Abstract

Based on the matrix description of the fractional Talbot effect, a new and effective method to numerically optimize diffractive optical elements that work in the Fresnel diffraction regime is described. When the investigation is restricted to spatially quantized phase-only gratings, diffraction can be described in terms of the fractional Talbot effect and the diffraction amplitude is efficiently evaluated from a finite set of sampling points. As an illustrating example we numerically optimize Talbot array illuminators. Our results show that a limited number of discrete phase levels does not imply a limited compression ratio but does lead to a reduced diffraction efficiency. Experimental results obtained from lithographically fabricated surface-relief gratings are compared with our theoretical designs.

© 1999 Optical Society of America

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