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Supporting quadric method for collimated beams
A.A. Mingazov 1, L.L. Doskolovich 1,2, D.A. Bykov 1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

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DOI: 10.18287/2412-6179-CO-783

Pages: 29-37.

Full text of article: Russian language.

Abstract:
We consider the problem of calculating a refractive element with two surfaces, forming a flat front and a given distribution of illumination. The supporting quadrics method is formulated for calculating a given optical element and it is shown that this method coincides with the gradient method for some functional related to the problem of the Monge-Kantorovich mass transfer problem. This enables adaptive selection of the step in the supporting quadric method. At the end of the article a design example is given.

Keywords:
geometric optics, non-imaging optics, inverse problem, Monge-Kantorovich mass transfer problem.

Citation:
Mingazov AA, Doskolovich LL, Bykov DA. Supporting quadric method for collimated beams. Computer Optics 2021; 45(1): 29-37. DOI: 10.18287/2412-6179-CO-783.

Acknowledgements:
This work was supported by Ministry of Science and Higher Education of the Russian Federation (FSRC "Crystallography and Photonics" RAS) in part of parts of the numerical implementation of the calculation algorithm and Russian Foundation for Basic Research (18-29-03067, 18-07-00982) in part of of formulating the supporting quadric method and proving the coincidence with the gradient method for the corresponding functional.

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