Analysis of partial coherence in grating-based phase-contrast X-ray imaging

We report here a quantitative analysis of the effect of partial coherence on grating-based phase-contrast X-ray imaging. The self-image intensity has been derived through the phase-space formulation in the framework of the Wigner distribution. Based on the behavior of the self-image visibility, the minimum required spatial coherence length is given for three different types of gratings. Furthermore, we show that the coherence requirement, at different fractional Talbot distances, increases linearly with the Talbot order for the three types of gratings. The approach we presented can also be successfully applied to the Talbot–Lau geometry.