Tolerance analysis on decenter error of multilayer diffractive optical elements based on polychromatic integral diffraction efficiency.

The decenter error can determine the polychromatic integral diffraction efficiency (PIDE) over a broad wave band of hybrid optical systems and further the imaging quality. The mathematical model of the relationship between the decenter error and the PIDE of multilayer diffractive optical elements (MLDOEs) is presented, and the expressions are derived based on phase delay of diffractive optical elements for both normal and oblique incident situations. Finally, the sensitivity of PIDE to the decenter error for MLDOEs used in a long-infrared wave band with a material combination of ZNS-ZNSE is analyzed, and then the decenter error tolerance is proposed to ensure high PIDE over a broad wave band as well as diffraction efficiency at the designed wavelengths. The analysis methods and results could be useful for guiding the decenter error of MLDOEs in hybrid optical systems for optical engineers.