Differential common path interferometry for picometre surface metrology

Abstract

Future space based missions for gravitational wave research call for an improved inertial reference sensor with acceleration noise levels of fm/s^(2). Spherical test masses can enable increased performance by suspension-free operation, contrary to cuboid solutions suffering from cross-coupling of attitude control noise. However, interferometric readout is affected by surface irregularities and test mass tumbling [Gerardi et al. 2014]. An accurate surface map for compensation must be established for compensation, either by characterisation a priori or in flight, when optical path length changes due to surface occur in the measurement band. We demonstrate a method for generating a surface map of a spherical body with optical point sensors using a differential method to suppress common mode errors present, taking advantage of the excellent performance of heterodyne interferometry at sub-nanometer levels. A measurement setup is proposed in which two beams of a Nd:YAG Michelson interferometer are used to scan the surface, which is afterwards reconstructed from the differential measurement. Such a method could potentially benefit other research areas, such as the precise determinations of the Avogadro constant [Azuma et al. 2015] or aspheric surface metrology.