Martin Hewitson and the GEO team

Measuring gravitational waves with GEO600

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Overview

GEOGEOh(t)

v(t) [V]

Noisee.g., seismic, laser

1 GEO

1 GEO

v(t) [V] h(t) + noise

calibrate

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Inside the GEO box

Opticalcavity

Opticalcavity+

h(t)

Seismicnoise

v(t) [V]

filterfilter

P(t) [V]

Keep detector at its operating point (dark fringe)

h(t) detected

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In the steady state….

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Optical transfer function

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Optical transfer function - equations

For each quadrature, P and Q, Overall gain Pole frequency Pole Q Zero frequency

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Measured optical response - P

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Measured optical response - Q

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Calibration overview

calibration

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Calibration software tasks

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On-line measurement of optical TF

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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

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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

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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

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Calibration pipeline

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S3 II recovered parameters

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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

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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

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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

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Calibration simulations

Simulations done for only open-loop detector

Red signals are output to frame files Normal calibration code is run on these

frames

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Simulation results - 2 v SNR

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Parameter recovery – SNR = 100

2

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Measured2 behaviour

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Measured2 behaviour

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Measured2 behaviour

noise estimation (2)

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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 ?