Based on the expression function of diffraction efficiency, and the phase delay function of diffractive optical elements (DOEs), the diffraction efficiency for multilayer diffractive optical elements (MLDOEs) is described with tilt and decenter assembling errors. A mathematical model of the relationship between diffraction efficiency and assembling errors of MLDOEs is proposed to analyze the effect of assembling errors on the diffraction efficiency of MLDOEs. The analyzed results from the mathematical model provide a range of values for the effect of assembling errors on the diffraction efficiency of MLDOEs. Assembling errors are important parameters for hybrid diffractive refractive optical systems, including MLDOEs, and so the proposed model will be useful for guiding the design and fabrication of such optical systems.
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