Establishment and Solution for a Mathematical Model of Multiple Diffuse Reflection

The indirect illumination system with diffuse reflection light-emitting diode (LED) is widely applied in various fields that require high illumination uniformity. On the basis of the Lambertian characteristic of LEDs and the ideal diffuse surface, a design method that features a multiple diffuse reflectance freeform surface is proposed and its related mathematical model is established in this paper. A nonlinear algebraic equation is solved to redistribute the energy emitted by the LED to a uniformity illuminated scene. The outline of the diffuse surface is obtained by solving equations numerically. With the use of the ray tracing software TracePro, simulation results show that the effect is generally the best and the uniformity and efficiency are significantly improved compared with other methods when the proportion between the radius of the target surface and the distance between the LED light source and the target surface is 1:4.