analysis of the virgo runs sensitivities raffaele flaminio, romain gouaty, edwige tournefier summary...
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Analysis of the Virgo runs sensitivities
Raffaele Flaminio, Romain Gouaty, Edwige Tournefier
Summary :
- Introduction : goal of the study / Overview on Virgo Commissioning
- Analysis techniques using the data taken during Commissioning Runs / Results for C5 run
- Analysis techniques using Siesta simulation / Last results
Hannover, April 8th, 2005 ILIAS WG1 : 4th meeting
Introduction
What are the goals of this analysis :
To identify the sources of instrumental noises that limit the interferometer sensitivity
To understand how these noises propagates through the interferometer
Two approaches are used :
Analysis of the data taken during Commissioning runs
Simulation
2
Virgo Commissioning : Overview
Laser
North arm
West arm
History :
- November 2003 : C1 (lock of one single Fabry Perot cavity)
- February 2004 : C2 (one FP cavity + Automatic angular alignment)
- April 2004 : C3 (one FP cavity + Auto angular alignment + laser frequency stabilisation)
3
Virgo Commissioning : Overview
Laser
North arm
West arm
History :
- November 2003 : C1 (lock of one single Fabry Perot cavity)
- February 2004 : C2 (one FP cavity + Automatic angular alignment)
-April 2004 : C3 (one FP cavity + Auto angular alignment + laser frequency stabilisation)
- April 2004 : C3 (first lock of the Recombined Mode, 2 arms)
- June 2004 : C4 (Recombined + Auto angular alignment + laser frequency stabilisation)
- December 2004 : C5 (Recombined + improvements)
4
Virgo Commissioning : Overview
Laser
North arm
West arm
History :
- November 2003 : C1 (lock of one single Fabry Perot cavity)
- February 2004 : C2 (one FP cavity + Automatic angular alignment)
-April 2004 : C3 (one FP cavity + Auto angular alignment + laser frequency stabilisation)
- April 2004 : C3 (first lock of the Recombined Mode, 2 arms)
- June 2004 : C4 (Recombined + Auto angular alignment + laser frequency stabilisation)
- October 2004 : first lock of the Recycled Mode
- December 2004 : C5 (Recombined + improvements and Recycled)
2 main goals of Commissioning :
• To manage to control the full Virgo (recycled mode) achieved at the end of 2004
• To reach Virgo nominal sensitivity “noise hunting”
5
The sensitivity curves of Virgo Commissioning
To reach Virgo nominal sensitivity :
Instrumental noises have to be identified in order to be cured
x 100
recombined
north armnorth arm
6
I - First approach :Analysis techniques using the data taken from Commissioning runs
7
Method used to identify a noise limiting the sensitivity curve
1. First step : To identify the possible noise sources
Method : to look at the coherence function between the dark fringe signal and other channels (correction signals sent to the mirrors, monitoring signals)
2. Second step : To understand how the noise propagates from the source to the dark fringe signal
Method : to find a mathematical model of propagation
3. Final step : The model is compared to the sensitivity curve
Validation of the analysis : the noise is identified and its propagation mechanism is understood
8
Examples of identified noise sources during C4 and C5 :
- C4 & C5 recombined
- C5 recycled
9
Recombined locking scheme
Laser0
B1_ACp
+
-
Differential Mode control loop
Dark fringe signal
sensitive to differential displacements
10
Laser0
B2
+
-
Beam Splitter
B2_ACq
Recombined locking scheme
B1_ACpDifferential Mode
control loop
Signal reflected
by the ITF
11
Laser0
B2
B1_ACp
+
-
Beam Splitter
Laser frequency stabilisation
B2_ACp B2_ACqDifferential Mode
control loop
Recombined locking scheme
12
Recombined locking scheme
Laser0
B2
B1_ACp
+
-
Beam Splitter
Laser frequency stabilisation
B2_ACp B2_ACqDifferential Mode
control loop
Reference cavity (sensitive to laser frequency noise)
+
+Common Mode control
loop (low frequency)
13
Identification of Beam Splitter longitudinal control noise
14
C4 run : Noise Sources
Hz
m/Hz R. Flaminio
Beam Splitter longitudinal control noise (introduced by the locking loop) : 10 - 60 Hz15
Laser0
B2
