工作环境温度的改变会降低衍射光学元件的衍射效率,影响混合光学系统的成像质量。基于斜入射时衍射效率的表达式,在双层衍射光学元件的设计中考虑温度变化,提出了工作在一定温度范围内和入射角度范围内的双层衍射光学元件微结构高度误差与衍射效率和带宽积分平均衍射效率的数学模型。以工作在可见光波段的双层衍射光学元件为例进行分析。结果表明,当环境温度确定后,随入射角度范围的增大,最高带宽积分平均衍射效率对应的最优相对微结构高度误差逐渐减小。当双层衍射光学元件工作在0°~15°的入射角度范围内、环境温度范围为-40~80 ℃时,其带宽积分平均衍射效率最高为96.81%,对应的最优相对微结构高度误差为4.42%。该方法进一步完善了双层衍射光学元件加工误差的设计理论。

The change in environmental temperature can reduce the diffraction efficiency of diffractive optical elements (DOEs) and thus affect the imaging quality of a hybrid optical system. Based on the expression of diffraction efficiency at oblique incidence, the temperature change is considered in the design of the double-layer diffractive optical elements (DLDOEs). The mathematical model of microstructure height error and diffraction efficiency/polychromatic integral diffraction efficiency (PIDE) of the DLDOEs within a certain temperature range and at certain incident angles is developed. The DLDOE that works in a visible waveband is taken as an example. The result shows that when a range of environmental temperature is determined, the optimal relative microstructure height error corresponding to the maximum PIDE decreases with the increase of the incident angle range. For the DLDOEs working within the incident angle range of 0°--15° and the environmental temperature range of 40--80 ℃, the maximum PIDE is 96.81%, and the corresponding optimal relative microstructure height error is 4.42%. Accordingly, the proposed model can further improve the design theory of the manufacturing error of the DLDOEs.