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Athermalization and thermal characteristics of multilayer diffractive optical elements.

A mathematical model to analyze the thermal characteristics of the multilayer diffractive optical elements (MLDOEs) is presented with consideration of the thermal characteristics for the refractive optical elements and single-layer diffractive optical elements. The analysis process of athermalization for MLDOEs by using the opto-thermal expansion coefficient of optical materials is given. Meanwhile, the microstructure heights of surface relief MLDOEs, the optical path difference, and the polychromatic integral diffraction efficiency with the ambient temperature changed are analyzed. The analysis results can be used to guide an athermalization design for the hybrid refractive-diffractive optical systems with MLDOEs.