A Freeform Lens System Design and Simulation in the Polar Coordinate

Abstract

In the field of illumination engineering, freeform technology is playing a more and more important role. Several methods have been reported in recent papers. The paper introduce a design method to generate an ellipse spot in the polar coordinate using the polar grids based on flux transportation mapping. In this method, the source is a point and the point is divided along the azimuth angle and zenith angle in the polar coordinate system. Then we divided the flux target in the polar coordinate, the grids of the target are achieved by the mapping between the source and the target. Based on the mapping and energy conservation, we can derive a set of the first-order PDE according to Snell’s law. We can acquire a points cloud after solving the PDE numerically, then we will construct a smooth freeform using Rhino. Finally, we will test the freeform using Light Tools. With this method, we can design a lens with the light utilization efficiency over 0.8. Keywords: LED; Freeform; Mapping; Polar coordinate.