A Symmetry-Preserving Neural Operator for Finite-Source Reflector Design

Freeform reflectors are mirrors shaped to transform some light source into some prescribed light pattern at some target, for example in road lighting. For a perfectly parallel source beam and a single reflector, this problem can be formulated to be exactly equal to optimal transport with a quadratic cost; real sources, however, emit light from many different points in many different directions, blurring the target pattern. While there are techniques to design such freeform reflectors under the assumption of more realistic sources—such as differentiable ray tracing—these techniques can be relatively slow, even on a powerful GPU. We therefore present a preliminary result on a neural operator which takes the source and target densities and directly predicts a corresponding reflector in about 20 ms. It builds in the symmetries of the problem, reduces to a quadratic-cost optimal-transport solver for a parallel source, and is trained in under an hour with a differentiable ray-tracing loss. On typical problems it removes about 90% of the error of the optimal-transport solution alone, though wide sources with sharp-edged targets remain challenging.