基于单层衍射二元光学元件的相位延迟表达式, 将双层衍射光学元件的衍射面用二元光学元件的台阶表面近似模拟, 推导出光束斜入射时双层衍射光学元件的衍射面产生的相位延迟, 揭示出含有斜入射角度的双层衍射光学元件衍射效率表达式。实例分析结果表明, 双层衍射光学元件衍射效率仅在一定角度范围内对入射角的变化不敏感, 当入射角度持续增大时, 衍射效率随入射角的增加快速下降。当入射角从0°增大到4.5°时, 衍射效率几乎没有下降; 当入射角从4.5°增大到6.7°时, 衍射效率开始缓慢下降到95％; 当入射角从6.7°增大到9.5°时, 衍射效率明显下降到80％; 当入射角从9.5°增大到18°时, 衍射效率快速下降到0。

Diffractive surface of a two-layer diffractive optical element (DOE) is simulated approximately by step surface of binary optical element, and phase shift of a two-layer DOE for light of oblique incidence is deduced from phase shift of a single-layer binary optical element. The expression of diffraction efficiency of the two-layer DOE is presented. Simulation shows that the diffraction efficiency of a two-layer DOE changes slightly when the incident angle is small, but it decreases greatly when incident angle increases. Diffraction efficiency changes little when the incident angle increases to 4.5°, decreases slowly to 95% when the incident angle increases 6.7°, decreases to 80% when the incident angle change increases to 9.5°, and decreases rapidly to zero when the incident angle increases to 18°.