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

The paper focused on the design problem of a refracting surface forming a prescribed irradiance distribution in the far field in the case of a plane incident beam. We give the formulation of this problem as a mass transfer problem (MTP) and obtain the cost function for the MTP. We propose effective design method of a refracting surface based on MTP. We give the example of calculating of the refractive surface which forms a chessboard pattern.