基于NURBS曲线的LED扩展光源双自由曲面匀光透镜优化设计

Optimization design of double freeform surface uniform lenses for LED extended light sources based on NURBS curve

摘要: 基于边缘光线理论，提出一种针对LED扩展光源的双自由曲面匀光透镜优化设计方法，旨在提升照明系统的匀光效果。通过斯涅尔折射定律和能量守恒定律计算自由曲面初始面型，利用NURBS（non-uniform rational B-splines）曲线拟合并参数化自由曲面，优化过程以模拟照明与期望照明的相对标准差（relative standard deviation, RSD）以及能量利用率为指标。仿真结果表明：优化后的透镜高度与光源直径比为2.32∶1，实现了RSD<0.113，能量利用率高达98%，目标面照度均匀度高达95.9%，有效提升了照明均匀性和光学系统紧凑性。

Abstract: Based on the edge ray theory, an optimization method for the design of double freeform surface uniform lenses for LED extended light sources was proposed. The initial surface shape was calculated by Snell's law of refraction and energy conservation law. The NURBS (non-uniform rational B-splines) curve was used to fit and parameterize the free surface. The RSD (relative standard deviation) and energy efficiency of simulated illumination and desired illumination were taken as the indexes in the optimization process. The simulation results show that the ratio of lens height to light source diameter is 2.32∶1, RSD<0.113, energy efficiency up to 98%, uniformity of target surface illumination up to 95.9%, illumination uniformity and optical system compactness are effectively improved.