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设计的传感器结构如图 1所示。它包括在两段SMF之间拼接一段内径为75μm的HCF而制造的FPI,以及在两段SMF之间拼接一段内径为5μm的HCF制造的MZI。当光源的光进入复合干涉仪时,光强可以分为3个部分:首先,由于存在HCF,来自SMF的一部分光被HCF的两个表面反射回SMF的纤芯,此时发生法布里-珀罗干涉; 其次,另一部分光进入SMF,在SMF-HCF拼接点激发了沿HCF包层传播的包层模式; 最后,还剩余一部分光作为HCF纤芯模式传播,在HCF-SMF拼接点,SMF的包层模式被耦合回纤芯模式,HCF的包层模式和纤芯模式之间发生马赫-曾德尔干涉。
对于法布里-珀罗干涉,入射光I1光可以分为从SMF进入HCF的I2,在SMF-HCF拼接处发生的菲涅耳反射光I3,以及在HCF-SMF拼接处发生的菲涅耳反射光I4。FPI的干涉光谱强度可以表示为:
$ I_{\mathrm{F}-\mathrm{P}}=I_3+I_4+2 \sqrt{I_3 I_4} \cos \left(\frac{4 \pi n L_{\mathrm{F}-\mathrm{P}}}{\lambda}+\varphi_0\right) $
(1) 式中,n是腔体的折射率,LF-P是FPI的腔体长度,λ是传输光的波长,φ0是初始相位。
可求得FPI的反射光的光程差为:
$ l=2 n L_{\mathrm{F}-\mathrm{P}} $
(2) 而FPI干涉光谱的第k级波谷处的波长λk, F-P为:
$ \frac{4 \pi n L_{\mathrm{F}-\mathrm{P}}}{\lambda_{k, \mathrm{~F}-\mathrm{P}}}+\varphi_0=2 k \pi $
(3) 联立(2)式和(3)式,可得FPI光程差为:
$ l=\left(k-\frac{\varphi_0}{2 \pi}\right) \lambda_{k, \mathrm{~F}-\mathrm{P}} $
(4) 由(4)式可知,FPI光程差与该第k级波谷处的波长λk, F-P成正比。
当外界温度发生变化时,依据热膨胀和热光效应,会导致FPI的腔长发生变化,最终导致光程差的变化,因此此时(2)式可转化为:
$ \begin{gathered} \Delta l=2 \Delta n L_{\mathrm{F}-\mathrm{P}}+2 n \Delta L_{\mathrm{F}-\mathrm{P}}= \\ 2 n \Delta T L_{\mathrm{F}-\mathrm{P}}(\xi+\alpha) \end{gathered} $
(5) 式中,α为HCF的热膨胀系数,ξ为HCF的热光系数。由(5)式可知,FPI的光程差变化量Δl与温度的变化量ΔT成正比。
联立(4)式和(5)式,可得:
$ \begin{gathered} \Delta T=\frac{\Delta l}{l(\xi+\alpha)}=\frac{\Delta \lambda_{k, \text { F-P }}}{\lambda_k(\xi+\alpha)}= \\ \frac{\Delta \lambda_{k, \text { F-P }}}{(\xi+\alpha)} \cdot \frac{2 k \pi-\varphi_0}{4 \pi n L_{\mathrm{F}-\mathrm{P}}} \end{gathered} $
(6) 由(6)式可知,对FPI干涉光谱的波谷进行波长漂移量的测量,即可得到温度的变化量。
进行折射率测量时,由于SMF和HCF的有效折射率差异,在SMF-HCF和HCF-SMF拼接点会产生菲涅耳反射,在拼接点处反射率为:
$ R_1=\left|\frac{n_{\mathrm{HCF}}-n_{\mathrm{SMF}}}{n_{\mathrm{HCF}}+n_{\mathrm{SMF}}}\right|^2 $
(7) 式中,nHCF为HCF光纤的有效折射率,nSMF为SMF光纤的有效折射率。当传感器置于不同折射率的外界环境时,外界环境折射率为nex,拼接点处反射率变为:
$ R_2=\left|\frac{n_{\mathrm{HCF}}-n_{\mathrm{ex}}}{n_{\mathrm{HCF}}+n_{\mathrm{ex}}}\right|^2 $
(8) 由多光束干涉的公式可知:
$ I_{\mathrm{r}}=\frac{\left(R_1+R_2\right)\left[1-\cos \left(\frac{4 \pi n L_{\mathrm{F}-\mathrm{P}}}{\lambda}\right)\right]}{1+R_1 R_2-\left(R_1+R_2\right) \cos \left(\frac{4 \pi n L_{\mathrm{F}-\mathrm{P}}}{\lambda}\right)} I_0 $
