The purpose of the secondary optical design for light emitting diodes (LED) illumination is to rearrange the direct output
of LED and then achieve the desired illumination. Usually a lens is applied to realize this function in an LED
illumination system, and a freeform lens can do better than the traditional spherical ones. The method in this paper can
be used to design a freeform lens in short time, just less than 10 seconds. And this freeform lens is constructed using the
numerical solutions of a set of first-order partial differential equations, which are deduced from the Snell's law according
to the conservation of energy. Using an LED as the source while immersing it in the lens, a uniform rectangle can be
gotten through single refraction, and with uniformity near to 90%. The rectangular illumination also has a relatively clear
cut-off line with little blur at the edge. This method can shorten the designing time and improve the performance of LED
illumination system. Furthermore, not only rectangle, but other illumination figures can be achieved by freeform lens
designed by this method, which can broaden the scope of freeform lens's usage.
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