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.
@article{arxiv.1711.04227,
title = {Phase-and-amplitude recovery from a single phase contrast image using partially spatially coherent X-ray radiation},
author = {Mario A. Beltran and David M. Paganin and Daniele Pelliccia},
journal= {arXiv preprint arXiv:1711.04227},
year = {2019}
}