Retrieval of a phase-and-amplitude submicrometric object from images obtained in partially coherent microscopy

A one-dimensional submicrometric object and its image obtained by partially coherent microscopy can be optimally expanded on a basis of linear prolate spheroidal wave functions. Hence the bilinear transfer becomes a product of the vector that represents the object and of an imaging system tensor. This formalism permits a phase-and-amplitude object to be retrieved from differently focused images. The number of degrees of freedom of the object that can be effectively retrieved is shown to be a logarithmic function of the signal-to-noise ratio in the image. The method is extended to the retrieval of the sum of a space-limited object and a constant background with infinite support.