Overlapping-based optical freeform surface construction for extended lighting source.

The freeform optical system for an extended source was constructed by partially overlapping a few numbers of point-source freeform surfaces (PFSs) and extracting their contour. Each PFS redistributed the Lambertian emission of a point source into the prescribed light distribution or more frequently into a modified distribution. By adjusting the relative positions of the PFSs and the pattern of the modified light distribution, the optimized freeform surface could be obtained. As an example, an optical system with a height only four times the source radius is designed for achieving a uniform-illuminance distribution on the target. The optimized freeform surface was formed by two PFSs. The virtue-point-sources of the PFSs were located symmetrically on the extended source with a distance of a quarter of the source diameter from each other. Each PFS achieved an increasing-illuminance distribution. The illumination uniformity of this model can be improved by 55.4%, while the optical efficiency within the target area is maintained above 80%.