Optimal mass transportation problem and freeform optics design – the identity of optimization scheme and the numerical solution method

Due to outstanding light shaping potential, freeform optical surfaces have been considered theoretically from centuries. Recently, they gained increased interest due to the availability of manufacturing technologies. Nevertheless, the design of freeform surfaces still becomes a challenge, associated with advanced mathematical concepts and significant computing power. In this work, a very interesting unification of theories is mentioned. It is shown how the problem of optimal redistribution of mass, analyzed in the 18th century, corresponds to the problem of optical beam shaping realized by freeform surface. Both issues are governed by the same partial differential equation. In the paper, a novel numerical algorithm for solving this partial differential equation is discussed. As an example, a design of freeform lens, capable of casting completely arbitrary shapes, is presented.