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反应室以经典圆筒形来进行整个系统建立, 其示意图如图 1所示。
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图 1中虚线框为激发光路部分,假设激发光源处的双凸透镜1焦距为f1,由于反应室前端结构安装存在误差,难以保证荧光采集区域(记为:图 1中A′-B′截面处)的弥散斑的稳定性,激发光路采用物远心光学系统结构[4-6],克服物距变化带来的误差不足的同时, 提高了设备的互换性,即以一定的平行光束经双凸透镜、光阑进入反应室,初定荧光的采集位置在物远心系统的弥散斑A′-B′截面处。光阑中通孔直径为d1,当光强与透镜1的焦距一定时,为保证激发光束完全进入反应室,同时抑制光阑边缘菲涅耳衍射效应,光束入射发散半角α的正切值应大于光阑孔径d1与2倍焦距的比值[7-9],即:
$ \tan \alpha \geqslant \frac{d_{1}}{2 f_{1}} $
(1) 假设反应室的直径为d2, 长度为a,荧光采集出口面积为S1,光子单位时间被反应室吸收率为A,则激发光被反应室内壁吸收的概率为:
$ P_{1}=\left(\pi a d_{2}-S_{1}\right) A /\left(\pi a d_{2}\right) $
(2) 当激发光强、光阑光通量、SO2气体体积分数一定时,假设激发光散射光子数为N1,通过光阑后光子数至少为N2=k1d1/N1,k1为比例系数,与光阑通光直径成正比,与杂散光光子数成反比。则有:
$\frac{N_{2}-N_{1}}{N_{2}}=\frac{k_{1} d_{1} / N_{1}-N_{1}}{k_{1} d_{1} / N_{1}} $
(3) -
SO2分子被214nm的紫外光激发后产生微弱荧光光子,荧光的采集需要将微弱的光进行汇集才能更好地被探测器检测。通常,凸透镜又称聚光镜,常见分类有双凸透镜[10-13]和平凸透镜。针对这两类透镜聚光特性分析如下。
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如图 2所示,r1为左凸曲率半径,r2为右凸曲率半径,n为折射率,H和H′分别为左右主点,O1和O2分别为左右顶点,δ为透镜总厚度,F和-F分别为左右焦点,f和-f为左右焦距。
可知左右焦距公式为:
$\left\{\begin{array}{l} f=n r_{1} /(n-1) \\ -f=n r_{2} /(n-1) \end{array}\right. $
(4) 若平行光左侧入射,光路通过透镜必经过F焦点。
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平凸透镜相当于一端曲率半径为无穷大的双凸透镜,且有方向性,如图 3所示。
图 3a为右凸r1取无穷大,则由焦距公式有:
$ f=n r_{2} /(n-1) $
(5) 图 3b为左凸r2取无穷大,则由焦距公式有:
$ f=n r_{1} /(n-1) $
(6) 图 3中对比计算发现,像方主点H′距焦点距离右凸透镜将大于左凸透镜,若将图 3中透镜以图所示位置组合后,由于左侧透镜的存在可将左侧透镜出射光再次汇聚,同时,能够缩小左侧透镜在组合透镜出射的汇聚点,扩大视场角度,符合荧光采集光路汇聚且微型化减小反应室结构尺寸的要求,故拟定此光路系统。
当激发光强、SO2气体体积分数一定时,SO2分子被激发的效率为常数η,激发总有效荧光光子数为N3=η(N2-N1), 通过荧光采集口的光子数至少N4=k2S1/d2,k2为比例系数,与荧光采集口面积成正比,与反应室直径成反比。杂散光子数与反应室长度成正比,即为N1=k3a。
综上所述,当反应室内光子处于平衡状态,通过被反应室壁吸收后剩余杂散光子与有效采集的荧光光子数的比值,就可以了解光路系统对信噪比的影响。荧光采集光子数N4与剩余杂散光子数ΔN1之比为:
$ \frac{N_{4}}{\Delta N_{1}}=\frac{k_{2} \frac{S_{1}}{d_{2}}}{\eta N_{1}\left(1-\frac{\pi a d_{2}-S_{1}}{\pi a d_{2}} A\right)} $
(7) 将N1=k3a代入可得:
$ \frac{N_{4}}{\Delta N_{1}}=\frac{k_{2} \frac{S_{1}}{d_{2}}}{\eta k_{3} a\left(1-\frac{\pi a d_{2}-S_{1}}{\pi a d_{2}} A\right)} $
(8) -
针对(3)式,当d1,N1,k1一定时,经数值计算,(N2-N1)/N2随d2的变化情况如图 4所示。
对于此光路,经计算分析可知,反应室直径一定,当有效激发光比率随光阑孔径变化时,出现峰峰值后,随光阑孔径的增大,有效激发光比率反而下降了,最后趋于稳定。因此,当光阑孔径存达到最佳值时,使得有效激发光比率达到最大,光阑抑制杂散光的效果较好。
针对(8)式,当a,k1,k3,S1,η,A一定时,经数值计算,N4/ΔN1随d2的变化情况如图 5所示。
对于反应室不同直径时,随内壁吸收率的增加,有效采集的荧光光子数与剩余杂散光子比率增加;当内壁吸收率相同时,直径增加,反而比率下降。若反应室中激发光,激发后产生的荧光光子数不随d2增加而降低,而保持与某个直径d相对应的荧光光子数,则(8)式中分子成为了常数,N4/ΔN1比率的分母随d2的增加而减少,最终趋于一个极限值,故存在一个分析模块的微型化最佳半径。
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为了验证物方远心光学系统与双平凸透镜组合光学系统在SO2分析模块中的应用的可行性,采用间接测量光路法,对整个光学系统进行分析。因不同体积分数的气体,引起探测器的电压值变化,进而分析电压值的线性度来验证光路系统。
实验中利用TR1BKD型动态校准仪配比不同体积分数的SO2气体,设定流量为1L/min;利用已有的信号采集系统进行电压信号的采集,其实验数据如表 1所示。
Table 1. Relationship between volume fraction and voltage value with flow rate of 1 L/min
