Models using optimal mass transport for inverse design in nonimaging optical systems

The key problem in computational illumination optics is to find the shapes of optical surfaces given a light source and desired target distribution. Our mathematical model is based on the principles of geometrical optics, formulated in terms of the optical map connecting source and target domain, and energy conservation. This leads to a fully nonlinear partial differential equation of generalized Monge-Ampère type subject to the transport boundary condition. We show the derivation of this equation for several model problems using optimal mass transport theory. The numerical solution method is a two-stage procedure. In the first stage it computes the optical map. In the second stage it constructs the shapes of the optical surfaces from the optical map. Both stages are solved using a least-squares method. The computation is an iterative process with fast convergence.