Using spherical aberrations of a singlet lens to get a uniform LED illumination

In order to get a simple LED illumination system with a short length, the LED needs a large irradiant angle (2ω = 90°) and the lens needs a large aperture. This would conduce a severe non-uniformity on the illuminated area and a very low F-number. So it is rather difficult to design a singlet lens for LED illumination system with a better uniformity in certain area because of the non-uniform irradiation of the LED and the contradiction between the focal length and the aperture. For an on-axial point source, the spherical aberrations in different apertures can change the propagating direction of the rays; therefore it is possible to get a uniform illumination with the help of spherical aberrations. Light density function on the illuminated plan is deduced, and the merit function for uniform illumination in certain area is defined in this paper. By using the optical design software ZEMAX EE, the search of the optimal value for the given focal length is done. The computer simulation results show that by producing spherical aberrations correctly a better uniformity illumination can be obtained on the illuminated area in certain distance successfully.