Analysis of sensitivity and noise sources for the Virgo

Analysis of sensitivity and noise sources for the Virgo gravitational wave interferometer Author: Supervisors: Scuola Normale Superiore di Pisa G. Vajente prof. F. Fidecaro prof. L. Foà Pisa, May 21th 2008 Summary Introduction Interferometric detection of gravitational waves Virgo Longitudinal control of Virgo Brief description Characterization Noise sources Linear noise projection technique Discussion of Virgo noise budget after the first science run Analysis of noise non-stationarity Monitoring of band-limited RMS Linear regression analysis Short transient detection Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 2 Introduction Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 3 Interferometric detection /1 Gravitational waves generate a differential distance change between free falling masses Interferometers are very sensitive instruments h L L  10  21 Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 4 Interferometric detection /2 Michelson interferometer at dark fringe: the field recombination at the antisymmetric port is destructive LASER Beam splitter: semi-transparent mirror Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 Photo-detector 5 Interferometric detection /3 Michelson interferometer at dark fringe: the field recombination at the antisymmetric port is destructive The amplitude of output signal is proportional to length and to circulating power LASER Gravitational waves creates a differential phase shift in the two arms Interference is no more destructive A signal can be detected Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 6 Resonant cavities Techniques to increase the detector sensitivity to GWs Fabry-Perot resonant cavities: arms replaced by resonant cavities to increase the optical gain (dephasing / equivalent displacement) Power Recycling: light reflected back to symmetric port is recycled by a semi-transparent mirror, to increase circulating power Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 7 The Virgo interferometer Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 8 Virgo design sensitivity h ~ 3 x 10-21 Hz-1/2 @ 10 Hz h ~ 7 x 10-23 Hz-1/2 @ 100 Hz Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 9 Seismic isolation Super-attenuators: multi-stage passive seismic isolation system MODEL Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 10 Actuation system Force is applied To the mirror using coil/magnet pairs and a reaction mass suspended to the same seismic isolation system To the marionette: using coil/magnets pair and the upper suspension stage as reaction mass To the uppermost stage of the super-attenuator (Filter 0) with coil/magnets, from ground Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 Last two stages of the super-attenuator 11 Longitudinal control Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 12 Longitudinal control Mirrors relative distances must be kept fixed in order to maintain correct resonant conditions inside the cavities CARM is equivalent to lWE laser frequency change Mean length of arms is used to stabilize laser frequency l NI  lWI PRCL  l PR  2 MICH  l NI  lWI CARM  l NE  lWE 2 DARM  l NE  lWE lNE lNI 13 lWI lPR Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 Feed-back control systems Seismic motion Optical system (plant) Error signal Actuator Correction signal Control filter (corrector) Error signals for the longitudinal control are extracted from interferometric beams with a frontal modulation technique Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 14 Pound-Drever-Hall technique Field is phase-modulated RF sidebands are reflected by the cavity RF sidebands do not enter the cavity They are (almost) insensitive to cavity length They can be used as fixed phase reference Aeit Aeit  eim cost  EOM Resonant cavity ~ Error signal sensitive to cavity length change Photo-detector Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 15 Longitudinal control topology MICH 8MHz CARM PRCL DARM 6MHz 6MHz Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 FREQ 6MHz 16 Characterization of longitudinal control Adding a suitable external pertubation to a feed-back system it is possible to measure transfer functions The feed-back loop change the signal response The goal is to extract the optical response from the measurement Seismic motion Optical system (plant) Error signal Actuator Correction signal Control filter (corrector) External perturbation Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 17 Characterization of longitudinal control In the Virgo case the system is multidimensional 4 degrees of freedom It can be solved using linear algebra The result is the optical response of photo-diode demodulated signals to MICH / PRCL / DARM / CARM displacements Optical matrix Driving matrix Sensing matrix Control filter matrix Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 18 An example: dark fringe response Transfer function from d.o.f. motions to the main gravitational channel Expected cavity pole at 500 Hz Requirements Measurements (VSR1) Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 19 Noise budget Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 20 Linear noise projection A feed-back loop can re-introduce noise (actuation or sensor noise) Linear noise projection is a well-known technique to measure the contribution of a feed-back loop GW channel error signal ITF TF correction signal Control Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 21 Automatic measurement in Virgo Noise budgets for longitudinal and angular controls are automated Two examples from April 2008 Longitudinal control loops Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 Angular control loops 22 Other sources of noise / 1 Technical noises Actuation noise (DAC and coil driver) Sensing noise (shot noise) Local oscillator phase noise Laser input power noise Laser frequency noise Power noise (upper limit) Frequency noise Actuation noise (VSR1 estimate) Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 23 Other sources of noise / 2 Environmental noise Magnetic, seismic and acoustic coupling through clipping, diffused and scattered light, etc. Typically non-linear Deep modulation and large up-conversion Difficult to identify and project Impossible to measure environmental noise at the point of scattering Magnetic noise Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 24 Other sources of noise / 2 Environmental noise Magnetic, seismic and acoustic coupling through clipping, diffused and scattered light, etc. Typically non-linear Deep modulation and large up-conversion Difficult to identify and project Impossible to measure environmental noise at the point of scattering Dark fringe Seismometer Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 25 Environmental noise projection Main source of coupling: window at Brewster angle between main interferometer and detection tower Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 26 Typical noise budget during VSR1 Control noise Frequency noise Environmental noise Shot noise Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 27 Typical NS-NS inspiral range during VSR1 Mpc Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 