B1_ACp
+
-
Beam Splitter
B2_ACpB2_ACq
+
+
C4 run : Noise Sources
Beam Splitter longitudinal control noise 16
First step : looking for coherent channels to identify the sources
Coherence function between the dark fringe signal and the correction signal sent to the Beam Splitter
Good coherence up to 50 Hz : noise introduced by the Beam Splitter longitudinal control loop ? 17
Goal : to convert the noise introduced by the Beam Splitter control loop into an equivalent displacement (Differential Mode)
Model : fft(Correction signal) x TF(Actuators) x 2 x 1/32
Second step : Building of a propagation model
Longitudinal correction sent to the
Beam Splitter (Volts)
Actuators
Volts meters
Resonant Fabry-Perot 32 round-trips
Global control
B2 quadrature
Due to geometry of the Beam Splitter
18
L (meters)
DAC
DAC
Correction signal (Volts)
Coil Driver
Coil Driver
i (Ampères)
Newton
Electronics of the actuators
Pendulum
Zoom on the actuators
TF(Actuators) = TF(electronics) x TF(pendulum) x K(voltsmeters)
Volts/m1045K
6.0f
1
1)pendulum(TF
425f
1
1)selectronic(TF
6)metersvolts(
2
2
fft : “amplitude spectrum”
TF : “Transfer Function”
C4 sensitivity
Beam Splitter longitudinal control noise model
Conclusion : the model is validated noise is introduced by the Beam Splitter control loop
Final step : The model is compared to the Sensitivity curve
• 10-30Hz : model is 2 times lower than sensitivity
there is another source of noise (Beam Splitter angular corrections)
• 30-50Hz : good agreement between model and sensitivity (Input Bench resonances region, see R. Flaminio’s talk, last WG1 meeting, Jan 2005)
19
Remember what happened during C4 ...
Low frequency : C4 sensitivity dominated by Beam Splitter control noise (B2_ACq) and tx angular control noise (sent to the mirror, Sc_BS_txCmir)
20
Low frequency : Coherence between control signals and dark fringe signal
1-100 Hz : coherence between B1_ACp and Beam Splitter control signals (longitudinal z + angular tx)
How the contribution of Beam Splitter control noises (z and tx) in sensitivity can be estimated ?
the coherence between the two noise sources (Sc_BS_zCorr and Sc_BS_txCmir) has to be taken into account
21
Dark fringe & BS z Correction Dark fringe & BS tx Correction
Computation of BS longitudinal & angular control noise contributions in sensitivity
Notation :
X0 = noise on dark fringe signal
X1 = noise from Sc_BS_zCorr (BS z correction) ; X2 = noise from Sc_BS_txCmir (BS angular correction) ;
X3 = another noise (not coherent with X1 and X2)
Assuming : X0 = a . X1 + b . X2 + c . X3
complex coefficients a and b have to be computed
Method : Solve the following system
where : refers to the complex coherence between the variables X and Y
Then the total contribution of Beam Splitter control noise in sensitivity is given by :
2X2Xb1X2XaX2X
2X1Xb1X1XaX1X
YX 1XX
2X1XbaRe2ba)ACp_1B(fft *22
a)ACp_1B(fft
b)ACp_1B(fft
Individual contribution of BS length control noise
Individual contribution of BS tx control noise
Remark : X0, X1, X2, X3 are normalised
22
BS longitudinal (z) & angular (tx) control noise contributions in sensitivity : obtained from coherence functions
txCmir
Input Bench mechanical resonances
BS z Correction
BS_zCorr
txCmir + BS_zCorr
C5 recombined sensitivity
BS z control noise
BS tx angular control noise
m/s
qrt
(Hz)
Common contribution between the 2 sources of noise (z & tx control) has been substracted
23
BS longitudinal control noise : Model compared to Coherence computation
C5 recombined sensitivity
model : BS z control noise
Estimation from coherence : BS z control noise
Good agreement for IB mechanical resonances
Same result for C4 and C5 :
Input bench resonances propagated by BS z control loop
Error signal : B2_ACq
Model : fft(Correction signal) x TF(Actuators) x 2 x 1/32
24
How do Input Bench (IB) resonances couple into B2_ACq ?
Summary of R. Flaminio’s talk (3rd WG1 meeting, Jan 2005) :
• Mechanical resonances driven by IB local control noise & coil driver noise
produce IMC length variations
• Frontal modulation : if mistuning of modulation frequency with respect to IMC length :
A-A+
A0
lIMC (a.u.)
