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Abstract
This paper investigates a method for measuring SO2 concentration using Fabry–Perot interferometer correlation spectroscopy. In this method, the experimental system is designed as a separated beam, with the beam entering the F–P cavity at two incidence angles simultaneously to match the peak and valley positions of the SO2 absorption cross-section. The system achieves a 2σ detection limit of 28.2 ppm·m(15 cm) at a sampling frequency of 10 Hz. An outfield comparison experiment with the differential optical absorption spectroscopy method shows good agreement for the simultaneous measurement of SO2 concentration from sulfur combustion, with a correlation coefficient of R2 = 0.93. This study introduces a non-dispersive, highly accurate, and fast gas detection technique.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Major air pollutants such as SO2 and the resultant sulfate aerosol production can seriously harm ecosystems, agricultural productivity, human health, and global warming [1–4]. Because volcanic emissions are the largest source of SO2 in nature, long-term monitoring of volcanic SO2 emissions is crucial for understanding how the Earth’s interior moves. Industrial emissions are the principal anthropogenic sources of SO2, although considerable volumes of SO2 are also produced by the combustion of high-sulfur fuels in ships and automobiles [5–8]. The monitoring of anthropogenic sources of SO2 can help to evaluate and formulate better emission reduction policies as studies show that global anthropogenic SO2 emissions peaked in the 1970s and have been declining year by year, with an upward trend in recent years due to the industrial development and international shipping in developing countries [9].
Currently, the main monitoring methods for SO2 are electro-chemical sensors and optical methods represented by absorption spectroscopy. While electro-chemical sensors can meet the conventional measurement needs, there are still certain defects in terms of data quality, stability, and response time [10,11]. The optical monitoring method represented by absorption spectroscopy technology is gradually replacing the traditional chemical approach for monitoring air trace gases due to its advantages of non-contact, high precision, and good stability [12–14]. Correlation spectroscopy was originally used to monitor SO2 emissions from volcanoes using remote sensing in the 1970s by Moffat et al. [15]. Since that time, correlation spectroscopy has been gradually superseded by spectral measurements made with micro-spectrometers, and the differential optical absorption spectroscopy (DOAS) approach developed by Platt et al. is still the most precise way to quantify SO2 in smoke plumes to date [14,16].
Some low-cost and simple-to-use non-dispersive SO2 measurement techniques have recently been developed due to the development of optoelectronic devices. To measure two-dimensional images of SO2 emitted from volcanoes quickly, Mori et al. first suggested a non-dispersive measurement method in 2006, using a UV camera and a UV bandpass filter. Since then, this method has been further improved and theoretically validated and is now widely used in volcano telemetry and in situ measurements [17–22]. Utilizing UV LEDs and photodiodes, Tirpitz et al. created a non-dispersive UV SO2 in-situ measurement device, and their measurements were in good agreement with electrochemical sensors [13]. However, non-dispersive measurement methods based on narrowband filters can obtain higher light throughput by sacrificing spectral resolution, and have faster measurement speed and imaging advantages, but it is difficult to ensure the accuracy of SO2 measurement(the variation in optical thickness of adjacent bands cannot eliminate the cross interference). In his early study, Georgieva used a Fabry–Perot interferometer (F–P) as a wavelength-selective device to filter out the spectra corresponding to the absorption peaks of gas molecules to measure gases like O2 and CH4 with greater sensitivity [23–26]. F–P correlation spectroscopy was suggested by Kuhn et al. for extremely sensitive image studies of SO2. They suggested changing the F–P cavity length or tilt angle to change the F–P transmission spectrum. However, changing the length of the F–P cavity is expensive, while changing the angle using a motor is simple, but mechanical control has certain limitations on time resolution and instrument stability [27–30].
In this study, we measure the concentration of SO2 using non-dispersive F–P interferometer correlation spectroscopy and the angular dependence of spectral transmittance. First, a forward inversion model is developed, the linear approximation between the measured signal and gas concentration is established, the viability of this method to measure gas concentration is confirmed through simulation, and the measurement bias introduced by this method to potential cross-interference is considered. Following the experimental setup design for the simultaneous measurement of two optical paths, the system's ideal parameters were calculated theoretically and experimentally, a standard gas calibration experiment established its calibration curve, and its detection limit was established using the Allen variance and standard deviation. To confirm initially that the experimental system could be used to measure real emission sources, the SO2 concentration from sulfur combustion was measured in the field and compared with the findings of contemporaneous measurements made by the DOAS system. In contrast to non-dispersive measurements, the experimental setup developed in this study has a greater anti-cross interference capability, and the mechanical structure is entirely fixed to guarantee the system’s stability for long-term applications. Although SO2 analyzers based on laser technology have improved unparalleled time resolution and measurement precision in the kHz regime, the method described in this paper may offer a low-cost alternative while maintaining a certain level of accuracy and time resolution.
