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

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

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,...

Full description

Bibliographic Details
Main Authors: Nikolay Kazanskiy, Sergey Kharitonov, Irina Kozlova, Mikhail Moiseev
Format: Article
Language:English
Published: Samara National Research University 2018-08-01
Series:Компьютерная оптика
Subjects:
optimal mass transport
phase problem in optics
Monge–Ampere equation
Online Access:http://computeroptics.smr.ru/KO/PDF/KO42-4/420407.pdf
id doaj-f1bce3faf8524be1882264bc2fabe008
record_format Article
spelling doaj-f1bce3faf8524be1882264bc2fabe0082020-11-24T22:20:30ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792018-08-0142457458710.18287/2412-6179-2018-42-4-574-587The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problemNikolay Kazanskiy0Sergey Kharitonov1Irina Kozlova 2Mikhail Moiseev 3IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, Russia; Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, RussiaSamara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, RussiaSamara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, RussiaIPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, RussiaWe 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.http://computeroptics.smr.ru/KO/PDF/KO42-4/420407.pdfoptimal mass transportphase problem in opticsMonge–Ampere equation
collection DOAJ
language English
format Article
sources DOAJ
author Nikolay Kazanskiy
Sergey Kharitonov
Irina Kozlova
Mikhail Moiseev
spellingShingle Nikolay Kazanskiy
Sergey Kharitonov
Irina Kozlova
Mikhail Moiseev
The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem
Компьютерная оптика
optimal mass transport
phase problem in optics
Monge–Ampere equation
author_facet Nikolay Kazanskiy
Sergey Kharitonov
Irina Kozlova
Mikhail Moiseev
author_sort Nikolay Kazanskiy
title The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem
title_short The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem
title_full The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem
title_fullStr The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem
title_full_unstemmed The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem
title_sort connection between the phase problem in optics, focusing of radiation, and the monge–kantorovich problem
publisher Samara National Research University
series Компьютерная оптика
issn 0134-2452
2412-6179
publishDate 2018-08-01
description 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.
topic optimal mass transport
phase problem in optics
Monge–Ampere equation
url http://computeroptics.smr.ru/KO/PDF/KO42-4/420407.pdf
work_keys_str_mv AT nikolaykazanskiy theconnectionbetweenthephaseprobleminopticsfocusingofradiationandthemongekantorovichproblem
AT sergeykharitonov theconnectionbetweenthephaseprobleminopticsfocusingofradiationandthemongekantorovichproblem
AT irinakozlova theconnectionbetweenthephaseprobleminopticsfocusingofradiationandthemongekantorovichproblem
AT mikhailmoiseev theconnectionbetweenthephaseprobleminopticsfocusingofradiationandthemongekantorovichproblem
AT nikolaykazanskiy connectionbetweenthephaseprobleminopticsfocusingofradiationandthemongekantorovichproblem
AT sergeykharitonov connectionbetweenthephaseprobleminopticsfocusingofradiationandthemongekantorovichproblem
AT irinakozlova connectionbetweenthephaseprobleminopticsfocusingofradiationandthemongekantorovichproblem
AT mikhailmoiseev connectionbetweenthephaseprobleminopticsfocusingofradiationandthemongekantorovichproblem
_version_ 1725774856876720128

Similar Items