IMC length variation produces sidebands amplitude variation
if A+ , then A-
noise seen on the quadrature signals (B2_ACq)
Conclusion : Now, the propagation mechanism of IB resonances into “Beam Splitter longitudinal control noise” is understood
25
Identification of DAC noise
26
C4 run : Noise Sources
Hz
m/Hz R. Flaminio
DAC / coil drivers (used to send corrections to mirrors) noise : 70 - 400 Hz
27
Laser0
B2
B1
+
-
Beam Splitter
B2 phaseB2 quad
+
+
C4 run : Noise Sources
DAC noise
DAC noise
28
DAC noise
Laser
WI
WE
NENI
DAC noise measurement ( i)
DAC
DAC
Coil driver
Coil driver
i (Ampères)
Newton
Electronics of the actuators
Pendulum
L (meters)
First step : Measurement of DAC noise (at the coil drivers level)
29
Second step : Model to propagate DAC noise in the ITF
• Model for 1 DAC : fft(DAC noise measured) x TF(Pendulum) x K(Volts DAC meters)
• Model for the total DAC noise (4 towers, 2 coils per tower) : quadratic sum
DAC
DAC
Coil driver
Coil driver
i (Ampères)
Newton
Electronics of the actuators
Pendulum
L (meters)
30
C4 recombined sensitivity
DAC noise (WI+WE+NI+NE)
Conclusion : DAC noise limits C4 sensitivity between 80 Hz and 300 Hz
Final step : The DAC noise model is compared to the Sensitivity curve
31
DAC noise & C5 recombined sensitivity
After C4 : new coil drivers installed to DAC noise
C5 recombined sensitivity
DAC noise (WI+WE+NI+NE)
x 1/30
DAC noise from west & north towers does not limit C5 sensitivity
But : what about DAC noise from Beam Splitter (with coil drivers still in high noise) ?
Hz
m/s
qrt
(Hz)
32
BS contribution for DAC noise of C5
Hz
m/s
qrt
(Hz)
Model for BS DAC noise : fft(DAC noise) x TF(Pendulum) x K(Volts DAC meters) x 2 x 1/32
Number of round-trips in Fabry-Perot cavityFor BS : DAC noise is extrapolated from measurement done on west and north
towers
C5 recombined sensitivity
DAC noise on (WI+WE+NI+NE)
DAC noise on Beam Splitter
Beam Splitter DAC noise 3 times higher than the contribution of arms towers
But still lower than sensitivity curve
33
Other noise sources in C5 recombined
34
Models for B1_ACp electronic noise & shot noise
• B1_ACp electronic noise : dark fringe signal
Model : fft(B1_ACp electronic noise) x TF(calibration : Wm)
• B1 shot noise :
Model : 2 x sqrt(2.PDC h) x TF(calibration : Wm)
Measured during the run by injecting noise in differential mode on the end mirrors
Electronic noise measured when photodiode shutter is closed
Power read on B1_DC
35
Noise sources in C5 recombined
C5 recombined sensitivity
Beam Splitter control noise (length and angular) estimated with coherences
Electronic noise (B1_ACp)
Shot noise
DAC noise (NI,NE,WI,WE)
Hz 36
In low noise mode
Examples of identified noise sources during C4 and C5 :
- C4 & C5 recombined
- C5 recycled
37
Recycled locking scheme
Laser
B1 ACp
+
-
Differential Mode control loop
38
Recycled locking scheme
Laser
B2_3fACp B1
ACp
+
-
Differential Mode control loop
Recycling mirror
39
Recycled locking scheme
Laser
B2_3fACp B1
ACp
+
-
Differential Mode control loop
B5
Recycling mirror
Beam Splitter
B5_ACq
40
Recycled locking scheme
Laser0
B2_3fACp B1
ACp
+
-
Differential Mode control loop
B5
Recycling mirror
Beam Splitter
B5_ACp
B5_ACqLaser frequency stabilisation
41
Low frequency : Coherence between control signals and dark fringe signal
• low frequency (120Hz) : coherence between B1_ACp and the angular correction signal sent to WI (in tx) (local control noise)
• 15 - 100 Hz, B1_ACp is coherent with :
BS longitudinal control signal
BS angular control signal (BS_txCmir)
Already seen with recombined
PR longitudinal control signal
(maybe due to coupling between
BS and PR displacements)
42
Contribution of mirror control noise (BS_zCorr, BS_txCmir, PR_zCorr, WI_txCorr) in the sensitivity curve
C5 recycled sensitivity
WI tx control noise (with coherence)
BS txCmir control noise (with coherence)
