Theory of angular dispersive imaging hard x-ray spectrographs

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).