有振幅调制和相位畸变光束通过硬边光阑的M2因子

光束传输M^2因子是表征激光束的有用参量。利用矩形函数的复高斯函数的近似展开方法，给出部分相干光通过硬边光阑后强度二阶矩的近似计算公式，由此可得到部分相干光通过硬边光阑后的推广M^2因子。以有振幅调制和相位畸变光束为例，推导出相应的推广M^2因子的解析表达式，通过数值计算对提出的近似算法的计算精度进行了分析。研究结果表明，使用该近似方法计算得到的推广M^2因子的计算误差小于1％，且通过该方法可直接得到相应的近似解析计算公式，从而使计算得以简化，并有效地提高了计算效率。

Generalized M2 Factor of Laser Beams with Amplitude Modulations and Phase Distortion Passing Through Hard-Edge Apertures

The beam propagation M2 factor is a useful parameter for characterizing laser beam. By using the treatment that the rectangular function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, approximate formulas for the second-order moments of partially coherent beam after it passes hard -edge diaphragm are given. The generalized M2 factor of partially coherent beam after it passes hard -edge diaphragm can be obtained. A laser beam with amplitude modulation and phase distortion is taken as a typical example of partially coherent beams. The analytical expression for the generalized M2 factor is derived. The calculation precision of our method is analyzed by numerical calculations. It can been seen from the study that by making use of the approximate calculation method proposed, the calculation error for the generalized M2 factor is less than 1% and the approximate analytic expressions can be obtained immediately. Consequently, the calculation can be simplified and the calculation efficiency can be improved efficiently.