I'm PIAMETER
STEEL WIRES
TEST MASS
AUXILIAR Y . ~ ~ . ........ ~ LASER ~~ / MIRROR , . '-V . ! ~OURCE '- P.ITC,H AXIS
POSITION ~ SENSING PHOTODIOOE
I 'YAW' AX IS
-
SU
SP
EN
SIO
N I
SO
LAT
ION
ME
AS
UR
EM
EN
T
5T~1r 'F~c,
rAT
/OIII
! s,.~
C()4J~tJ(,'f'r "
L
Sta
ck S
uppo
rt B
eam
s
"\.
To
-le
st ~
'S'-
'Sp
e-.
-.sI
O' ..
.. 5
p~or""'~c ..
. L"
"' ...
. ~
-br;
;>"'
.s~ ~ .... c
.-l;."
" -c.
..""
Jt"\
),,~
~ M"~~~ ~.
"
\ :..
..~~
r .-
-\.v
, o
.... ~~)
S v>
P!t
rSIO
tV
E-)
l.C
liR
TIO
IV
Flex
ible
Bea
m
Mag
net C
oil
Perm
anen
t Mag
net
,.:;
-
r--.
..
m
·U
'---
'"
c 0 .. ' U 0 (f) c 0 (f) c: (J o.
(f)
::l
(/)
TOP
P
LAT
E S
HA
KE
R v
s.
INTE
RFE
RO
MET
ER
OU
TPU
T In
-a
ir a
cce
lero
me
ter
calib
rati
on
o
f sh
ake
r u
sed
a
--
21 J
une
91
··2
0
--
25 J
uly
(unc
erta
in c
alib
ratio
n)
·40
""
dl.N'
lItAI
JL!
I
I . I
·60
.
\I p
M~'N-W
~IJ'J
Jh
I \,
Q _
r
--8
0 .
-1
00
- i
--1
20
1-1
--
to
I'
'""-.
-'--
_-'
---J
....
....
...!
..-L
.. J
I
I I
10
0
f (H
z)
a -·20
I I
-·-
40
I~I
--6
0
" Hl
/lljl
---
80
II '
100
J ~-'-
_J b
,I
-12
0 1
00
0
It!
-
.s V
SP
EIV
SI_
_
RE-SoNANC~3
E~/D
~""-
I",
!,.,rH
rrG
t?o,
..(T
6/?
OtJT
""0J
7
Dis
plac
emen
t S
ensi
tivity
of
Cal
tech
40
m I
nte
rfe
rom
ete
r
-12
m
2J4
.-,
10
~ II
i tp
:q
I;'
il
, i
• • iii
;:;
10-1
2
10-1
3 ~v
1
' V
y
S~~~
Si-
\ J
10-1
3
10-1
• ~ I'
\.-.'1
"11
\,.
r--
lit.
J 10
-1•
1O-1~
I 1 0
-1~
,....
.. N
)(
"-)
N
~ "
. . I
10-1
• ~
'-....
10-1
• L
J ~ E
I
'-"
.1. N
~ -
)(
1 L
"-1\
11
, • ,I.
I. II j
lllL11
.. 10
-17
I.
... 10
-17
'-"
• 1
~''''~Ifr\MIJ1YI~
,.-" [
1r J
I, '-_
_ ... ~
10-1
• I
10-1
8
10-1
•
w.c
.-.d
upp
er I
mIt
to M
IIm
ic b
==
;'lI
h n
at: E
DIt
£nd
,/
10-2
0 • _
_ -L
__
L-~~~ __
=~LJ1~
'~'
100
10
00
10
-20
Fre
quen
cy (
Hz)
.~-
-
( SOME- ') Rt:D~t:TIDtV OF s~spetV~en., RE-SoIVI'VuCE5 8'( (S~/GHr) S II"'IP~/F/CRT~ cF S t.J:SP~~5/0t1/
~ONSTRAI NT WIRES REMOVED FROM H-MASS CONTROL BLOCK l OU .
, ' , ' "
,"",0 ~; {:, .... :'"'"\
.. .. ' . " , .
t
~ i: 0, I; .: ~ I :'
( " ~ .
10-6L-__ ~~--~~~-L~LL~---L~~~~~-L~~ 1 0 100 II. SIP 92; wccmp,prbOOO
Frequency (Hz) wcJ, Mphf
2. .
-
.,
-----
N "- - N
SE
1 ..s11
1C.
l">
c>4A
TIO
f./
~7t\
c:.1
c 'f
IIIP
Eq
F"f
C.T
/<:>
N:
INTE
f?FY
ibI'
1E7~
IS
jtfofl~
. RE~/~
70
t-
'Efn
"IC
f}t.
~~
C/MT
~O(J
1
Sei
smic
10-9
10-1
0
10-1
1
10-1
2
10-1
J
Fee
dthr
ough
at
Eas
t E
nd.
Com
pare
d to
Tot
al N
oise
se
is-p
red2
.xvg
r;
13 D
ec 9
3
-..
_x
.dot
; pR
d1ct
ion
....
....
on
..tl
cal
trano
IaIIo
n --
....
.. x.
dot;
P..c
lctlo
n ...
.....
on r
oddn
g --
caI"
2x
.do
t;
Pr.d
kIIo
n ...
.....
on h
oriz
onta
l Ihc
IIdng
t p
,..
I'
,..e«
1-I.L
"'-'o
.... J.
"=
'~..
stcJ
. 6
""
)."
...II!
";II.
..$lA
r-eJ
jrov
. ... .\
. ""
'. ~;o
'"
';;I"
, <l
"'"' u
;,~ '
" <' .
. J
-hr~~~ ~-L
bl b~
I "-
1 0-1
4
E
........
. x
10-1
5
10-1
6
10-1
7
10-1
8
10-1
9
10
100
Fre
quen
cy (
Hz)
Tota
l ..
..
J/2
t/1
4 , .
500
,.,
-
, ;.,
1) e51~V"\
~ .
~)
-
/1vQ TyP6 c': I"'nfts I.,..., ~€
[ I. e ~""'''E -'J I, - '''J ,) (,.,b",/o.nce.) ro.~jM:o-. ptr.ssu~ -t'l"'~'-'H_.i
i:::\ 6 F1vC.1W1f"J' 1,'
-
!:! I o -
!! I o -
Ill"';:' III ~ .0.2 z:o >-0 ~c.. III 0 C "-1Il--__ x .£ III ... ... 0 III III III C
.3~
~ I o -
. , o' 0··· . 0°· · • , ..
'" ! I I
:
0 0 - -
.. ... ... .
.. ! ! ~ I I I 0 0 0 - - -
o " o ~
o
~-ct
o o .n
0 0
N I .........~
-p .. ... I-4)
~
II -I 0 -
\r ("
-
vPcew"t~.3Ic:w 8~ .scl:rf"J:.RING
[ ~ E ,,.,,yt t- IS
~T ~ E P
~'I!>. "J,=IO).1 f.: l ~ ~ -::t' t p ~ 100 Hi (·~~lIflt~-)
REOUCE Ef"ffCf {3y DI9I'1PJ1J' f?p~('£J (~~119('(')
EFF £ CT'hJf If: 'X p ~ 1. - (110 vPCCNIIEIP~) flrv'O Sy t>P71cAt. 1,S6'4r1OlV
j