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A simple method of phase-and-amplitude extraction is derived that correctsfor image blurring induced by partially spatially coherent incidentillumination using only a single intensity image as input. The method is basedon Fresnel diffraction theory for the case of high Fresnel number, merged withthe space-frequency description formalism used to quantify partially coherentfields and assumes the object under study is composed of a single material. Apriori knowledge of the object's complex refractive index and informationobtained by characterizing the spatial coherence of the source is required. Thealgorithm was applied to propagation-based phase contrast data measured with alaboratory-based micro-focus X-ray source. The blurring due to the finitespatial extent of the source is embedded within the algorithm as a simplecorrection term to the so-called Paganin algorithm and is also numericallystable in the presence of noise.

Phase-and-amplitude recovery from a single phase contrast image using partially spatially coherent X-ray radiation