Correlated Ricean noise and resolution in coherent imaging

This paper presents a probabilistic resolution criterion for quantifying the performance of a coherent imaging system incorporating within its formulation the effects of noise. A deterministic field is corrupted by noise whose statistics are assumed to have a correlated Gaussian distribution, giving intensities at the detection plane described by a joint-correlated Ricean random process. The joint-correlated Ricean distribution is obtained and used to formulate a resolution criterion in terms of the joint probability of making two intensity measurements at different locations at the detector plane. Results are presented for two special cases that are equivalent to probabilistic analogues of the familiar Sparrow and Rayleigh resolution criteria used in incoherent imaging. Qualitative comparisons between these criteria are made in terms of the signal-to-noise ratio.