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激光光束质量M2因子在测量过程中,数据不可避免的存在随机和非随机两类误差,为了减小测量过程中受到误差的影响以提高系统的测量精度和稳定性,针对不同误差影响进行分析并提出相应的解决方法。在随机误差情况下,对传统双曲线拟合的正规方程组解法进行了改进并提出了加权拟合的正规方程组解法;而对于非随机误差情况,双曲线拟合尚未发现有效的解决方案,为此提出了基于稳健估计的双曲线拟合方法,并对此进行了深入的理论研究。实验表明,在数据存在非随机的情况下采用稳健估计的方法,可以克服非随机误差对参数估值产生的影响,使其拟合优度接近最优值,稳健估计的误差要比正规方程组的误差低一个数量级。因此,稳健估计可有效地提高测量M2因子的测量精度,对评价光束质量方面有着重要的应用价值。
M2 factor of laser beam quality There are two kinds of random and non-random error inevitably in the data during the measurement. In order to reduce the influence of error in the measurement process to improve the measurement accuracy and stability of the system, we analyze and analyze the influence of different errors Put forward the corresponding solution. In the case of random error, the normal equations solution of traditional hyperbola fitting is improved and the normal equations solution of weighted fitting is proposed. For non-random errors, hyperbola fitting has not found an effective solution, For this reason, a hyperbolic fitting method based on robust estimation is proposed, and an in-depth theoretical study is carried out. Experiments show that using the robust estimation method in the presence of non-random data can overcome the influence of non-random error on the parameter estimation and make the goodness of fit close to the optimal value. The error of robust estimation is better than that of normal equations The error is an order of magnitude lower. Therefore, the robust estimation can effectively improve the measurement accuracy of the M2 factor measurement, which has an important application value in evaluating the beam quality.