X-ray dark-field imaging from intensity flow: A Fokker-Planck approach to grating interferometry

TL;DR

This paper introduces a novel Fokker-Planck based algorithm for X-ray grating interferometry that improves image quality, reduces artifacts, and enhances performance in low-exposure, noisy conditions.

Contribution

It develops a new Fokker-Planck derived retrieval algorithm for grating interferometry, outperforming conventional sinusoidal-fitting methods in artifact suppression and noise robustness.

Findings

Fokker-Planck method produces images consistent with conventional methods.

It suppresses artifacts caused by grating perturbations and reduced flux.

It performs better in fast imaging with high noise and short exposure times.

Abstract

Grating interferometry is a promising diagnostic technique that enables simultaneous acquisition of three complementary, synergistic X-ray images: transmission, differential phase, and dark-field. Its key advantage over other setups is its ability to use large pixels and, hence, large-area detectors, as well as its compatibility with low-coherence, compact X-ray sources, both of which are key factors for human-scale imaging. It has already demonstrated strong potential for chest imaging applications, including the diagnosis of pulmonary emphysema, fibrosis, and cancer. To retrieve transmission, differential phase, and dark-field images from data, an algorithm is required to separate the distinct mechanisms contributing to measured contrast. Since its realization, this image-retrieval step has remained fundamentally unchanged. In this work, we develop a novel transmission- and dark-field retrieval algorithm for grating-interferometry derived from the X-ray Fokker-Planck equation. To demonstrate and validate our Fokker-Planck algorithm, we apply it to experimental measurements of a test sample and to data from a mouse chest acquired with varying exposure times and added Poisson noise. The retrieved images were qualitatively and quantitatively compared with those retrieved using a conventional sinusoidal-fitting approach. Across both samples, the Fokker--Planck method produced images consistent with conventional retrieval, with a comparable signal-to-noise ratio. Notably, our Fokker-Planck method suppresses artefacts arising in the conventional approach under grating perturbations (e.g., structural defects like scratches) and reduced flux or visibility, yielding smoother and more reproducible images. Additionally, we demonstrate that our Fokker-Planck method has an advantage over the conventional dark-field retrieval method for fast sample imaging with short exposure times and high noise.