Open AccessLinear assignment problem in the design of freeform refractive optical elements generating prescribed irradiance distributions
Author(s) -
Dmitry A. Bykov,
Leonid L. Doskolovich,
Albert A. Mingazov,
Evgeni A. Bezus,
Nikolay L. Kazanskiy
Publication year - 2018
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.26.027812
Subject(s) - eikonal equation , paraxial approximation , irradiance , ray tracing (physics) , optics , refraction , iterative method , geometrical optics , nonimaging optics , surface (topology) , eikonal approximation , distribution (mathematics) , function (biology) , beam (structure) , physics , mathematics , mathematical optimization , mathematical analysis , geometry , evolutionary biology , biology
We consider the problem of calculating the eikonal function defined on a certain curved surface from the condition of generating a prescribed irradiance distribution on a target surface. We show that the calculation of the "ray mapping" corresponding to the eikonal function is reduced to the solution of a linear assignment problem (LAP). We propose an iterative algorithm for calculating a refractive optical surface from the condition of generating a prescribed near-field irradiance distribution in a non-paraxial case. The algorithm is based on sequential calculation of eikonal functions defined on curved surfaces using the LAP-based approach. The proposed algorithm is applied to the calculation of refractive optical elements generating uniform irradiance distributions in a rectangular region and in a region in the form of the letters "IPSI" in the case of a circular incident beam. The presented ray-tracing simulations of the designed optical elements demonstrate high efficiency of the proposed iterative algorithm.