Design of double freeform-surface lens by distributing the deviation angle for light-emitting diode uniform illumination

In the conventional freeform lens design, people usually assume the inner surface as hemispherical and only the outer surface is designed. An important design degree of freedom on the inner surface is abandoned. In this study, by distributing the deviation angle, we proposed a method to design the inner and outer surfaces of freeform lens simultaneously. Detailed design method was presented and several examples were designed to verify the method. It was found when the distribution ratio is 0.75, the simulated illumination is the most uniform and its Fresnel light loss is the rather smaller than that conventional freeform lens. By overall consideration of the illumination uniformity and the Fresnel loss, the distribution ratio of 0.75 is the optimal extra condition and corresponds to best performance.