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TDLAS的测量原理基于Beer-Lambert定律。DAS利用电流调谐激光器实现对特征吸收峰的扫描,无需复杂的实验标定,系统结构简单。由Beer-Lambert定律定义吸光度
$\tau \left( \nu \right)$ 为:$$ \begin{array}{*{20}{c}} {\tau \left( \nu \right) = {\rm ln}\dfrac{{{I_0}\left( \nu \right)}}{{{I_t}\left( \nu \right)}} = \alpha \left( \nu \right)CL = PS\left( T \right)\varphi \left( \nu \right)CL} \end{array} $$ (1) 式中:
${I_0}\left( \nu \right)$ 为激光光源强度;$\nu $ 为频率;经待测气体吸收后,出射光强为${I_t}\left( \nu \right)$ ;$\alpha \left( \nu \right)$ 为待测气体分子的吸收系数;$C$ 为光路上气体的平均浓度;$L$ 为光传播的有效光程;$P$ 为气体压强;$S\left( T \right)$ 表示分子吸收线强,与温度$T$ 相关;$\varphi \left( \nu \right)$ 为经归一化后的吸收线形函数,其积分数值为1。对吸光度进行积分,消去线形函数,则得到简化后的积分吸光度$A$ :$$ \begin{array}{*{20}{c}} {A = \smallint \tau \left( \nu \right){\rm{d}}\nu = PS\left( T \right)CL} \end{array} $$ (2) 由公式(2)可知,当压强、温度、光程一定时,获得气体吸收光谱积分吸光度,即可计算气体浓度
$C$ :$$ \begin{array}{*{20}{c}} {C = \dfrac{A}{{PS\left( T \right)L}}} \end{array} $$ (3) -
对乙醇吸收进行谱线筛选,从PNNL数据库中调取温度为296 K、压力为1 atm、光程为1 m时,浓度为1 ppm的乙醇吸收光谱(见图1)。由图可知,近红外7180 cm−1处存在一个相对较窄的乙醇吸收峰。
开放光程的气体检测受到空气背景吸收的影响,美国HITRAN数据库给出标准空气模型(Institute of Atmospheric Optics, IAO)的八种组成及浓度,在7175~7185 cm−1进行干扰分析。排除无吸收组分,图2显示了IAO模型及H2O、CO2、N2O、CH4和C2H5OH的模拟吸收光谱。由图2可知,除水蒸气外,其余组分对气相乙醇吸收的干扰可忽略不计。
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基于干扰光谱内标的激光遥测技术利用干扰物质作内标从而修正被测物质吸收光谱,通过差分扣除干扰,数据处理流程如图3所示。
推导基线重构公式解决由宽带吸收带来的基线偏移问题。采集参考路原始数据
${Y_r}$ 和测量路原始数据${Y_a}$ ,利用去峰拟合法[15]分别得到参考路基线${I_{r0}}$ 和测量路基线${I_{a0}}$ 的函数表达式:$$ \begin{array}{*{20}{c}} {{I_{r0}} = a{\nu ^2} + b\nu + c} \end{array} $$ (4) $$ \begin{array}{*{20}{c}} {{I_{a0}} = m{\nu ^2} + n\nu + p} \end{array} $$ (5) 联立公式可以得到:
$$ \begin{array}{*{20}{c}} {{I_{a0}} = W\cdot{I_{r0}} + Q} \end{array} $$ (6) 由公式(4)~(6)可知,
$W$ 为仅与2阶系数相关的常数。$Q$ 是一个数组,大小与自变量$\nu $ 有关,包含所有自变量$\nu $ 对应的两个背景曲线之间的偏移量。采用均值趋势迭代获得使两曲线偏移方差最小的偏移常量${Q_i}$ 。迭代过程遵循:$$ \begin{array}{c}N=\sum {\left({Q}_{{i}}-{Q}_{{j}}\right)}^{2}\text{,}i,j\in \left[0,n\right]\end{array} $$ (7) 式中:
$n$ 为数组$Q$ 的元素个数。此时,可以得到重构后测量路基线Ia0_new的解析式:$$ \begin{array}{*{20}{c}} {{I_{a0\_{\rm{new}}}} = W \cdot {I_{r0}} + {Q_i}} \end{array} $$ (8) 当测量路包含乙醇时,参考路吸收光谱
