用于弱磁场测量的光纤光栅法布里—珀罗干涉仪研究
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摘要
本文在研究磁致伸缩规律和光纤光栅法布里-珀罗干涉仪(Fabry-PerotInterferometer，FPI)传感特性的基础上，提出了一种用于弱磁场测量的光纤FPI，即利用磁致伸缩材料随外加磁场的变化关系，将光纤光栅FPI作为传感元件，由自相关解调达到磁场测量的目的。相对于其他FPI，光纤光栅FPI具有许多优点：制作简单、复用潜力大，并保留了普通FPI测量精度高和光纤布拉格光栅(FBG)传感器可绝对测量的特点，扩大了测量范围。围绕着将光纤光栅FPI用于磁场测量的研究，本文的主要内容如下：
(1)通过相干旋转模型推导了磁致伸缩材料在外加磁场中的变化规律，并求出了考虑应力以及磁场方向与测量方向不一致时的磁致伸缩计算公式。利用迈克耳孙干涉仪光路对Tb-Dy-Fe和Fe-Ga合金两种材料的磁致伸缩曲线进行了测量，得到的测量曲线与理论的平方规律相吻合。
(2)从光纤中的麦克斯韦方程组出发，推导了描述模式耦合的耦合方程，并用耦合模理论对FBG的传输特性进行了分析，讨论了光栅长度和折射率调制对反射光谱的影响。在此基础上，通过光束传播法和传输矩阵法分别推导了光纤光栅F-P腔反射率和透射率的严格表达式。数值模拟分析了光纤光栅F-P腔的光谱特性，并研究了光栅长度和F-P腔长对反射光谱的影响。
(3)分析了光纤光栅FPI对温度和应变的传感特性，并给出了相应的实验结果。在此基础上，介绍了一种适用于光纤光栅FPI的自相关解调法，即通过线性拟合得到的两个参量A和B来计算布拉格波长的漂移。该方法使光纤光栅FPI同时具有了测量精度高和可绝对测量的优点，利用温度传感实验验证了解调方法的可行性。为了将光纤光栅FPI用于磁场传感，对换能器的等效磁致伸缩系数进行了计算，并将光纤光栅FPI的磁场测量结果与特斯拉计进行了比较。
(4)分析了光纤光栅FPI的频分复用技术，并通过数值模拟说明了频分复用的过程，同时推广了自相关解调法的应用范围。为提高光纤光栅FPI的复用数目，最后提出了一种波分复用与频分复用相结合的复用系统。
Based on the research of magnetostrictive principles and sensing properties of a fiber grating Fabry-Perot interferometer (FPI), an optical fiber FPI used for weak magnetic field detection is present in this thesis. Where, the fiber grating FPI works as a sensing element and the magnetostrictive material works as a transducer when applied magnetic field changes. The purpose of magnetic field detention is achieved after the autocorrelation demodulation. Compared with other FPIs, the fiber grating FPI possesses many merits: ease of manufacture, large potential for multiplexing, the fiber grating FPI keeps the advantages of FBG sensors and common FPIs both, which means that it can provide high precise measurements and absolute measurements at the same time. As a result, the measurement range is enlarged. Encircling the research on magnetic field detection by using the fiber grating FPI, the main work in the thesis is as follows:
(1) The magnetostrictive laws are derived through the coherent rotation model, and the formulas between magnetostriction and magnetic field are given. The magetostrictive formulas are deduced in such situations, where magnetostrictive material is under stress and the direction of magnetic field is different from that of measurement. The magnetostrictive curves of Tb-Dy-Fe and Fe-Ga alloy are measured by an experiment set up of Michelson interferometer. These curves agreed with the theoretical result.
(2) Starting from the Maxwell-field equations in optical fiber, we derived the coupled-mode equations that describe the interaction between the modes. Then, FBG is analyzed with coupled-mode theory, relationships between the spectra and grating length as well as index modulation are discussed. Relying on the transmission characters of FBG, the strict expressions of transmissivity and reflectivity for the fiber grating F-P cavity are deduced through the transfer matrix method and light propagating method. The spectrum of fiber grating F-P cavity is analyzed by numerical simulation, the effects of the grating length and cavity length on the reflective spectrum shape are investigated.
