X-ray dark-field via spectral propagation-based imaging

Dark-field X-ray imaging visualizes scattering from unresolved microstructure. Most dark-field imaging techniques rely on crystals or structured illumination, but recent work has shown that dark-field effects are observable in straightforward propagation-based imaging (PBI). Based on the single-material X-ray Fokker–Planck equation with an a priori dark-field energy dependence, we propose an algorithm to extract phase and dark-field effects from dual-energy PBI images. We successfully apply the dark-field retrieval algorithm to simulated and experimental dual-energy data, and show that by accounting for dark-field effects, projected thickness reconstruction is improved compared to the classic Paganin algorithm. With the emergence of spectral detectors, the method could enable single-exposure dark-field imaging of dynamic and living samples.