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Light Beams Refractor

In this note, our goal is to find a refractor lens that refracts all prescribed light rays, in different directions, to the origin. Similar problems have been studied recently; see [2], [3] and [4]. The main difference between this problem and the near field refractor problem, which was studied in [4], is that now we are given the initial positions and directions of light beams and we are looking for a surface which refracts all of them to the origin. On the contrary, in the near field refractor problem we had a point which was emitting light with different illumination densities in different directions and our goal was to design a lens to illuminate a surface with a prescribed illumination density.