Design of cascaded diffractive optical elements operating at several wavelengths for generating color images and solving classification problems

We consider the design of cascaded phase diffractive optical elements (DOEs) operating at several different wavelengths. The problem of DOE design is formulated as the problem of minimizing a certain error functional that depends on the functions of diffractive microrelief height of the cascaded DOE and evaluates its performance at different design wavelengths. Explicit expressions are obtained for the Fréchet derivatives of the error functional. The presented expressions for the derivatives of the error functional constitute the basis for gradient design of cascaded multiwavelength DOEs in various problems including the beam shaping and optical classification problems. As particular example, we consider the calculation of cascaded DOEs focusing radiation of three different wavelengths into different letter-shaped areas.