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 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 Laser 0 B1_ACp + - Differential Mode control loop Dark fringe signal sensitive to differential displacements 10

Laser 0 B2 + - Beam Splitter B2_ACq Recombined locking scheme B1_ACp Differential Mode control loop Signal reflected by the ITF 11

Laser 0 B2 B1_ACp + - Beam Splitter Laser frequency stabilisation B2_ACp B2_ACq Differential Mode control loop Recombined locking scheme 12

Recombined locking scheme Laser 0 B2 B1_ACp + - Beam Splitter Laser frequency stabilisation B2_ACp B2_ACq Differential 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) : Hz 15

Laser 0 B2 B1_ACp + - Beam Splitter B2_ACp B2_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 Correction signal (Volts) Coil Driver  i (Ampères) Newton Electronics of the actuators Pendulum Zoom on the actuators TF(Actuators) = TF(electronics) x TF(pendulum) x K( volts  meters) 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 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 : 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/sqrt(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- A+A+ A0A0 l IMC (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 : Hz 27

Laser 0 B2 B1 + - Beam Splitter B2 phase B2 quad + + C4 run : Noise Sources DAC noise 28

DAC noise Laser WI WE NE NI DAC noise measurement (   i) DAC 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 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/sqrt(Hz) 32

BS contribution for DAC noise of C5 Hz m/sqrt(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 cavity For 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 : W  m) B1 shot noise : Model :  2 x sqrt(2.P DC h ) x TF(calibration : W  m) 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_3f ACp B1 ACp + - Differential Mode control loop Recycling mirror 39

Recycled locking scheme Laser B2_3f ACp B1 ACp + - Differential Mode control loop B5 Recycling mirror Beam Splitter B5_ACq 40

Recycled locking scheme Laser 0 B2_3f ACp B1 ACp + - Differential Mode control loop B5 Recycling mirror Beam Splitter B5_ACp B5_ACq Laser frequency stabilisation 41

Low frequency : Coherence between control signals and dark fringe signal low frequency (1  20Hz) : coherence between B1_ACp and the angular correction signal sent to WI (in tx) (local control noise) 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= S p + S q = s p cos (  t) + s q sin (  t) with  =2  f mod Demodulation process  S multiplied by the oscillator : LO=cos (  t+  0 ) ACp = S x LO p = (s p cos (  t) + s q sin (  t)) x cos (  t) = s p /2 (  0 = 0) ACq = S x LO q = (s p cos (  t) + s q sin (  t)) x sin (  t) = s q /2 (  0 = 90) If there is phase noise  : LO = cos (  t +  +  0 ) ACp = (s p cos (  t) + s q sin (  t)) x cos (  t +  ) = (s p + s q  ) /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

Laser 0 B2 B1 ACp + - B2 ACp Reference cavity + + B2 ACq Laser 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 B5B5 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 ACp SSFS 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 ACp SSFS 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 (P laser = 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 (P laser = 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 B1B1 Injection Common Mode noise (  ) Hypothesis : sensitivity limited by Common Mode noise Definition : 62

C4 sensitivity limited by a « Laser frequency noise » above 2000 Hz Motivations for this study 63

C4 configuration B1_phase B2_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  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 lWlW lNlN Hz Measurement with simulation  Simplified model : asymmetry between the FP reflectivities (  N   W ) Finesse asymmetry 66 r 2N  r 2W  2 effects

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 : 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 ) 69

|a| 2 + |b| 2 |a| 2 + |b| Re(a*b ) 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 (l 1 -l 2 )  sidebands amplitude variation  B2 signal in quadrature  B2_ACp = 0 ACp ACq B2B2 AC p AC q l 1 -l 2 (a.u.) A-A- A+A+ A0A0

B2 Effect of IMC length noise (I) ACp ACq l IMC (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- A+A+ A0A0

B2 Effect of IMC length noise (II) ACp ACq A-A- A+A+ A0A0 l IMC (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- A+A+ A0A0 l IMC (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- A+A+ A0A0 l IMC (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)