${A_r}$ 和测量路吸收光谱${A_a}$ 满足:$$ \begin{array}{*{20}{c}} {{A_r} = {A_{w1}} = {\rm ln}\dfrac{{{I_{r0}}}}{{{Y_r}}}} \end{array} $$ (9) $$ \begin{array}{*{20}{c}} {{A_a} = {A_{w2}} + {A_e} = {\rm ln}\dfrac{{{I_{a0}}}}{{{Y_a}}}} \end{array} $$ (10) 其中,
${A_e}$ 为乙醇吸收光谱,由水蒸气浓度相等,即参考路水蒸气光谱${A_{w1}}$ 与测量路水蒸气光谱${A_{w2}}$ 满足关系:$$ \begin{array}{*{20}{c}} {{A_{w2}} = k \times {A_{w1}}} \end{array} $$ (11) 其中,常数k为两路有效光程的比值。联立公式(10)~(12),通过差分得
${A_e}$ 为:$$ \begin{array}{*{20}{c}} {{A_e} = {\rm ln}\dfrac{{{I_{a0}}}}{{{Y_a}}} - k \times {\rm ln}\dfrac{{{I_{r0}}}}{{{Y_r}}}} \end{array} $$ (12) -
实验系统主要包括激光控制单元、光学接收单元和信号处理单元,如图4所示。通过激光控制器(LDC-3908,ILX)使激光器输出波长范围为7178~7182 cm−1。系统光源经分束器按5%和95%的强度分成参考和测量两路信号。光学接收单元设置参考路光程为60 cm,采用对射方式接收。测量路等效光程为336 cm,激光从离轴抛面镜底部通孔出射,由非合作目标(墙面)漫反射后,经离轴抛面镜会聚到探测器。数据采集卡(PCI-4474,NI)采集实验信号,采样率为100 kS/s。部分实验装置实物如图5所示。
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为验证基线重构公式的准确性,在实验室环境下测量水蒸气背景吸收。为消除探测器暗电流、非线性等因素对光谱检测的影响,对齐两探测器无信号输出时的基准信号。由拟合结果知两路基线解析式为:
$$ {I_{a0}} = - 5.42 \times {10^{ - 10}}{\nu ^2} + 4.29 \times {10^{ - 5}}\nu \begin{array}{*{20}{c}} { - 4.64 \times {{10}^{ - 5}}} \end{array} $$ (13) $$ {I_{r0}} = - 1.26 \times {10^{ - 9}}{\nu ^2} + 1.00 \times {10^{ - 4}}\nu - 9.79 \times {10^{ - 5}} $$ (14) $$ \begin{array}{*{20}{c}} {{I_{a0\_{\rm{new}}}} = 0.428\;37 \times {I_{r0}} - 4.271\;41 \times {{10}^{ - 6}}} \end{array} $$ (15) 通过F-P标准具结合自由光谱区定义实现光谱波数标定,波长分辨率为0.05 cm−1。
图6(a)为重构前后的基线对比,图(b)为波数标定后的吸收光谱,图(c)为光谱偏差。由图可知,测量路原始光谱与参考路等效光谱的绝对偏差最大值为0.1525,基线重构后的偏差最大仅为0.0847,远小于重构前偏差,由此证明了基线重构在一定程度上的有效性。
为验证测量所得吸光度的准确性,选择水蒸气吸收峰值最大的实测吸光度作为基准,计算环境中的水蒸气浓度为0.6706%。实测吸光度与HITRAN数据库中相同水蒸气浓度下四个吸收峰的理论吸光度进行比较,结果如表1所示,吸光度偏差最大仅为0.00181。
表 1 吸光度偏差表
Table 1. Absorbance deviation of peaks
No. Theoretical absorbance Measured absorbance Absolute deviation Relative deviation 1 2.48344 2.48344 0 0 2 0.14914 0.15087 0.00174 1.164% 3 0.10572 0.10415 −0.00157 −1.482% 4 0.03309 0.03490 0.00181 5.46% -
为验证系统准确性,对乙醇标气进行测量。实验室环境温度恒为26 ℃,对应乙醇饱和蒸气压为8
${\text{kPa}}$ ,由理想气体状态方程(Ideal Gas Law)计算乙醇的质量浓度为:$$ \begin{array}{*{20}{c}} {{C_m} = \dfrac{{PM}}{{RT}} = \dfrac{{8\;000 \times 46}}{{\left( {26 + 273.15} \right) \times 8.314}} \approx 147.96\;{\text{g}}/{{\text{m}}^3}} \end{array} $$ (16) 式中:
