We present a method for the design of a single freeform reflector that converts the light distribution of a point source to a desired light distribution in the far field. Using the geometrical-optics law of reflection and requiring energy conservation, this optical design problem can be represented by a generalized Monge–Ampère equation for the shape of the reflector with transport boundary condition. We use a generalized least-squares algorithm that can handle a logarithmic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate reflector surfaces for a number of complicated target distributions.
- Geometrical optics
- Optimal mass transport
- Logarithmic cost function
- Generalized Monge-Ampère equation
- Least-squares method
- Stereographic coordinates
- Generalized Monge–Ampère equation