  A simple method of phase-and-amplitude extraction is derived that corrects
for image blurring induced by partially spatially coherent incident
illumination using only a single intensity image as input. The method is based
on Fresnel diffraction theory for the case of high Fresnel number, merged with
the space-frequency description formalism used to quantify partially coherent
fields and assumes the object under study is composed of a single material. A
priori knowledge of the object's complex refractive index and information
obtained by characterizing the spatial coherence of the source is required. The
algorithm was applied to propagation-based phase contrast data measured with a
laboratory-based micro-focus X-ray source. The blurring due to the finite
spatial extent of the source is embedded within the algorithm as a simple
correction term to the so-called Paganin algorithm and is also numerically
stable in the presence of noise.
