Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution
Mingazov A.A., Bykov D.A., Doskolovich L.L., Kazanskiy N.L.

 

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

Abstract:
The problem of calculation of the light field eikonal defined on a certain surface from the condition of generating a prescribed irradiance distribution on another surface is formulated as a Monge-Kantorovich mass transportation problem. We show that the cost function in this mass transportation problem corresponds to the distance between a point on the initial surface (on which the eikonal function is defined) and a point on the target surface, where the prescribed irradiance distribution is to be generated. An analytical expression for the gradient of a “cost functional” describing the mass transportation problem is derived. It enables using gradient descent methods for the calculation of the eikonal function.

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

Citation:
Mingazov AA, Bykov DA, Doskolovich LL, Kazanskiy NL. Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution. Computer Optics 2018; 42(4): 568-573. DOI: 10.18287/2412-6179-2018-42-4-568-573.

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