Relationships Between Smooth- and Small-Phase Conditions in X-Ray Phase-Contrast Imaging

We analyze some relationships between the small- and smooth-phase conditions in propagation-based X-ray phase-contrast imaging. Although these conditions are generally well-understood, our analysis yields the identification of physical conditions under which they are mathematically equivalent. We also demonstrate that the smooth-phase condition depends not only on the imaging system resolution and object-to-detector distance, but also on the topography of the wavefield phase function.