(3) Sensing properties to temperature and strain are analyzed for the fiber grating FPI, and related experiment results are given. An autocorrelation demodulation method applied for the fiber grating FPI is introduced. Using the two parameters, A and B, which are got from the linear fit, wavelength demodulation is achieved. This method has the advantages of high precision and a wide measurement range. A temperature experiment is demonstrated to confirm the feasibility of this method. For sensing the magnetic field by proposed fiber grating FPI, the effective magnetostrictive coefficient is calculated. Then, measurement results of a fiber grating FPI are compared with those of a Tesla meter.
(4) The frequency division multiplexing technology of a FPI system is discussed and analyzed. By numerically simulating, processes of frequency division multiplexing are explained, and the applied area of autocorrelation demodulation is extended. A multiplexing system based on the wavelength division multiplexing and frequency division multiplexing is suggested to increase the number of multiplexed FPIs.
(1)通过相干旋转模型推导了磁致伸缩材料在外加磁场中的变化规律，并求出了考虑应力以及磁场方向与测量方向不一致时的磁致伸缩计算公式。利用迈克耳孙干涉仪光路对Tb-Dy-Fe和Fe-Ga合金两种材料的磁致伸缩曲线进行了测量，得到的测量曲线与理论的平方规律相吻合。
(2)从光纤中的麦克斯韦方程组出发，推导了描述模式耦合的耦合方程，并用耦合模理论对FBG的传输特性进行了分析，讨论了光栅长度和折射率调制对反射光谱的影响。在此基础上，通过光束传播法和传输矩阵法分别推导了光纤光栅F-P腔反射率和透射率的严格表达式。数值模拟分析了光纤光栅F-P腔的光谱特性，并研究了光栅长度和F-P腔长对反射光谱的影响。
(3)分析了光纤光栅FPI对温度和应变的传感特性，并给出了相应的实验结果。在此基础上，介绍了一种适用于光纤光栅FPI的自相关解调法，即通过线性拟合得到的两个参量A和B来计算布拉格波长的漂移。该方法使光纤光栅FPI同时具有了测量精度高和可绝对测量的优点，利用温度传感实验验证了解调方法的可行性。为了将光纤光栅FPI用于磁场传感，对换能器的等效磁致伸缩系数进行了计算，并将光纤光栅FPI的磁场测量结果与特斯拉计进行了比较。
(4)分析了光纤光栅FPI的频分复用技术，并通过数值模拟说明了频分复用的过程，同时推广了自相关解调法的应用范围。为提高光纤光栅FPI的复用数目，最后提出了一种波分复用与频分复用相结合的复用系统。
Based on the research of magnetostrictive principles and sensing properties of a fiber grating Fabry-Perot interferometer (FPI), an optical fiber FPI used for weak magnetic field detection is present in this thesis. Where, the fiber grating FPI works as a sensing element and the magnetostrictive material works as a transducer when applied magnetic field changes. The purpose of magnetic field detention is achieved after the autocorrelation demodulation. Compared with other FPIs, the fiber grating FPI possesses many merits: ease of manufacture, large potential for multiplexing, the fiber grating FPI keeps the advantages of FBG sensors and common FPIs both, which means that it can provide high precise measurements and absolute measurements at the same time. As a result, the measurement range is enlarged. Encircling the research on magnetic field detection by using the fiber grating FPI, the main work in the thesis is as follows:
(1) The magnetostrictive laws are derived through the coherent rotation model, and the formulas between magnetostriction and magnetic field are given. The magetostrictive formulas are deduced in such situations, where magnetostrictive material is under stress and the direction of magnetic field is different from that of measurement. The magnetostrictive curves of Tb-Dy-Fe and Fe-Ga alloy are measured by an experiment set up of Michelson interferometer. These curves agreed with the theoretical result.
(2) Starting from the Maxwell-field equations in optical fiber, we derived the coupled-mode equations that describe the interaction between the modes. Then, FBG is analyzed with coupled-mode theory, relationships between the spectra and grating length as well as index modulation are discussed. Relying on the transmission characters of FBG, the strict expressions of transmissivity and reflectivity for the fiber grating F-P cavity are deduced through the transfer matrix method and light propagating method. The spectrum of fiber grating F-P cavity is analyzed by numerical simulation, the effects of the grating length and cavity length on the reflective spectrum shape are investigated.
