与平面目标面相比，在曲面目标面产生均匀的照度分布时，LED阵列的设计更复杂。通过优化LED阵列排布，使其在复杂曲面的目标面上产生了均匀的照度分布。构建了反映照度均匀性的目标函数，目标函数以阵列中各LED的位置坐标为变量，利用模拟退火算法对阵列中各LED的位置进行优化，使目标函数获得最小值。为了验证算法的可行性，针对圆柱形目标面、抛物线形柱状面以及正弦形柱状面，优化设计了3种不同排布的LED阵列，优化后的LED阵列在相应目标面上的照度分布均匀性分别达到99.0%、99.3%和97.0%。分析了LED阵列中各LED的装配公差对目标面照度均匀性的影响，模拟结果表明：装配公差在0.2 mm以内，目标的均匀度下降不超过0.3%，说明这种设计方法具有一定的实用价值。

Compared with the plane target surface, it is more complex for designing light emitting diode (LED) array to produce a uniform illumination distribution on the curved surface. In this paper, the uniform illumination distribution in curved target surface is produced by optimizing the LED array arrangement. In the optimization, firstly, the objective function is constructed to reflect the uniformity of illumination distribution. The objective function takes the coordinates of each LED in the array as variables. Then, the location coordinates of each LED in the array is optimized by simulated annealing algorithm, so that the objective function is minimization. In order to verify the feasibility of the algorithm, we design the cylindrical curved surface, parabolic and sinusoidal curved surface as target surfaces. With the three different kinds of target surfaces, three different LED array arrangements are designed. The three arrays produce uniform illumination distribution on the corresponding target surfaces with the uniformity of 99.0%, 99.3% and 97.0%, respectively. The influence of assembly tolerance of LED arrays on the illumination uniformity of the target surface is also analyzed. The simulation results show that the decrease of the uniformity is no more than 0.3% when the assembly tolerance is within 0.2 mm. This indicates that the design method has good practical value.