${C_m}$ 为气体质量浓度,单位为${\text{g}}/{{\text{m}}^3}$ ;$P$ 为压强,单位为${\text{Pa}}$ ;$M$ 为摩尔质量,单位为${\text{g}}/{\text{mol}}$ ;$R$ 为摩尔气体常数,具体数值为8.314$ {\text{J}}/\left( {{\text{mol}} \cdot {\text{K}}} \right) $ ;$T$ 表示绝对温度,单位为${\text{K}}$ 。实验选用长度
$L$ 为25 cm,直径$D$ 为9 cm的塑料管,将其置于测量路径任一位置均不影响测量结果。计算容积为:$$ {V_G} = \pi {\left( {\frac{D}{2}} \right)^2}L = 3.14 \times {\left( {4.5} \right)^2} \times 25 \approx 1.59\;{\text{L}} $$ (17) 系统测量目标为大气中的痕量乙醇气体,乙醇标气浓度应选择在ppm量级。当测量路乙醇平均体积浓度为10 ppm时,换算标气池内的乙醇体积浓度
${C_V}$ 为134.4 ppm,对应无水乙醇的体积为:$$ {V_e} = \dfrac{{{m_e}}}{{{\rho _e}}} = \dfrac{{{C_V}{V_G}{M_e}}}{{22.4{\rho _e}}} = \dfrac{{134.4 \times 1.59 \times 46}}{{22.4 \times 0.789\;3}} \approx 0.556\;\text{μ} {\text{L}} $$ (18) 式中:
${m_e}$ 为无水乙醇质量;${\rho _e}$ 表示无水乙醇密度,标准状态下为0.7893${\text{g}}/{\text{c}}{{\text{m}}^3}$ 。用量程为0.2~2 µL的可调式微量移液器准确获取实验所需无水乙醇用量,滴入两端封好的透明塑料管中,充分挥发后测量路径上的乙醇平均体积浓度。分别取0.5、1.0、1.5、2.0、2.5 µL的无水乙醇,制备五组不同浓度的乙醇气体进行测量验证。实验得到的参考路原始信号及基线和五组测量路原始信号及重构基线如图7(a)所示,图7(b)为参考路水蒸气吸收光谱Ar和测量路为混合吸收光谱Aa。为消除噪声影响,对差分所得乙醇蒸气吸收光谱进行平滑滤波。Savitzky-Golay(S-G)平滑滤波法是光谱预处理中常用滤波方法,设置S-G滤波参数为三阶,窗宽为乙醇吸收特征信息宽度的0.6倍,即窗口覆盖1.4 K个数据点,获得平滑后的乙醇吸收光谱如图8所示。
对实验结果进行分析评价。计算五组不同体积的无水乙醇经充分挥发的理论浓度,由Beer-Lambert定律反演测量系统检测到的气体浓度。通过两者之间的绝对误差和相对误差,评价系统的准确性。
由表2可知,乙醇气体浓度绝对误差小于3.5 ppm。当配置乙醇气体浓度较小时,误差较大。微量移液器(FINNPIPETTE F3)量程为0.2~2 µL,当排液容量接近移液器最小容量时,其准确度和精度均最低,对应的相对系统误差最大。实验数据符合该规律。
表 2 不同浓度乙醇标气测量结果
Table 2. Measurement results of ethanol standard gas with different concentrations
Volume/µL 0.50 1.00 1.50 2.00 2.50 Theoretical concentration/ppm 8.9795 17.959 26.9385 35.918 44.8975 Measured concentration/ppm 12.462 19.022 25.575 34.939 45.514 Absolute error/ppm 3.4825 1.063 −1.3635 −0.979 0.6165 Relative error 38.783% 5.919% 5.062% 2.726% 1.373% -
Allan方差应用于气体检测领域,评价系统检测限。对于测量系统而言,存在一个最佳积分时间,使系统在最佳积分时间内保持稳定,对应的测量值即为系统的检测限。
系统连续运行30 min,采集空气中水蒸气的吸收信号,对系统进行Allan方差评价,如图9所示。
由图9可知,系统最佳积分时间为15.1 s,水蒸气检测限为5.7 ppm,对应积分吸光度为1.96×10−4,即乙醇检测限为2.6 ppm。
Stand-off detection of ethanol by laser absorption spectrometry with interference-based internal standard
