Performance of diffractive lenses with nonunity diffraction efficiency

Abstract

The unique optical properties of diffractive optical elements make them attractive candidates for a wide variety of applications. Unlike conventional optical elements, however, diffractive optics can simultaneously produce more than one image, resulting from the various diffracted orders. Rigorous electromagnetic grating diffraction theory shows that, in general, the diffraction efficiency can be a function of pupil position and field angle. If the diffractive lens is not 100% efficient in diffracting the incident light into the desired diffracted order, the resulting image can be degraded by the increased background illumination. We consider the effects of the unwanted diffracted orders on the point-spread function and modulation transfer function (MTF) of systems that contain diffractive lenses. With a nonunity diffraction efficiency, the diffraction-limit MTF at low spatial frequencies is reduced by an amount equal to the fraction of energy in the diffraction order of interest. Fourier theory shows that this amount of degradation is given by the pupil-averaged efficiency. This average efficiency thus makes a convenient merit function for estimating image quality. For scanned imaging systems, the average efficiency acts as the equivalent of system transmittance in reducing the flux incident on the detector.