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

Abstract

The location of the beam focus when monochromatic X-ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It 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.

Crystal bending in triple-Laue X-ray interferometry. Part I. Theory

“…Our interest is in the phase of the diffracted waves, rather than the intensity profile arising when using bent crystals e.g. to focus X-rays or as analysers for X-ray spectroscopy (Nesterets & Wilkins, 2008;Kaganer et al, 2020;Qi et al, 2021;Guigay & Sanchez del Rio, 2022).…”

Crystal bending in triple-Laue X-ray interferometry. Part II. Phase-contrast topography

“…Bent silicon crystals have been extensively studied because they are used as optics for the conditioning of X-ray beams and analysers for X-ray spectroscopy (Nesterets & Wilkins, 2008;Qi et al, 2021;Kaganer et al, 2020;Guigay & Sanchez del Rio, 2022), and to infer the stresses in thin films and devices on substrates (Vaudin et al, 2011). We are motivated by the search for systematic errors in the measurement of the silicon lattice parameter by crystal X-ray interferometry and the realization of the kilogram by counting silicon atoms (Massa et al, 2011(Massa et al, , 2015(Massa et al, , 2020aKessler et al, 2017;Yang et al, 2020).…”