A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution
We consider an approach to the calculation of a refractive optical element generating a prescribed irradiance distribution in the far field for a plane incident beam based on a certain variational problem. We consider an explicit formulation of this problem in the form of the Monge-Kantorovich mass...
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| Language: | English |
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Samara National Research University
2024-06-01
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| Series: | Компьютерная оптика |
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| Online Access: | https://www.computeroptics.ru/eng/KO/Annot/KO48-3/480305e.html |
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| author | D.V. Soshnikov A.A. Mingazov L.L. Doskolovich |
| author_facet | D.V. Soshnikov A.A. Mingazov L.L. Doskolovich |
| author_sort | D.V. Soshnikov |
| collection | DOAJ |
| description | We consider an approach to the calculation of a refractive optical element generating a prescribed irradiance distribution in the far field for a plane incident beam based on a certain variational problem. We consider an explicit formulation of this problem in the form of the Monge-Kantorovich mass transfer problem. We also demonstrate a connection between the mass transfer problem and the dual linear variational problem. A numerical solution of the linear variational problem is also considered. The direct solution of this type of problem presents a huge computational complexity. To overcome this difficulty we use the so-called multiscale approach based on constructing a chain of approximations that are solutions on refining grids. |
| format | Article |
| id | doaj-art-df184777938d4ab186ecb9f0b20495d3 |
| institution | Kabale University |
| issn | 0134-2452 2412-6179 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj-art-df184777938d4ab186ecb9f0b20495d32025-02-05T12:12:36ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792024-06-0148335636210.18287/2412-6179-CO-1379A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distributionD.V. Soshnikov0A.A. Mingazov1L.L. Doskolovich2Image Processing Systems Institute, NRC "Kurchatov Institute"; Samara National Research UniversityImage Processing Systems Institute, NRC "Kurchatov Institute"; Samara National Research UniversityImage Processing Systems Institute, NRC "Kurchatov Institute"; Samara National Research UniversityWe consider an approach to the calculation of a refractive optical element generating a prescribed irradiance distribution in the far field for a plane incident beam based on a certain variational problem. We consider an explicit formulation of this problem in the form of the Monge-Kantorovich mass transfer problem. We also demonstrate a connection between the mass transfer problem and the dual linear variational problem. A numerical solution of the linear variational problem is also considered. The direct solution of this type of problem presents a huge computational complexity. To overcome this difficulty we use the so-called multiscale approach based on constructing a chain of approximations that are solutions on refining grids.https://www.computeroptics.ru/eng/KO/Annot/KO48-3/480305e.htmloptical designgeometric opticsmonge-kantorovich problemlinear variational problemlinear programming |
| spellingShingle | D.V. Soshnikov A.A. Mingazov L.L. Doskolovich A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution Компьютерная оптика optical design geometric optics monge-kantorovich problem linear variational problem linear programming |
| title | A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution |
| title_full | A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution |
| title_fullStr | A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution |
| title_full_unstemmed | A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution |
| title_short | A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution |
| title_sort | multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far field illumination distribution |
| topic | optical design geometric optics monge-kantorovich problem linear variational problem linear programming |
| url | https://www.computeroptics.ru/eng/KO/Annot/KO48-3/480305e.html |
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