Further study on radial distortion model for photographic objective

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.