Phase unwrapping in spectral X-ray differential phase-contrast imaging with an energy-resolving photon-counting pixel detector

Grating-based differential phase-contrast imaging has proven to be feasible with conventional X-ray sources. The polychromatic spectrum generally limits the performance of the interferometer but benefit can be gained with an energy-sensitive detector. In the presented work, we employ the energy-discrimination capability to correct for phase-wrapping artefacts. We propose to use the phase shifts, which are measured in distinct energy bins, to estimate the optimal phase shift in the sense of maximum likelihood. We demonstrate that our method is able to correct for phase-wrapping artefacts, to improve the contrast-to-noise ratio and to reduce beam hardening due to the modelled energy dependency. The method is evaluated on experimental data which are measured with a laboratory Talbot-Lau interferometer equipped with a conventional polychromatic X-ray source and an energy-sensitive photon-counting pixel detector. Our work shows, that spectral imaging is an important step to move differential phase-contrast imaging closer to pre-clinical and clinical applications, where phase wrapping is particularly problematic.