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本文提出了一种实现目标面特定区域照度均匀性为常数的方法设计自由曲面轮廓，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 LED（Light Emitting Diode）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 Trace Pro 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 50mm 圆形区域，照明距离为 200mm，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方式照明情况，漫反射间接照明照度均匀性更高。以上仿真结果验证了方案的正确性和有效性。
In this paper, a method of designing a free-form surface profile with a uniform illuminance in a specific area of the target surface is proposed, which can be applied to the indirect lighting system of diffuse reflectance surface. Based on the ideal diffuse surface and the Lambert property of LED (Light Emitting Diode), the equations of illumination distribution of target surface are deduced. Solve the equation set to get the surface data, and rotate the axis to get the diffuse free-form surface. The evaluation function is established according to the illumination of the target surface to optimize the array spacing. The trace Pro software was used to simulate the non-sequential ray tracing system. The simulation results show that the diffuse free-form surface indirectly illuminates a circular area with the target area of 50mm, the illumination distance is 200mm, the uniformity is 91.5% and the efficiency is 6.73%. Compared with indirect illumination and direct illumination illumination of diffusely reflecting free-form surface under linear array, circular array and rectangular array, diffuse reflectance indirect illumination illumination uniformity is higher. The above simulation results verify the correctness and effectiveness of the scheme.