(9) 式中,Ir是FPI反射光的光强;I0是FPI入射光的光强。
由(9)式可知,当外界环境的折射率发生变化时,FPI反射光谱的波长不会随着折射率的变化而发生改变,即FPI反射光谱对折射率的变化不敏感。
对于马赫-曾德尔干涉,光可以分为在HCF纤芯中传输的I5以及被激发到HCF包层中传输的I6,MZI形成的干涉光谱强度可以表示为:
$ I_{\mathrm{M}-\mathrm{Z}}=I_5+I_6+2 \sqrt{I_5 I_6} \cos \left(\frac{2 \pi \Delta n_{\mathrm{f}} L_{\mathrm{M}-\mathrm{Z}}}{\lambda}+\varphi_0\right) $
(10) 式中,IM-Z为MZI干涉谱光强;Δnf为纤芯模式和包层模式的相对折射率差;LM-Z为MZI腔体的长度;λ为传输光的波长。
当外界环境发生变化时,光纤的热光效应和热膨胀效应会导致HCF的包层模和纤芯模的相对折射率差Δnf和腔长LM-Z发生变化,有:
$ \begin{gathered} \frac{\Delta \lambda_{\mathrm{M}-\mathrm{Z}}}{\lambda_{\mathrm{M}-\mathrm{Z}}}=\left(\frac{1}{L_{\mathrm{M}-\mathrm{Z}}} \frac{\partial L}{\partial T}+\frac{\xi_1 n_{\mathrm{f}, 1}-\xi_2 n_{\mathrm{f}, 2}}{n_{\mathrm{f}, 1}-n_{\mathrm{f}, 2}}\right) \Delta T+ \\ \left(-\frac{\partial n_{\mathrm{f}, 2}}{\partial n_{\mathrm{ex}}} \frac{1}{n_{\mathrm{f}, 1}-n_{\mathrm{f}, 2}}\right) \Delta n_{\mathrm{ex}} \end{gathered} $
(11) 式中,ξ1为纤芯的热光系数;ξ2为包层的热光系数;nf, 1为纤芯的有效折射率;nf,2为包层的有效折射率。
当相位差φ56满足φ56=(2k+1)π时(k是正整数),干涉波峰对应的波长λk, M-Z可表示为:
$ \lambda_{k, \mathrm{M}-\mathrm{Z}}=\frac{2 \Delta n_{\mathrm{f}} L_{\mathrm{M}-\mathrm{Z}}}{2 k+1} $
(12) 由(11)式可知,MZI的波峰变化量与外界温度和折射率的变化量线性相关。
当外界温度T和C12H22O11溶液质量分数w发生变化时,所产生的温度变化ΔT和溶液折射率变化Δn与FPI的反射光谱特征波长变化系数ΔλF-P和MZI的透射光谱特征波长变化系数ΔλM-Z相关关系为:
$ \left\{\begin{array}{l} \Delta \lambda_{\mathrm{F}-\mathrm{P}}=m_{T, 1} \Delta T+m_{n, 1} \Delta n \\ \Delta \lambda_{\mathrm{M}-\mathrm{Z}}=m_{T, 2} \Delta T+m_{n, 2} \Delta n \end{array}\right. $
(13) 式中,mT, 1和mn, 1分别为FPI的温度灵敏度和折射率灵敏度;mT, 2和mn, 2分别为MZI的温度灵敏度和折射率灵敏度,由(13)式构建灵敏度系数矩阵有:
$ \left[\begin{array}{c} \Delta T \\ \Delta n \end{array}\right]=\left[\begin{array}{ll} m_{T, 1} & m_{n, 1} \\ m_{T, 2} & m_{n, 2} \end{array}\right]^{-1}\left[\begin{array}{l} \Delta \lambda_{\mathrm{F}-\mathrm{P}} \\ \Delta \lambda_{\mathrm{M}-\mathrm{Z}} \end{array}\right] $
(14) 将测量得到的特征波长漂移变化量进行线性拟合,得到FPI和MZI灵敏度,再与(14)式灵敏度系数矩阵相结合,即可同时进行温度和溶液质量分数的监测。
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将制作好的传感器连接至图 3所示温度传感实验装置,进行温度特性测试表征实验。所采用温度传感实验装置由超辐射发光二极管光源(super luminescent diode,SLD)、光纤环行器、高温炉(high temperature furnace,HTF)和光谱分析仪(optical spectrum analyzer,OSA)构成。
固定传感器,将温度变化范围设置为40℃~150℃,每隔10℃在光谱仪中收集一次数据。FPI和MZI的频谱漂移如图 4和图 5所示。
