  X-ray phase-contrast imaging enhances soft tissue visualization by leveraging
the phase shift of X-rays passing through materials. It permits to minimize
radiation exposure due to high contrast, as well as high resolution imaging
limited by the wavelength of the X-rays. Phase retrieval extracts the phase
shift computationally, but simulated images fail to recreate low-frequency
noise observed in experimental images. To this end, we propose a new method to
simulate phase contrast images using the Wigner Distribution Function. This
permits the simulation of wave and particle effects simultaneously and
simulates images photon by photon. Here, we give a first demonstration of the
method by simulating the Gaussian double-slit experiment. It has the potential
for realistic simulation of low-dose imaging.
