Theory of angular dispersive imaging hard x-ray spectrographs

TL;DR

This paper develops theoretical designs for hard x-ray spectrographs capable of high energy resolution and spectral imaging, using Bragg crystals and ray-transfer matrix techniques, to enhance inelastic x-ray scattering spectroscopy.

Contribution

It introduces several optical designs for hard x-ray spectrographs with high energy resolution, analyzing their performance for IXS and RIXS applications.

Findings

Achievable energy resolution of 0.1 meV for inelastic x-ray scattering.

Spectrographs with 1 meV spectral resolution and 85 meV imaging window.

Feasibility of high-resolution hard x-ray spectrographs demonstrated.

Abstract

A spectrograph is an optical instrument that disperses photons of different energies into distinct directions and space locations, and images photon spectra on a position-sensitive detector. Spectrographs consist of collimating, angular dispersive, and focusing optical elements. Bragg reflecting crystals arranged in an asymmetric scattering geometry are used as the dispersing elements. A ray-transfer matrix technique is applied to propagate x-rays through the optical elements. Several optical designs of hard x-ray spectrographs are proposed and their performance is analyzed. Spectrographs with an energy resolution of 0.1 meV and a spectral window of imaging up to a few tens of meVs are shown to be feasible for inelastic x-ray scattering (IXS) spectroscopy applications. In another example, a spectrograph with a 1-meV spectral resolution and 85-meV spectral window of imaging is considered for Cu K-edge resonant IXS (RIXS).