从图 6和图 7可以看出,传感器的FPI和MZI都随温度变化而漂移,FPI的变化较大,MZI的变化较小。对FPI和MZI的温度响应进行线性拟合。FPI和MZI的温度响应曲线如图 8所示。FPI温度拟合线的斜率约为10pm /℃,截距约为1577.70,调整后拟合优度R2≈1;MZI温度拟合线的斜率约为3.45pm /℃,截距约为1575.15,调整后拟合优度R2≈0.93。因此,MZI的温度灵敏度为3.45pm /℃,线性度为0.93。FPI的温度敏感度为10pm /℃,线性度为1。实验结果表明,该传感器对温度变化具有良好的灵敏度和线性度。
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根据C12H22O11溶液质量分数和折射率的经验公式可计算得出折射率值,再计算溶液折射率与光谱波长的关系,即可间接求得溶液质量分数和波长的关系。
利用蒸馏水和质量分数为0.25(20℃)的C12H22O11溶液分别配置了质量分数为0.05,0.10,0.15,0.20,0.25,0.30,0.35,0.40的C12H22O11溶液。如表 1所示,C12H22O11溶液质量分数与折射率成正比。
Table 1. Solution mass fraction refractive index table
group mass fraction w refractive index 1 0.05 1.340 2 0.10 1.348 3 0.15 1.356 4 0.20 1.364 5 0.25 1.373 6 0.30 1.381 7 0.35 1.389 8 0.40 1.397 将制作好的传感器连接至图 9所示溶液质量分数传感实验装置,进行溶液质量分数特性测试实验。所采用质量分数传感实验装置由SLD光源、光纤环行器、装盛不同质量分数C12H22O11溶液的培养皿和光谱分析仪构成。
将制备的溶液倒入培养皿中并测量溶液的温度。当溶液的温度稳定在20℃时,记录传感器在不同溶液质量分数下的光谱数据。FPI和MZI的频谱漂移如图 10和图 11所示。从图 12和图 13可以看出,当溶液的质量分数从0.05增加到0.40、折射率从1.340增加到1.397时,FPI特征波谷的波长没有明显的漂移,MZI波峰向右漂移,波长变化约为15nm。对FPI和MZI的折射率响应进行线性拟合,响应曲线如图 14所示。FPI折射率拟合线的斜率约为0pm /℃,截距约为1565.70,调整后拟合优度R2≈1;MZI折射率拟合线的斜率约为232.29pm /℃,截距约为1274.15,调整后拟合优度R2≈0.97。
Figure 14. Response curve of the sensor to the wavelength change in solutions with different refractive index
实验结果表明,FPI对折射率不敏感,折射率与波长之间没有明显的线性关系,FPI的溶液折射率灵敏度约为0nm/RIU;MZI的溶液折射率灵敏度为232.3nm/RIU,线性度为0.975。
结合上述实验数据,将温度特性研究所得的温度灵敏度,与溶液质量分数特性研究所得折射率灵敏度代入下式的灵敏度系数矩阵,可得该FPI-MZI双参数传感器的温度-折射率传感矩阵方程为:
$ \begin{gathered} {\left[\begin{array}{c} \Delta T \\ \Delta n \end{array}\right]=\left[\begin{array}{ll} m_{T, 1} & m_{n, 1} \\ m_{T, 2} & m_{n, 2} \end{array}\right]^{-1}\left[\begin{array}{l} \Delta \lambda_{\mathrm{FPI}} \\ \Delta \lambda_{\mathrm{MZI}} \end{array}\right]=} \\ {\left[\begin{array}{cc} 0.00345 & 0 \\ 0.01 & 232.3 \end{array}\right]^{-1}\left[\begin{array}{l} \Delta \lambda_{\mathrm{FPI}} \\ \Delta \lambda_{\mathrm{MZI}} \end{array}\right]} \end{gathered} $
(15)
级联FPI-MZI复合干涉光纤传感器双参数特性研究
Research on dual-parameter characteristics of composite interference fiber sensor based on cascade FPI-MZI