PR z control noise (with coherence)
BS z control noise (model)
Hz
WI_tx_Corr
PR_zCorr + BS_zCorr + BS_txCmir
For WI_tx, BS_tx, PR_z : the common contribution is not substracted results to be checked
BS_zCorr model suits well to IB mechanical resonances
43
High frequency : Electronic noise (B1_ACp)
x 40
• Electronic noise (shutter closed) at the same level as Shot noise
• when power reaches B1 : noise of B1_ACp by a factor 40 follows linearly the amount of signal seen on the B1_ACq
Suspected origin : phase noise from LO board (Oscillator distribution board) or Marconi (Oscillator generator)
C5 recycled sensitivity
Electronic noise (with closed shutter)
Shot noise
Phase noise ( model with = 0.45 rad/(Hz) )
44
Phase noise from the LO signal to B1_ACp
The signal arriving on the photodiode is the sum of “in phase” and “in quad” components :
S= Sp + Sq = sp cos (t) + sq sin (t) with =2fmod
Demodulation process S multiplied by the oscillator : LO=cos (t+0)
ACp = S x LOp = (sp cos (t) + sq sin (t)) x cos (t) = sp/2 (0 = 0)
ACq = S x LOq = (sp cos (t) + sq sin (t)) x sin (t) = sq/2 (0 = 90)
If there is phase noise : LO = cos (t + + 0)
ACp = (sp cos (t) + sq sin (t)) x cos (t + ) = (sp+ sq ) /2
ACp contains phase noise proportionally to the ACq level.
45
« B1_ACp noise » versus « B1_ACq signal »
B1_ACp high frequency noise (Volts / sqrt(Hz))
B1_ACq integral: spectrum integrated from 0 to 100 Hz (Volts)
B1 electronic noise with closed shutter
• ACp noise proportional to ACq integral
B1_ACp sensitive to phase noise
• Estimation of :
~ 0.48 rad/Hz
46
What is being done :
- upgrade of the LO board (replaced by a more simple version)
- looking for a less noisy oscillator generator
- phase noise should be reduced after the implementation of Linear Alignment (ACq )
Noise sources in C5 recycled
47
II - Second approach : Simulation
48
What are the goals of simulation ?
• Simulation can confirm results extracted from Commissioning runs data
useful to check the agreement between models and simulation
• In recycled mode : we can expect strong coupling between several degrees of freedom of the ITF
more difficult to find simple models
simulation is needed to understand propagation mechanism of noises
example : simulation has been used to analyse the introduction of photodiodes electronic noise by the locking control loops of the recycled
• Models can depend on not well known parameters : simulation is needed to obtain an estimation of these parameters
example : Common Mode Rejection Ratio (which depends on the 2 arms asymmetry)
49
SIESTA simulation
SIESTA : time domain simulation developed by Virgo collaboration
What can be simulated ?
- Mirrors characteristics (curvature, losses, reflectivity)
- Locking control loops
- Mirror actuators & Super attenuators
- Photodiodes electronics
- TEM laser modes
- Dynamical effects (Fabry-Perot cavities)
- all sources of noise (laser frequency/power noise, DAC noise, electronic & shot noise, thermal noise, seismic noise …)
50
An example of analysis using simulation :
Introduction of photodiodes electronic noise by the locking control loops
51
C4 sensitivity limited by a « Laser frequency noise » above 2000 Hz how this « laser frequency noise » is produced ?
Motivations for this study
52
Laser0
B2
B1 ACp
+
-
B2 ACp
Reference cavity
+
+
B2 ACqLaser frequency control loop (SSFS) Electronic noise of B2 ACp propagated by
the SSFS
gives a « Laser frequency noise »
Differential mode
Common mode
Motivations for this study
53
Conclusion :
The photodiodes electronic noise can be injected in the ITF by the control loops
Motivations for this study
54
Photodiodes electronic noise & control loops in Siesta simulation (RECYCLED)
Why do we need simulation ?
strong coupling of the different degrees of freedom due to the recycling cavity
approximated models can be wrong
What is simulated ?
