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Formulation of the inverse problem of calculating the optical surface for an illuminating beam with a plane wavefront as the Monge–Kantorovich problem

L.L. Doskolovich1,2, A.A. Mingazov1, D.A. Bykov1,2, E.A. Bezus1,2

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

 PDF, 807 kB

DOI: 10.18287/2412-6179-2019-43-5-705-713

Pages: 705-713.

Full text of article: Russian language.

Abstract:
A problem of calculating a refractive surface that forms a required irradiance distribution in the far field in the case of a plane illuminating beam is considered. We show that this problem can be formulated as a mass transportation problem. The specific form of the cost function for this problem is obtained. It is shown that with a certain choice of coordinates, the cost function becomes quadratic. The resulting mass transportation problem also describes a problem of calculating a mirror, which can be considered as a special case of the problem of calculating a refractive surface.

Keywords:
geometrical optics, optical design, nonimaging optics, illumination design, Monge-Kantorovich problem, mass transportation problem.

Citation:
Doskolovich LL, Mingazov AA, Bykov DA, Bezus EA. Formulation of the inverse problem of calculating the optical surface for an illuminating beam with a plane wavefront as the Monge-Kantorovich problem. Computer Optics 2019; 43(5): 705-713. DOI: 10.18287/2412-6179-2019-43-5-705-713.

Acknowledgements:
This work was supported by the Russian Foundation for Basic Research (RFBR) under grants ## 18-07-00982, 18-29-03067, 18-07-00514 (formulation of the problem of calculating refractive or reflective optical surface as an optimal mass transportation problem) and the RF Ministry of Science and Higher Education within the State assignment to FSRC “Crystallography and Photonics” RAS under agreement 007-ГЗ/Ч3363/26 (formulation of the weak solution of the problem).

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