Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination

Analytical expressions for the spatial distribution of the spectral density and intensity of projection images are derived for a broad class of object transmission functions in the case of partially coherent Schell-model-type incident illumination. The expressions are linear with respect to the phase distribution in the transmitted wave. Associated methods for phase retrieval are discussed with the emphasis on a technique that allows simultaneous “automatic” phase retrieval and deconvolution of projection images of homogeneous objects by means of mutual cancellation at a specified defocus distance of the Fresnel diffraction effects and the image blurring due to the point-spread function of the imaging system.