为了获得LED扩展光源大角度均匀照明, 采用双自由曲面, 设计了大角度紧凑型透镜。利用角度扩大函数使内自由曲面对光线发散 , 根据矢量Snell定律确定点源透镜的外自由曲面。采用交叠法优化双自由曲面扩展光源透镜模型, 通过BreedPSO算法进一步优化。对于h/d=2.5的紧凑型系统, 均匀度和光效分别为88.12%和84.54%, 照明均匀度明显提高。照明系统横向安装位移误差在［0, 0.3mm］内, 均匀度及光效分别在85%及84%以上, 纵向安装位移误差在［-0.04mm, 0.05mm］, 均匀度及光效均在82%以上。

A compact double freeform-surface lens with large view angle is designed to make a uniform illumination for LED extended source with double free-form surfaces. The angle magnification function is proposed to make rays diverge from the inner surface. The outer freeform-surface of the lens for a dot light source is achieved according to Snell’s law in vector form. The overlapping method is used to optimize the double freeform lens with extended source. The lens is further optimized by BreedPSO algorithm. For a compact system with h/d=2.5, the uniformity and luminous efficiency are 88.12% and 84.54% respectively, and the uniformity is significantly improved. The uniformity and luminous efficiency are more than 85% and 84% respectively when the displacement error in the horizontal direction is within ［-0.04mm, 0.05mm］. The uniformity and luminous efficiency are both over 82% when the displacement error in the longitudinal direction is within ［-0.04mm, 0.05mm］.