Tracking Length and Differential-Wavefront-Sensing Signals from Quadrant Photodiodes in Heterodyne Interferometers with Digital Phase-Locked-Loop Readout

We propose a method to track signals from quadrant photodiodes (QPDs) in heterodyne laser interferometers that employ digital phase-locked loops for phase readout. Instead of separately tracking the four segments from the QPD and then combining the results into length and differential-wavefront-sensing signals, this method employs a set of coupled tracking loops that operate directly on the combined length and angular signals. The benefits are an increased signal-to-noise ratio in the loops and the possibility of adapting the loop bandwidths to the differing dynamical behavior of the signals being tracked, which now correspond to physically meaningful observables. We demonstrate an improvement of up to 6 dB over single-segment tracking, which makes this scheme an attractive solution for applications in precision intersatellite laser interferometry in ultralow light conditions.