Heterodyne efficiency of a detection system for partially coherent beams

We consider the heterodyne efficiency as a measure of quality for a coherent detection system. The heterodyne efficiency reflects the matching between the received beam and the local oscillator beam on the detector surface, and one can use this property for the alignment of the system. In this paper we derive a general expression for the heterodyne efficiency of a detection system for beams at any state of coherence, assuming that the propagation directions for the two signals (the received signal and the locally generated one) are slightly different. We derive an analytical expression for the heterodyne efficiency when mixing coherently two partially coherent Gaussian Schell-model beams on a photodetector surface. Numerical examples are given for the variation in the heterodyne efficiency with the misalignment angle, the detector radius, and the parameters of the overlapping beams. We show that partially coherent beams, although they suffer more than coherent beams from a decrease in the heterodyne efficiency, are less affected than coherent beams by the misalignment of the detection system.