Computer aided design of diffractive beam-shaping elements

Diffractive beam-shaping elements focus a given aperture with intensity and phase distributions with high efficiency into a pregiven intensity pattern in their focal planes. The design of appropriate phase-only hologram functions can be carried out in a very illustrative and convenient way through the use of geometrical optics. Using inverse raytracing, wavefronts performing geometrical transformations between the hologram and the reconstruction plane can be easily designed. Such geometrical transformations allow to compensate for the intensity and phase distributions of the impinging laser beam as well as for the shape of the hologram aperture. For seperable beam-shaping tasks it is often possible to solve the design problem directly by analytical or numerical integrations. In other cases a numerical approach based on iterative finite element mesh adaption can be used. In this way a variety of elementary reconstruction objects like points, straight line segments, circles, rings, triangles, rectangles etc. in various types of apertures can be handled. More complex reconstruction patterns are decomposed into as few of those elementary objects as possible. The total hologram function if then found by the subsequent superposition of its constituents, with a relative amplitude and phase weighting for each of them, This concept leads to a modular construction kit for diffractive optical elements which on the one hand is easy to use and to understand and on the other hand is a very powerful design tool.