Quasi-static displacement calibration system for a "Violin-Mode" shadow-sensor intended for gravitational wave detector suspensions

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 ‘Violin-Mode’ (VM) resonances in the 0.4 mm diameter silica fibre suspensions of the test-masses / mirrors of advanced LIGO gravitational wave interferometers. Each sensor illuminated the fibre under test, so as to cast its narrow shadow onto a ‘synthesized split photodiode’ detector, the shadow falling over adjacent edges of the paired photodiodes. The apparatus described here translated a vertically orientated silica test fibre horizontally through a collimated Near InfraRed illuminating beam, whilst simultaneously capturing the separate DC ‘shadow notch’ outputs from each of the paired split photodiode detectors. As the ratio of AC to DC photocurrent sensitivities to displacement was known, a calibration of the DC response to quasi-static shadow displacement allowed the required AC sensitivity to vibrational displacement to be found. Special 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 of this work, gave a vibrational responsivity in voltage terms of (9.45 ± 1.20) MV (rms) / metre (rms), yielding a VM displacement sensitivity of (69 ± 13) picometres (rms) / √Hz, at 500 Hz, over the required measuring span of ±0.1 mm.