2. Measurement principle
2.1 Fabry–Pérot interferometer correlation spectroscopy
The Fabry–Perot interferometer is typically composed of two parallel glass substrates, as shown in Fig. 1. The inner surfaces of the glass substrates that are in close proximity to each other are coated with a reflective film layer to form a mirror with a reflectivity of R. The incident light undergoes multiple reflections between the parallel mirrors, resulting in multiple-beam interference, and the phase difference between the two successive beams is
where $\alpha $ is the angle of incidence of the beam entering the F–P cavity, h is the length of the F–P cavity, and n is the refractive index of the medium between the mirrors. When the surface layer's absorption is not considered, the spectral transmittance of F–P is
Fig. 1. F–P structure and transmittance schematic representation. (a) An air gap F–P is made up of two parallel flat plates that are positioned parallel to the inner surface film layer's reflectivity R; (b) The red line represents the transmittance curve at a beam incidence angle of 7.39°; the blue line represents the transmittance at a beam incidence angle of 4.95°, and the gray portion represents the SO2 molecule absorption cross-section.
The reflectivity of the film layer on the inner surface of the F–P cavity is represented by R in Eq. (2). The F–P spectral transmittance shows a near-periodic comb-like transmittance spectral structure in the narrow-band spectral range when the interference level is high. Equation (2) shows that the F–P cavity length h, the inner surface reflectivity R, and the beam incidence angle $\alpha $ are the key factors affecting the F–P spectral transmittance (for air gap F–P, the medium refractive index nair = 1.0003 remains almost unchanged). The F–P transmittance curves have a near-periodic comb-like transmittance structure, such as the red and blue curves in Fig. 1(b).
F–P can be thought of as a filter with periodic transmittance using the periodic comb transmittance spectral structure, and its transmittance can be varied within a specific range by altering its beam incidence angle $\alpha $ and cavity length h. The molecular absorption cross-sections of some gases also have the same near-periodic structural characteristics; Fig. 1(b) shows the transmittance curve set by F–P with the SO2 molecular absorption cross-section. Therefore, specific F–P parameters can be designed to match the periodic absorption structure of gas molecules to achieve spectral measurements of specific gases. Designing the F–P parameter to align the transmission peaks with the absorption peaks and valleys of the gas absorption cross-section is a classic approach. By adjusting the F–P cavity length h or the beam incidence angle $\alpha $ so that the F–P spectral transmission peak position switches between the absorption peaks and absorption valleys of the gas absorption cross-section, the measured differential signal highly correlates with the gas [28].
A point detector is placed at the receiving end to measure the light intensity signal and configure the F–P interferometer's parameters to serve as a wavelength selection device. When there is no absorption of the gas to be measured in the measurement path, the reference light intensity signal is
The difference between the optical thicknesses of the two settings can eliminate the extinction caused by the absorption and scattering of other gases in the measurement path. The differential optical thickness $\Delta \tau$ is approximately linear with the column concentration S of the target gas, thus enabling the inversion of the target gas concentration.
2.2 Angular dependence of F–P spectral transmittance
According to Eqs. (1) and (2), the F–P spectral transmittance can be changed by varying parameters such as the beam incidence angle, cavity length, and inner surface reflectivity. Figure 2 shows the effects of the UV band parameters beam incidence angle $\alpha $, cavity length h, and inner surface reflectivity R on the F–P spectral transmittance. The horizontal coordinate in the graph indicates the wavelength, the vertical coordinate indicates the adjusted parameter, and the color indicates the transmittance. From Fig. 2(a), the position of the F–P transmission peak gradually shifts to the short-wave direction with the increase of the beam incidence angle, and this change is nonlinear. Figure 2(b) shows the effect of the change in F–P cavity length h on the transmittance, and a change in cavity length at the micron level can dramatically affect the transmittance structure. The reflectivity of the inner surface layer only affects the fineness of the transmission peak and does not affect the free spectral range (FSR) and position of the transmission peak (Fig. 2(c)), while changes in both the cavity length and the beam incidence angle can affect the position and free spectral range of the transmission peak to some extent.
