Measurement of the absolute wavefront curvature radius in a heterodyne interferometer

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.