以衍射光学元件(DOE)相位延迟表达式为基础，研究并给出了多层衍射光学元件(MLDOE)的带宽积分平均衍射效率(BIADE)与相应设计波长关系的表达式。在MLDOE的基底材料确定后，由所给出的表达式可以得到最大BIADE及相应的设计波长，由此可以实现MLDOE的BIADE最大化、精确化设计。在0.4～0.7 μm可见光波段，以聚甲基丙烯酸酯和聚碳酸酯为基底材料，通过优化得到最大BIADE为99.3%，相应的设计波长为0.435 μm和0.598 μm，各层谐衍射元件(HDE)的微结构高度分别为16.460 μm和12.813 μm，所得到的BIADE比以0.4 μm和0.7 μm为设计波长时高4%。

The relation between bandwidth integrated average diffraction efficiency (BIADE) of multi-layer diffractive optical elements (MLDOE) and corresponding phase retardation expression is discussed, and the maximum BIADE and the corresponding design wavelengths are determined when the optical materials are selected, then the design of the BIADE of the MLDOE is realized exactly and maximumly. Based on the principle, to design a MLDOE with (PMMA) and polycarbonate as materials respectively, the maximum BIADE is 99.3% in visible waveband (0.4～0.7 μm), the corresponding design wavelengths are 0.435 μm and 0.598 μm, the heights of harmonic diffractive element (HDE) are 16.460 μm and 12.813 μm respectively, and the BIADE of the MLDOE designed with this method is 3.9% higher than that with the former method in which design wavelengths are 0.4 μm and 0.7 μm.