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 derivative...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2023-10-01
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| Series: | Компьютерная оптика |
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| Online Access: | https://www.computeroptics.ru/eng/KO/Annot/KO47-5/470502e.html |
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| author | D.V. Soshnikov L.L. Doskolovich E.V. Byzov |
| author_facet | D.V. Soshnikov L.L. Doskolovich E.V. Byzov |
| author_sort | D.V. Soshnikov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e67b60d1a9f949a580ab11acb289d281 |
| institution | Kabale University |
| issn | 0134-2452 2412-6179 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj-art-e67b60d1a9f949a580ab11acb289d2812025-01-21T11:12:03ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792023-10-0147569170110.18287/2412-6179-CO-1314Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digitsD.V. Soshnikov0L.L. Doskolovich1E.V. Byzov2IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS; Samara National Research UniversityIPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS; Samara National Research UniversityIPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS; Samara National Research UniversityWe 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.https://www.computeroptics.ru/eng/KO/Annot/KO47-5/470502e.htmldiffractive optical elementphase functionscalar diffraction theorygradient methodimage classification |
| spellingShingle | D.V. Soshnikov L.L. Doskolovich E.V. Byzov Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits Компьютерная оптика diffractive optical element phase function scalar diffraction theory gradient method image classification |
| title | Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits |
| title_full | Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits |
| title_fullStr | Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits |
| title_full_unstemmed | Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits |
| title_short | Gradient method for designing cascaded DOEs and its application in the problem of classifying handwritten digits |
| title_sort | gradient method for designing cascaded does and its application in the problem of classifying handwritten digits |
| topic | diffractive optical element phase function scalar diffraction theory gradient method image classification |
| url | https://www.computeroptics.ru/eng/KO/Annot/KO47-5/470502e.html |
| work_keys_str_mv | AT dvsoshnikov gradientmethodfordesigningcascadeddoesanditsapplicationintheproblemofclassifyinghandwrittendigits AT lldoskolovich gradientmethodfordesigningcascadeddoesanditsapplicationintheproblemofclassifyinghandwrittendigits AT evbyzov gradientmethodfordesigningcascadeddoesanditsapplicationintheproblemofclassifyinghandwrittendigits |