SO2 volume fraction/10-9 voltage value per measurement/mV average voltage value /mV 1 2 3 4 5 6 0 20.0 21.0 20.5 20.7 19.5 20.0 20.3 50 429.5 430.0 420.5 440.0 425.8 435.2 430.2 100 838.8 840.0 836.2 838.5 838.0 838.5 849.3 150 1247.0 1247.5 1246.9 1250.0 1237.6 1246.5 1245.9 200 1656.0 1658.5 1660.5 1652.0 1654.5 1656.0 1656.3 如图 10所示,将实验数据经散点拟合,得出其相关系数R2=0.9999,说明SO2体积分数与探测器的电压值有着较好线性关系,间接表明物方远心光学系统与双平凸透镜组合光学系统在SO2分析模块中的应用效果较好,起到了光路优化的作用。
大气SO2检测模块的光路研究
Optical path study of atmospheric SO2 detection module
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摘要: 为了适应当下网格化大气监测中低体积分数的SO2气体检测需要, 针对紫外荧光法模块化应用的光路关键性问题, 将物远心光学系统与双平凸组合光学系统相结合, 应用于SO2检测模块的激发光路和采集光路上。采用多光学系统优势互补的方法, 进行了理论分析和实验验证。通过模型的建立, 分析了光路系统对反应室信噪比的影响, 结合ZEMAX软件仿真、蒙特卡洛法公差评价分析与整个光学系统的间接实验验证, 取得了该优化光路系统应用。结果表明, 其仪器线性度的相关系数的平方能够达到0.9999。该光学系统具有较强的应用价值, 能够为紫外荧光法模块化光路系统设计提供理论依据与实验数据支持。Abstract: In order to meet the requirement of low volume fraction SO2 gas detection in grid atmospheric monitoring, aiming at the key problem of optical path in modular application of ultraviolet fluorescence method, object telecentric optical system was combined with double-plane-convex optical system to apply the excitation and acquisition paths of SO2 detection module. Theoretical analysis and experimental verification were carried out by complementary advantages of multi-optical systems. Through the establishment of the model, the influence of optical system on signal-to-noise ratio of reaction chamber was analyzed. Combining ZEMAX software simulation, Monte Carlo tolerance evaluation analysis and indirect experimental verification of the whole optical system, the application of the optimized optical system was achieved. The results show that, the square of correlation coefficient of instrument linearity can reach 0.9999. The optical system has strong application value. It can provide theoretical basis and experimental data support for the design of modular optical system of ultraviolet fluorescence method.
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Key words:
- optical design /
- light path research /
- optical path modeling /
- ZEMAX simulation /
- experimental analysis
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Table 1. Relationship between volume fraction and voltage value with flow rate of 1 L/min
SO2 volume fraction/10-9 voltage value per measurement/mV average voltage value /mV 1 2 3 4 5 6 0 20.0 21.0 20.5 20.7 19.5 20.0 20.3 50 429.5 430.0 420.5 440.0 425.8 435.2 430.2 100 838.8 840.0 836.2 838.5 838.0 838.5 849.3 150 1247.0 1247.5 1246.9 1250.0 1237.6 1246.5 1245.9 200 1656.0 1658.5 1660.5 1652.0 1654.5 1656.0 1656.3 -
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