28 Improvements after VSR1 Many improvements Longitudinal and angular control noise reduction Actuator noise reduction Mitigation of diffused and scattered light problems Brewster window removal Calibration improvements … NS-NS range [Mpc] Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 29 Typical noise budget today Eddy currents Actuation Environmental Shot noise Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 30 Non-stationary noise analysis Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 31 Noise is non-stationary Dark fringe noise (sensitivity) changes with time Typical time constants from seconds to days Need of a technique to monitor the non-stationarities Band-limited RMS (BRMS) Integral of power in a limited frequency band Typical dark fringe signal spectrum BRMSi( t ) Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 32 Line identification algorithm A narrow and large spectral line can dominate the BRMS in a band An algorithm has been developed to estimate the noise floor and identify lines Useful also as a line identification tool Very old data! Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 33 BRMS monitoring during VSR1 An on-line process monitoring BRMS all over Virgo band-width BRMS is computed every second Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 34 Typical non-stationarity Noise is almost stationary on short time-scale (up to about 1 hour) Large noise floor variations over longer times Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 35 Multi-dimensional linear regression / 1 The goal: Correlate noise BRMS variation with slow changes in other interferometric signals Angular positions, powers, temperatures, residual RMS motions, etc… The technique used is a multi-dimensional linear regression Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 36 Multi-dimensional linear regression / 2 Each BRMS is a random variable, linear combination of auxiliary channels, plus some gaussian noise BRMS in a given frequency band Unknown coefficients Auxiliary channels Additive gaussian noise Best estimate of coefficients is given by least square method (in matrix notation) Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 37 Multi-dimensional linear regression / 3 The coefficients covariance matrix can be computed Having an estimate of the noise variance Finally confidence intervals on coefficients: Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 38 Practical application More than 100 auxiliary channels have been used for the analysis Downsampled to 10 mHz, using only Science Mode periods (excluded initial and final parts of each segment) Full linear regression computed Coefficients compatible with 0 within 3 are discarded Linear regression computed again with remaining channels Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 39 Some results / 1 Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 40 Some results / 2 Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 41 Linear regression: conclusions It is possible to reconstruct very well the slow noise nonstationarities It is also possible to select the most relevant auxiliary channels Suspended benches position Micro-seismic conditions and alignment accuracy After the end of the run, noise is much more stationary But no long enough periods of stable operations to repeat the analysis Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 42 Glitches Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 43 Fast noise variations Dark fringe signal is affected by short (< 1s) periods of increased noise Glitches Need of a fast tool to track the largest one HACR = hierarchical algorithm for curves and ridges developed by the GEO600 group and implemented in Virgo VirgoHACR Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 44 HACR: principles Compute short Fourier Transforms to obtain a timefrequency map Simulated white noise + sine gaussian burst Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 45 HACR: principles Compute mean spectrum with a running time-average Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 46 HACR: principles Distance of each bin from mean, normalized with variance Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 47 HACR: principles Bins above high threshold generate a trigger Adjacent bins above lower threshold are clustered One trigger Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 48 HACR: principles For each cluster several parameters are computed Mean time and frequency Time and frequency width Total power Maximum and mean SNR … During VSR1 HACR ran on-line, writing triggers to a database Allows easy storage and retrevial of trigger lists Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 49 Dark fringe triggers Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 50 Dark fringe triggers Many classes distributed in different frequency regions Different origins identified Frequency noise Beam jitter Power supplies Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 51 Coincidence with auxiliary channels Time-shift analysis: count time coincidence between two channels adding different time shifts Beam Monitoring System: steers the input beam Before and after There are physical fixing BMS problem coincidences This signal could be used as a veto Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 52 Conclusions Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 53 Conclusions Commissioning of the Virgo detector Angular and (mainly) longitudinal control systems Other control system improvements Noise studies Measurement of control noise budget Estimation of frequency / power noise Collaboration with environmental noise group On-line data analysis tools NonStatMoni: BRMS monitor LineMonitor: line extraction and tracking VirgoHACR: glitch monitor Slow noise non-stationarity analysis Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 54 Spare slides Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 55 PSR 1916+13 Orbital period about 8 hours E.M. waves Gravitational waves Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 56 VSR1 duty cycle Duty Cycle Science Mode 81.4% Longest Lock 94.3 h Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 57 Laser lab benches Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 58 Suspended benches Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 59 DARM open loop transfer function Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 60 PRCL open loop transfer function Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 61 MICH open loop transfer function Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 62 Noise subtraction One auxiliary loop correction is filtered and added to DARM one TF computed from measurements to cancel the noise coupling Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 63 Virgo sensitivity history Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 64 Virgo-LSC detectors Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 65 Coil drivers Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 66 Suspended detection bench noise Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 67 Faster noise non-stationarities Gabriele Vajente – Analysis of Sensitivity etc. – May 21st 2008 68