We propose two energy-mapping methods to produce a uniformly illuminated area for a nontilted (straight) and a tilted light source toward a target plane. These energy-mapping methods define the positions of the desired points (the destination points of the refracted rays of a light source) on an illuminated area. The surface of the lenses can then be formed through the position of the desired points. Based on these design methods, two freeform lenses, (i) a symmetric lens and (ii) an asymmetric lens, were designed to provide uniformity within a rectangular illumination footprint for a nontilted and a tilted light source, respectively. This method can produce uniformity for a tilted light source within 0 deg to 45 deg toward the normal vector on the target plane. Two freeform lenses for 0 deg and 20 deg tilted toward a target plane were designed. The illumination footprint of the symmetric and asymmetric freeform lenses was evaluated through ray-tracing simulations and experiments. Both models produce over 90% uniformity within an illuminated area.
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