Quantitative characterization of the contrast mechanisms of ultra-small-angle X-ray scattering imaging

A general treatment of X-ray imaging contrast for ultra-small-angle X-ray scattering (USAXS) imaging is presented; this approach makes use of phase propagation and dynamical diffraction theory to account quantitatively for the intensity distribution at the detector plane. Simulated results from a model system of micrometre-sized spherical SiO₂ particles embedded in a polypropyl­ene matrix show good agreement with experimental measurements. Simulations by means of a separate geometrical ray-tracing method also account for the features in the USAXS images and offer a complementary view of small-angle X-ray scattering as a contrast mechanism. The ray-tracing analysis indicates that refraction, in the form of Porod scattering, and, to a much lesser extent, X-ray reflection account for the USAXS imaging contrast.