Fig. 2. Effects of beam incidence angle, cavity length, and inner surface reflectivity on the transmittance of F–P spectra. (a) Variation of transmittance with beam incidence angle; (b) Variation of transmittance with cavity length; (c) Variation of transmittance with inner surface reflectivity.
It is difficult and expensive to adjust the F–P cavity length h with nanometer-level precision and to ensure that the two parallel plates of F–P are always parallel to each other during the adjustment process. Therefore, the F–P etalon with a fixed cavity length is chosen in this paper. The cavity length h and the refractive index n of the film layer are fixed for the F–P etalon. According to Eq. (2), the spectral transmittance is only affected by the angle of incidence of the beam. The F–P transmittance can be adjusted within a specific range by changing the incident angle of the light beam entering the F–P cavity.
3. Forward model
3.1 Numerical simulation
To verify the feasibility of measuring SO2 using the F–P transmittance angle-dependent matching of SO2 molecular absorption cross-sections, a forward model is developed for simulation study in this section. The influence of the spectral shape of the light source spectrum in the 290-310 nm band is assumed not to be considered in the forward model when the beam enters the F–P cavity at the incident angles on and off, and the spectral signals acquired at the on and off receiver ends, respectively. When an SO2 column concentration of 1 × 1018 molec.cm-2 is present on the measurement path, the measured spectral signal is shown in Fig. 3. The gray line is the SO2 absorption spectrum with no F–P in the path, the red line is the spectrum when the F–P is in the on position, and the blue line is the spectrum with the F–P in the off position. The SO2 absorption cross-section has different absorption coefficients at different wavelengths, where the difference between absorption peaks and absorption valleys is the largest. Using F–P, the light intensity signals can be selectively screened after the extinction of multiple absorption peak positions (red line in Fig. 3) and multiple absorption valleys (blue line in Fig. 3).
Fig. 3. Spectrum after forward simulation of SO2 absorption at 1 × 1018 molec.cm-2, the gray line is the absorption spectrum, the red line is the transmission spectrum when matching the on position; the blue line is the transmission spectrum when matching the off position.
The optical intensity signal can be seen as the integration of the spectral signal along the wavelength. The optical density is calculated from the directly measured optical intensity signal according to Beer-Lambert’s law, and the optical density is approximately linearly related to the concentration of the absorbing gas (described in Section 3.2). In contrast, the difference in optical density between on and off is only affected by the absorption properties of the SO2 molecule itself (differences in peak and valley between molecular absorption cross-sections). Cross-interference is removed to the maximum extent.
3.2 Linear approximation
The difference between the light intensity signals is entirely generated by the molecular absorption properties of SO2; this enables highly sensitive detection of SO2 molecules directly based on the difference in optical thickness of the light intensity signals. When the effect of light source spectrum and detector quantum efficiency is not considered in the narrow band range, the effective absorption cross-section can be approximated as
The effective absorption cross-section of SO2 is influenced only by the absorption cross-section of SO2 molecules and the F–P transmittance setting. The system concentration-response curves are calculated using the effective absorption cross-section coefficient and the exact numerical simulation, as shown in Fig. 4. The blue curve in Fig. 4 is the system response curve using the linear approximation of the effective absorption cross-section coefficient; the red is the exact numerical simulation result, and the black is the relative deviation. The figure shows that when the concentration of the gas to be measured is low, the linear approximation curve is in good agreement with the exact numerical simulation results, and the relative deviation of the system response using linear approximation does not exceed 2% when the SO2 column concentration does not exceed 1 × 1018 molec.cm-2. Therefore, when the measured gas concentration is less than 1 × 1018 molec.cm-2, the system calibration curve can be obtained through approximation with the linear fitting method.
Fig. 4. SO2 column concentration versus optical thickness response curves, the red line is the exact numerical simulation result, the blue line is the linear approximation curve, and the black line indicates the relative deviation caused by the linear approximation.
