Smooth Energy Mappings of Freeform Lens Design for Non-circular Distribution of Luminance

Energy mappings of edge rays are required in design of a freeform lens for LED illumination. The mappings dominate the outcome of the lens design and the final distribution of the LED light illumination. Smoothness of the mappings is critical to assure the edge-ray principle hold. Design of energy mappings with good smoothness for circular distribution of uniform luminance is known, but the design for non-circular distribution is not well discussed in the literature yet. In this paper, a design method of smooth energy mappings for rectangular distribution of uniform luminance is proposed. It will be demonstrated by the Monte Carlo ray tracing simulations that the proposed mappings can generate luminance distribution with a clear-cut horizon and a 15° slope.