Tailoring freeform illumination optics in a double-pole coordinate system

We have developed a new method to design freeform illumination optics by introducing a double-pole coordinate system in ray mapping. This method establishes a much more accurate ray mapping by moving the two poles of the spherical coordinate system to the southernmost point of the sphere and overlapping them together. It can reduce surface error and improve illumination uniformity significantly. The residual surface error (RSE) of the freeform lens designed in the double-pole coordinate system is one magnitude smaller than that of the lens designed in the (θ; φ) coordinate system and is only 1/3 of that of the freeform surface designed in the (u; v) coordinate system.