Optimal design of depth-scaling error for multilayer diffractive optical elements with oblique incidence.

The mathematical analytic models of the relationship between depth-scaling error and diffraction efficiency/polychromatic integral diffraction efficiency (PIDE) for multilayer diffractive optical elements (MLDOEs) with oblique incidence are presented. A method for optimal design of the depth-scaling error for MLDOEs with consideration of comprehensive PIDE working within a range of incident angle is established. The effect of depth-scaling error on diffraction efficiency and PIDE of MLDOEs working in the visible wavelength with oblique incidence is analyzed. For the MLDOEs working within the range of incident angle 0-20°, the maximum comprehensive PIDE is 98.24%, and the optimal relative depth-scaling error is -6.55%. The analytic method and conclusion provide a theoretical basis for the determination of manufacturing tolerance of depth-scaling error for MLDOEs with oblique incidence.