2D grating simulation for X‐ray phase‐contrast and dark‐field imaging with a Talbot interferometer

Talbot interferometry is a recently developed and an extremely powerful X‐ray phase‐contrast imaging technique. Besides giving access to ultra‐high sensitivity differential phase contrast images, it also provides the dark field image, which is a map of the scattering power of the sample. In this paper we investigate the potentialities of an improved version of the interferometer, in which two dimensional gratings are used instead of standard line grids. This approach allows to overcome the difficulties that might be encountered in the images produced by a one dimensional interferometer. Among these limitations there are the phase wrapping and quantitative phase retrieval problems and the directionality of the differential phase and dark‐field signals. The feasibility of the 2D Talbot interferometer has been studied with a numerical simulation on the performances of its optical components under different circumstances. The gratings can be obtained either by an ad hoc fabrication of the 2D structures or by a superposition of two perpendicular linear grids. Through this simulation it has been possible to find the best parameters for a practical implementation of the 2D Talbot interferometer.