Designation of lenses with a single freeform surface for multiple point sources.

Optical lenses with a freeform surface can be designed for diverse illumination profiles with uniformity. However, most of the previous studies formulate the problem for a single point source, and the lens topology has freeform top and spherical bottom surfaces. In this study, the formulation is extended for multiple point sources, and a flat surface is included in the lens bottom topology for ease of prototyping and manufacturing. The extended formulation for multiple point sources requires only a freeform surface to design. The formulation of overdetermined coupling equations is solved by applying the weighted least-square method. The weightings are correlated with the emitting intensities of sources in terms of an inverse gamma function. The weighting scheme gives a parameter space for designation of illumination profile fit and uniformity. The adequacy of the extended formulation is demonstrated by simulation. Examples of circular and rectangular illumination for single and multiple point sources are studied. The simulation results show that unbalanced luminance distribution can be induced by an offset source and collimated by a lens, which is designated by taking the offset into account. For multiple point sources, illumination profile fit and uniformity are designated in trade off based on the parameter design.