为了验证柯林斯公式的一种近似计算方法，对光波通过方形孔径光阑及一薄透镜时的衍射图像进行理论计算，并与实验结果进行比较。研究结果表明，理论计算与实验结果一致。利用该方法对透镜的焦距进行了测量，将测量结果与传统方法测得的焦距进行比较，两者误差不到1%。

The concept of the beam propagation factor M2 is extended for chromatic laser beams. The definition of the beam propagation factor can be generalized with the weighted effective wavelength. Using the new definition of factor M2, the propagation of chromatic beams can be analyzed by the beam propagation factor M2 as same as that of monochromatic beams. A simple method to measure the chromatic beam factor M2 is demonstrated. The chromatic factor M2 is found invariable while the laser beam propagates through the dispersion-free ABCD system.

利用Collins公式,推导出厄米-拉盖尔-高斯(HLG)光束通过近轴ABCD光学系统的解析传输公式,并用来研究通过自由空间和薄透镜的传输特性.结果表明,除模指数m,n之外,对HLG光束新引入的α参数,它影响光强分布和对称性;HLG光束在传输中保持形状不变;HLG光束的焦移与模指数m,n和α参数无关,这意味着m,n和α不同的HLG光束聚焦在同一位置.并给出了HLG光束的M2因子.