3.3 Bandpass filter
Previous work on comb filter-based correlation spectroscopy has indicated that the specificity and sensitivity of the correlation method increase with the number of overlapping gas and comb filter lines [31]. However, F–P resonances and SO2 absorption lines can only be in register over a limited bandwidth, as the periodicity of both combs varies with wavelength at different rates. Therefore, selecting an appropriate bandpass filter is necessary to restrict the range in which the comb filter and gas absorption lines match.
As shown in Fig. 1(b), when the parameters of the F–P etalon are set to R = 0.7 and h = 22.4 µm, the on-off structure of the F–P matches the molecular absorption cross-section of SO2 best within the 290 to 310 nm band-pass segment. Beyond this range, the matching degree of the comb structure decreases significantly. In order to quantitatively evaluate the effect of the width of the selected bandpass segment on the sensitivity of SO2 measurement, we performed the following simulations. We assume that there exists 1 × 1018 molec/cm2 of SO2 gas on the path, and its absorption spectrum is shown in the figure. We use a high-order Gaussian function to simulate a band-pass filter
in Eq. (8), A represents the transmittance of the filter, p represents the order of the Gaussian function, ${\lambda _c}$ represents the center wavelength, and c is the bandwidth. We use an 8th-order Gaussian function to simulate the filter function of different bandwidths with a center wavelength of 300 nm, as shown in Fig. 5. For a known concentration of SO2, the measurement sensitivity can be quantified by the on-off optical thickness difference of the measured signal. Figure 6 shows the simulated on-off optical thickness difference varying with increasing filter pass bandwidth. As the filter's passband increases, the sensitivity of the spectroscopic measurement of SO2 increases initially and then gradually decreases. This is due to the decreasing match between the SO2 molecular cross-section and the F–P comb structure as the passband increases. The original position of the F–P on-end that matches the SO2 absorption peak may coincide with the SO2 absorption valley, as shown in Fig. 5(f), eventually leading to a decrease in the OD difference between on-off, resulting in a decrease in the sensitivity of the measurement of SO2. Therefore, we suggest that the selected filter's passband should not exceed 20 nm, and the filter's passband should not be less than 10 nm. This is because if the filter's passband is too narrow, the passband may only contain one or two F–P interference peaks, and the number of interference peaks will affect the OD difference, as shown in Fig. 5(a). The fluctuation of OD difference within 10 nm in the pass band in Fig. 6 is mainly due to the difference in the number of F-P interference peaks within the pass band.Fig. 5. Absorption spectra of different filter pass bands when the simulated SO2 concentration is 1 × 1018 molec/cm-2. (a) Filter pass band 300 ± 2.5 nm; (b) Filter pass band 300 ± 5 nm; (c) Filter pass band 300 ± 7.5 nm; (d) Filter pass band 300 ± 10 nm; (e) Filter pass band 300 ± 12.5 nm; (f) Filter pass band 300 ± 15 nm.
3.4 Cross interference
SO2 is not the only absorbing gas in the UV wavelength near 300 nm. In addition to O3, NO2, HCHO, and other gas absorption, Fig. 7(a) shows several major gas absorption cross-sections that may exist near 300 nm. Cross interference between gases often affects the accuracy of measurements on a single gas. For conventional non-dispersive measurement methods, cross interference between gases can only be evaluated by predicting the concentration of the interfering gas to assess the effect that cross interference has on the measured gas, but it cannot be eliminated. F–P correlation spectroscopy uses the differential signal between the absorption peaks and valleys of adjacent gases to measure the gas with good selectivity and sensitivity for a single gas. We introduce different proportions of interferent gases in the simulation model and define the relative deviation of SO2 measurement after introducing interferent gases as
in Eq. (9), $\Delta {\tau _{SO2 + others}}$ represents the differential optical thickness calculated according to formula 6 after adding interferent gases, and $\Delta {\tau _{SO2}}$ represents the differential optical thickness of SO2 absorption only without adding interferent gases. The relative deviation $RD$ quantifies the cross-interference of other gases on SO2 measurement.Fig. 7. (a) Absorption cross-section of gas in 290-310 nm, (b) Measurement deviation caused by interfering gas.
