Relationship between machining accuracy and optical properties of convex blazed grating in ultra-precision cutting

For ultra-precision machining of convex blazed grating elements there are inevitable machining errors, surface defects, and surface roughness, all of which can have an impact on their diffraction efficiency. In this paper, we use PCGrate software based on the integration method to establish the machining error model, surface defect model, and surface roughness model of convex spherical blazed grating with a curvature radius of 41.104 mm, a substrate diameter of 14 mm, a grating density of 53.97 line/mm and a blazed angle of 3.86° as the basic specification. To investigate the effect of base curvature radius error, grating period error, blazed angle error, grating ridge and valley passivation radius, Poisson burr height, and blaze surface roughness on their -1 order diffraction efficiency in the 0.95-2.5 µm spectral range. The results show that when the curvature radius error of the spherical base is less than ±80µm, the influence on diffraction efficiency can be ignored. Among the three groups of grating microstructure parameters, the influence of blazed angle on grating diffraction efficiency is the largest, followed by a grating period, and the influence of grating apex angle is the smallest, among which when the error of blazed angle is less than ±0.1° and the error of grating period is less than ±0.1µm, the influence on diffraction efficiency can be ignored. The effect of the passivation radius of the grating valley on the diffraction efficiency is smaller than that of the passivation radius of the grating ridge, and the maximum reduction of diffraction efficiency is 0.096 and 0.144 when the grating ridge and valley passivation radius are 50nm∼650 nm, respectively. The diffraction efficiency decreases significantly in the wavelength range of 1.9-2.5 µm with the increase of Poisson burr height and blaze surface roughness, and its effect on the diffraction efficiency can be neglected when the Poisson burr height is less than 0.5 µm and the blaze surface roughness value is less than RMS 1 nm. The machining error, surface defect, and surface roughness models of the convex blazed grating are optimized to provide a comprehensive machining accuracy basis for ultra-precision cutting of convex grating components.