Branch cut effects in optimally estimating a coherent diffracted field

In optical imaging systems that image coherently illuminated diffuse scattering objects, the complex field in both the object plane and the measurement plane of the object are described by a circularly complex random process1 with a spatial correlation function for the phase of the field given by2, where k o is the complex coherence factor3 in the measurement plane, and x→ and x→ are arbitrary positions in the measurement plane. The parameters γ and Ω depend solely on the complex coherence factor and so equation (1) depends only on the object’s ensemble statistics and does not model branch cut effects.