激光束廓形高斯拟合的稳健估计

Robust Estimation in Laser Beam Profile Gaussian Fitting

在对激光束廓形进行高斯拟合时一般采用最小二乘法,但是采集数据的噪声会严重影响拟合优度。将稳健估计中的M估计应用到最小二乘算法中,经过算法的迭代,赋予每个观测点不同的权值,正常点的权值为1,异常点的权值为0,其他观测点的权值根据异常程度在0到1之间取值。提高最小二乘算法的稳健能力,从而克服异常点对高斯拟合的拟合优度的影响。实验结果表明:采用稳健估计的方法,可以克服噪声对高斯拟合的拟合优度的影响,与一般高斯拟合相比拟合优度提高了0.1107。稳健估计可有效地提高高斯拟合的拟合优度,在激光束的分析方面有着重要的应用价值。

The least squares algorithm was generally used when gaussian fitting for laser beam profile,but the noise of the data can seriously affect the goodness of fit. In this paper, M estimation will be applied to the least square algo-rithm. After iteration algorithm,each image data different right value is given,the right value of normal point is 1,ab-normal point is 0, and the right value of the other observation datas are according to its abnormal degree taking 0 to 1. The robust ability of the least square algorithmhis can be improved, which can overcome the influence of abnormal point data on the goodness of fit of guassian fitting. The experimental results show that the influence of abnormal point data on the goodness of fit of guassian fitting can be overcomed by using robust estimation method and being compared with the general gaussian fitting the goodness of fit is improved by 0.1107. Robust estimation can effectively improve the goodness of fit of gaussian fitting and has important application value in the analysis of the laser beam.