Numerical optimization of spherical VLS grating X-ray spectrometers

TL;DR

This paper presents a method for optimizing spherical VLS grating X-ray spectrometers to achieve high resolution and minimal aberrations across a broad energy range, using ray-tracing and analytical techniques.

Contribution

It introduces a comprehensive optimization approach for spherical VLS gratings, enhancing spectrometer performance over extended energies with minimized aberrations.

Findings

Achieved resolving power above 20400 at 930 eV.

Optimized VLS coefficients to cancel asymmetry and reduce broadening.

Developed operational modes for energy-independent focal curves.

Abstract

Operation of an X-ray spectrometer based on a spherical variable line spacing grating is analyzed using dedicated ray-tracing software allowing fast optimization of the grating parameters and spectrometer geometry. The analysis is illustrated with optical design of a model spectrometer to deliver a resolving power above 20400 at photon energy of 930 eV (Cu L-edge). With this energy taken as reference, the VLS coefficients are optimized to cancel the lineshape asymmetry (mostly from the coma aberrations) as well as minimize the symmetric aberration broadening at large grating illuminations, dramatically increasing the aberration-limited vertical acceptance of the spectrometer. For any energy away from the reference, we evaluate corrections to the entrance arm and light incidence angle on the grating to maintain the exactly symmetric lineshape. Furthermore, we evaluate operational modes when these corrections are coordinated to maintain either energy independent focal curve inclination or maximal aberration-limited spectrometer acceptance. The results are supported by analytical evaluation of the coma term of the optical path function. Our analysis gives thus a recipe to design a high-resolution spherical VLS grating spectrometer operating with negligible aberrations at large acceptance and over extended energy range.