Mathematical modeling analysis of freeform reflector for rectangular uniform illumination with surface source

Since the general reflectors cannot control the surface source effectively and there is unavoidable chromatic dispersion in lens, we proposed a freeform reflector design method. In our scheme, the surface source was located at the top of the reflector, whose luminous surface back faced the target plane. The surface source was divided to micro surfaces by finite element method, which were treated as point sources. According to the rectangular illumination distribution, the energy relationship between surface source and target plane was established. Meanwhile, the mathematical model of the reflector could be directly computed based on the theory of the differential geometry and Snell's law, then the numerical solution of freeform reflector could be calculated by Matlab software without feedback optimizing. By example,the numerical solution of the reflector of the table lamp was obtained by using associated software and the performance of the reflector was simulated by optical software. It is revealed that the illumination uniformity on target plane is above 0.8, while the energy efficiency can reach about 0.9.