Adaptive trajectories for variable-included angle monochromator with variable line spacing gratings, and computation of diffraction efficiency using Reticolo

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Abstract
With diffraction-limited storage rings, the power load on the pre-mirror in grating monochromators can cause deformation that adversely affects the effective photon-energy resolution of the beamline. For variable included angle with variable line-spacing (VIA-VLS) grating monochromators, it is possible to compensate for some deformation effects and achieve nominal resolution by adapting the relative angles of the pre-mirror and grating across the entire energy range. We derive a simplified analytical formulation for grating and mirror positions that can be used for automatically tuning photon energies in simulations and digital twins. We also demonstrate the use of the open-source Rigorous Coupled-Wave Analysis software Reticolo for soft X-ray gratings to compute diffraction efficiency using Python for lamellar, blazed, and arbitrary groove profiles, including higher-order diffraction efficiencies. We provide experimental comparisons from various gratings mea sured at the Advanced Light Source, showing agreement well within 5%. These calculations facilitate grating design and enable more effective prediction of flux and harmonic contamination.