正规方程组求解激光束质量M^2因子方法的研究

Research on Solving Laser Beam Quality Factor M^2 with Normal Equations

为提高双曲线拟合精度和速度,克服M2因子测量过程中受到随机误差的影响,采用正规方程组拟合双曲线的方法,给出了三角分解法求解正规方程组的快速数值算法。实验结果表明,采用正规方程组求解光束质量M2因子与奇异值分解法所得结果是一致的,且该方法速度快、精度高,运算速度可提高一个数量级。

To improve the precision and speed of fitting hyperbola, and to overcome the influence of random errors between the measurement of laser beam quality factor M2, the method for fitting hyperbola with NE （ Normal Equations） is adopted. The fast numerical algorithm of solving tion is presented. It is shown by experiments that the M^2 factors the normal equations with triangular decomposiobtained by the normal equations method is consistent with that solved with SVD （Singular Value Decomposition） method, but the first one is faster and more accurate, the operation speed can be improved by one order of magnitude.