Problem of maximization of the sharpness functions in observation of objects in coherent light through a randomly inhomogeneous medium

A study is made of the problem of the possibility of adaptive formation of images of objects in coherent light transmitted by a randomly inhomogeneous medium. A comparison is made of two sharpness functions of similar type related to the spectrum of the spatial frequencies of the images. It is shown that in the absence of a priori information on the object and on the distorting medium, maximization of the sharpness function does not result in image reconstruction, whereas in the case of an arbitrarily assumed a priori information and illumination of an object by a radiation field with a known spatial distribution of the amplitude it is possible to reconstruct images unambiguously. A specific amplitude distribution in the form of mutually orthogonal spatial harmonics is suggested for the investigated sharpness function.