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

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.

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

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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