为了探究不同发光半角对圆形LED阵列辐照特性的影响, 利用单颗LED芯片的照度公式推导出圆形阵列的照度公式、光斑半径和发散角公式。使用Tracepro软件对不同发光半角的圆形LED阵列仿真并利用MATLAB进行函数数值拟合。结果表明: 在有效光斑区域下, 随着单颗LED发光半角的增大, 圆形阵列的中心照度值逐渐降低, 降低的速率近似线性增长; 光斑半径和发散角逐渐增大, 变化率先增大后减小。辐照均匀度随着单颗LED发光半角的增大而增大, 而后保持稳定, 单颗LED发光半角为60°时, 圆形阵列辐照均匀度最好, 且相同发光半角时接收面面积越小辐照均匀度越高。这些结论对实现圆形LED阵列照明设计提供了定量的参考和理论依据。

In order to investigate the influence of different luminous half angles on the radiation characteristics of circular LED array, the formula of illuminance, radius of spot and divergence angle of circular array are derived by using the illuminance formula of single LED chip. The Tracepro software is used to simulate the circular LED arrays with different luminous half angles, and MATLAB is used to fit the function values. The results show that, under the effective light spot area, with the increase of the single LED luminescence half angle, the central illuminance value of the circular array decreases gradually. The rate of the decrease is approximately linear, the radius of the spot and the divergence angle increase gradually, and the change first increases and then decreases. The radiation uniformity increases with the increase of the single LED luminescence half angle, and then keeps stable. The radiation uniformity of the circular array is the best when the single LED luminescent half angle is 60°, and the smaller the area of the receiving surface is, the higher the uniformity is. These conclusions provide a quantitative reference and theoretical basis for realizing the circular LED array lighting design.