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

• Published in: IEEE transactions on medical imaging Vol. 42; no. 6; p. 1
• Main Authors: Leatham, Thomas A., Paganin, David M., Morgan, Kaye S.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01-06-2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; dark-field retrieval; Datasets; Detectors; Fokker-Planck equation; Gratings (spectra); Histology; homogeneous samples; Image contrast; Imaging; Mathematical models; Medical imaging; Microstructure; Optical imaging; Optical scattering; Optics; Phase retrieval; Propagation; propagation-based imaging; Radiography; Spatial discrimination; Spatial resolution; Thickness; X ray imagery; X ray sources; X-ray imaging; X-Rays
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2023.3234901

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 a 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 both the projected thickness and the dark-field signal 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 sample thickness 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.