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This article is cited in 5 scientific papers (total in 5 papers)
OPTO-IT
Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution
A. A. Mingazovab, D. A. Bykovab, L. L. Doskolovichab, N. L. Kazanskiiab a IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, Russia
b Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, 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.
Received: 27.07.2018 Accepted: 28.07.2018
Citation:
A. A. Mingazov, D. A. Bykov, L. L. Doskolovich, N. L. Kazanskii, “Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution”, Computer Optics, 42:4 (2018), 568–573
Linking options:
https://www.mathnet.ru/eng/co539 https://www.mathnet.ru/eng/co/v42/i4/p568
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