An alternative approach to the design and fabrication of diffractive optical elements

As a simple, demonstrative example, consider the generation of two diffraction-limited spots with an optical element of a given size. It is well known how to generate a single spot by a Fresnel lens that is characterized by a relatively simple phase structure. A frequently adopted procedure to generate two spots is to position two Fresnel lenses side by side. This procedure, however, reduces the size of the aperture available for each spot resulting in a degraded diffraction limit. To maintain the diffraction limit of the whole aperture for both spots one has to design and fabricate a quite complicated phase structure given by a coherent superposition of two waves propagating backward from the two spots. It is easy to see that an ideal element to regenerate this more complex wave front has a transfer function where the two phase functions represent two spherical wave fronts.