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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 ?