• Control loops in the recycled configuration
• Realistic simulation of the detection system with photodiodes electronic noise
Laser
0
B2_3f ACp B1
ACp
+
-
Differential mode
B5
PR
Laser frequency control loop
B5_ACp
B5_ACq
BS
55
Simulation with electronic noise put on B5_ACq
Laser
0
B2_3f ACp B1
ACpSSFS
B5 ACp
B5 ACq
C5 recycled sensitivity
simulated sensitivity with electronic noise on B1_ACp (dark fringe)
simulation : electronic noise on B1_ACp + B5_ACq
B5_ACq electronic noise is injected in the ITF by the control loops (at least one of them)
to find a model which explains how the noise is propagated 56
Propagation of electronic noise from B5_ACq
TF(actuators) : Volts meters
B2 quadrature electronic noise : measured when shutter is closed (Watts)
Global control : TF(GC filter) (for michelson)
Correction signal Sc_BS_zCorr (Volts)
Beam Splitter
control loop
Resonant Fabry-Perot : 32 round-trips
Beam Splitter control noise model :
fft(B5_ACq electronic noise) x 1/(1-G) x TF(GC filter) x TF(actuators) x 2 x 1/32
G : open loop transfer function for the Beam Splitter longitudinal control
Noticing that : fft(B5_ACq electronic noise) x 1/(1-G) fft(B5_ACq)B5_ACq spectrum when
ITF is locked
57
C5 recycled sensitivity
simulation : electronic noise on B1_ACp + B5_ACq
Model : BS control noise model
Simulation and model are in a perfect agreement
propagation of B5_ACq noise well understood : due to Beam Splitter control loop
Simulation with electronic noise put on B2_3f_ACp
Laser
0
B2_3f ACp B1
ACpSSFS
B5 ACp
B5 ACq
C5 recycled sensitivity
simulation : electronic noise on B1_ACp + B2_3f_ACp
BS control noise model
Electronic noise is put on B2_3f_ACp (PR error signal), but :
simulation agrees with BS control noise model
B2 3f electronic noise :
- seen by B5 ACq (coupling between different degrees of freedom)
- reintroduced into the ITF by BS control loop 58
Summary : Simulation results for the recycled
C5 recycled sensitivity (Plaser = 0.7 W)
simulation : electronic noise on B1_ACp (dark fringe)
simulation : electronic noise on B1_ACp + B5_ACp
simulation : electronic noise on B1_ACp + B2_3f_ACp
simulation : electronic noise on B1_ACp + B5_ACq
simulation : electronic noise on all the photodiodes
Virgo nominal sensitivity (Plaser = 20 W)
m/sqrt(Hz)
What this simulation shows :
• electronic noise introduced by control loops does not limit C5 sensitivity
• could be a problem below 100 Hz to reach Virgo nominal sensitivity
Above 500 Hz : C5 sensitivity limited by
phase noise in B1_ACp
59
Conclusions
60
• Analysis from Commissioning runs data :
- Recombined (C4/C5) :
Low frequency : BS control noises, IB resonances, DAC noise
High frequency : B1_ACp electronic noise
- Recycled (C5) :
Low frequency : Mirrors Control noises
High frequency : phase noise in B1_Acp
• Simulation : study of the introduction of the electronic noise by the control loops
- electronic noises propagated through BS longitudinal control loop
- anticipate the noise which could limit sensitivity in the next future
Simulation also used: - to test analytical models, - to estimate some parameters which are required by the models (Common Mode Rejection Ratio)
Comparison between C4 and C5 recombined sensitivities
High frequency :
C4 : laser frequency noise (B2_ACp)
will be explained in a few slides …
C5 : B1_ACp electronic noise
power reduced by a factor of 10 the inpact of electronic noise (B1_ACp) has increased
During C4 : DAC (Coil Drivers) noise
Now (with new coil drivers) : does not limit the sensitivity any more another noise ?
C4 & C5 : Noise quite at the same level
Input Bench mechanical resonances still visible
61
Common Mode Rejection Ratio (CMRR) definition
North arm
West arm
B1
InjectionCommon
Mode noise ()
Hypothesis : sensitivity limited by Common Mode noise
Definition :
L
meters) into (converted B1_ACpCMRR
62
C4 sensitivity limited by a « Laser frequency noise » above 2000 Hz
Motivations for this study
63
C4 configuration
B1_phaseB2_quad
North arm
West arm
B2_phase
laser
Reference cavity
IMC
Sc_IB_zErrGC
Common Mode noise correction
+
+
+
-
Differential Mode noise correction
B2_ACp electronic noise is propagated in the ITF through the laser frequency control loop Common Mode noise
G
64
B2_ACp electronic noise propagation (Common Mode noise), CMRR measurement
Hz
m/sqrt(Hz)
Sensitivity FFT(B2 electronic noise) x 1/OG x 1/TF_cavity x CMRR
Common Mode noise (m)
Raffaele Flaminio – Edwige Tournefier measurement :
CMRR 0.005
Expected Finesse asymmetry :
0.01 (or a few %)
Why CMRR better than 0.01 at high frequency ?
