Design of coma-free Hettrick-Underwood type spectrometers for high energy resolution RIXS experimental station.

The Hettrick-Underwood (HU) type design, consisting of a pre-focusing mirror and a varied-line-spacing planar grating (VLS-PG), for the high resolution resonant inelastic x-ray scattering spectrometer is considered. The light path of the HU design is analyzed, and the analytical functions determining the groove parameters of VLS-grating are given. Efforts are made to compare the different choices of the pre-focusing mirrors, circular cylindrical (HU-CM) and elliptical cylindrical (HU-EM).