The effect of a crystal monochromator on the local angular divergence of an X-ray beam

The performance of an X-ray optical system often depends critically on the local angular divergence of the X-ray beam. For example, in systems for radiography, tomography and diffraction topography, the angular divergence of the incident beam at a point in the sample determines the limiting spatial resolution. In this paper, formulas are derived for the local divergence in the diffracted beam of the non-dispersive asymmetric reflection double-flat-crystal monochromator, illuminated by synchrotron or characteristic radiation. The formulas are analyzed to determine the general behavior of the local divergence as a function of the asymmetry factors of the crystal reflections. For synchrotron radiation, one surprising conclusion is that the local divergence of the magnifying monochromator is always greater than that of the symmetric monochromator, significantly so for even moderate magnification factors. This result, which contradicts a claim in the literature, is attributed to a prismatic property of asymmetric reflection that has not previously been identified.