Martin Hewitson and the GEO team

1
Measuring gravitational waves with GEO600

• Martin Hewitson and the GEO team

2
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
In the steady state.
4
Transfer functions h(t)?P,Q
5
Optical transfer function - equations

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

6
Measured optical response - P
7
Calibration overview
8
Calibration software tasks
9
On-line measurement of Tp(f)
10
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 c2

11
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
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
Fast path (UG 100 Hz) electronics model
14
Slow path (UG 8 Hz) electronics model
15
Calibration pipeline hp(t)
16
Parameter estimation results - P
17
Parameter estimation results - Q
18
c2 behaviour

• The measure of success from the optimisation
  routine tells us something about data quality
• c2 depends on SNR of calibration lines in P

19
Quality channel

• One 16-bit sample per second
• Encodes information from
• Lock status
• Maintenance status
• c2 threshold crossings
• So far, c2 thresholds have been chosen arbitrarily

This will be extended soon see data quality
indicators talk ? 32 bit sample per sec
20
Measured c2 behaviour
21
Measured c2 behaviour
22
Measured c2 behaviour
noise estimation (s2)
23
hp(f) and hq(f) validation I
24
ESD calibration - Validation II
Labbook pages 1587, 1596, 1602
25
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
Simple mean combination
h(t) hp(t) hq(t) / 2
27
Simple mean combination phase check
28
Filtered combination highpasslowpass
h(t) lowpasshp(t) highpasshq(t)
29
Filtered combination results
h(t) lowpasshp(t) highpasshq(t)
30
Filtered combination phase check
31
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 c2 values for PQ simulations
• More studies of c2 values for PQ 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
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 (gt1Hz) 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
Intermission (Pause)
34
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 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
• c2 values
• Lock lists and duty cycle
• Will be extended to include GEO monitor outputs
  (see Ajiths talk)

36
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

Lets have a look