Figure 7(b) shows the deviation of the measured SO2 results relative to the non-interference measurements after simulating the mixing of different proportions of interfering gases with SO2 using the forward model without considering the possible chemical reactions between the gases. As the model simulation results show, the interference caused by NO2 and HCHO is almost negligible (1:1 mixing measurement deviation is less than one thousandth). The cross-interference caused by BrO and O3 is relatively large, and when BrO/SO2 is less than or equal to 1%, the measurement deviation caused by cross-interference reaches 0.4%. O3, as the absorbing gas with the strongest interference in the UV band, causes the largest cross-interference to the SO2 measurement, and when O3/SO2 is 10%, the cross-interference reaches 0.5%. Overall, using F–P correlation spectroscopy can effectively eliminate the effect of cross-interference between gases on the measurement results.
4. Experimental system and parameters
4.1 Experimental setup
We designed the experimental system, as shown in Fig. 8, using a xenon lamp (GLORIA-X150A) as the light source to provide a continuous spectrum in the UV band. The beam is emitted from the xenon lamp and passes through collimated lens set Lens1 (GCL-010827 and GCL-010811) and UV bandpass filter F1 (XBPA300). Then the beam enters the cuvette approximately parallel to the cuvette, with the fused silica material at both ends of the cuvette allowing the UV beam to pass through. In the experiment, SO2 gas (gas to be measured) and high-purity nitrogen (reference gas) are introduced into the sample cell. The beam passes through the cell and is divided by the UV beam splitter (UVBS15-1, Newport) into two beams of approximately equal intensity. The F–P etalon (SLS Optics Ltd.) is placed on a rotary table (GCM-1106 M), and the tilt angle of the F–P etalon is adjusted so that the beam enters the F–P etalon at an incidence angle of ${\alpha _{\textrm{on}}}$, and the reflected beam is reflected by the reflector M1 (GCC-102122) and enters the F–P etalon at an incidence angle of ${\alpha _{\textrm{off}}}$. The incident angles ${\alpha _{\textrm{on}}}$ and ${\alpha _{\textrm{off}}}$ correspond to the transmittance Ton and Toff of the F–P etalon, respectively. By adjusting the angle, the spectral transmission peak at the transmittance of Ton matches the absorption peak of the SO2 molecule absorption cross-section, and the spectral transmission peak at the transmittance of Toff matches the absorption valley of the SO2 molecule absorption cross-section. The two beams of light passing through the F–P etalon were focused by lens-coupled Lens2 and Lens3, and the transmitted spectral signal was measured by a fiber optic spectrometer (Maya2000, Ocean Optics), and the light intensity signal was measured by a photodiode (LSGSPD-UV1.5). The position of the F–P transmission peak is changed by adjusting the F–P placement angle according to the spectrum at the measurement end. The photodiode receives the light intensity signal directly at the measurement end, and the photocurrent generated by the diode is converted into a voltage signal via the IV amplifier module. The voltage signal is received using the low-power MSP430F5529 microcontroller ADC sampling channel, and the measurement signal is processed according to Eq. (6) to calculate the gas concentration in the cell.
4.2 Calculation of F–P etalon parameters
In this paper, SO2 is used as the target gas for measurement, so the F–P parameter needs to be selected to match the molecular absorption cross-section of SO2. According to the high-resolution SO2 absorption cross-sections obtained from the Hitran database [32], SO2 was found at several consecutive absorption peak positions near 300 nm as 296.195, 298.074, 300.093, 302.126, and 304.238 nm, with an average absorption peak interval of about 2.01 nm. Thus, the cavity length h of the F–P etalon was first determined so that the free spectral range of F–P coincided with the average spacing of the SO2 absorption peaks, and the ideal cavity length of 22.4 µm was calculated according to the equation
corresponding to the central wavelength of 300.1 nm when the free spectral range of F–P was 2.01 nm. The free spectral range of F–P after determining the cavity length h is almost identical to the spacing of the absorption peaks of the SO2 cross-section, while the position of the transmitted peaks needs to be adjusted by adjusting the beam incidence angle to match the peaks and valleys of the SO2 absorption cross-section. Figure 9(a) shows the variation curve of F–P transmittance with beam incidence angle at the SO2 absorption peak of 300.1 nm; with the increase of angle, multiple transmittance peaks and valleys appear at 300.1 nm. Among them, when the beam incidence angle is 7.39°, the F–P transmission peak matches with the SO2 molecular cross-sectional absorption peak, and similarly, the beam incidence angle of 4.95° can be determined to match with the SO2 molecular absorption valley.Fig. 9. (a) F–P transmittance curve at 300.1 nm with angle; (b) Signal-to-noise ratio curve with reflectivity.
