DOEs for color correction in broad band optical systems: validity and limits of efficiency approximations

Diffractive optical elements (DOE) are well-suited for the correction of longitudinal and transverse chromatic aberrations in broadband optical systems such as photographic lenses, HMDs or infrared lenses. Unfortunately, the diffraction efficiency η for the working order of DOEs is often clearly below 100% which causes stray light from unwanted diffraction orders and prevents a more frequent use of DOEs in practice. The main reasons for the decrease of diffraction efficiency η are spectral bandwidth, variation of the incidence angle of impinging light and manufacturing errors of the DOE. In the present paper, several scalar approximations for the diffraction efficiency η as a function of these parameters are compared with rigorous electromagnetic calculations. The validity of these formulae are shown to extend over a surprisingly large range of parameters.