提出一种设计自由曲面轮廓的方法以实现目标面特定区域照度均匀性为常数的目标, 该方法可应用于漫反射曲面间接照明系统。基于理想漫反射曲面和发光二极管朗伯特性, 推导了目标面照度分布函数的方程组。求解方程组得到曲面面型数据, 绕轴旋转得到漫反射自由曲面。根据目标面照明情况建立评价函数用于优化求解阵列间距。对系统用TracePro软件进行非序列光线追迹仿真, 仿真结果表明漫反射自由曲面间接照明目标面大小为50 mm圆形区域, 照明距离为200 mm, 均匀度达到91.5%, 效率为6.73%。对比间距优化的线性阵列、环形阵列和矩形阵列下的漫反射自由曲面间接照明与直射照明, 漫反射间接照明照度均匀性更高。仿真结果验证了方案的正确性和有效性。

A method is proposed to design a freeform surface profile, which can make the illumination uniformity of the target surface location be a constant and can be used in the diffuse reflection surface indirect illumination system. Based on the ideal diffuse reflection freeform surface and light emitting diode Lambertian characteristics, equations of target plane illuminance distribution function are derived. The surface profile data is obtained by solving the equations. The diffuse reflection freeform surface is obtained by rotating around the axis. According to the illumination of the target surface, the evaluation function is built to optimize the solution of the array spacing. The non-sequential ray tracing simulation of the system is carried out by using TracePro software. The simulation results show that the target surface size is 50 mm circular area, the illumination distance is 200 mm under the indirect illumination of diffuse reflection freeform surface, the uniformity is 91.5%, and the effectiveness is 6.73%. Indirect illumination and direct illumination at diffuse reflection freeform surface for space optimized linear array, circular array and rectangular array are compared. Illumination uniformity of diffuse reflection freeform surface indirect illumination is better than that of direct illumination. The simulation results verify the correctness and effectiveness of the scheme.