Geometrical optics and optimal transport

被引：7

作者：

Rubinstein, Jacob ^{[1
]}

Wolansky, Gershon ^{[1
]}

机构：

[1] Technion, Dept Math, IL-32000 Haifa, Israel

来源：

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION | 2017年 / 34卷 / 10期

基金：

以色列科学基金会;

关键词：

MASS-TRANSFER PROBLEM; DISPERSIVE WAVES; PHASE RETRIEVAL; INTENSITY; PRINCIPLE;

D O I：

10.1364/JOSAA.34.001817

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

The Fermat principle is generalized to a system of rays. It is shown that all the ray mappings that are compatible with two given intensities of a monochromatic wave, measured at two planes, are stationary points of a canonical functional, which is the weighted average of the actions of all the rays. It is further shown that there exist at least two stationary points for this functional, implying that in the geometrical optics regime the phase from intensity problem has inherently more than one solution. The caustic structures of all the possible ray mappings are analyzed. A number of simulations illustrate the theoretical considerations. (C) 2017 Optical Society of America

引用

页码：1817 / 1823

页数：7

共 17 条

[1] Minimizing flows for the Monge-Kantorovich problem [J].

Angenent, S ;

Haker, S ;

Tannenbaum, A .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 35 (01) :61-97

[2]

[Anonymous], 2003, TOPICS OPTIMAL TRANS

[3]

[Anonymous], 1995, OPTICAL COHERENCE QU

[4]

Benamou JD, 2000, NUMER MATH, V84, P375, DOI 10.1007/s002119900117

[5] POLAR FACTORIZATION AND MONOTONE REARRANGEMENT OF VECTOR-VALUED FUNCTIONS [J].

BRENIER, Y .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (04) :375-417

[6] CONNECTIONS BETWEEN OPTIMAL TRANSPORT, COMBINATORIAL OPTIMIZATION AND HYDRODYNAMICS [J].

Brenier, Yann .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2015, 49 (06) :1593-1605

[7] COHERENCE AND THE SPATIAL-DISTRIBUTION OF INTENSITY [J].

GORI, F ;

SANTARSIERO, M ;

GUATTARI, G .

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1993, 10 (04) :673-679

[8] Phase retrieval with the transport-of-intensity equation .2. Orthogonal series solution for nonuniform illumination [J].

Gureyev, TE ;

Nugent, KA .

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1996, 13 (08) :1670-1682

[9] AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM [J].

Haber, Eldad ;

Rehman, Tauseef ;

Tannenbaum, Allen .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (01) :197-211

[10] On design of free-form refractive beam shapers, sensitivity to figure error, and convexity of lenses [J].

Oliker, Vladimir .

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 2008, 25 (12) :3067-3076

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