Multiscale approach and linear assignment problem in designing mirrors generating far-field irradiance distributions.

We propose a multiscale approach for designing mirrors generating prescribed irradiance distributions in the far field. Our design method is based on calculating a ray mapping from a Monge-Kantorovich mass transportation problem and on reducing this problem to a linear assignment problem (LAP). The proposed multiscale formulation of the LAP allows one to efficiently calculate freeform mirror surfaces defined on meshes with a size of up to at least 1000×1000. As an example requiring a mesh of this size, we design a mirror generating a grayscale image of A. Einstein on a zero background. The proposed multiscale approach is general and can be applied to a wide range of inverse problems of nonimaging optics.