Abstract

We consider the problem of calculating a refracting surface generating a prescribed irradiance distribution in the far field in the case of a plane incident beam. We demonstrate that this problem can be formulated as a mass transportation problem (MTP) and obtain the cost function for the MTP. It is shown that with a special choice of coordinates, the cost function becomes quadratic. The obtained mass transportation problem also describes the problem of calculating a mirror, which can be considered as a special case of the problem of calculating a refracting surface. We propose a method of calculating a refracting surface based on the reduction of the MTP to a linear assignment problem. This method is applied to the design of several optical elements generating prescribed intensity distributions. The simulation results demonstrate high performance of the proposed approach.

© 2019 Optical Society of America

Optimal mass transportation and linear assignment problems in the design of freeform refractive optical elements generating far-field irradiance distributions

Leonid L. Doskolovich, Dmitry A. Bykov, Albert A. Mingazov, and Evgeni A. Bezus
Opt. Express 27(9) 13083-13097 (2019)

Design and fabrication of freeform mirrors generating prescribed far-field irradiance distributions

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Linear assignment problem in the design of freeform refractive optical elements generating prescribed irradiance distributions

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Opt. Express 26(21) 27812-27825 (2018)

On the use of the supporting quadric method in the problem of designing double freeform surfaces for collimated beam shaping

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Opt. Express 28(15) 22642-22657 (2020)

Designing double freeform surfaces for collimated beam shaping with optimal mass transportation and linear assignment problems

Leonid L. Doskolovich, Dmitry A. Bykov, Evgeniy S. Andreev, Evgeni A. Bezus, and Vladimir Oliker
Opt. Express 26(19) 24602-24613 (2018)