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

Abstract

We consider the problem of calculating a refractive surface generating a prescribed irradiance distribution in the far field in the case of a point light source. We show that this problem can be formulated as a mass transportation problem with a non-quadratic cost function. A method for calculating the refractive surface is proposed, which is based on reducing the problem of calculating an integrable ray mapping to finding a solution to a linear assignment problem. We discuss the application of the developed method for the design of optical elements with two working refractive surfaces. The method was applied to the calculation of refractive optical elements generating uniform irradiance distributions in a square and in a region in the form of the letters AB on a zero background. The results of the simulations of the designed optical elements demonstrate high performance of the proposed method.