Optimizing and characterizing grating efficiency for a soft X-ray emission spectrometer

The efficiency of soft X‐ray diffraction gratings is studied using measurements and calculations based on the differential method with the S‐matrix propagation algorithm. New open‐source software is introduced for efficiency modelling that accounts for arbitrary groove profiles, such as those based on atomic force microscopy (AFM) measurements; the software also exploits multi‐core processors and high‐performance computing resources for faster calculations. Insights from these calculations, including a new principle of optimal incidence angle, are used to design a soft X‐ray emission spectrometer with high efficiency and high resolution for the REIXS beamline at the Canadian Light Source: a theoretical grating efficiency above 10% and resolving power E/ΔE > 2500 over the energy range from 100 eV to 1000 eV are achieved. The design also exploits an efficiency peak in the third diffraction order to provide a high‐resolution mode offering E/ΔE > 14000 at 280 eV, and E/ΔE > 10000 at 710 eV, with theoretical grating efficiencies from 2% to 5%. The manufactured gratings are characterized using AFM measurements of the grooves and diffractometer measurements of the efficiency as a function of wavelength. The measured and theoretical efficiency spectra are compared, and the discrepancies are explained by accounting for real‐world effects: groove geometry errors, oxidation and surface roughness. A curve‐fitting process is used to invert the calculations to predict grating parameters that match the calculated and measured efficiency spectra; the predicted blaze angles are found to agree closely with the AFM estimates, and a method of characterizing grating parameters that are difficult or impossible to measure directly is suggested.