Effects of partial coherence on the scattering of x rays by matter

We discuss the scattering of x rays by matter using the Huygens-Fresnel method, i.e., in the kinematic regime. We derive expressions for how the mutual coherence function (MCF) of the scattered radiation defined across an exit aperture, arises from the MCF of the incident radiation across the entrance aperture and the electron density distribution of the scatterer, and in particular calculate the intensity measured in a detector placed behind the exit aperture as a function of the nominal wave vector transfer q. We discuss the exact relationship between this intensity function and the usual density-density correlation function of the scatterer, and discuss the relationship between coherence and instrumental resolution effects in various regimes. The Fraunhofer and Fresnel regimes are distinguished and the incoherent and coherent limits are discussed. We illustrate the results with explicit calculations for (a) Bragg reflections from crystals and (b) scattering from surfaces.