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

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.