光腔衰荡法数据截取对时间常数测量精度的影响分析

张金玉; 金尚忠; 张彪; 吴磊; 俞兵; 袁良; 黎高平

doi:10.5768/JAO202344.0103006

光腔衰荡法数据截取对时间常数测量精度的影响分析

doi: 10.5768/JAO202344.0103006

张金玉^1,,
金尚忠¹,
张彪²,
吴磊²,
俞兵^{2, 3},
袁良^{2, 3},
黎高平²

1.
中国计量大学光学与电子科技学院，浙江杭州 310018
2.
西安应用光学研究所，陕西西安 710065
3.
北京理工大学光电学院，北京 100081

基金项目: 浙江省科技计划项目（2020C03095）；技术基础科研项目（JSJL2020208A003）；测试仪器项目（2006ZCGG0103-2）

详细信息

作者简介:
张金玉（1994—），男，硕士研究生，主要从事光学计量测试研究工作。E-mail：1731135828@qq.com

中图分类号: TN248
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- 被引次数: 0
出版历程
- 收稿日期: 2022-03-28
- 修回日期: 2022-04-28
- 网络出版日期: 2022-08-05
- 刊出日期: 2023-01-17

Influence of cavity ring-down data interception on time constant measurement accuracy

1.
College of Optical and Electronic Science Technology, China Jiliang University, Hangzhou 310018, China
2.
Xi'an Institute of Applied Optics, Xi'an 710065, China
3.
School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 光腔衰荡方法是目前测量光学元件超高反射率（反射率>99.9%）的唯一方法。介绍了一种对光腔衰荡法中激光信号强度与时间关系的优化提取方法。设计了基于光腔衰荡法的光学元件超高反射比的测试系统，通过对采集的光腔衰荡曲线数据进行分段指数拟合，将光腔衰荡曲线数据分为5段，对每段指数拟合结果对应的R² (R-square)和RMSE（root mean squared error）值进行对比分析，计算每段指数拟合的衰荡时间。实验结果表明：截取光腔衰荡曲线数据40%～60%部分拟合得到的结果最接近真实值，求得对应的腔镜的反射率为99.988 977%。最后通过与腔镜的自身反射率进行比较，表明该种数据拟合方法能有效地测量腔镜的反射率，并能减小实验数据本身带来的误差。
- 光腔衰荡技术 /
- 一次指数函数拟合 /
- R² /
- RMSE
Abstract: The cavity ring-down method is currently the only method for measuring ultra-high reflectivity (reflectivity is greater than 99.9%) of optical elements. An optimal extraction method for the relationship between laser signal intensity and time in cavity ring-down method was introduced, and a test system for ultra-high reflection ratio of optical elements based on cavity ring-down method was designed. The data of cavity ring-down curve were divided into five sections by piecewise exponential fitting, the R² (R-square) and root-mean-square error (RMSE) values corresponding to the index fitting results of each section were compared and analyzed, and the ring-down time of each index fitting was calculated. The experimental results show that the results obtained from 40%~60% of the cavity ring-down curve data are closest to the real value, and the reflectivity of the corresponding cavity mirror is 99.988 977%. Finally, by comparing with the reflectance of the cavity mirror, it is shown that this data fitting method can effectively measure the reflectivity of the cavity mirror and reduce the error caused by the experimental data.
- cavity ring-down technology /
- first order exponential function fitting /
- R² /
- root mean square error

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图 1 初始光腔测量系统框图

Fig. 1 Block diagram of initial optical cavity measurement system

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图 2 测试光腔测量系统框图

Fig. 2 Block diagram of test optical cavity measurement system

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图 3 折叠腔示意图

Fig. 3 Schematic diagram of folding cavity

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图 4 实验装置系统连接示意图

Fig. 4 System connection diagram of experimental device

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图 5 第23组一次指数函数拟合曲线图

Fig. 5 Fitting curve of primary exponential function of group 23

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图 6 第23组二次指数函数拟合曲线图

Fig. 6 Fitting curve of quadratic exponential function of group 23

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图 7 第1组数据拟合曲线图

Fig. 7 Fitting curve of data of group 1

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图 8 第2组数据拟合曲线图

Fig. 8 Fitting curve of data of group 2

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图 9 第3组数据拟合曲线图

Fig. 9 Fitting curve of data of group 3

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图 10 第4组数据拟合曲线图

Fig. 10 Fitting curve of data of group 4

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图 11 第5组数据拟合曲线图

Fig. 11 Fitting curve of data of group 5

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表 1 6组实验数据的处理值

Table 1 Processing values of six groups of experimental data

试验组数	第3组	第8组	第13组	第18组	第23组	第28组
${ {R} }^{2}$	0.994 6	0.994 3	0.994 2	0.994 1	0.994 3	0.994 3
$ {\rm{RMSE}} $	4.922	4.952	4.913	4.950	4.820	4.851

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表 2 第23组指数函数拟合统计值

Table 2 Fitting statistics of exponential function of group 23

拟合函数次数	一次指数拟合	二次指数拟合
${ {R} }^{2}$	0.994 3	0.999 0
$ {\rm{RMSE}} $	4.820	1.999

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表 3 5段数据求得的参数值

Table 3 Parameter values obtained from five segments of data

数据	1～500	501～1 000	1 001～1 500	1 501～2 000	2 001～2 500
$\tau $	16.949 15	19.801 98	30.238 887	70.821 53	228.519 56
$R$	0.999 803	0.999 831 7	0.999 889 77	0.999 952 9	0.999 985 4
${ {R} }^{2}$	0.994 8	0.980 9	0.906 8	0.633 1	0.164 5
$ {\rm{RMSE}} $	4.812	2.021	1.059	0.609 2	0.444 6

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