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摘要: 乙醇是具有宽带吸收特征的大分子挥发性有机物气体,其宽带吸收受空气背景光谱的干扰,这给遥测带来了极大的困难。文中提出通过准确测量干扰光谱、用干扰光谱作为差分吸收谱内部标准的宽带谱气体分析方法,修正光谱分析系统可能的基线偏移和非线性,该方法成功应用于乙醇气体的激光遥测。针对乙醇的近红外特征吸收(7180 cm−1),在实验室条件下,以近红外DFB激光器构建了开放式的遥测实验系统,测量结果表明乙醇浓度测量误差小于3.5 ppm,由Allan方差评价结果表明在积分时间15.1 s时,检测限2.6 ppm,比目前报道的最低检测限低近2个数量级。实现了乙醇的高灵敏开放光程遥测,为进一步研制小型化的乙醇气体遥测系统奠定了基础。Abstract: Ethanol is a macromolecular volatile organic compound (VOC) with broadband absorption characteristics, which is always disturbed by the air background absorption for remote sensing. In this paper, it was proposed that a novel differential absorption spectroscopy for stand-off detection of VOCs with broadband absorption, in which accurately measured the interference spectrum and used as internal standard to correct the possible baseline offset and nonlinearity in the spectrometer. The method has been successfully applied to stand-off detection of gaseous ethanol. An open-air experimental system was constructed with a DFB diode laser under laboratory conditions for the near-infrared characteristic absorption (7180 cm−1) of ethanol. The results showed that the measurement error of ethanol concentration was less than 3.5 ppm, and the detection limit of 2.6 ppm with the integration time 15.1 s by Allan variance evaluation, which was nearly 2 orders of magnitude lower than the lowest detection limit reported at present. The proposed method laid a foundation of highly sensitive miniaturized optical system for VOCs stand-off detection.
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Key words:
- stand-off detection /
- gaseous ethanol /
- open optical path /
- broadband absorption
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表 1 吸光度偏差表
Table 1. Absorbance deviation of peaks
No. Theoretical absorbance Measured absorbance Absolute deviation Relative deviation 1 2.48344 2.48344 0 0 2 0.14914 0.15087 0.00174 1.164% 3 0.10572 0.10415 −0.00157 −1.482% 4 0.03309 0.03490 0.00181 5.46% 表 2 不同浓度乙醇标气测量结果
Table 2. Measurement results of ethanol standard gas with different concentrations
Volume/µL 0.50 1.00 1.50 2.00 2.50 Theoretical concentration/ppm 8.9795 17.959 26.9385 35.918 44.8975 Measured concentration/ppm 12.462 19.022 25.575 34.939 45.514 Absolute error/ppm 3.4825 1.063 −1.3635 −0.979 0.6165 Relative error 38.783% 5.919% 5.062% 2.726% 1.373% -
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