Fast freeform optics design for high-contrast irradiance tailoring using optics-heuristic auction algorithm and rejection sampling

Freeform lens design for producing a high-contrast irradiance distribution from a zero-étendue source can be related to an optimal transport problem. This problem can be discretized into a linear assignment problem, but existing solutions are often computationally expensive and time-consuming. To accelerate the process, we introduce rejection sampling for faster discretization and a heuristic auction algorithm with an optimization step size adapted to optical features enabling the rapid solution of the linear assignment problem. Furthermore, freeform surface construction is automatically calculated to ensure surface continuity. The effectiveness of the proposed method is demonstrated through four examples designed to generate near-field and far-field distributions. These examples involve generating distributions in the shape of zero-background letters "BIT" and an Einstein portrait, from either parallel beams or point sources. In these examples, our method exhibits improved optical performance while significantly increasing the overall computational efficiency.