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 that 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 can be used as the dispersing elements in the hard-x-ray regime. 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.