DuMond analysis of bending in single crystals by Laue diffraction using sigma-pi polarization geometry

A DuMond analysis of X-ray diffraction patterns has been carried out in the case of a combined sigma-pi polarization configuration, obtained using a setup with a double-crystal monochromator in reflection (Bragg) geometry and an analyser in transmission (Laue) geometry. The derived analytical expressions allow the characterization of the bending of the analyser and the quantitative estimation of the curvature radius and its sign from the width of the crystal rocking curves. The theoretical analysis is applied to the case of a thin, accidentally bent, Si crystal.