Martin Hewitson and the GEO team Measuring gravitational waves with GEO600

R&D Hannover July Overview GEO h(t) v(t) [V] Noise e.g., seismic, laser 1 GEO 1 GEO v(t) [V] h(t) + noise calibrate

R&D Hannover July Inside the GEO box Optical cavity Optical cavity + h(t) Seismic noise v(t) [V] filter P(t) [V] Keep detector at its operating point (dark fringe) h(t) detected

R&D Hannover July In the steady state….

R&D Hannover July Optical transfer function

R&D Hannover July Optical transfer function - equations For each quadrature, P and Q, Overall gain Pole frequency Pole Q Zero frequency

R&D Hannover July Measured optical response - P

R&D Hannover July Measured optical response - Q

R&D Hannover July Calibration overview calibration

R&D Hannover July Calibration software tasks

R&D Hannover July On-line measurement of optical TF

R&D Hannover July Optimisation routine Fit models of the optical transfer functions to the measured ones 8 parameter fit Gp, Ppf, Ppq, Pzf, Gq, Qpf, Qpq, Qzf Algorithm uses various minimisation methods to find the best parameter set that describes the data It also returns a measure of success –  2

R&D Hannover July Undoing the effect of the optical response The parameters from sys id can be used to generate inverse optical response Poles to zeros, zeros to poles, invert gains IIR filters are designed for these inverted responses Overall gains are treated separately Filters are applied to up- sampled error-point to give better filter response

R&D Hannover July Generating loop-gain correction signals A full set of IIR filters has be constructed to match the response of the feedback electronics in the detection band One set for fast feedback, one set for slow feedback Error-point signal is filtered through these electronics filters and then through actuator filters This produces two ‘displacement’ signals that correct for the loop gain of the MI servo

R&D Hannover July Calibration pipeline

R&D Hannover July S3 II recovered parameters

R&D Hannover July Pros and cons Pros Calibration is updated once per second Accuracy to ~10% from 50Hz to 6kHz Runs on-line with 2 min latency – time-domain! Produces calibrated time-series – h(t) Cons Fast (>1Hz) optical gain fluctuations ignored Outwith valid frequency range, accuracy is poorer Bottom line is ESD calibration – good to about 5% Need independent check of ESD Photon pressure calibrator

R&D Hannover July  2 behaviour The measure of success from the optimisation routine tells us something about data quality  2 also depends on SNR of calibration lines in P

R&D Hannover July Quality channel Is one 16-bit sample per second Encodes information from Lock status Maintenance status  2 threshold crossings So far,  2 thresholds have been chosen arbitrarily

R&D Hannover July Calibration simulations Simulations done for only open-loop detector Red signals are output to frame files Normal calibration code is run on these frames

R&D Hannover July Simulation results -  2 v SNR

R&D Hannover July Parameter recovery – SNR = 100 22

R&D Hannover July Measured  2 behaviour

R&D Hannover July Measured  2 behaviour

R&D Hannover July Measured  2 behaviour noise estimation (  2 )

R&D Hannover July Current and future work Q quadrature parameters are now successfully estimated Something not fully understood about Q response Makes unstable IIR filter More studies of  2 values for P+Q simulations More studies of  2 values for P+Q ‘real’ data How to combine h(t)_P and h(t)_Q ?