X-ray focusing by bent crystals: focal positions as predicted by the crystal lens equation and the dynamical diffraction theory

The location of the beam focus when monochromatic x-ray radiation is diffracted by a thin bent crystal is predicted by "crystal lens equation". We derive this equation in a general form valid for Bragg and Laue geometries. This equation has little utility for diffraction in Laue geometry. The focusing effect in the Laue symmetrical case is discussed using concepts of dynamical theory and an extension of the lens equation is proposed. The existence of polychromatic focusing is considered and the feasibility of matching the polychromatic and monochromatic focal positions is discussed.