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Measurement of optical fiber geometry parameters by gray distribution fitting with Gaussian function
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摘要:
光纤的几何参数影响着光纤的光学传输和机械性能等，是衡量光纤质量的重要指标。近场光分布法是国标GB 15972.20-2008中推荐的几何参数测量方法。该方法在对光纤纤芯的测量中需对光纤通光照明，以区分纤芯和包层的边界。通光的纤芯端面是一个边缘并不清晰的发光亮斑，因而无法准确判断纤芯与包层的真实边缘。本文分析了光纤内光传播模场的分布，理论上光纤模场电磁矢量的解满足贝塞尔函数，但在近似情况下也可以用高斯函数代表光纤模场分布。因此本文利用高斯函数拟合光纤纤芯端面灰度分布，进而由拟合后的高斯函数得到纤芯与包层的真实边缘。本方法是对国标GB15972.20-2008的测量方法的进一步完善。实验测量结果表明，当光纤的切割效果不佳或成像质量较差时，模场灰度分布的高斯函数拟合法仍能保证测量的重复精度和测量数据的稳定性。
Abstract:The geometry parameters of optical fiber affect the optical transmission and mechanical properties, which are the important indexes to measure the quality of fiber. Near-field light distribution method is recommended in GB15972.20-2008 for the measurement of geometry parameters. In order to distinguish the boundary between fiber core and cladding, the method needs to illuminate the fiber. The end face of the fiber core is a bright spot with unclear edge, so the true edge of the core and cladding cannot be accurately judged. In this paper, the distribution of mode field in optical fiber is analyzed. Theoretically, the solution of electromagnetic vector of mode field satisfies Bessel function, but Gaussian function can also be used under approximate conditions. Therefore, Gaussian function is used to fit the distribution of the fiber core in this paper, and the real edge of the fiber core and cladding can be obtained from the Gaussian function after fitting. This method is a further improvement on the measurement method of GB15972.20-2008. The experimental results show that when the cutting effect of the fiber is not good or the imaging quality is poor, the Gaussian function method fitting with mode distribution can still ensure the repeatability of the measurement and the stability of the measured data.
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Key words:
- optical fiber geometry parameters /
- mode distribution /
- Gaussian function /
- edge detect
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Overview: The geometry parameters of optical fiber affect the optical transmission and mechanical properties of optical fiber. The near-field optical distribution method is a measurement method recommended in GB15972.20-2008. The main parameters to be measured include the diameter of cladding and core, the roundness of cladding and core, and the concentricity of cladding and core. In order to distinguish the boundary between fiber core and cladding, the fiber core should be illuminated during the measurement of the geometry parameters. Actually, the end face of fiber core is a bright spot with unclear edges, so it is impossible to accurately judge the true edges of fiber core, which will bring errors to the measurement of geometry parameters of fiber core. In this paper, the distribution of optical mode field in fiber was analyzed. Theoretically, the solution of electromagnetic vector of optical fiber mode field satisfies Bessel function, but Gaussian function can also be used to approximately describe the distribution of optical fiber mode field.
Therefore, Gaussian function was used to fit the gray distribution of fiber core, and the true edge of fiber core was obtained from the Gaussian function. Gaussian function fitting method mainly includes the following three steps. The first step is to obtain the image of the end face of the optical fiber by CCD and conduct appropriate image preprocessing. The image contrast is stronger and more conducive to subsequent gray data extraction by image preprocessing. The second step is to find the best Gaussian function by the fitting with gray data of the image. 3D fitting with all the gray data of fiber core end face can effectively filter out error data and reflect the true mode field distribution of fiber core. The third step is to find the true edge of the fiber core through the best-fitting Gaussian function, and fit the edge data with elliptical curves. Finally, the geometry parameters of the fiber core will be obtained. For the measurement of cladding geometry parameters, because of the high contrast of the edge, Canny operator can be directly used to extract the edge of the cladding. The cladding geometry parameters with high precision can be obtained by elliptical curves fitting.
The real edge of optical fiber core can be accurately obtained by Gaussian function fitting, and the error points in the image can be effectively filtered through fitting, so as to improve the measurement accuracy of optical fiber geometry parameters. Taking fiber core data as an example, the data of diameter and roundness measured by the standard instrument are 8.420 μm and 0.670%, respectively. When cutting effect of fiber end face or lighting condition is poor, the instrument data change to 9.044 μm and 1.457%, while the data measured in this paper are 8.425 μm and 0.480%, respectively.
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图 8 非正常条件下光纤灰度的高斯函数拟合图
Figure 8. 2D Gaussian function fitting rendering of abnormal fiber
表 1 正常条件下FGM-5几何参数测试仪的测量结果
Table 1. Data measured by FGM-5 under normal conditions
实验组数 包层直径/μm 包层不圆度/% 纤芯直径/μm 纤芯不圆度/% 芯—包同心度/μm 1 125.073 0.116 8.421 0.865 0.241 2 125.094 0.117 8.409 0.335 0.236 3 125.120 0.118 8.431 0.666 0.246 4 125.101 0.098 8.449 0.616 0.247 5 125.093 0.102 8.388 0.868 0.221 平均值 125.096 0.110 8.420 0.670 0.238 最大偏差 0.024 0.012 0.032 0.335 0.017 
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表 2 正常条件的高斯函数拟合法测量结果
Table 2. Data measured by Gaussian function fitting under normal conditions
实验组数 包层直径/μm 包层不圆度/% 纤芯直径/μm 纤芯不圆度/% 芯—包同心度/μm 1 125.081 0.108 8.379 0.116 0.226 2 125.101 0.114 8.368 0.423 0.247 3 125.125 0.111 8.413 0.102 0.238 4 125.108 0.122 8.413 0.096 0.244 5 125.097 0.114 8.412 0.269 0.237 平均值 125.102 0.114 8.397 0.201 0.238 最大偏差 0.023 0.008 0.029 0.222 0.013
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表 3 非正常成像条件下FGM-5仪的测量数据
Table 3. Data measured by FGM-5 under abnormal conditions
实验组数 包层直径/μm 包层不圆度/% 纤芯直径/μm 纤芯不圆度/% 芯—包同心度/μm 1 124.832 0.077 9.092 1.529 0.288 2 124.83 0.094 9.037 1.148 0.302 3 124.869 0.089 9.037 1.754 0.302 4 124.862 0.095 9.045 0.837 0.283 5 124.837 0.091 9.01 2.016 0.278 平均值 124.846 0.089 9.044 1.457 0.291 最大偏差 0.023 0.012 0.048 0.62 0.013
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表 4 非正常成像条件下高斯函数拟合法的测量结果
Table 4. Data measured by Gaussian function fitting under abnormal conditions
实验组数 包层直径/μm 包层不圆度/% 纤芯直径/μm 纤芯不圆度/% 芯—包同心度/μm 1 124.874 0.084 8.427 0.570 0.305 2 124.857 0.072 8.410 0.295 0.300 3 124.897 0.069 8.428 0.380 0.314 4 124.885 0.078 8.416 0.736 0.310 5 124.862 0.055 8.442 0.421 0.320 平均值 124.875 0.072 8.425 0.480 0.310 最大偏差 0.022 0.016 0.017 0.256 0.011
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