基于数学分析的高斯光束光斑半径测量方法

Measurement method of spot radius of Gaussian beam based on mathematical analysis

采用光阑法和光点法测量高斯光束光斑半径时,未对光斑图像进行增强处理,导致测量精准度较低,为了解决该问题,提出了基于数学分析的高斯光束光斑半径测量方法研究。根据高斯光束瞬时辐射照度示意图,求解电场振幅和辐照度时域平均值,从而得到高斯光束光强分布情况。依据分析结果采用数学分析法建立光斑几何模型,重构多维度数据,将重构数据块映射到一个新的坐标系之中,使数据差异性达到最大,并增强处理光斑图像。参考光斑图像增强结果获取光斑边缘特征中的最佳特征点,使用最小二乘法进行边缘拟合,以此来提高拟合精准度,最终完成对高斯光束光斑半径的测量。通过实验结果表明,该方法测量误差最大为230μm,最小为20μm,相比于其他两种测量方法来说测量结果较为精准,充分验证了该方法的可行性与优势性。

When using aperture method and spot method to measure the spot radius of Gaussian beam,the spot image is not enhanced,resulting in low measurement accuracy.In order to solve this problem,a method of measuring the spot radius of Gaussian beam based on mathematical analysis is proposed.According to the schematic diagram of instantaneous irradiance of Gaussian beam,the average values of electric field amplitude and irradiance in time domain are calculated,and the light intensity distribution of Gaussian beam is obtained.According to the analysis results,the geometric model of facula is established by mathematical analysis method,the multi-dimensional data is reconstructed,and the reconstructed data block is mapped into a new coordinate system to maximize the data difference and enhance the processing of facula image.In order to improve the fitting accuracy,the least square method is used to fit the edge.Finally,the measurement of the spot radius of Gaussian beam is completed.The experimental results show that the maximum measurement error of this method is 230μm and the minimum is 20μm.Compared with the other two methods,the measurement results are more accurate,which fully verifies the feasibility and advantages of this method.