Design and fabrication of a freeform mirror generating a uniform illuminance distribution in a rectangular region

The design of a freeform mirror generating a uniform illuminance distribution in a rectangular region with angular dimensions of $30^\circ\times15^\circ$ is presented. The design method is based on the formulation of the problem of calculating the "ray-mapping" as a Monge-Kantorovich mass transportation problem and its subsequent reducing to a linear assignment problem. We describe a mirror fabrication process with the use of milling technology and present results of experimental measurements of the light distribution generated by the mirror. The experimental results are in good agreement with the results of numerical simulations and thus confirm the manufacturability of mirrors designed by the method proposed.