Validity of ray trace based performance predictions of optical systems with diffractive optical elements (DOE)

Color aberrations in broadband imaging optics can be effectively corrected for by use of diffractive optical elements (DOE) such as kinoforms. Typically, the DOE groove width increases with wavelength range and is in the range of several ten to several hundreds of micrometers. Since the footprint diameter of a light bundle originating from a single object point at the diffractive surface is often in the range of millimeters, the number of grooves crossed by this light bundle can be small. In addition, the groove width varies and the grooves are curved. For DOE optimization and prediction of optical performance, optical design software is widely used being based on the ray trace formula, i.e. the law of refraction including DOEs. This ray trace formula relies on two assumptions. First, the footprint diameter of a light beam at the diffractive surface is assumed to be large compared to the groove width. Second, the local grating approximation is used saying that at the footprint area the groove width is constant and the grooves are straight lines. In realistic optical systems, these assumptions are often violated. Thus, the reliability of optical performance predictions such as MTF is in question. In the present paper, the authors re-examine the limits of the ray trace equation. The effect of a finite footprint diameter at the diffractive surface is investigated as well as variations of the groove width. Also, the Fraunhofer diffraction pattern of a light bundle after crossing a grating with a finite number of grooves is calculated.