Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping
We develop a method for calculating the eikonal function (or the phase function) of the light field, ensuring the formation of a prescribed irradiance distribution in the geometrical optics approximation. In the proposed method, the problem being solved is formulated in a semi-discrete form as a pro...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2022-04-01
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| Series: | Компьютерная оптика |
| Subjects: | |
| Online Access: | https://computeroptics.ru/eng/KO/Annot/KO46-2/460201e.html |
| _version_ | 1797826167292559360 |
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| author | L.L. Doskolovich A.A. Mingazov E.V. Byzov D.A. Bykov E.A. Bezus |
| author_facet | L.L. Doskolovich A.A. Mingazov E.V. Byzov D.A. Bykov E.A. Bezus |
| author_sort | L.L. Doskolovich |
| collection | DOAJ |
| description | We develop a method for calculating the eikonal function (or the phase function) of the light field, ensuring the formation of a prescribed irradiance distribution in the geometrical optics approximation. In the proposed method, the problem being solved is formulated in a semi-discrete form as a problem of the maximization of a concave function. For finding the solution to the latter problem, a gradient method is used, with analytical expressions obtained for the gradient. Using the developed method, we calculate an eikonal function that provides the formation of a “discontinuous” hexagram-shaped irradiance distribution. We demonstrate that the use of the solution obtained in the framework of the geometrical optics as an initial approximation in iterative Fourier transform algorithms allows one to calculate diffractive optical elements having a quasi-regular microrelief. |
| first_indexed | 2024-03-13T11:03:41Z |
| format | Article |
| id | doaj.art-b169b4154b6f42cebb024575df306391 |
| institution | Directory Open Access Journal |
| issn | 0134-2452 2412-6179 |
| language | English |
| last_indexed | 2024-03-13T11:03:41Z |
| publishDate | 2022-04-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj.art-b169b4154b6f42cebb024575df3063912023-05-16T12:26:28ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792022-04-0146217318310.18287/2412-6179-CO-1029Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shapingL.L. Doskolovich0A.A. Mingazov1E.V. Byzov 2D.A. Bykov3E.A. Bezus4IPSI 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 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 develop a method for calculating the eikonal function (or the phase function) of the light field, ensuring the formation of a prescribed irradiance distribution in the geometrical optics approximation. In the proposed method, the problem being solved is formulated in a semi-discrete form as a problem of the maximization of a concave function. For finding the solution to the latter problem, a gradient method is used, with analytical expressions obtained for the gradient. Using the developed method, we calculate an eikonal function that provides the formation of a “discontinuous” hexagram-shaped irradiance distribution. We demonstrate that the use of the solution obtained in the framework of the geometrical optics as an initial approximation in iterative Fourier transform algorithms allows one to calculate diffractive optical elements having a quasi-regular microrelief.https://computeroptics.ru/eng/KO/Annot/KO46-2/460201e.htmlgeometrical opticsinverse problemeikonaldiffractive optical elementfresnel approximationgerchberg-saxton algorithm |
| spellingShingle | L.L. Doskolovich A.A. Mingazov E.V. Byzov D.A. Bykov E.A. Bezus Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping Компьютерная оптика geometrical optics inverse problem eikonal diffractive optical element fresnel approximation gerchberg-saxton algorithm |
| title | Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping |
| title_full | Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping |
| title_fullStr | Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping |
| title_full_unstemmed | Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping |
| title_short | Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping |
| title_sort | method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping |
| topic | geometrical optics inverse problem eikonal diffractive optical element fresnel approximation gerchberg-saxton algorithm |
| url | https://computeroptics.ru/eng/KO/Annot/KO46-2/460201e.html |
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