利用微分方程数值解构造自由曲面反光器  

Using numerical solutions of differential equations to form free reflector

作　　者：丁毅[1] 顾培夫[1] 陆巍[1] 郑臻荣[1] 

机构地区：[1]浙江大学现代光学仪器国家重点实验室,浙江杭州310027

出　　处：《浙江大学学报（工学版）》2007年第9期1516-1518,共3页Journal of Zhejiang University：Engineering Science

摘　　要：为在特定平面上得到均匀照明,构造了一种自由曲面反光器.根据已知的光源发光特性和所需实现的照明面上的光分布,基于理论模型,结合立体坐标系和能量守恒定理,推导得到微分方程组.采用差分法求解微分方程组得到自由曲面反光器的面形数据.对得到的曲面进行了光线追迹模拟,光源分别采用均匀发光的点光源和面光源.模拟得到的照明面为旋转对称的圆形,两种光源的照明均匀性均接近90%,面光源的均匀性更高.通过单一自由曲面反射器实现均匀照明,不依靠方棒、复眼透镜等器件,有助于实现整个照明系统的小型化.A free reflector was designed to get uniform illumination on a specific planar. According to the source characteristics and the desired illumination on the target plane, a set of differential equations were detruded based on the existing theoretical model by using the solid coordinate system and the energy conservation theory. Then the equation sets were solved by difference method to get the surface data of the free reflector. The illumination condition using the free reflector was ray-tracing simulated with point source and extended source, respectively. Simulation showed that the lightening plane was an symmetrical circle, and that the illumination uniformity of the two sources were near to 90%, and the extended source had higher uniformity. The illumination system is simple and compact and uniform illumination can be realized just through a single free reflector without light tunnel or any fly eyes.

关 键 词：自由曲面 均匀照明 微分方程组 差分方法 

分 类 号：TN94[电子电信—信号与信息处理]