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

TL;DR

This paper compares the crystal lens equation and dynamical diffraction theory in predicting x-ray focus positions for bent crystals, extending the lens equation for Laue geometry and discussing polychromatic focusing.

Contribution

It derives a general crystal lens equation valid for Bragg and Laue geometries and extends it for Laue cases, enhancing understanding of x-ray focusing in bent crystals.

Findings

The lens equation is accurate for Bragg geometry.

Dynamical theory provides better predictions for Laue geometry.

Polychromatic focusing feasibility is discussed.

Abstract

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.