非球面波记录全息光栅理论公式的误差分析

本文针对使用两块球面镜产生非球面波记录球面光栅的光路，分析条纹函数解析表达式的误差来源，指出当光栅基底半径或辅助球面镜半径较小时，理论公式推导过程中的级数展开会引入较大误差。采用基于光线追迹的数值方法，计算实际光栅条纹分布。全息光栅设计实例表明，有必要采用数值方法对记录参数设计结果进行验证。

Theoretic equations of holographic gratings recorded with aspherical wavefronts: error analysis

Considering the analytical equations of groove parameters to fourth order and using two spherical mirrors to generate aspherical wavefronts and a spherical blank as a grating blank, we have analyzed the error of groove function and indicated that when the radius of grating blank or the radii of auxiliary mirrors are comparatively small, the series expansion in derivation procedure will introduce comparatively large error. A numerical method based on ray tracing was adopted and the practical groove pattern was calculated. Design example of holographic grating shows that it is necessary to validate the design result of recording parameters through numerical method.