Photoelectron statistics for two independent, uniuniform random-phase sinusoids plus additive Gaussian noise with application to optical heterodyne detection

The purpose of this paper is to study the first-order photoelectron statistics for the ideal optical heterodyne situation (perfect alignment of the incident signal wave and the local oscillator wave) in the presence of a Gaussian noise background. The phases of the signal wave and the local oscillator wave are taken to be nonuniformly distributed over (-pi, pi). The probability density of the time-integrated intensity, the probability distribution of the detected photoelectrons, and the corresponding means and variances are investigated. Two different optical heterodyning situations are studied.