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

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. (C) 2019 Optical Society of America