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Computer Optics, 2018, Volume 42, Issue 4, Pages 574–587
DOI: https://doi.org/10.18287/2412-6179-2018-42-4-574-587 (Mi co540) 		 
This article is cited in 19 scientific papers (total in 19 papers)

OPTO-IT

The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem

N. L. Kazanskiyab, S. I. Kharitonovb, I. N. Kozlovab, M. A. Moiseeva

a IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, Russia
b Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, Russia
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DOI: https://doi.org/10.18287/2412-6179-2018-42-4-574-587
Abstract: We discuss the use of variational principles for solving the phase problem in optics. In this paper, we consider the connection between four fundamental problems: the phase problem in optics, the inverse problem of focusing coherent radiation, the Monge – Kantorovich optimal mass transport problem, and the variational methods for solving the equation of a modified Monge – Ampere equation. It is shown that the solution of the phase problem in optics within the framework of the asymptotic approach is closely related to the solution of the problem of optimal mass transport with a nonquadratic cost function.
Keywords: optimal mass transport, phase problem in optics, Monge–Ampere equation.
Funding agency Grant number
Russian Science Foundation 18-19-00326
Russian Academy of Sciences - Federal Agency for Scientific Organizations 007-ÃÇ/×3363/26
Russian Foundation for Basic Research 17-47-630164 ð_à
16-29-09528 îôè_ì
This work was supported by the Russian Science Foundation (Project No. 18-19-00326) (calculation of the variation in the Monge–Kantorovich mass transportation problem, Section 2), by the RF Ministry of Science and Higher Education within the State assignment to the FSRC «Crystallography and Photonics» RAS (calculation of the Laplacian and derivation of the Monge–Ampere equation, Appendices A and B – Agreement No 007-ÃÇ/×3363/26), and by Russian Foundation for Basic Research (Projects Nos. 17-47-630164, 16-29-09528) (derivation of the basic equations describing the phase problem, Section 1).
Received: 27.06.2018
Accepted: 28.06.2018
Document Type: Article
Language: Russian
Citation: N. L. Kazanskiy, S. I. Kharitonov, I. N. Kozlova, M. A. Moiseev, “The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem”, Computer Optics, 42:4 (2018), 574–587
Citation in format AMSBIB
\Bibitem{KazKhaKoz18}
\by N.~L.~Kazanskiy, S.~I.~Kharitonov, I.~N.~Kozlova, M.~A.~Moiseev
\paper The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem
\jour Computer Optics
\yr 2018
\vol 42
\issue 4
\pages 574--587
\mathnet{http://mi.mathnet.ru/co540}
\crossref{https://doi.org/10.18287/2412-6179-2018-42-4-574-587}
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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