Martin Hewitson and the GEO team Measuring gravitational waves with GEO600

GEO meeting Sept 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)

GEO meeting Sept In the steady state….

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

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

GEO meeting Sept Measured optical response - P

GEO meeting Sept Calibration overview calibration

GEO meeting Sept Calibration software tasks

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

GEO meeting Sept 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

GEO meeting Sept 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

GEO meeting Sept 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

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

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

GEO meeting Sept Calibration pipeline – hp(t)

GEO meeting Sept Parameter estimation results - P

GEO meeting Sept Parameter estimation results - Q

GEO meeting Sept  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

GEO meeting Sept 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

GEO meeting Sept Measured  2 behaviour

GEO meeting Sept Measured  2 behaviour

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

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

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

GEO meeting Sept 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

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

GEO meeting Sept Simple mean combination – phase check

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

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

GEO meeting Sept Filtered combination – phase check

GEO meeting Sept 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

GEO meeting Sept 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

GEO meeting Sept Intermission (Pause)

GEO meeting Sept 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?

GEO meeting Sept 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)

GEO meeting Sept Where to look Index of reports appears at 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…