65
With OG = B2 Optical Gain (W/m)
Effect of an asymmetry between the 2 Fabry-Perot cavities (open loop model)
West arm
North arm
21r
2N2r
21r
lW
lN
2W2r
22t
22t
Hz
Measurement with simulation
Simplified model :
• asymmetry between the FP reflectivities (N W)
• Finesse asymmetry
66
21
21
rr1
rr
2
c
NW
ff
1
1
F
F
2CMRR
r2N r2W 2 effects
NN
NN
rr
rrF
21
21
1
With dF/F=0.01
Finesse asymmetry = 1%
DC gains asymmetry = 10%
At low frequency, CMRR is limited by the DC gains asymmetry (and no more by the finesse asymmetry)
High frequency:
CMRR limited by finesse asymmetry effect
Effect of an asymmetry on the DC gains of the control filters (added to a finesse asymmetry)
An asymmetry of the Mechanical responses have a similar effect as an asymmetry on the DC gains of the filters
67
Computation of BS longitudinal & angular control noise contributions in sensitivity (from coherence functions)
Notation :
X0 = noise on dark fringe signal
X1 = noise from Sc_BS_zCorr (BS z correction) ; X2 = noise from Sc_BS_txCmir (BS angular correction) ;
X3 = another noise (not coherent with X1 and X2)
Assuming : X0 = a . X1 + b . X2 + c . X3
complex coefficients a and b have to be computed
Method : Solve the following system
where : refers to the complex coherence between the variables X and Y
Then the total contribution of Beam Splitter control noise in sensitivity is given by :
2X2Xb1X2XaX2X
2X1Xb1X1XaX1X
YX 1XX
2X1XbaRe2ba)ACp_1B(fft *22
a)ACp_1B(fft
b)ACp_1B(fft
Individual contribution of BS length control noise
Individual contribution of BS tx control noise
! X0, X1, X2, X3 are normalised by their modulus
68
BS z control noise individual contribution (|a|2)
BS tx angular control noise individual contribution (|b|2)
common contribution 2.Re(a*b<X1X2>)
69
|a|2+ |b|2
|a|2+ |b|2+ 2.Re(a*b<X1X2>)
70
Input Bench resonances
B1_ACp (C1)
TF IB (Feb 04)
B2
Signals: B2_ACp & B2_ACq• Variation of cavity common mode length ( = laser frequency variation):
carrier phase shift
B2 signal in phase
B2_ACq = 0
• Variation of Michelson differential length (l1-l2)
sidebands amplitude variation
B2 signal in quadrature
B2_ACp = 0
ACp ACq
B2
ACp
ACq
l1-l2 (a.u.)
A- A+
A0
B2
Effect of IMC length noise (I)
ACp ACq
lIMC (a.u.)
• Variation of IMC length (due to input bench resonances)
1) carrier phase shift = sideband phase shift
2) carrier and sidebands amplitude variation:
second order effect
B2_ACp = 0 , B2_ACq = 0
A- A+A0
B2
Effect of IMC length noise (II)
ACp ACq
A-A+
A0
lIMC (a.u.)
• Variation of IMC length (due to input bench resonances)
sidebands amplitude variation: if A+ then A-
first order effect
signal on B2_ACq (and on all quadratures)
B2
Effect of IMC length noise (III)
ACp ACq
A-A+
A0
lIMC (a.u.)
• Variation of IMC length (due to input bench resonances)
compensated with a frequency variation by the fast frequency
stabilization loop (300 kHz bandwidth)
no sidebands amplitude variation
no spurious signal
Signal here is zero
B2
Effect of IMC length noise (IV)
A-A+
A0
lIMC (a.u.)
• Laser frequency locked to interferometer
IMC length variation (due to input bench resonances) not
completely compensated by the SSFS
sidebands amplitude variation: if A+ then A-
signal on B2_ACq (and on all quadratures)
Signal here is zero
Signal here is NOT zero
(= SSFS_Corr)
Signal here is NOT zero
(= - SSFS_Corr)