Previous secondary optical designs, however, have approximated the LED light distribution curve as a Lambertian
distribution which is unable to suit all custom sources. In this paper, a freeform surface lens is utilized to redistribute the
light rays emitted from a LED device with a random light distribution curve in order to effect a prescribed illumination
distribution on the target area. A mapping relationship is also established between the spatial light intensity distribution of
a light source and the rectangular uniform illumination used for road-going cases. A set of first-order partial differential
equations is deduced according to Snell’s Law and the Law of Energy Conservation. A numerical solution is obtained
through MATLAB software, and freeform surface data of the secondary optical lens is recorded to aid in modeling the
freeform surface lens. Simultaneously, an analysis and comparison of different differential algorithm and mapping
methods is carried out in order to solve the differential equations and designate the most superior mapping relationship.
With the help of 3D software, a 3D model of the freeform surface lens is established, and Light Tools software is employed
to simulate the effects of illumination. In this model, the light distribution curve of the LED source is described as an
eighth-order polynomial. According to the simulated results, a 10m height, 40m×40m road uniform illumination is realized
by the secondary optical design. The energy efficiency and uniformity of this illumination is 99.7% and 91.52%
respectively. This method of secondary optical design is easy to operate and can be applied to any other lighting systems
with random LED sources.