1. Martin Hewitson and the GEO team Measuring gravitational waves with GEO600

2. R&D Hannover July 20042 Overview GEO h(t) v(t) [V] Noise e.g., seismic, laser 1 GEO 1 GEO v(t) [V] h(t) + noise calibrate

3. R&D Hannover July 20043 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

4. R&D Hannover July 20044 In the steady state….

5. R&D Hannover July 20045 Optical transfer function

6. R&D Hannover July 20046 Optical transfer function - equations For each quadrature, P and Q, Overall gain Pole frequency Pole Q Zero frequency

7. R&D Hannover July 20047 Measured optical response - P

8. R&D Hannover July 20048 Measured optical response - Q

9. R&D Hannover July 20049 Calibration overview calibration

10. R&D Hannover July 200410 Calibration software tasks

11. R&D Hannover July 200411 On-line measurement of optical TF

12. R&D Hannover July 200412 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

13. R&D Hannover July 200413 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

14. R&D Hannover July 200414 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

15. R&D Hannover July 200415 Calibration pipeline

16. R&D Hannover July 200416 S3 II recovered parameters

17. R&D Hannover July 200417 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

18. R&D Hannover July 200418  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

19. R&D Hannover July 200419 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

20. R&D Hannover July 200420 Calibration simulations Simulations done for only open-loop detector Red signals are output to frame files Normal calibration code is run on these frames

21. R&D Hannover July 200421 Simulation results -  2 v SNR

22. R&D Hannover July 200422 Parameter recovery – SNR = 100 22

23. R&D Hannover July 200423 Measured  2 behaviour

24. R&D Hannover July 200424 Measured  2 behaviour

25. R&D Hannover July 200425 Measured  2 behaviour noise estimation (  2 )

26. R&D Hannover July 200426 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 ?