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在波长调制光谱中,激光通过样品吸收池后的透射光光强It与入射光光强I0遵循Beer-Lambert定律并展开为傅里叶余弦级数:
$ \begin{array}{c} \tau (\nu ) = \frac{{{I_{\rm{t}}}}}{{{I_0}}} = \exp [ - N\sigma (\nu )] = \\ \exp \left[ { - pS(T){L\chi }\varphi (\nu )} \right] = \sum\limits_{k = 0}^\infty {{A_k}} \cdot \cos (k\omega t) \end{array} $
(1) 式中, τ(ν)称为透射率,N为每立方厘米待测气体分子个数,σ(ν)为吸收横截面,ν为中心波数,p为吸收池内压强,S(T)为对应温度T下单位压强的谱线吸收强度,L为有效光程,χ为待测分子体积分数,φ(ν)为吸收谱线线型函数,Ak可表示为:
$ \left\{\begin{aligned} A_{0}=& \frac{1}{2 \pi} \int_{-\pi}^{\pi} \exp \left[-p S(T) L{\chi \varphi}(\nu)\right] \mathrm{d} \theta \\ A_{k}=& \frac{1}{2 \pi} \int_{-\pi}^{\pi} \exp \left[-p S(T) L{\chi \varphi}(\nu)\right]\cdot \\ & \cos \theta \mathrm{d} \theta, (k=1, 2, 3, \cdots) \end{aligned}\right. $
(2) 当叠加上频率为ω的调制信号时,I0可表示为:
$ I_{0}=\bar{I}_{0}\left[1+i_{1} \cos \left(\omega t+\psi_{1}\right)+i_{2} \cos \left(2 \omega t+\psi_{2}\right)\right] $
(3) 式中, I0为平均光强,i1和ψ1分别为线性强度调制幅值与相位移动,i2和ψ2分别为非线性强度调制幅值与相位移动。将(3)式代入(1)式中进行谐波探测,可得1f信号S1f与2f信号S2f在吸收线型中心的表达式为[11, 15, 18]:
$ \left\{\begin{aligned} S_{1 f}=& \frac{G \bar{I}_{0}}{2}\left\{\left[i_{1}\left(A_{0}+\frac{A_{2}}{2}\right) \cos \psi_{1}\right]^{2}+\right.\\ &\left.\left[i_{1}\left(A_{0}-\frac{A_{2}}{2}\right) sin \psi_{1}\right]^{2}\right\}^{\frac{1}{2}} \\ S_{2 f}=& \frac{G \bar{I}_{0}}{2}\left\{\left[A_{2}+i_{2}\left(A_{0}-1+\frac{A_{4}}{2}\right) \cos \psi_{2}\right]^{2}+\right.\\ &\left.\left[i_{2}\left(A_{0}-1-\frac{A_{4}}{2}\right) \sin \psi_{2}\right]^{2}\right\}^{\frac{1}{2}} \end{aligned}\right. $
(4) 式中,G为系统光电增益。
从(4)式中可以发现,波长调制2f与1f信号均会受到系统增益系数G和光强I0的影响,通过在吸收线中心使用1f信号对2f信号进行归一化,可以有效避免系统增益及光强对测量信号的影响,归一化后的信号S2f/1f可表示为:
$ S_{2 f / 1 f}=\frac{S_{2 f}}{S_{1 f}} $
(5)
基于免校准波长调制的多光程吸收光谱
Multipass absorption spectroscopy based on calibration- free wavelength modulation
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摘要: 为了研究免校准波长调制光谱技术对激光光强变化及外界干扰的免疫能力, 采用基于免校准波长调制技术的多光程吸收光谱, 以乙炔为测量目标, 进行了理论分析和实验验证。结果表明, 不同激光功率下得到的波长调制二次谐波信号幅值发生明显变化, 但通过免校准的方法得到的信号变化较小, 且受气流影响、部分遮光、系统振动等外界干扰影响较小; 采用免校准方法实验得到的体积分数在5×10-6 ~9×10-5范围内的光谱信号拥有较好的线性度, 相关系数达0.9997;采用Allan方差分析得到该实验系统的最小探测极限可达1.2×10-8。免校准波长调制光谱技术能较好地避免光强抖动、气流干扰、系统振动等干扰, 从而提高系统稳定性和探测灵敏度。
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关键词:
- 光谱学 /
- 可调谐半导体激光吸收光谱 /
- 免校准波长调制光谱 /
- 气体测量 /
- 乙炔(C2H2)
Abstract: In order to study the immunity of calibration-free wavelength modulation spectroscopy to laser intensity change and external interference, multi-path absorption spectra based on calibration-free wavelength modulation technology were adopted. Taking acetylene as the measurement target, theoretical analysis and experimental verification were carried out. The results show that, the amplitude of wavelength modulated second harmonic signal varies significantly under different laser power. But the signal obtained by the calibration-free method changes little. It is less affected by external disturbance such as airflow, partial shading and system vibration. The spectral signals with volume fraction in the range of 5×10-6 ~9×10-5 obtained by calibration-free method have good linearity. The correlation coefficient is 0.9997. Allan variance analysis shows that the minimum detection limit of the experimental system can reach 1.2×10-8. This study shows that calibration-free wavelength modulation spectroscopy can avoid the interference of light intensity jitter, air flow and system vibration. The system stability and detection sensitivity are improved. -
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