基于径向半径偶次幂级数的相对畸变表达式在相机校准中被广泛地采用。对于一个具体镜头,它的物理精确性却没有可靠的理论做依据。基于自变量(径向半径和视场角)不同项数和幂次的组合多项式作为相对畸变的拟合函数,以Zemax软件平台上的一组已知镜头的栅格畸变结果为已知数据,借助于Matlab的最优化工具箱进行数据拟合。结果表明,包含径向半径2、3次幂的表达式在精度上更有益; 基于视场角幂次的展开式可以提供更为精确的畸变描述; 多项和高阶的拟合函数反而不利于提供一个精准的畸变表达。

The expression of relative distortion based on even-power series of a radial radius is commonly used in camera calibration. But there is not any reliable theoretical source for the physical accuracy of this model of a substantial lens. Based on a numerical result of grid distortion by Zemax and the optimization toolbox of Matlab, data fitting with combined multinomial of different number of terms and powers of independent variable (radial radius or field) is done. The results show that the expression of relative distortion including terms of the two and three powers of the radial distortion is beneficial in terms of accuracy, and the expression by powers of field angle may give a much better fitting, but the fitting function with multi-term and high-order is not of advantage to provide a more accurate expansion.