Transcript hewitson_amaldi6 - Albert Einstein Institute

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.
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
P and Q
Calibration signal
optical
actuator
Signal processing
pipeline
Figure 5: A summary of the signal processing tasks used to calibrate
each of the detector outputs.
Figure 3: Snap-shot amplitude spectral densities of the injected calibration lines
and the two detector output signals.
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 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).
Optimal combination of the two calibrated strain outputs
Both calibrated outputs of GEO contain the
same strain signal but different noise
sPP
sQQ
sPQ
Form a maximum likelihood estimator for h(t) (Eq. 1)
Al density estimates
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)
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.
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.