Inverse design method for generalized zero-étendue sources and two targets

We present an inverse method to compute freeform optical surfaces that transform a light distribution, parameterized by two source planes, into two separate target distributions. The surfaces can be reflectors or lenses, and control both the spatial and directional source and target coordinates of light rays. From energy conservation, we derive Jacobian equations for optical mappings, and the optical path length provides generating functions for the optical surfaces. A three-stage least-squares algorithm numerically solves the resulting equations. We present examples with complex source and target distributions.