Absorption and secondary scattering of X-rays with an off-axis small beam for a cylindrical sample geometry

Expressions for X-ray absorption and secondary scattering are developed for cylindrical sample geometries. The incident-beam size is assumed to be smaller than the sample and in general directed off-axis onto the cylindrical sample. It is shown that an offset beam has a non-negligible effect on both the absorption and multiple scattering terms, resulting in an asymmetric correction that must be applied to the measured scattering intensities. The integral forms of the corrections are first presented. A small-beam limit is then developed for easier computation.