martin hewitson and the geo team measuring gravitational waves with geo600

Martin Hewitson and the GEO team

Measuring gravitational waves with GEO600

R&D Hannover July 2004 2

Overview

GEOGEOh(t)

v(t) [V]

Noisee.g., seismic, laser

1 GEO

1 GEO

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

calibrate

R&D Hannover July 2004 3

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

R&D Hannover July 2004 4

In the steady state….

R&D Hannover July 2004 5

Optical transfer function

R&D Hannover July 2004 6

Optical transfer function - equations

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

R&D Hannover July 2004 7

Measured optical response - P

R&D Hannover July 2004 8

Measured optical response - Q

R&D Hannover July 2004 9

Calibration overview

calibration

R&D Hannover July 2004 10

Calibration software tasks

R&D Hannover July 2004 11

On-line measurement of optical TF

R&D Hannover July 2004 12

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 2004 13

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 2004 14

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 2004 15

Calibration pipeline

R&D Hannover July 2004 16

S3 II recovered parameters

R&D Hannover July 2004 17

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 2004 18

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 2004 19

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 2004 20

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 2004 21

Simulation results - 2 v SNR

R&D Hannover July 2004 22

Parameter recovery – SNR = 100

2

R&D Hannover July 2004 23

Measured2 behaviour

R&D Hannover July 2004 24

Measured2 behaviour

R&D Hannover July 2004 25

Measured2 behaviour

noise estimation (2)

R&D Hannover July 2004 26

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 ?