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 photodiode. This technique, also referred to as differential wavefront sensing, 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 what we believe to be a new measurement method to accurately determine the absolute wavefront curvature of a single measurement beam. We also investigate the change in the 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.