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摘要: 为了实现工业生产过程中温度和溶液质量分数的同时测量和传感检测, 提出了一种由法布里-珀罗干涉仪(FPI)和马赫-曾德尔干涉仪(MZI)级联干涉结构构成的双参数传感器。该传感器由融合在一起的单模光纤(SMF)和空芯光纤(HCF)组成。采用同时测量FPI反射光谱和MZI透射光谱的特征波长位移的方法, 获得了FPI和MZI对温度和折射率的灵敏度差, 建立了传感器温度-质量分数灵敏度矩阵, 实现了传感器双参数的测量。结果表明, 在40℃~150℃的温度范围内, FPI的温度敏感度为10pm/℃, 而MZI的对温度不敏感; 在质量分数0.05~0.40的范围内, FPI对折射率不敏感, 而MZI质量分数灵敏度是232.3nm/RIU; 该传感器可以实现温度与溶液质量分数的同时测量。该研究为石油、化工、电力、钢铁、机械等加工行业中双参数的动态测量提供了参考。Abstract: In order to achieve the simultaneous measurement and sensing detection of temperature and solution mass fraction in the industrial production process, a new dual-parameter sensor, which was composed of Fabry-Perot interference (FPI) and Mach-Zehnder interference (MZI) cascading interference structure was proposed. This new type of dual-parameter sensor cascade structure was composed of a single mode fiber (SMF) and a hollow core fiber (HCF) fused together. A method of simultaneously measuring the characteristic wavelength shift of the FPI reflection spectrum and the MZI transmission spectrum was adopted, and then the sensitivity difference between FPI and MZI to temperature and refractive index was obtained. The measurement of dual parameters of the sensor was realized by establishing the sensor temperature-mass fraction sensitivity matrix. The results show that the temperature sensitivity of FPI is 10pm/℃ in the temperature range of 40℃~150℃, while MZI is not sensitive to temperature. In the range of mass fraction 0.05~0.40, FPI is not sensitive to refractive index, while the sensitivity of MZI mass fraction is 232.3nm/RIU. The temperature and solution mass fraction can be measured by using this sensor. The study provides a reference for the dynamic measurement of dual-parameter in the processing industries such as petroleum, chemical, electricity, steel, and machinery.
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Key words:
- optical fiber sensor /
- Fabry-Perot cavity /
- Mach-Zehnder interference /
- hollow core fiber
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Table 1. Solution mass fraction refractive index table
group mass fraction w refractive index 1 0.05 1.340 2 0.10 1.348 3 0.15 1.356 4 0.20 1.364 5 0.25 1.373 6 0.30 1.381 7 0.35 1.389 8 0.40 1.397 -
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