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

TL;DR

This paper introduces a method to recover phase and amplitude from a single X-ray image, correcting for blurring caused by partial coherence, applicable in laboratory settings with stable, noise-tolerant results.

Contribution

It presents a novel correction algorithm that extends the Paganin method to account for partial coherence effects using only one image.

Findings

Successfully applied to micro-focus X-ray data

Corrects for source-induced blurring

Numerically stable with noisy data

Abstract

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.