This paper presents methods for designing and recording optimal comput
er-generated diffractive optical elements, The design method is based
on an analytic ray-tracing procedure for minimizing aberrations, The r
ecording involves computer-generated mask and multiple lithographic pr
ocesses in order to form reflective and transmissive multilevel, surfa
ce relief-phase, diffractive elements. As a result, the elements can h
ave high diffraction efficiencies over a broad range of incidence angl
es. Even generalized diffractive elements that operate with highly uni
form diffraction efficiency and polychromatic radiation can be designe
d and recorded by optimizing the shape and height of the relief gratin
gs. To illustrate the effectiveness of the diffractive optical element
s, they have been incorporated into a number of applications, involvin
g visible as well as infra-red radiation. Some that deal with coordina
te transformation beam shaping, and polarization control are briefly r
eviewed.