The F–P inner surface reflectivity R affects the fineness of the F–P transmission peak, affecting the F–P filtering effect. Figure 9(b) shows the effect of the inner surface reflectivity on the signal-to-noise ratio for the SO2 measurement. As R increases, the F–P filtering effect is more significant, and the signal-to-noise ratio gradually increases, while when R is higher than 0.65, the signal-to-noise ratio decreases due to the decrease of the transmission light intensity, so the optimal selection interval of F–P reflectivity is 0.6-0.7.
In summary, the results of the F–P parameters selected for the theoretical best match with the SO2 molecular absorption cross-section are shown in Table 1.
Table 1. Theoretical calculation of F–P parameters
4.3 Measuring the actual best angle of incidence
After theoretical calculations, we can roughly determine the F–P custom parameters and the placement angle during measurement. However, errors are inevitable in the integration process, and the placement position and clamping device also affect the F–P tilt angle. Therefore, we experimentally determine the optimal F–P placement position in this paper. N2 was introduced into the 15 cm quartz gas cell, and the F–P etalon apparatus was placed on an electronically controlled rotary table. The rotary table rotation was controlled with a rotation accuracy of 0.01°, and the transmission spectrum of the corresponding angle was recorded at the measurement end (on end) using a spectrometer (Maya200), as shown in Fig. 10(a). The above angular measurement experiment was repeated by passing 1200, 1600, and 2000ppm of SO2 standard gas into the sample cell, and the transmission spectra were recorded, and the spectra were recorded when 2000ppm of SO2 standard gas was passed into the gas cell are shown in Fig. 10(e). Figures 10(b), (c), and (d) show the variation of the integrated light intensity signal with the incident angle when the SO2 gas of 1200, 1600, and 2000ppm is introduced, respectively. The red-filled area shows the weakening of the light intensity caused by SO2 absorption, and the higher the SO2 concentration, the larger the red-filled area. Figures 10(f), (g), and (h) show the variation curves of absorbance with an angle corresponding to 1200, 1600, and 2000ppm SO2. The angles ${\alpha _{\textrm{on}}}$ (8.2°) and ${\alpha _{\textrm{off}}}$ (6.45°) when the transmission peak of F–P matches with the absorption peak and absorption valley of SO2 can be seen in the figure. The F–P at the tilt angle ${\alpha _{\textrm{on}}}$ is fixed to match the SO2 absorption peak, and the distance d1 between the beam splitter and the F–P is measured. The distance between the reflector M2 and the beam splitter should be
according to the formula, and the reflector M2 is adjusted to make the beam enter the F–P.Fig. 10. (a) The variation of F–P transmission spectrum with the angle of incidence of the beam measured by passing N2 into the 15 cm gas chamber; (b) Light intensity curves with angle when 1200 ppm SO2 was passed into the 15-cm gas chamber; (c) Light intensity curves with angle when 1600 ppm SO2 was passed into the 15-cm gas chamber; (d) Light intensity curves with angle when 2000ppm SO2 was passed into the 15-cm gas chamber; (e) Variation of the F–P transmission spectrum with the angle of incidence of the beam measured by passing 2000ppm SO2 into the 15 cm gas chamber; (f) Curve absorbance curve with angle when 1200 ppm SO2 was passed into the 15 cm gas chamber. (g) Absorbance curve with angle when 1600 ppm SO2 was passed into the 15 cm gas chamber. (h) Absorbance curve with angle when 2000ppm SO2 was passed into the 15 cm gas chamber.
Based on the measurement results of the rotating F–P etalon, the actual beam incidence angles matching the absorption peaks and absorption valleys of the SO2 molecular absorption cross-section were determined to be 8.2° and 6.4°, respectively (there may be some tilt in the F–P mounting during the rotating table, and there is a discrepancy between the rotating table rotation angle and the actual incidence angle). Because the SO2 absorption cross-section and the F–P transmission spectral structure are not ideal periodic structures, achieving an exact match between the absorption peak and valley and the F–P transmission peak positions is difficult. A narrow band filter with a center band of 300 nm and a half height width of 10 nm is used outside the best matching band to filter out the interference caused by poor matching.
