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空域无源光纤腔衰荡乙炔气体体积分数检测系统如图 1所示。它由可调谐半导体激光器(tunable semiconductor laser, TSL)、隔离器、环形器、3 dB光纤耦合器(coupler, C)C0、光纤偏振控制器(polarization controller, PC)PC1、声光调制器(acousto-optic modulation, AOM)、光纤衰荡腔(fiber ring-down cavity, FRDC)、平衡探测器(balanced detector, BD)、数据采集卡(data acquisition board, DAQ)、计算机组成。其中,AOM的功能为实现对激光产生频移,光纤衰荡腔通常采用如图 1所示的光纤环形腔,它由两个高分光比光纤耦合器(C1和C2)、单模光纤、气室(gas cell, GC)和偏振控制器PC2组成。
图 1 空域无源光纤腔衰荡乙炔气体体积分数传感系统原理图
Figure 1. Schematic diagram of space-domain passive fiber cavity ring-down acetylene gas volume fraction sensing system
由图 1可以看出,本文作者提出的传感系统是在频移干涉仪的萨格奈克环中插入光纤环形腔而形成的,其传感原理可描述为:当可调谐激光器产生的连续光通过隔离器、环形器和3 dB光纤耦合器C0后,分成顺时针和逆时针传播的两束连续光,接着这两束连续光分别从光纤耦合器C1和C2进入到光纤环形腔中循环传输。当它们在光纤环形腔内每传输1圈后,两束连续光均有少量连续光从光纤环形腔内返回到3 dB耦合器C0。当可调谐激光器的相干长度比光纤环形腔的腔长短时,则从光纤环形腔内环行不同圈数的光返回到C0处不会产生干涉,也就是说,只有环行相同圈数的光返回到C0处才会产生干涉。由于逆时针传播的连续光较顺时针传播的连续光先经过频移器,因此这两束连续光产生的相位差不再为0,从而在3 dB光纤耦合器C0的左侧两个输出端均有干涉光输出,从而可采用差分探测来消除直流噪声,故传感系统的信噪比得到了极大的改善。由频移干涉技术的原理[19-20],并考虑传感系统的噪声,差分信号的强度ΔI可表示为:
$ \begin{aligned} \Delta I= & \sum\limits_{m=0}^{\infty} I_m \cos \left[2 \pi \frac{n\left(m L+L_0\right)}{c} f\right]= \\ & \sum\limits_{m=0}^{\infty} I_m \cos \left(2 \pi F_m f\right)+P_{\text {noise }} \end{aligned} $
(1) 式中,L是光纤衰荡腔的腔长;L0是顺时针传输的连续光在频移器前后所走的路程差;n是纤芯的折射率;c为光在真空中的速度;f是声光调制器产生的频移量;Pnoise为系统的噪声,且可认为是高斯白噪声;Fm=n(mL+L0)/c是光纤衰荡腔的振荡频率,由于c的值很大,所以传感系统的振荡频率较低,即无需快速探测器和高速采集卡,就能实现气体体积分数的高灵敏度探测,从而降低了传感系统的成本;m是连续光在光纤衰荡腔中往返的次数;Im是连续光经过m次往返之后的光强。
对采集到的干涉信号作快速傅里叶变换,就可以得到傅里叶谱的信息,且该傅里叶谱呈现出一系列谱峰的特征,每个谱峰的位置由振荡频率Fm决定,由于Fm是空间位置的函数,并且激光受到气体样品吸收的影响,这些谱峰的强度随空间位置呈现出指数的衰减规律,故将其称为空域的衰荡信号。对这些谱峰进行峰值提取和指数拟合,并调整好PC1和PC2的偏振态,就可以得到空域的衰荡曲线。
将衰荡曲线中的谱峰强度下到初始强度的1/e时,激光在光纤环形腔内传输的长度定义为衰荡距离。当气室充入氮气时,衰荡距离d0与固有腔损耗αc之间的关系可表示为:
$ d_0=\frac{L}{\alpha_{\mathrm{c}}} $
(2) 当气室充入待测气体时,气体产生吸收损耗αs,此时,衰荡距离变为:
$ d=\frac{L}{\alpha_{\mathrm{c}}+\alpha_{\mathrm{s}}} $
(3) 由(2)式和(3)式,可得衰荡距离的倒数差与待测气体的吸收损耗之间满足如下关系:
$ \frac{1}{d}-\frac{1}{d_0}=\frac{\alpha_{\mathrm{s}}}{L} $
(4) 式中,气体的吸收损耗与气体体积分数φ之间的关系为αs=αgLGCφ,其中,αg=Sgasg(ν)p/(kBT)是气体的吸收系数, Sgas是气体吸收线的强度,g(ν)为线型函数,ν为激光的频率,p是气压, kB是玻尔兹曼常数, T是温度,LGC是光纤型气室的长度。
将(4)式改写成与气体体积分数的关系,则可表示为:
$ \frac{1}{d}-\frac{1}{d_0}=k^{\prime} \varphi $
(5) 式中,k′=αgLGC/L。(5)式表明:衰荡距离的倒数差与待测气体体积分数之间满足线性关系,所以,通过测量衰荡距离的倒数差就可以实现待测气体体积分数的检测,这就是空域无源光纤腔衰荡气体体积分数传感系统的工作原理。此外,斜率k′代表的是气体体积分数传感系统的灵敏度,k′越大,灵敏度越高。
