analysis of the virgo runs sensitivities raffaele flaminio, romain gouaty, edwige tournefier summary...

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


Laser

North arm

West arm

History :



-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


Laser

North arm

West arm

History :



-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


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


12


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

+

+


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


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


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

+

+


DAC noise

DAC noise

28

DAC noise

Laser

WI

WE

NENI

DAC noise measurement ( i)

DAC

DAC

Coil driver

Coil driver

i (Ampères)

Newton


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


Pendulum

L (meters)

30


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


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


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


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

+

-


38


Laser

B2_3fACp B1

ACp

+

-


Recycling mirror

39


Laser

B2_3fACp B1

ACp

+

-


B5

Recycling mirror

Beam Splitter

B5_ACq

40


Laser0

B2_3fACp B1

ACp

+

-


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)


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


53

Conclusion :

The photodiodes electronic noise can be injected in the ITF by the control loops


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


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



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


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 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


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.)


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.)


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)

analysis of the virgo runs sensitivities raffaele flaminio, romain gouaty, edwige tournefier summary...

Documents

recombined mode

virgo recycled mode

commissioning runs

c5 recombined improvements

single fabry perot cavity

c1 lock

interferometer sensitivity

possible noise sources