Supporting quadric method for collimated beams
We consider the problem of calculating a refractive element with two surfaces, forming a flat front and a given distribution of illumination. The supporting quadrics method is formulated for calculating a given optical element and it is shown that this method coincides with the gradient method for s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Samara National Research University
2021-02-01
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| Series: | Компьютерная оптика |
| Subjects: | |
| Online Access: | http://computeroptics.ru/KO/PDF/KO45-1/450104.pdf |
| _version_ | 1831641110656581632 |
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| author | A.A. Mingazov L.L. Doskolovich D.A. Bykov |
| author_facet | A.A. Mingazov L.L. Doskolovich D.A. Bykov |
| author_sort | A.A. Mingazov |
| collection | DOAJ |
| description | We consider the problem of calculating a refractive element with two surfaces, forming a flat front and a given distribution of illumination. The supporting quadrics method is formulated for calculating a given optical element and it is shown that this method coincides with the gradient method for some functional related to the problem of the Monge-Kantorovich mass transfer problem. This enables adaptive selection of the step in the supporting quadric method. At the end of the article a design example is given. |
| first_indexed | 2024-12-19T12:19:32Z |
| format | Article |
| id | doaj.art-1ffc1c5596dd4aa392ffad4af20fb54f |
| institution | Directory Open Access Journal |
| issn | 0134-2452 2412-6179 |
| language | English |
| last_indexed | 2024-12-19T12:19:32Z |
| publishDate | 2021-02-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj.art-1ffc1c5596dd4aa392ffad4af20fb54f2022-12-21T20:21:51ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792021-02-01451293710.18287/2412-6179-CO-783Supporting quadric method for collimated beamsA.A. Mingazov 0L.L. Doskolovich1D.A. Bykov2IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS, 443001, Samara, Russia, Molodogvardeyskaya 151IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS, 443001, Samara, Russia, Molodogvardeyskaya 151; Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS, 443001, Samara, Russia, Molodogvardeyskaya 151; Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34We consider the problem of calculating a refractive element with two surfaces, forming a flat front and a given distribution of illumination. The supporting quadrics method is formulated for calculating a given optical element and it is shown that this method coincides with the gradient method for some functional related to the problem of the Monge-Kantorovich mass transfer problem. This enables adaptive selection of the step in the supporting quadric method. At the end of the article a design example is given.http://computeroptics.ru/KO/PDF/KO45-1/450104.pdfgeometric opticsnon-imaging opticsinverse problemmonge-kantorovich mass transfer problem |
| spellingShingle | A.A. Mingazov L.L. Doskolovich D.A. Bykov Supporting quadric method for collimated beams Компьютерная оптика geometric optics non-imaging optics inverse problem monge-kantorovich mass transfer problem |
| title | Supporting quadric method for collimated beams |
| title_full | Supporting quadric method for collimated beams |
| title_fullStr | Supporting quadric method for collimated beams |
| title_full_unstemmed | Supporting quadric method for collimated beams |
| title_short | Supporting quadric method for collimated beams |
| title_sort | supporting quadric method for collimated beams |
| topic | geometric optics non-imaging optics inverse problem monge-kantorovich mass transfer problem |
| url | http://computeroptics.ru/KO/PDF/KO45-1/450104.pdf |
| work_keys_str_mv | AT aamingazov supportingquadricmethodforcollimatedbeams AT lldoskolovich supportingquadricmethodforcollimatedbeams AT dabykov supportingquadricmethodforcollimatedbeams |