The Fokker–Planck Equation for Speckle-based X-ray Microscopy

X-rays are attenuated, refracted, and diffused as they pass through an object. In the context of X-ray microscopy, these three mechanisms can be individually exploited to render three complementary images of a sample. The attenuation image reveals sample density, the phase image (based on X-ray refraction) distinguishes weakly attenuating structures, and the dark-field image (using diffusion-induced contrast) highlights structures that are invisible to attenuation and phase imaging. In dark-field imaging, the contrast arises from small-scale structures that induce intensity variations below the spatial resolution of the imaging system, effectively diffusing the X-ray beam.