Abstract
LED has many advantages, such as high luminous efficiency, small size, low-voltage DC drive, etc. so it has been widely
used in many lighting situations. But in certain circumstances, such as uniform illumination requirements in the
micro-display projection system, because LED has an analogous Lambertian radiation distribution resulting in its
non-uniform light intensity, the secondary optical design should be done to achieve the specific illumination
requirements. In this paper, a freeform surface lens is designed to obtain a square area with uniform illumination on the
target plane with LED: Firstly, based on the law of conservation of energy, the source-target light energy mapping
relationship between the incident plane and the target plane is achieved. Secondly, according to the vector form of Snell’s
law, the differential equations of the freeform surface are established. Finally, in order to solve the problem of surface
discontinuity during the progress of designing the lens, the process of solving the differential equations is described in
detail and the integrability condition is introduced to modify and adjust the points’ position of freeform surface, thus
reducing the errors accumulating during the progress of numerical calculation and improving the continuity of the
freeform surface. By simulation, the continuity of the freeform surface and the uniform illumination improve a lot, so it
is validated that the results meet the requirements and the design method using integrability condition can improve the
continuity of the surface and lighting uniformity of the lighting system.
