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The two reflector design problem for forming a flat wavefront from a point source as an optimal mass transfer problem

A.A. Mingazov1, L.L. Doskolovich1,2, D.A. Bykov1,2, N.L. Kazanskiy1,2

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

 PDF, 776 kB

DOI: 10.18287/2412-6179-2019-43-6-968-975

Pages: 968-975.

Full text of article: Russian language.

Abstract:
The article deals with a problem of calculating two reflecting surfaces that form a given irradiance distribution with a flat wavefront, provided that a point source of light is used. A notion of a weak solution for the said problem is formulated and the equivalence of this problem and the Monge–Kantorovich mass transfer is proven.

Keywords:
geometric optics, optical design, nonimaging optics, inverse problem, Monge-Kantorovich mass transfer problem, optimal mass transportation.

Citation:
Mingazov AA, Doskolovich LL, Bykov DA, Kazanskiy NL. The two reflector design problem for forming a flat wavefront from a point source as an optimal mass transfer problem. Computer Optics 2019; 43(6): 968-975. DOI: 10.18287/2412-6179-2019-43-6-968-975.

Acknowledgements:
This work was supported by Russian Science Foundation (RSF) under grants 18-19-00326 (formulation of the problem of calculating of two reflector as an optimal mass transportation problem) and by Ministry of Science and Higher Education within the State assignment FSRC “Crystallography and Photonics” RAS under agreement 007-ГЗ/Ч3363/26 (formulation of the weak solution of the problem).

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