基于微分方程数值解的自由曲面透镜的设计

Freeform surface lens design based on numerical solutions of differential equations

为满足目标面上均匀照明的需求,设计了一款自由曲面透镜。根据LED光源的发光特点,结合光学成像的特性,非成像光学原理和能量守恒定理,推导出实现光能量在目标面上均匀分布的自由曲面面形的微分方程,采用matlab的ode算法求出面形上的离散坐标点,对离散坐标点拟合后得到透镜模型,通过光学模拟仿真软件对透镜模型进行光线追迹。结果表明,配光角度为80°的透镜,透镜的口径与光源发光面宽度之比大于等于9时,目标面上的照度均匀性大于0.9,光能利用率约为85%。该设计方法可以快速精确地设计出所需的透镜,而且透镜结构紧凑,单颗就能实现均匀照明,有利于LED光源照明系统的小型化。

In order to meet the required uniform illumination on a target plane, it is necessary to design a freeform surface lens. According to the emitting characteristics of LED light source, combining with the characteristics of optical imaging, the principles of optical non-imaging and the law of conservation of energy, a set of differential equations of free surface shape is deduced to realize light energy uniform distribution the target plane. Using ode formulas of matlab to cal- culate the discrete points of the surface, the lens model is established by fitting the discrete points. The lens model is sim- ulated with ray-tracing software. The results show that the lens with 80% divergence angle can keep the uniformity above 0. 9 and light energy utilization rate about 85% while the ratio of the lens aperture to the width of the LED emitting sur- face is not less than 9. The design can obtain the required lens quickly and accurately, what＇s more, the structure of the lens is compact which is good for miniaturization of LED lighting system.