Tilt sensor and servo control system for gravitational wave detection

Abstract

This paper describes the design of a novel double-flexure two-axis tilt sensor with a tilt readout based on an optical walk-off sensor. The performance of the device has been investigated theoretically and experimentally. The walk-off sensor has demonstrated a sensitivity of 10−11 rad Hz−1/2 at 1 Hz. The tilt sensor has measured seismic noise ∼10−9–10−10 rad Hz−1/2 for frequency in the 2–10 Hz range.

Cross-correlation studies with seismic noise

“…In figure 3(b) the tilt noise spectrum is shown and aside from the N-S/E-W difference in level (possibly due to the shape and attachment of the concrete slab of the floor) it is remarkably featureless. This measured tilt spectrum is significantly above the noise floor measured with a clamped sensor [10] and has not been corrected for transfer function variation. The transfer function was measured [10] by applying known tilts using piezo actuators in the legs and gave values of around 1 (±20%) for frequencies above 0.2 Hz, but rose to 10 (±10%) around 0.05 Hz, suggesting that the tilt spectra in figure 3(b) at this frequency are higher than actual.…”

“…This measured tilt spectrum is significantly above the noise floor measured with a clamped sensor [10] and has not been corrected for transfer function variation. The transfer function was measured [10] by applying known tilts using piezo actuators in the legs and gave values of around 1 (±20%) for frequencies above 0.2 Hz, but rose to 10 (±10%) around 0.05 Hz, suggesting that the tilt spectra in figure 3(b) at this frequency are higher than actual. Below this frequency the measured transfer function did not match the calculated one and so the tilt spectrum below 0.05 Hz may be suspect.…”

“…The tilt was measured using a double flexure inverse pendulum [8][9][10]. A massive disc (50 kg) was suspended from a rod with x-y flexures at each end.…”

Embedded model control: sub-microradian horizontality of the nanobalance thrust-stand

“…Details about control loops are seldom available, as they are standard analogue loops, very often converted to digital filters. In the present case, accuracy is not extreme as in [13], but it must approach 100 nrad, the tilt range must reach tens of mrad which requests millimeter-stroke actuators, the mass to be tilted is of the order of 50 kg, motors must be silent to avoid lateral accelerations, ofthe-shelf sensors and motors must be employed, coordination between different sensors and motors is needed to accommodate contrasting requirements.…”

“…The former is usually requested by leading scientific instruments like gravitational wave detectors [13], where nanoradian accuracy is approached with the help of custom-made horizontality sensors. Microradian tilt control aims to accurately point small-mass mirrors (< 1 kg) to a source, final accuracy being achieved by quality control of the source image.…”