Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits

We consider a gradient method for calculating cascaded diffractive optical elements (DOEs) consisting of several sequentially placed phase DOEs. Using the unitarity property of the operator describing the light propagation through the cascaded DOE, we obtained explicit expressions for the derivatives of the error functional with the respect to the phase functions of the cascaded DOE. We consider the application of the gradient method in the problem of focusing several different incident beams to several domains with different intensity distributions, and in the problem of image classification. The presented description of the gradient method treats the problems of designing cascaded DOEs for both focusing the laser radiation and performing image classification in the framework of a single general approach. It is shown that the difference of the problem of optical classification from the problem of generating required intensity distributions consists only in the form of error functionals, the calculation of the derivatives of which is reduced to the same general formula. Using the proposed gradient method, we designed single and cascaded DOEs for optical classification of handwritten digits. The obtained results may find application in the development of diffractive neural networks and optical systems for laser beam focusing.