Measurement of the absolute wavefront curvature radius in a heterodyne interferometer

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.

double-spaced, 21 pages, 5 figures

References in corpus (2)

• Coupling characterization and noise studies of the Optical Metrology System on-board the LISA Pathfinder Mission
• Real-time phasefront detector for heterodyne interferometers

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• Dynamic motion trajectory control with nanoradian accuracy for multi-element X-ray optical systems via laser interferometry
• Differential wavefront sensing and control using radio-frequency optical demodulation
• Fundamental Performance Determining Factors of the Ultrahigh-Precision Space-Borne Optical Metrology System for the LISA Pathfinder mission