Measuring Gravitational Waves with GEO600

Martin Hewitson, AEI Hannover for GEO600

DPG, March 2005

GEO600 optical layout

MC1

MC2

BSMSR MCn MFn

MCe

MFe

MPR

DPG, March 2005

Overview

GEOGEOh(t)

v(t) [V]

Noisee.g., seismic, laser

1 GEO

1 GEO

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

calibrate

DPG, March 2005

Inside the GEO box

Opticalcavity

Opticalcavity+

h(t)

Seismicnoise

v(t) [V]

Keep detector at its operating point (dark fringe)

h(t) detected

filterfilter

P(t) [V]Q(t) [V]

DPG, March 2005

Calibration of GEO600

Time-domain calibration method Optimisation routine is used to quasi-

continuously estimate parameters of optical response

Update rate is 1Hz

DPG, March 2005

Calibration procedure

Correct for MI loop and Optical transfer function(s)

x

=

Michelson servo model

Optical transfer functions Calibration functions

DPG, March 2005

On-line optical TF measurements

actuator optical

CALP and Q

DPG, March 2005

Calibration overview

calibration

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Idea is that

So we can form

Do this in the time-domain to fit in with the current calibration method

Combining hP(t) and hQ(t) - I

hopt(t) = a(t,f).hP(t)+b(t,f).hQ(t)hopt(t) = a(t,f).hP(t)+b(t,f).hQ(t)

hP(t) = h(t) + nP(t)

hQ(t) = h(t) + nQ(t)

hP(t) = h(t) + nP(t)

hQ(t) = h(t) + nQ(t)

DPG, March 2005

Combining hP(t) and hQ(t) – II

Form optimal frequency dependent weighting of hP(t) and hQ(t) by considering variance of noise components

Convert to time-domain filtersConvert to time-domain filters

DPG, March 2005

Combining hP(t) and hQ(t) – III

Simplification: consider only magnitude Create filters from noise floor estimates

h(t) = Pfilter{hP(t)} + Qfilter{hQ(t)}h(t) = Pfilter{hP(t)} + Qfilter{hQ(t)}

QQQQ

PPPP

PQPQ

DPG, March 2005

Combining hP(t) and hQ(t) – results

Get the best of hP and hQ plus a little extra!

Get the best of hP and hQ plus a little extra!

DPG, March 2005

Summary and future work

Online time-domain calibration of GEO600 output(s) to strain sensitivity

Both output demodulated output quadratures are calibrated and combined to give (almost) optimal h(t)

Extend this to allow for time variation of combining filters and to include non-linear phase correlations in the output quadratures