5. Results and discussion
5.1 Calibration
After filtering by the bandpass filter, only the light signal in the range of 290–310 nm was allowed to pass through, and a diode photodetector was used at the measurement end to measure the light intensity signal. The linear response of the measurement system was calibrated by passing SO2 standard gas with concentrations of 400, 800, 1200, 1600, and 2000ppm into the 15 cm sample cell in turn, and the SO2 column concentrations along the sample cell were 60, 120, 180, 240, and 300 ppm·m when the gas was mixed uniformly.
It can be seen from Fig. 11 that the spectral signal matching the SO2 absorption peak decreases significantly (about 65% at the maximum concentration) as the concentration of the incoming sample gas increases. In comparison, the spectral signal matching the SO2 absorption valley decreases by only about 20% of the light intensity signal at an SO2 concentration of 2000ppm in the sample cell.
The calibration curve using the standard gas is shown in Fig. 12, in which the red curve is the calibration curve when the F–P transmission peak matches the absorption peak of the SO2 cross-section. Blue indicates the calibration curve when the F–P transmission peak matches the absorption valley of the SO2 cross-section. Black indicates the calibration curve between the difference in the optical depth and the concentration of the SO2 column. According to the numerical simulation results, the difference in the optical depth between the SO2 column concentration and the two F–P settings, the calibration curve is approximately linear (when the SO2 absorption is not saturated). The calibration curve is
Fig. 12. SO2 calibration curve for the standard gas, the red line is the fitted curve when the F–P transmission peak matches the absorption peak, the blue line is the fitted curve when the F–P transmission peak matches the absorption valley, and the black line is the calibration curve for the differential optical thickness.
5.2 Detection limits and system stability
Figure 13(a) shows the value of the light intensity signal directly measured by the photodiode detector for N2 over a period. The measured concentration of SO2 is calculated from the light intensity signal by Eqs. (5) and (6) and the calibration curve. Because the actual concentration of SO2 is 0 ppm·m when N2 is passed in, the SO2 concentration obtained by inversion reflects the measurement uncertainty. Figure 13(b) shows the concentration time series for a period at a 10 Hz sampling frequency. Ideally, averaging the measurement signal and improving the integration time can reduce the random noise to improve the signal-to-noise ratio. Thus, the Allen variance can assess the system’s long-term stability and determine the best sensitivity when the integration time. Figure 13(c) shows the Allen variance of the measurement system. The Allen variance decreases with increasing sample averaging time, indicating the system's stability. Figure 13(d) presents the histogram distribution of the time series of measured concentrations. the standard deviation of the directly calculated measured values is 14.1 ppm·m. With a 2σ detection limit, the detection limit of the system at a 10 Hz sampling frequency is 28.2 ppm·m. According to the Allen variance calculation results, increasing the system integration time can further reduce the detection limit of the system, such as the 2σ Allen variance detection limit reaching a minimum of 1.4 ppm·m when the average sampling time is 40 s. Further, amplifying the measurement signal using a multiple reflection optical cavity and detecting it with a lock-in amplifier can improve the sensitivity and accuracy of the measurement of the percentage of concentration volume. The optical cavity increases the absorption optical path, while the lock-in amplifier filters out low frequency noise and enhances the signal-to-noise ratio. However, this paper only provides a preliminary theoretical validation of the measurement method and therefore does not integrate a measurement system with the goal of a lower detection lower limit.
Fig. 13. (a) Photodiode direct measurement of light intensity signal time series; (b) SO2 concentration inversion time series; (c) Allen variance; (d) Concentration statistics histogram with standard deviation 14.1188.
5.3 Comparison experiments
An external comparison experiment was conducted in this paper to verify the accuracy of the experimental setup in measuring SO2 in practice. The experimental setup is shown in Figs. 14(a) and (b). The same Xenon lamp was used as the reference light source, and the experimental setup and the fiber optic spectrometer were placed in parallel to measure the light signal after SO2 absorption in the same optical path (∼1 m). Moreover, the spectral signals measured by the fiber optic spectrometer were inverted to obtain an SO2 concentration according to the DOAS method. For safety reasons, the sulfur combustion experiment time was controlled at 10 min, and a set of data was collected every 0.3 s. Every ten measured values were averaged to remove noise interference. The sulfur burning process was divided into three stages (start burning, in burning, and stop burning). Comparing the experimental results shown in Fig. 14(c), it can be seen that after start burning, the SO2 concentration on the measurement path gradually increases; during the burning process, the average SO2 concentration in the path is maintained at about 200 ppm due to good diffusion conditions, and the change of SO2 concentration on the measurement path is affected by the change of wind field; at the end of the burning, the measured SO2 concentration on the path rapidly decreases to 0, again indicating good diffusion conditions in the experiment. The measured concentration results of the two sets of devices showed good agreement; the measured concentrations changed in the same trend; and the correlation coefficient R2 of the data fitting results reached 0.93, as shown in Fig. 14(d). The comparative test results illustrate that the method and device based on F–P correlation spectroscopy for SO2 measurement can be applied to the practical monitoring of SO2 emission sources.
