Lens-term- and edge-effect in X-ray grating interferometry

X-ray grating interferometry requires gratings with periods in the micrometer range and allows the acquisition of the dark-field contrast. The analyzer grating is designed to match the period of the interference pattern in order to translate it into a measurable intensity modulation. In this study, we explore the influence of a sample-induced mismatch between the interference pattern and the analyzer grating on the dark-field contrast. We propose a formula for the calculation of the signal due to a period mismatch and present estimations varying periods and detector pixel size. Furthermore, numerical simulations of the X-ray wave-front demonstrate that the wave-front curvature, described by the lens-term, e.g. behind a parabolic lens or edges of a sample can change the period of the interference pattern. Our results give a concrete explanation for the formation of a dark-field contrast from object edges and thus allow a better understanding of the dark-field signal obtained with a grating interferometer.