Variational approach to eikonal function computation
Doskolovich L.L., Mingazov A.A., Bykov D.A., Andreev E.S.

 

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

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Abstract:
The problem of calculating the eikonal function from the condition of focusing into a prescribed region is formulated as a variational problem and as a Monge-Kantorovich mass transportation problem. It is found that the cost function in the Monge-Kantorovich problem corresponds to the distance between a point of the original region (in which the eikonal function is defined) and a point of the focal region. The formalism proposed in this work makes it possible to reduce the calculation of the eikonal function to a linear programming problem. In this case, the calculation of the “ray mapping” corresponding to the eikonal function is reduced to the solution of a linear assignment problem. The proposed variational approaches are illustrated by examples of calculation of optical elements for focusing a circular beam into a rectangular region.

Keywords:
geometrical optics, eikonal function, variational problem, Monge-Kantorovich mass transportation problem.

Citation:
Doskolovich LL, Mingazov AA, Bykov DA, Andreev ES. Variational approach to eikonal function computation. Computer Optics 2018; 42(4): 557-567. DOI: 10.18287/2412-6179-2018-42-4-557-567.

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