Angular vibration analysis of a plane grating monochromator at the Hefei Advanced Light Facility

• A novel method based on elastic deformation is proposed to quantify planar microangle vibrations. • The elastic fitting method fully considers the nonuniform deformation and phase difference during PGM vibration. • The elastic fitting method provides a criterion for the design and optimization of high-precision optical systems. The stability of the plane grating monochromator in the Hefei Advanced Light Facility is highly important for beamline focusing, with angular vibration being a key indicator for assessing its stability. This paper proposes an elastic fitting method based on fifth-order polynomial fitting for the precise analysis of microangular vibrations on grating surfaces. Compared with the traditional rigid body method, this method fully considers the three major elastic characteristics exhibited by optical components during vibration: significant phase differences, nonuniform deformation gradients, and spatial distribution differences in angular deformation. The research results indicate that this method can accurately reflect the actual vibration state of the grating surface, not only enabling the quantitative prediction of local angular microvibration but also establishing a reliable theoretical analysis framework for the stability assessment of high-precision instruments.