An inverse problem of synthesis of nanooptical security elements for visual and automated authenticity verification

This paper is concerned with solving inverse problems of the synthesis of nanooptical security elements. The synthesis of a nanooptical element involves calculating its phase function via solving an inverse problem and fabricating the microrelief with high precision. The microrelief of the nanooptical element illuminated at any point with coherent radiation produces an image in the focal plane parallel to the plane of the optical element. This image is used for the automated authenticity verification. The area of the optical element is divided into elementary regions. In each elementary region, the image is formed using binary kinoforms whose phase function is calculated via solving a nonlinear Fredholm integral equation of the first kind. The depth of the microrelief is constant in each elementary region and determines the color of that region when the optical element is illuminated with white light. The developed elements can be used to protect documents, excise stamps, and brands.