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FBG为折射率沿光纤纤芯的周期性调制。FBG反射宽带入射光的窄带部分并透射其余大部分。根据耦合模理论,FBG反射峰的中心波长
$\lambda_{\mathrm{B}} $ 可以用布拉格条件表示为$\lambda_{\mathrm{B}}=2 n_{e f f} \varLambda$ [17]。其中$n_{e f f} $ 为光纤单芯模的有效折射率,$\varLambda$ 为光栅的周期性。在环境温度恒定的条件下,由应变引起的布拉格波长偏移可以表示为:$$ \lambda_{B}=2 n_{e f f} \varLambda=2 n_{e f f}(\varepsilon, T) \varLambda(\varepsilon, T) $$ (1) 对公式(1)进行全微分运算得到:
$$ \frac{\Delta \lambda_{B}}{\lambda_{B}}=\left(\frac{1}{n_{e f f}} \frac{\partial n_{e f f}}{\partial \varepsilon}+\frac{1}{\varLambda} \frac{\partial \varLambda}{\partial \varepsilon}\right) \Delta \varepsilon $$ (2) 公式(2)是FBG应变传感的基本模型,FBG的波长偏移为[18]:
$$ \frac{\partial n_{ {eff }}}{n_{e f f}}=-\frac{n_{ {eff }^{2}}}{2}\left[P_{12}-v\left(P_{11}+P_{12}\right)\right]\left|\varepsilon_{z z}\right| $$ (3) $$ P_{e}=\frac{n_{{e f f}^{2}}}{2}\left[P_{12}-v\left(P_{11}+P_{12}\right)\right] $$ (4) 式中:
$P_{e} $ 为光纤的应变光学系数;$P_{11} $ 和$P_{12} $ 为应变光学张量的两个分量;v为泊松比。结合公式(3)、(4),可将FBG的波长偏移表示为:$$\Delta \lambda_{B}=\left(1-P_{e}\right) \lambda_{B} \varepsilon $$ (5) 对于标准单模石英光纤,
$n_{e f f} $ =1.456,v=0.17,P11=0.121,P12 =0.270,Pe=0.216,因此,应变引起的FBG的波长偏移可由公式(6)给出:$$ \Delta \lambda_{B}=0.784 \lambda_{B} \varepsilon $$ (6) 由公式(6)可知,对于确定材料的光纤光栅,与材料相关的应变敏感系数为常数,因此应变导致FBG波长线性偏移。
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所提出的脉象传感器结构示意图的俯视图如图1(a)所示,光栅FBG 1和FBG 2组成级联光栅,并封装于硅胶腕带中。硅胶腕带宽16 mm,长330 mm,其中FBG 1距离硅胶腕带左端85 mm,FBG 2距离硅胶腕带右端25 mm,FBG 1和FBG 2间隔220 mm。基于FBG在柔性基体中的应变传递效果研究[14],选择硅胶腕带厚度为4 mm,光纤封装在距离硅胶腕带下表面1 mm处。脉象测试时,腕带左侧被弯曲而缠绕于腕关节,此时传感器前视图如图1(b)所示。测试过程中,FBG 1处于腕关节桡动脉处,用于感知脉搏信号。腕带右侧呈自然状态水平放置,FBG 2处有一“C型夹”,用于对FBG 2施加应变。
结合图2中的传感器反射光谱示意图对脉象测量原理进行介绍。FBG 1中心波长为
$\lambda_1 $ ,FBG 2中心波长为$\lambda_2 $ 。FBG 1和FBG 2参数相同,$\lambda_1 $ =$\lambda_2 $ ,两个光栅的反射峰重叠,传感器光谱表现为单一反射峰,如图2(a)所示。当脉搏信号作用于FBG 1时,在应变作用下其反射峰偏移,此时中心波长为${\lambda_1}' $ ,FBG 1反射峰和FBG 2反射峰分离,传感器反射光谱如图2(b)所示。因此,对传感器反射光的强度进行监测即可得到FBG 1反射峰的波长偏移量,进而获取脉象信息。脉搏测试中需要注意,当腕带被弯曲缠绕于腕关节时,FBG 1所承受的应变增加,其反射峰偏移。因此,在腕带缠绕于腕关节后,应通过“C型夹”对FBG 2施加应变,使得FBG 2反射峰以同FBG 1相同的方向偏移,进而使FBG 1反射峰和FBG 2反射峰重合。需要说明的是,由于FBG 1和FBG 2参数相同,当环境温度变化时,FBG 1反射峰和FBG 2反射峰以相同速率向同一方向偏移,二者相对位置不变,此时传感器反射光的强度恒定,因此该传感器在脉象测试时不受环境温度变化的影响。
Pulse sensor based on cascade grating using silica gel package
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摘要: 提出了一种基于级联光栅的脉象波传感器。相同参数的两个光纤光栅组成级联光栅并植入硅胶腕带中,其中一个光栅作为传感光栅被用于感知脉搏信号,另一个光栅作为匹配光栅被用于解调。由于两个光栅参数完全相同,其反射峰重叠,传感器反射光谱表现为单个反射峰。脉搏搏动产生的应变变化对传感光栅进行调制,导致传感光栅反射峰的中心波长产生偏移,进而导致传感器反射光的强度变化。通过对反射光的强度进行监测,即实现了脉象信息的测量和提取。实验中分别测试了健康男性青年和老年受试者,以及同一个健康男性受试者上午8时和下午8时的脉象信息。结果显示,传感器可有效提取不同受试者的脉象特征点,测试结果符合中医脉象理论。当环境温度变化时,级联光栅中两个光栅的反射峰以相同速率向同一方向偏移,传感器反射光谱的强度不变,因此该传感器不受环境温度影响。此外,该传感器具有结构简单、解调方便、成本较低等优点,在脉象测试中具有一定的应用潜力。Abstract: A pulse sensor based on cascaded grating is proposed. Cascaded gratings composed of two fiber Bragg gratings with the same parameters are implanted into the silicone wristband. One fiber Bragg grating is used as a sensing grating to sense the pulse signal, and the other grating is used as a matching grating for demodulation. Because the parameters of the two gratings are exactly the same, their reflection peaks overlap, and the reflection spectrum of the sensor shows a single reflection peak. The pulse signal modulates the strain state of the sensing grating under the action of stress, resulting in the shift of the central wavelength of the reflection peak of the sensing grating, which leads to the change of the reflected light intensity of the sensor. By monitoring the reflected light intensity of the sensor, the measurement and extraction of pulse are realized. In the experiment, the pulse of healthy young and old male subjects, and the same healthy male subjects at 8 am/pm are tested. The results show that the sensor can effectively extract the pulse feature points of different subjects, and the test results are in line with the pulse theory of traditional Chinese medicine. When the ambient temperature changes, the reflection peaks of the two gratings shift in the same direction at the same rate, and the reflected light intensity of the sensor remains stable, so the sensor is not affected by the ambient temperature. In addition, the sensor has the advantages of simple structure, convenient demodulation and low cost. There are potential applications in pulse measurement.
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Key words:
- cascaded grating /
- sensor /
- pulse /
- strain
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