X-ray dark-field and phase retrieval without optics, via the Fokker-Planck equation

TL;DR

This paper introduces a novel method for extracting x-ray phase and dark-field signals from simple bright-field images using the Fokker-Planck equation, eliminating the need for optics in propagation-based imaging.

Contribution

It presents a new computational approach based on the Fokker-Planck equation to retrieve phase and dark-field signals without additional optics, improving resolution and applicability.

Findings

Dark-field signals can be extracted from propagation images.

X-ray phase retrieval is enhanced by accounting for dark-field effects.

The method is validated with both simulated and experimental data.

Abstract

Emerging methods of x-ray imaging that capture phase and dark-field effects are equipping medicine with complementary sensitivity to conventional radiography. These methods are being applied over a wide range of scales, from virtual histology to clinical chest imaging, and typically require the introduction of optics such as gratings. Here, we consider extracting x-ray phase and dark-field signals from bright-field images collected using nothing more than a coherent x-ray source and detector. Our approach is based on the Fokker--Planck equation for paraxial imaging, which is the diffusive generalization of the transport-of-intensity equation. Specifically, we utilize the Fokker--Planck equation in the context of propagation-based phase-contrast imaging, where we show that two intensity images are sufficient for successful retrieval of the projected thickness and dark-field signals associated with the sample. We show the results of our algorithm using both a simulated dataset and an experimental dataset. These demonstrate that the x-ray dark-field signal can be extracted from propagation-based images, and that x-ray phase can be retrieved with better spatial resolution when dark-field effects are taken into account. We anticipate the proposed algorithm will be of benefit in biomedical imaging, industrial settings, and other non-invasive imaging applications.