Tailored freeform optical surfaces

Freeform optical surfaces embedded in three-dimensional space, without any symmetry, are tailored so as to solve the archetypal problem of illumination design: redistribute the radiation of a given small light source onto a given reference surface, thus achieving a desired irradiance distribution on that surface. The shape of the optical surface is found by solving a set of partial nonlinear differential equations. For most cases, a few topologically distinct solutions exist, given suitable boundary conditions.