AbstractIn coherent imaging the object of interest is complex but only its amplitude is to be estimated. The object phase yields nuisance variables and in a proper Bayesian approach it is necessary to obtain a phaseless likelihood function. We investigate a two‐dimensional case in which the target object is modelled as a collection of point scatterers having independent random phases. The phaseless likelihood function is determined exactly for a configuration of data samples in a uniformly spaced square array in spatial frequency when the target scatterers are confined to lattice positions of a “matched” spatial array. It is determined approximately when the target scatterers are arbitrarily positioned, at most one per conventional resolution cell. The relation between maximum likelihood and conventional Fourier transform imaging is explored and the feasibility of a CLEAN algorithmic technique in coherent imaging is considered.©1993 John Wiley & Sons Inc