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

2. GEO meeting Sept 20042 Introduction DRMI gives 2 output signals, each containing GW information – P(t) and Q(t) There is a transfer function from h(t) to P(t) and from h(t) to Q(t) Tp(f) = P(f) / h(f) and Tq(f) = Q(f)/h(f) Each comprise an optical part and an electronic part Each vary (slowly?) in time We want to calibrate P(t) and Q(t) to h(t) on-line Need to estimate Tp(f) and Tq(f)  hp(t) and hq(t) Combine hp(t) and hq(t) to get optimal h(t)

3. GEO meeting Sept 20043 In the steady state….

4. GEO meeting Sept 20044 Transfer functions h(t)  P,Q

5. GEO meeting Sept 20045 Optical transfer function - equations For each quadrature, P and Q, Overall gain Pole frequency Pole Q Zero frequency

6. GEO meeting Sept 20046 Measured optical response - P

7. GEO meeting Sept 20047 Calibration overview calibration

8. GEO meeting Sept 20048 Calibration software tasks

9. GEO meeting Sept 20049 On-line measurement of Tp(f)

10. GEO meeting Sept 200410 Optimisation routine Fit models of the transfer functions to the measured ones 8 parameter fit Gp, Ppf, Ppq, Pzf, Gq, Qpf, Qpq, Qzf Electronic parameters are fixed Algorithm uses various minimisation methods to find the best parameter set that describes the data It also returns a measure of success –  2

11. GEO meeting Sept 200411 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 Inverse P

12. GEO meeting Sept 200412 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

13. GEO meeting Sept 200413 Fast path (UG 100 Hz) electronics model

14. GEO meeting Sept 200414 Slow path (UG 8 Hz) electronics model

15. GEO meeting Sept 200415 Calibration pipeline – hp(t)

16. GEO meeting Sept 200416 Parameter estimation results - P

17. GEO meeting Sept 200417 Parameter estimation results - Q

18. GEO meeting Sept 200418  2 behaviour The measure of success from the optimisation routine tells us something about data quality  2 depends on SNR of calibration lines in P

19. GEO meeting Sept 200419 Quality channel One 16-bit sample per second Encodes information from Lock status Maintenance status  2 threshold crossings So far,  2 thresholds have been chosen arbitrarily This will be extended soon – see data quality indicators talk  32 bit sample per sec

20. GEO meeting Sept 200420 Measured  2 behaviour

21. GEO meeting Sept 200421 Measured  2 behaviour

22. GEO meeting Sept 200422 Measured  2 behaviour noise estimation (  2 )

23. GEO meeting Sept 200423 hp(f) and hq(f) – validation I

24. GEO meeting Sept 200424 ESD calibration - Validation II Labbook pages 1587, 1596, 1602

25. GEO meeting Sept 200425 Combining hp(t) and hq(t) With ‘correct’ hp(t) and hq(t) we can try to combine them to get some optimal h(t) Both signals represent (apparent) strain Each contain some differential arm-length change information (real strain) So, far only tried a couple of simple examples Simple mean High/low pass filter combination

26. GEO meeting Sept 200426 Simple mean combination h(t) = [hp(t) + hq(t)] / 2

27. GEO meeting Sept 200427 Simple mean combination – phase check

28. GEO meeting Sept 200428 Filtered combination – highpass+lowpass h(t) = lowpass{hp(t)} + highpass{hq(t)}

29. GEO meeting Sept 200429 Filtered combination – results h(t) = lowpass{hp(t)} + highpass{hq(t)}

30. GEO meeting Sept 200430 Filtered combination – phase check

31. GEO meeting Sept 200431 Current and future work Q quadrature parameters are now successfully estimated and signal is calibrated to hq(t) Updating of the optical filters needs more extensive studies to look for artefacts 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 ? Some simple ideas already exist Other possibilities should be explored The combined h(t) needs studied for artefacts Include more automation MI loop gains read from LabVIEW Add more data quality checks – extend quality channel bits Try using recorded feedback signals for loop-gain correction

32. GEO meeting Sept 200432 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 – hp(t), hq(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

33. GEO meeting Sept 200433 Intermission (Pause)

34. GEO meeting Sept 200434 Introducing GEO Summary Pages Track fixed measurements over lock stretches Same set of measurements is performed on each data segment Lock stretches can be overnight runs, weekend runs, science runs A report is produced (web page) for each data segment Quick-look way of comparing detector status over days Also gives information about data quality Q: Should this data segment be analysed?

35. GEO meeting Sept 200435 GEO Summary Pages – calibration quality GEO Summary pages focus primarily on calibration quality and sensitivity measures so far Min/Max spectra BLRMS sensitivity Data quality channel – locked?, Maintenance? Recovered parameters  2 values Lock lists and duty cycle Will be extended to include GEO++ monitor outputs (see Ajith’s talk)

36. GEO meeting Sept 200436 Where to look Index of reports appears at http://www.geo600.uni-hannover.de/georeports/index.html The list of reports is split into months Each entry is a summary of the full report Links take you to the full report Let’s have a look…