Measurement of the absolute wavefront curvature radius in a heterodyne interferometer

TL;DR

This paper derives an analytical expression for the coupling parameter in heterodyne interferometers used in gravitational wave detection, introduces a new method to measure wavefront curvature, and studies the impact of mirror displacement on phase signals.

Contribution

It provides a novel analytical derivation of the coupling parameter and proposes an improved measurement technique for wavefront curvature in heterodyne interferometers.

Findings

Derived an analytical expression for the coupling parameter.

Proposed a new method to measure wavefront curvature.

Analyzed the effect of mirror displacement on phase coupling.

Abstract

We present an analytical derivation of the coupling parameter relating the angle between two interfering beams in a heterodyne interferometer to the differential phase-signals detected by a quadrant photo-diode. This technique, also referred to as Differential Wavefront Sensing (DWS), is commonly used in space-based gravitational wave detectors to determine the attitude of a test-mass in one of the interferometer arms from the quadrant diode signals. Successive approximations to the analytical expression are made to simplify the investigation of parameter dependencies. Motivated by our findings, we propose a new measurement method to accurately determine the absolute wave-front curvature of a single measurement beam. We also investigate the change in coupling parameter when the interferometer "test-mirror" is moved from its nominal position, an effect which mediates the coupling of mirror displacement noise into differential phase-measurements.