Simulation of diffraction and scattering using the Wigner distribution function

We present a new, to the best of our knowledge, method to simulate diffraction images accounting for both coherent and incoherent effects, based on the Wigner distribution function of the exit wave. This permits the simulation of wave and particle effects simultaneously and simulates images photon by photon. It is motivated by artifacts observed in x ray phase-contrast images after phase retrieval, present as noise in the low spatial frequency range, which can make analysis of such images challenging. Classical simulations have so far not been able to reproduce these artifacts. We hypothesize that these artifacts are due to incoherent scatter present in the images, hence the interest in developing a simulator that permits the simulation of both diffraction and incoherent scattering. Here, we give a first demonstration of the method by simulating the Gaussian double-slit experiment. We demonstrate the capability of combining diffraction and incoherent scattering, as well as simulating images for any propagation distance.