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Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits
D.V. Soshnikov 1,2, L.L. Doskolovich 1,2, E.V. Byzov 1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151;
2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 1320 kB

DOI: 10.18287/2412-6179-CO-1314

Pages: 691-701.

Full text of article: Russian language.

Abstract:
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.

Keywords:
diffractive optical element, phase function, scalar diffraction theory, gradient method, image classification.

Citation:
Soshnikov DV, Doskolovich LL, Byzov EV. Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits. Computer Optics 2023; 47(5): 691-701. DOI: 10.18287/2412-6179-CO-1314.

Acknowledgements:
This work was performed within the State assignment of Federal Scientific Research Center "Crystallography and Photonics" of Russian Academy of Sciences in part of developing the gradient method for calculating cascaded DOEs, and was supported by the Ministry of Science and Higher Education of the Russian Federation (State assignment for research to Samara University (laboratory "Photonics for Smart Home and Smart City", project FSSS-2021-0016) in part of designing DOEs for classifying handwritten digits.

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