Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution
The problem of calculation of the light field eikonal defined on a certain surface from the condition of generating a prescribed irradiance distribution on another surface is formulated as a Monge-Kantorovich mass transportation problem. We show that the cost function in this mass transportation pro...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2018-08-01
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| Series: | Компьютерная оптика |
| Subjects: | |
| Online Access: | http://computeroptics.smr.ru/KO/PDF/KO42-4/420406.pdf |
| _version_ | 1818503170988441600 |
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| author | Albert Mingazov Dmitry Bykov Leonid Doskolovich Nikolay Lvovich Kazanskiy |
| author_facet | Albert Mingazov Dmitry Bykov Leonid Doskolovich Nikolay Lvovich Kazanskiy |
| author_sort | Albert Mingazov |
| collection | DOAJ |
| description | The problem of calculation of the light field eikonal defined on a certain surface from the condition of generating a prescribed irradiance distribution on another surface is formulated as a Monge-Kantorovich mass transportation problem. We show that the cost function in this mass transportation problem corresponds to the distance between a point on the initial surface (on which the eikonal function is defined) and a point on the target surface, where the prescribed irradiance distribution is to be generated. An analytical expression for the gradient of a “cost functional” describing the mass transportation problem is derived. It enables using gradient descent methods for the calculation of the eikonal function. |
| first_indexed | 2024-12-10T21:20:25Z |
| format | Article |
| id | doaj.art-9ed60de6615a457f8b758a77bab42c1d |
| institution | Directory Open Access Journal |
| issn | 0134-2452 2412-6179 |
| language | English |
| last_indexed | 2024-12-10T21:20:25Z |
| publishDate | 2018-08-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj.art-9ed60de6615a457f8b758a77bab42c1d2022-12-22T01:33:08ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792018-08-0142456857310.18287/2412-6179-2018-42-4-568-573Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distributionAlbert Mingazov0Dmitry Bykov1Leonid Doskolovich 2Nikolay Lvovich Kazanskiy3Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, Russia; IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, RussiaSamara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, Russia; IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, RussiaSamara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, Russia; IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, RussiaSamara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, Russia; IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, RussiaThe problem of calculation of the light field eikonal defined on a certain surface from the condition of generating a prescribed irradiance distribution on another surface is formulated as a Monge-Kantorovich mass transportation problem. We show that the cost function in this mass transportation problem corresponds to the distance between a point on the initial surface (on which the eikonal function is defined) and a point on the target surface, where the prescribed irradiance distribution is to be generated. An analytical expression for the gradient of a “cost functional” describing the mass transportation problem is derived. It enables using gradient descent methods for the calculation of the eikonal function.http://computeroptics.smr.ru/KO/PDF/KO42-4/420406.pdfgeometrical opticsnonimaging opticsinverse problemeikonal functionMonge-Kantorovich mass transportation problem |
| spellingShingle | Albert Mingazov Dmitry Bykov Leonid Doskolovich Nikolay Lvovich Kazanskiy Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution Компьютерная оптика geometrical optics nonimaging optics inverse problem eikonal function Monge-Kantorovich mass transportation problem |
| title | Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution |
| title_full | Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution |
| title_fullStr | Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution |
| title_full_unstemmed | Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution |
| title_short | Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution |
| title_sort | variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution |
| topic | geometrical optics nonimaging optics inverse problem eikonal function Monge-Kantorovich mass transportation problem |
| url | http://computeroptics.smr.ru/KO/PDF/KO42-4/420406.pdf |
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