Fig. 14. (a) Experimental setup of the FP system; (b) Comparison experimental setup; (c) Measurement of SO2 concentration change during sulfur combustion in real-time comparison, the red dot line is the measurement result of F–P experimental system, the blue dot line is the measurement result of DOAS system; (d) Comparison experimental linear fit with correlation coefficient R2 = 0.93.
6. Summary
This paper presented a method to measure SO2 concentration using F–P optical correlation spectroscopy by angularly adjusting the transmittance spectral structure of the F–P interferometer approximate period to match the molecular absorption cross-section of SO2 to achieve selective measurement of SO2 molecules. The feasibility of the measurement method described for SO2 concentration measurement, the use of linear fitting of standard concentrations to obtain calibration curves, and the possible problem of cross-interference between gases were investigated by establishing a forward model. A double-optical measurement system was designed so that the beam entered the F–P cavity at on and off incidence angles to match the absorption peaks and valleys of the SO2 cross-section; the ideal F–P etalon was theoretically calculated to match the absorption cross-section of the SO2 molecule near 300 nm, and the angle rotation experiment was performed to determine the tilt angle of the F–P placement under practical conditions. Furthermore, SO2 standard sample gas calibration experiments were conducted to verify the linear correlation between OD measurement results and SO2 concentration with the calibration curve. The detection performance of the experimental apparatus was measured, and the detection limit 2σ reached 1.4 ppm·m at an integration time of 40s according to the calculated Allen variance. Theoretically, the lower limit of measurement can be further reduced by using a longer absorbing optical path and a detector with lower noise. This paper is only a preliminary verification of the feasibility of the measurement method, and further work is needed in the aspect of system optimization. An external field comparison test was conducted on SO2 generated by sulfur combustion. Using the experimental setup in parallel with the DOAS system, the comparative experimental results showed a consistent trend, and the correlation coefficient R2 of the experimental results reached 0.93. Moreover, compared with differential optical absorption spectroscopy, the proposed method did not require a spectrometer to receive the spectral signal, which avoided the reduction of light flux caused by the spectrometer slit. The higher light flux could theoretically obtain a faster measurement speed and higher signal-to-noise ratio. Although the light intensity theoretically doubles by switching the F–P angle through a motor (without beam splitter), the large repeat positioning error of mechanical rotation has a significant impact on the measurement results and the time taken for the motor to rotate greatly limits the improvement of the measurement time resolution. The completely fixed mechanical structure of this paper can greatly avoid these disturbances. In addition, since the F–P non-dispersive system does not require a slit to limit the aperture, the use of a beam splitter can still meet a larger signal intensity even if the light intensity is halved. Therefore, the application prospect of portable measurement was achieved. The results of this paper could provide a new idea for using an F–P interferometer for high-precision gas measurement as well as a basis for further research on non-dispersive gas measurement methods. While our work represents a preliminary exploration of the measurement of gas concentration using F–P optical correlation spectroscopy, there are still many factors that have not been considered. For example, temperature and pressure can broaden the absorption lines of the gas, which can affect the accuracy of the measurement. While these effects may be negligible in the short term, they will need to be taken into account in future work. Additionally, incorporating a lock-in amplifier module in the system can further suppress low frequency noise and improve the signal-to-noise ratio of the measurement. In addition to SO2, other gases with approximately periodic absorption cross sections, such as BrO, CO2, NH3, etc., can also be detected using the same method as long as the F-P interferometer with matching parameters is designed.
Funding
National Natural Science Foundation of China (41975037, U19A2044); Key Technologies Research and Development Program of Anhui Province (202004i07020013).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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