Heterodyne detection with a weak local oscillator

Abstract

Heterodyne detection in the limit of weak (a few photons) local oscillator and signal power levels has been largely neglected in the past, as authors almost always assumed that the noise was dominated by the shot noise from a strong local oscillator. We present the theory for heterodyne detection of diffuse and specular targets at arbitrary power levels, including the case where the local oscillator power is only a few photons per coherent integration period. The theory was tested with experimental results, and was found to show good agreement. We show how to interpret the power spectral density of the heterodyne signal and how to determine the optimal number of signal and local oscillator photons per coherent integration.