Abstract

We propose a multiscale approach for designing mirrors generating prescribed irradiance distributions in the far field. Our design method is based on calculating a ray mapping from a Monge–Kantorovich mass transportation problem and on reducing this problem to a linear assignment problem (LAP). The proposed multiscale formulation of the LAP allows one to efficiently calculate freeform mirror surfaces defined on meshes with a size of up to at least $1000 \times 1000$. As an example requiring a mesh of this size, we design a mirror generating a grayscale image of A. Einstein on a zero background. The proposed multiscale approach is general and can be applied to a wide range of inverse problems of nonimaging optics.

© 2020 Optical Society of America

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

Leonid L. Doskolovich, Dmitry A. Bykov, Evgeniy S. Andreev, Egor V. Byzov, Mikhail A. Moiseev, Evgeni A. Bezus, and Nikolay L. Kazanskiy
Appl. Opt. 59(16) 5006-5012 (2020)

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)

Optimal mass transportation problem in the design of freeform optical elements generating far-field irradiance distributions for plane incident beam

Dmitry A. Bykov, Leonid L. Doskolovich, Albert A. Mingazov, and Evgeni A. Bezus
Appl. Opt. 58(33) 9131-9140 (2019)

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

Dmitry A. Bykov, Leonid L. Doskolovich, Albert A. Mingazov, Evgeni A. Bezus, and Nikolay L. Kazanskiy
Opt. Express 26(21) 27812-27825 (2018)

Variational approach to calculation of light field eikonal function for illuminating a prescribed region

Leonid L. Doskolovich, Albert A. Mingazov, Dmitry A. Bykov, Evgeniy S. Andreev, and Evgeni A. Bezus
Opt. Express 25(22) 26378-26392 (2017)