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Computer Optics, 2022, Volume 46, Issue 3, Pages 353–365
DOI: https://doi.org/10.18287/2412-6179-CO-1055 (Mi co1023) 		 
DIFFRACTIVE OPTICS, OPTICAL TECHNOLOGIES

Support quadric method in non-imaging optics problems that can be reformulated as a mass transfer problem

A. A. Mingazova, L. L. Doskolovichab, D. A. Bykovab, E. V. Byzova

a Image Processing Systems Institute of the RAS - Branch of the FSRC "Crystallography and Photonics" RAS, Samara, Russia, Samara
b Samara National Research University
Full-text PDF (1117 kB)
DOI: https://doi.org/10.18287/2412-6179-CO-1055
Abstract: The article deals with problems of generating desired illumination patterns, formulated in a special way. More precisely, we consider problems that can be reformulated as a Monge–Kantorovich mass transfer problem with some cost function. For all problems of this type, we uniformly formulate the support quadric method and show that it coincides with the gradient method for finding the maximum of a certain concave function.
Keywords: non-imaging optics, geometric optics, inverse problem, Monge-Kantorovich problem, support quadric method
Funding agency Grant number
Russian Science Foundation 18-19-00326
The work was funded by the Ministry of Science and Higher Education of the Russian Federation under a government project of the FSRC “Crystallography and Photonics” RAS (numerical implementation of the calculation algorithm) and the Russian Science Foundation under grant #18-19-00326 (proof of the coincidence with the gradient method for the corresponding functional).
Received: 29.09.2021
Accepted: 26.11.2021
Document Type: Article
Language: Russian
Citation: A. A. Mingazov, L. L. Doskolovich, D. A. Bykov, E. V. Byzov, “Support quadric method in non-imaging optics problems that can be reformulated as a mass transfer problem”, Computer Optics, 46:3 (2022), 353–365
Citation in format AMSBIB
\Bibitem{MinDosByk22}
\by A.~A.~Mingazov, L.~L.~Doskolovich, D.~A.~Bykov, E.~V.~Byzov
\paper Support quadric method in non-imaging optics problems that can be reformulated as a mass transfer problem
\jour Computer Optics
\yr 2022
\vol 46
\issue 3
\pages 353--365
\mathnet{http://mi.mathnet.ru/co1023}
\crossref{https://doi.org/10.18287/2412-6179-CO-1055}
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