LINKING EQUATIONS BETWEEN PHOTON STATISTICS AND PHOTOCURRENT STATISTICS FOR TIME-VARYING STOCHASTIC PHOTON RATES

Detected photons originating from classical light beams can be describ ed either by means of photon statistics or by means of photocurrent st atistics on a semiclassical basis. The statistical parameters of these two descriptions have, up to now, only been related to each other usi ng vague, effective-time-constant arguments. We show that these relati ons are invalid for the general case of time-varying stochastic photon rates and arbitrary detector impulse responses and derive generally v alid linking equations for the ensemble average, the shot noise varian ce and the excess noise variance of the photon statistics and the phot ocurrent statistics due to a random optical field. The derivations are based on a general definition of the time average that allows an eleg ant treatment in the Fourier domain.