光束质量稳健估计非线性拟合求解方法

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。

Robust estimation nonlinear fitting method for solving beam quality

Laser beam quality M2 factor inevitably exist two types errors in measurement process,random and non-random errors.To reduce the measurement error and improve measurement accuracy and stability,the impact of different errors and propose solutions were analyzed.For the random error,an improved method that using normal equations set of weighted fitting was proposed.While in the case of non-random error,no effective solutions were found for the hyperbolic fitting.As a result,the nonlinear hyperbolic fitting method based on robust estimation was proposed and conducted in-depth through theoretical study.The experiments prove that robust estimation method can overcome the impact caused by non-random error and make the estimate data approach to be optimal,robust estimation error is an order of magnitude lower than normal equations error.Therefore,robust estimation can effectively improve the measurement accuracy of M2 factor,and it has great application in evaluating laser beam quality.