Calculation of the diffraction efficiency on concave gratings based on Fresnel–Kirchhoff’s diffraction formula

Abstract

Fraunhofer diffraction formula cannot be applied to calculate the diffraction wave energy distribution of concave gratings like plane gratings because their grooves are distributed on a concave spherical surface. In this paper, a method based on the Kirchhoff diffraction theory is proposed to calculate the diffraction efficiency on concave gratings by considering the curvature of the whole concave spherical surface. According to this approach, each groove surface is divided into several limited small planes, on which the Kirchhoff diffraction field distribution is calculated, and then the diffraction field of whole concave grating can be obtained by superimposition. Formulas to calculate the diffraction efficiency of Rowland-type and flat-field concave gratings are deduced from practical applications. Experimental results showed strong agreement with theoretical computations. With the proposed method, light energy can be optimized to the expected diffraction wave range while implementing aberration-corrected design of concave gratings, particularly for the concave blazed gratings.