利用LED照度公式推导方形LED阵列的光斑半径和发散角公式, 建立了研究方形LED阵列光斑发散特性的数值计算方法.通过拟合得到方形LED阵列的光斑半径和发散角随目标距离、m值及阵列边长变化的幂函数公式.结果表明, 幂函数拟合方法与数值计算结果吻合, 平均相对误差小于1%.该方法弥补了数值计算方法不能对方形LED阵列光斑发散特性解析研究的缺陷.

Using LED illumination formula, the light spot radius formula and the divergence angle formula of LED square array are deduced. Using fitting method, the power function formula of the spot radius and divergence angle with target distance and m value and array length are obtained.. The results show that the formulas can be quite good agreement with the numerical calculation results which the average relative error is less than 1%. It makes up for the defects that numerical method can′t analytical study on the light spot divergence characteristics of LED square array.