Optimal on-line time-domain calibration of the dual-recycled GEO 600 M. Hewitson for the GEO 600 team Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) Institut für Atom- und Molekülphysik Introduction GEO 600 uses dual recycling (power and signal recycling) Gravitational wave signal appears in two output quadratures One quadrature is used as control signal for Michelson Transfer function from strain to main output signals is a function of frequency (see Figure 2); this includes: Optical response Michelson control servo response Calibration to interpret sensitivity of GEO: Provides one signal for analysis Helpful during commissioning Figure 2: Measured transfer functions from strain to two detector outputs. Figure 1: A simplified schematic of the optical layout of GEO 600. The two main detector outputs, P(t) and Q(t), are shown. Signal processing pipeline On-line transfer function measurement Injected calibration lines are used to induce known differential displacement (and hence, strain) – see Figure 3. By observing the magnitude and phase of the calibration lines in the two detector outputs, we get measurements of the transfer functions at these spot frequencies Measured once per second Parameterised models (see Figure 4) of the transfer functions are fit to the measurements using an optimisation routine Models are inverted and used to generate IIR filters Detector outputs, P(t) and Q(t), are filtered to give strain outputs, hP(t) and hQ(t) Figure 5: A summary of the signal processing tasks used to calibrate each of the detector outputs. Calibration signal P and Q actuator optical Figure 3: Snap-shot amplitude spectral densities of the injected calibration lines and the two detector output signals. Figure 6: A more detailed schematic of the signal processing pipeline used to calibrate each of the detector outputs to strain. Figure 4: Parameterised model of the Michelson control servo including the two model optical transfer functions that give the two detector outputs, P(t) and Q(t). Al density estimates Optimal combination of the two calibrated strain outputs Figure 7: Left: Amplitude and cross-spectral density estimates of hP and hQ. Noise floor estimates are shown; these are used to estimate the various sigma terms in the maximum likelihood estimator of h. Right: Combined responses of FIR filters made from maximum likelihood estimator of h. sPP sQQ sPQ Figure 8: Amplitude spectral density estimates of the two calibrated strain outputs of GEO and the combined strain signal, h(t). The induced strain from the injected calibration lines is shown for reference. Both calibrated outputs of GEO contain the same strain signal but different noise Form a maximum likelihood estimator for h(t) (Eq. 1) Estimate sigma terms from variance of noise in the two calibrated data streams Compute two sets of filters for hP(t) and hQ(t) Equation 1: A maximum likelihood estimator for h(t)