Self-similarity analysis of the fields diffracted from zone plates with complex geometry

We extend the results obtained for different cases of the product superposition of periodic functions, and the determination of the scattered fields, for the case of circular symmetry. The characteristics of focalization for such cases are studied. We name Cantor-Fresnel zone plate the structures obtained with this method. Also, in this study can be included the focalization by periodic, Cantor, incomplete structures and randomization. The self-similarity in the field, along the propagation, is finally studied, comparing with the Cantor-Ronchi linear grating associated to the zone plate. Key-Words: numerical analysis, theoretical design, optics and image processing, zone plates, Cantor set, periodic functions