Supporting quadric method for collimated beams

We consider the problem of calculating a refractive element with two surfaces, forming a flat front and a given distribution of illumination. The supporting quadrics method is formulated for calculating a given optical element and it is shown that this method coincides with the gradient method for some functional related to the problem of the Monge-Kantorovich mass transfer problem. This enables adaptive selection of the step in the supporting quadric method. At the end of the article a design example is given.