(3) Sensing properties to temperature and strain are analyzed for the fiber grating FPI, and related experiment results are given. An autocorrelation demodulation method applied for the fiber grating FPI is introduced. Using the two parameters, A and B, which are got from the linear fit, wavelength demodulation is achieved. This method has the advantages of high precision and a wide measurement range. A temperature experiment is demonstrated to confirm the feasibility of this method. For sensing the magnetic field by proposed fiber grating FPI, the effective magnetostrictive coefficient is calculated. Then, measurement results of a fiber grating FPI are compared with those of a Tesla meter.
(4) The frequency division multiplexing technology of a FPI system is discussed and analyzed. By numerically simulating, processes of frequency division multiplexing are explained, and the applied area of autocorrelation demodulation is extended. A multiplexing system based on the wavelength division multiplexing and frequency division multiplexing is suggested to increase the number of multiplexed FPIs.
引文
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2. F. Primdahl, "The fluxgate magnetometer," J. Phys. E. 12, 214-252 (1979).
3. H. Okamura, "Fiber-optic magnetic sensor utilizing the lorentzian force," J. Lightwave Technol. 8(1), 1558-1564 (1990)
4. G.. W. Day and A. H. Ross, "Faraday effect sensors: The state of the art," Fiber Optic and Laser Sensors 6,138-150 (1980)
5．周晓军，刘永智，光纤微弱磁场传感技术研究进展，半导体光电，18(1)，1-5，(1997)
6. A.Yariv and H.V.Winsor, "Proposal for detection of magnetic field through magnetostrictive perturbation of optical fibres," Opt. Lett. 5(3), 87-89 (1980).
7. A. Dandridge, A. B. Tveten, G H. Sigel, E. J. West and T. G. Giallorenzi, "Optical fiber magnetic field sensor," Electron. Lett. 16,408-409 (1980)
8. A.R. Davis, S. S. Patrick, A. Dandridge, and F. Bucholtz, "Remote fibre-optic ac magnetometer," Electron. Lett. 28(3), 271-273 (1992).
9. D.M. Dagenais, F. Bucholtz, and K. P. Koo, "Elimination of residual signals and reduction of noise in low-frequency magnetic fiber sensor,"Appl.Phys.Lett. 53, 1417-1426 (1988).
10. D. M. Dagenais, F. Bucholtz, K. P. Koo, and A. Dandridge, "Demonstration of 3pT/(Hz)~(1/2) at 10 Hz in a fibre-optic magnetometer," Electron. Lett. 24(23), 1422-1423 (1988).
11. F. Bucholtz, D. M. Dagenais, and K. P. Koo, "High-Frequency Fibre-Optic magnetometer of 7fr/(Hz) 1/2 Resolution," Electron. Lett. 25(25),1719-1721 (1989)
12. F. Bucholtz, C. A. Villarruel, D. M. Dagenais, J. A. McVicker, K. P. Koo, C. K. Kirkendall, A. R. Davis, S. P. Patrick, and A. Dandridge, "Fiber Optic Magnetic Sensor Technology. for Undersea Applications," Fiber Optic and Laser Sensors 22, 2-13 (1994)
13. M. Sedlar, V. Matejec, and I. Paulicka, "Optical fibre magnetic field sensors using ceramic magnetostrictive jackets," Sensors and Actuators A 84, 297-302 (2000)
14. A. D. Kersey, M. Corke, D. A. Jackson, and J. D. C. Jones, "Detection of dc and low-frequency AC magnetic fields using an all single-mode fiber magnetometer," Electron. Lett. 19, 469-471 (1983)
15. A. D. Kersey, D. A. Jackson, and M. Corke, "Single-mode fibre-optic magnetometer with DC bias field Stabilization," J. Lightwave Technol. 3(4), 836-840 (1985)
16．袁纵横，光纤微弱磁场传感技术研究，博士学位论文，电子科技大学，21-23，(1999)
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