This paper deals with the mathematical modeling and the synthesis of nano-optical elements for the forming of 2D images used for automated identification. The inverse problem of synthesis is considered in Fresnel's scalar wave approximation. The problem is reduced to the solution of a nonlinear Fredholm operator equation of the first kind. Some efficient numerical iterative methods are developed to solve the inverse problem. When illuminated by a coherent light, the designed nano-optical elements produce 2D images used for the automated identification. The proposed identification procedure is invariant with respect to rotations and shifts of images. The electron beam lithography was used to produce samples of nano-optical elements for the case of 650 nm wavelength. The microfabrication technology allows forming a microrelief with 20 nm accuracy. Such nanooptical elements are resistant against the damage of microreliefs and can be used for the verification of banknotes, documents, etc.

Keywords: nano-optical elements, flat computer optics, electron beam lithography, inverse problems, computer generated hologram, protection against counterfeiting, pattern recognition.

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