LIGO Document P1400104-v2

Quasi-static displacement calibration system for a ‘Violin-Mode’ shadow-sensor in Advanced LIGO suspensions

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This paper describes the design of, and results from, a calibration system for optical linear displacement- (shadow-) sensors. The shadow-sensors were designed to detect, and to help damp-out, ‘Violin-Mode’ (VM) resonances in the fused silica fibre suspensions of the test-masses / mirrors of advanced LIGO (aLIGO) gravitational wave interferometers. In aLIGO, four, 400 µm diameter, highly-tensioned silica fibres, support each 40 kg test-mass. The fibres’ fundamental resonance is at a frequency of ~ 500 Hz, and the target displacement sensitivity for the shadow-sensors, at this frequency, was 100 picometres (rms) / SQRT(Hz), over a span of ± 0.1 mm in fibre position. The four shadow-sensors of this work employed ‘synthesized split photodiode’ (i.e., dual) photo-detectors, in which lateral VM fibre- (and hence, shadow-) resonances generated differential AC photocurrents, whereas quasi-static fibre movements, due to pendulum-motion of the test-masses, generated differences in their two, steady, DC photocurrents. The apparatus described here moved a vertically orientated silica test fibre horizontally through a collimated Near InfraRed illuminating beam, whilst simultaneously capturing the DC ‘shadow notch’ outputs from a pair of split photodiode detectors. The AC and DC photocurrents were routed through separate transimpedance channels, and so the ratio of AC to DC gain was known. A calibration of the DC responsivity to quasi-static displacement thereby allowed the required AC responsivity to vibrational displacement to be found. Low-cost techniques are described for generating the required constant scan-rate for the test-fibre, using a DC motor driven stage, for removing ‘jitter’ at such low translation rates from a linear magnetic encoder, and so for capturing the two shadow-notch signals at each micrometre of the test-fibre’s travel. Calibration, across the four detectors, gave a vibrational displacement responsivity of (9.45 ± 1.20) MV (rms) / metre (rms), yielding a displacement sensitivity of (69 ± 13) picometres (rms) / SQRT(Hz), at 500 Hz, over a span of ± 0.1 mm in fibre position. This sensitivity exceeded the design target.
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The paper has been modified in response to the helpful comments of the LSC reviewer.

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