Full-field quantitative X-ray phase nanotomography via space-domain Kramers–Kronig relations

Abstract

Given the low absorption contrast of X-rays, phase shift has been playing an important role as an alternative source of contrast in X-ray nanoimaging. Numerous phase-measuring techniques have been proposed, most of which, however, are based on significant assumptions or sample translations. In this study, we propose the application of Kramers–Kronig (KK) relations in the spatial domain as a solution to allow the X-ray quantitative phase image to be directly calculated from the measured intensity image without any additional requirements. Based on this straightforward principle, we have presented KK nanotomography by introducing a spatial-frequency cutoff filter into a conventional tomographic setup. The robustness and versatility of the proposed method were experimentally verified based on various sample tomograms. We expect KK nanotomography to be widely adopted as a powerful and easy-to-adapt phase quantification solution for X-ray microscopes.