Inverse freeform design of a parallel-to-two-target reflector system

We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target coordinates of light rays. To determine the shape and position of the reflectors, we derive generating functions and use Jacobian equations to find the optical mappings to the two targets. The model is solved numerically by a three-stage least-squares algorithm. A feasibility condition is derived, which ensures that the reflectors are not self-intersecting. Several examples validate this condition and demonstrate the algorithm's capability of realizing complex distributions.