Optical motion sensor for resonant-bar gravitational wave antennas

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Abstract
An experiment is described in which an optical method was used to measure fluctuations in the separation between two mirrors of a Fabry-Perot sensor cavity. Noise measurements were made to determine the sensitivity of this device to vibration amplitudes in the frequency range 1.1–2.1 kHz, which is of interest for resonant-bar gravitational wave antennas. The rms spectral noise density for length fluctuations in this range was 3.7 × 10−15 m/Hz1/2 and can be related to electronic noise of the circuitry plus vibrational noise from the environment. The cavity finesse was relatively low at 117, and the power dissipated in the mirrors was estimated to be 1.9 (μW. On a multimode gravitational wave detector, the sensor cavity would be formed by one reference mirror and by one mirror mounted on the last resonator. For a 1200-kg bar, 1.2-g last resonator system operating at 1600 Hz, the sensor described here would exhibit a noise temperature of 18 μK; the resolution in h in the case of negligible thermal noise from the mechanical system would be 3.7 × 10−18/Hz1/2. Improvements in the sensitivity in a quiet antenna-like environment should be possible with higher finesse mirrors.