除灵敏度之外,检测极限(detection limit, DL)也是传感系统的关键指标。通常将气体检测系统的检测极限定义为最小可检测的气体体积分数,其大小表示为:
$ \varphi_{\min }=\frac{1}{\alpha_{\mathrm{g}} L_{\mathrm{GC}} h} \frac{\sigma_d}{\bar{d}} $
(6) 式中,σd为未充入待测气体时,衰荡距离的1阶标准偏差,d为衰荡距离的平均值。σd/d代表气体体积分数检测系统的稳定性,很明显,σd/d的值越小,则表示气体体积分数检测系统的稳定性越好。h=d0/L表示衰荡距离内连续光与气体发生相互作用的次数,显然,与传统的直接吸收光谱技术相比,空域无源光纤腔衰荡传感技术的检测极限提高了h倍。由(2)式可知,固有腔损耗αc越小,衰荡距离d0越长,则连续光与气体发生相互作用的次数越多,检测极限越高。所以,科研人员一般采用降低光纤环形腔的固有腔损耗或者用掺铒光纤放大器来补偿光纤腔固有腔损耗的方法以提高传感系统的检测极限。
仿真实验中,利用MATLAB中randn函数产生了均值为0、方差为8×10-6的高斯白噪声,用于模拟传感系统产生的噪声。为了获得较低的固有腔损耗,选用了两个耦合比为99.5/0.5的光纤耦合器来形成光纤环形腔,光纤环形腔的腔长为65 m、气室长度为5 cm。为了检测乙炔气体的体积分数,可调谐半导体激光器(型号为Santec TSL-550)的中心波长为1530.37 nm,即对着乙炔最强的吸收峰,输出功率为8 mW。声光调制器(型号为美国Brimrose公司的AMM-100-20-25-1550-2FP)的扫频范围是90 MHz~110 MHz,扫描步长为0.02 MHz。平衡探测器(型号为美国New Focus公司的Model 2117)的增益设为为103,数据采集卡(型号为美国NI公司的USB-6361)的采样率为105 /s。
空域无源光纤腔衰荡乙炔体积分数检测仿真
Simulation of space-domain passive fiber cavity ring-down acetylene gas volume fraction detection
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摘要: 为了更准确地分析空域无源光纤腔衰荡乙炔体积分数检测系统,建立了考虑系统噪声的气体体积分数传感理论模型。采用该模型对空域无源光纤腔衰荡乙炔体积分数检测系统的性能进行了仿真和讨论。结果表明,利用空域无源光纤腔衰荡传感技术,通过测量衰荡距离,可实现灵敏度高达56.226 km-1的乙炔体积分数的测量,稳定性达0.47%,检测极限达260.577×10-6,且稳定性和检测极限还可通过减少光纤腔的固有腔损耗得到进一步的提高。此研究对于体积分数传感系统的优化设计应用具有理论指导意义。
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关键词:
- 传感器技术 /
- 体积分数 /
- 空域无源光纤腔衰荡传感系统 /
- 频移干涉 /
- 灵敏度
Abstract: In order to analyze space-domain passive fiber cavity ring-down acetylene gas volume fraction detection system more accurately, a theoretical model of gas volume fraction sensing system considering system noise was established in this paper. The performance of space-domain passive fiber cavity ring-down acetylene gas volume fraction detection system was simulated and discussed by using this model. Simulation results show that, by using the space-domain passive fiber cavity ring-down sensing technology, the acetylene volume fraction can be monitored by measuring the ring-down distance and the sensitivity of 56.226 km-1 is achieved, the corresponding stability and detection limit can reach 0.47% and 260.577×10-6, which can be further improved by reducing the inherent cavity loss of the fiber cavity. This research has theoretical significance for the optimization design of volume fraction sensing system. -
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