双层衍射光学元件可以在宽波段范围内获得高的衍射效率。加工误差会导致带宽积分平均衍射效率的下降，进而影响折衍射混合成像光学系统的传递函数。基于位相延迟和带宽积分平均衍射效率的表达式，建立了双层衍射光学元件加工误差与带宽积分平均衍射效率的数学关系。分析了应用于8~12 μm 长波红外光学系统中的两种加工误差对双层衍射光学元件衍射效率的影响。采用带宽积分平均衍射效率，可以直接评价宽波段光学系统的成像质量。通过带宽积分平均衍射效率和双层衍射光学元件加工误差的关系，可以分析含有双层衍射元件混合光学系统的调制传递函数。

Two- layer diffractive optics can achieve high diffraction efficiency at broad wavelength band. Manufacturing errors can result in loss of diffraction efficiency and further, influence modulation transfer function (MTF) of refractive and diffractive hybrid imaging optical system. Based on the expression of phase delay and polychromatic integral diffraction efficiency (PIDE), mathematical analysis model of relationship between manufacturing errors and polychromatic integral diffraction efficiency is presented. Two kinds of manufacturing errors applied in 8~12 μm far infrared optical system which results in diffraction efficiency of two-layer diffractive optics are studied. Method of PIDE can evaluate image quality of optical system over broadband wavelength. According to the relationship between PIDE and manufacturing errors, MTF for hybrid optical system consisting of two-layer diffractive optics can be analyzed.