Heterodyne efficiency for a partially coherent optical signal

Heterodyne efficiency is discussed for a partially coherent signal and a coherent local oscillator beam. Both fileds are assumed to have Gaussian amplitude distributions. An input aperture is used to reduce the background noise. As the coherence of the signal decreases, the efficiency also decreases. However, there is a simple relation between the beam parameters and the detector dimensions to maintain optimum efficiency. The effect of the offset of the signal from the detector axis is also discussed, assuming the Gaussian probability of the deviation. In this case, the optimum parameters that give the maximum efficiency change with the average deviation.