Design of two- and three-element diffractive Keplerian telescopes.

Design procedures for simple two- and three-element diffractive telescopes, suitable for monochromatic applications, are described. We obtained the basic configuration for the two-element design analytically by solving design equations to set the Seidel aberrations to target values. Computer optimization is used to complete the design of the doublet and triplet telescopes. The two- and three-element designs exhibit similar optical performance and diffraction efficiency. We show that diffraction-limited performance can be obtained from these all-diffractive systems.

Effects of diffraction efficiency on the modulation transfer function of diffractive lenses.

Diffractive lenses differ from conventional optical elements in that they can produce more than one image because of the presence of more than one diffraction order. These spurious, defocused images serve to lower the contrast of the desired image. We show that a quantity that we define as the integrated efficiency serves as a useful figure of merit to describe diffractive lenses. The integrated efficiency is shown to be the limiting value for the optical transfer function; in most cases it serves as an overall scale factor for the transfer function. We discuss both monochromatic and polychromatic applications of the integrated efficiency and provide examples to demonstrate its utility.

Design of diffractive singlets for monochromatic imaging.

The Seidel aberrations of a rotationally-symmetric diffractive lens with an arbitrary phase profile are presented. It is shown that by a proper choice of phase function and aperture stop position, third-order coma and astigmatism can be eliminated for any chosen conjugate ratio. Since a diffractive lens has an inherent zero value for the Petzval sum, the image plane is flat in both tangential and sagittal meridians. The substrate curvature of the lens may be chosen to introduce a prescribed amount of distortion to allow for use as a Fourier transform lens or a laser scan lens. Examples are given of lens performance in finite conjugate imaging and laser scanning, where the f - theta condition is satisfied.

Optical performance of holographic kinoforms.

The optical properties of holographic kinoforms are described. It is shown that paraxial designs are not adequate for f/Nos. less than F/10. A nonparaxial design is introduced that retains the high diffraction efficiency of the paraxial designs, yet also produces an unaberrated diffracted wavefront for the design wavelength. Aberration calculations and computer calculations, based on the Huygens-Fresnel principle, of the point spread functions for these elements show the necessity of using the nonparaxial design. Specifications for a surface profile that takes account of the finite thickness of the diffracting surface are given. A model for kinoforms which can be used in optical design programs is proposed.

Design of a wide field diffractive landscape lens.

The third-order aberrations of a diffractive optical element with paraxial zone spacings are derived as a function of aperture stop position. It is shown that by placing the stop in the front focal plane, coma and astigmatism are identically zero, assuming an infinitely distant object. In addition, since the element is diffractive, the Petzval sum is also zero. Modulation transfer function comparisons with other lenses are given. The correction of spherical aberration using an aspheric plate located in the aperture stop and nonmonochromatic imaging performance are discussed. The distortion of the resulting system is shown to be the proper amount for use as a Fourier transform lens. An estimate for the space-bandwidth product of this Fourier transform system is given.