A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution

We consider an approach to the calculation of a refractive optical element generating a prescribed irradiance distribution in the far field for a plane incident beam based on a certain variational problem. We consider an explicit formulation of this problem in the form of the Monge-Kantorovich mass...

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Bibliographic Details
Published inKompʹûternaâ optika Vol. 48; no. 3; pp. 356 - 362
Main Authors Soshnikov, D.V., Mingazov, A.A., Doskolovich, L.L.
Format Journal Article
LanguageEnglish
Russian
Published Samara National Research University 01.06.2024
Subjects
geometric optics
linear programming
linear variational problem
monge-kantorovich problem
optical design
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Summary:We consider an approach to the calculation of a refractive optical element generating a prescribed irradiance distribution in the far field for a plane incident beam based on a certain variational problem. We consider an explicit formulation of this problem in the form of the Monge-Kantorovich mass transfer problem. We also demonstrate a connection between the mass transfer problem and the dual linear variational problem. A numerical solution of the linear variational problem is also considered. The direct solution of this type of problem presents a huge computational complexity. To overcome this difficulty we use the so-called multiscale approach based on constructing a chain of approximations that are solutions on refining grids.
ISSN:0134-2452
2412-6179
DOI:10.18287/2412-6179-CO-1379