Abstract

Phase transfer function Φ of thin surface-microrelief diffractive optical element (DOE) is usually considered proportional to its microrelief height h in accordance with relation Φ = kμ h, where k = 2π/λ, λ is the wavelength, μ is the scaling factor. Conventional approximate equations¹ are μ = n-1 for transmitting and μ = 2cosθ₀ for reflective elements, where n is the refractive index of the microrelief material and θ₀ is the angle of incidence. This relations are approximate even within scalar diffraction approach because they do not take into consideration the local slopes of the incident and the output beam as well as the curvature of the substrate surface, orientation of microrelief with respect to incident beam. Solutions of rigorous diffraction theory² are much more precise, but limited to the cases of regular diffraction gratings, while most of DOEs and computer generated holograms feature more complicated spatial structure. Piecewise-smooth surface considerations^3,4 are related to the definite type of DOE and require numerical solutions even for simple phase functions.

© 1998 Optical Society of America