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A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution
D.A. Soshnikov 1,2, A.A. Mingazov 1, L.L. Doskolovich 1,2

1 Image Processing Systems Institute, NRC "Kurchatov Institute",
443001, Samara, Russia, Molodogvardeyskaya 151;
2 Samara National Research University,
443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 898 kB

DOI: 10.18287/2412-6179-CO-1379

Pages: 356-362.

Full text of article: Russian language.

Abstract:
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.

Keywords:
optical design, geometric optics, Monge-Kantorovich problem, linear variational problem, linear programming.

Citation:
Soshnikov DA, Mingazov AA, Doskolovich LL. A multiscale approach to a linear programming problem for calculating a refractive optical element forming a given far-field illumination distribution. Computer Optics 2024; 48(3): 356-362. DOI: 10.18287/2412-6179-CO-1379.

Acknowledgements:
This work was performed within the State assignment for scientific research to Samara University (project FSSS-2024-0014) in part of the development and implementation of the multiscale approach and the State assignment of the NRC "Kurchatov Institute" in part of establishing the relationship between the linear functional and the cost functional.

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