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Abstract
For wide dynamic range gas concentration detection based on tunable diode laser absorption spectroscopy (TDLAS), direct absorption spectroscopy (DAS) and wavelength modulation spectroscopy (WMS) are usually used in combination. However, in some application scenarios such as high-speed flow field detection, natural gas leakage, or industrial production, the requirements of wide-range, fast response and calibration-free must be met. Taking applicability and cost of TDALS-based sensor into consideration, a method of optimized direct absorption spectroscopy (ODAS) based on signal correlation and spectral reconstruction is developed in this paper. This method can achieve adaptive selection of the optimal benchmark spectrum for spectral reconstruction. Moreover, methane (CH4) is taken as an example to carry out the experimental verification. Experimental results proved that the method satisfies wide dynamic range detection of more than 4 orders of magnitude. It is worth noting that when measuring large absorbance with concentration of 75 × 104 ppm with DAS and ODAS method, respectively, the maximum value of residual is reduced from 3.43 to 0.07. Furthermore, whether measuring gas of small or large absorbance with different concentrations, which vary from 100 ppm to 75 × 104 ppm, the correlation coefficient between standard concentrations and inverted concentrations is 0.997, showing the linear consistency of the method in wide dynamic range. In addition, the absolute error is 1.81 × 104 ppm when measuring large absorbance of 75 × 104 ppm. It greatly improves the accuracy and reliability with the new method. In summary, the ODAS method can not only fulfill the measurement of gas concentration in wide range, but also further expand the application prospects of TDLAS.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Thanks to their advantages of non-contact, high sensitivity and strong selectivity [1], sensors based on tunable diode laser absorption spectroscopy (TDLAS) have been widely applied in industrial process control [2], combustion diagnostics [3], environmental monitoring [4,5] and other fields [6,7]. When the absorbance is less than 0.05, wavelength modulation spectroscopy (WMS) has a significant advantage of strong anti-interference ability compared with direct absorption spectroscopy (DAS) [8–10]. However, the second harmonic (2f) peak value measured by WMS is no longer a liner with gas concentration when the absorbance is closer to 0.05 or more than 0.05 [11]. Therefore, DAS still plays an important role in measuring large absorbance. For instance, a sensor combining DAS and WMS is proposed for monitoring methane (CH4) in full range [12]. And in essence, it takes into account both detecting small absorbance with WMS method and large absorbance with DAS method.
Unfortunately, when detecting large-scale changes of gas concentration in high-speed flow fields, in flames and in combustion fields [13–15], the scanning frequency of the DFB laser is required to be close to kilohertz (KHz) or even higher. Correspondingly, the frequency of WMS will reach hundreds of KHz or even megahertz (MHz), which undoubtedly greatly increases the complexity and cost of the lock-in-amplifier, nay impossible. In contrast, the TDLAS-based sensor using only DAS method has the advantages of simple circuit structure, higher scanning frequency and easy data processing, which makes it more suitable for various occasions. However, it is difficult for DAS method to meet the requirements of wide range and precise detection at the same time. More specifically, with large absorbance, the spectrum obtained based on DAS will show nonlinearity or even spectral distortion, which will be analyzed in detail in the second and third parts. On the other hand, when measuring small absorbance, it is difficult to meet the demand of weak signal extraction since DAS is easily affected by troublesome noise, such as random noise and coherent noise [8,16,17].
Based on above analysis, the biggest problem is that neither WMS method nor DAS method can carry out wide-range adaptive gas measurement. In order to solve above generic technical problems and expand the applicability of TDLAS, an optimized direct absorption spectroscopy (ODAS) method based on signal correlation and spectral reconstruction is proposed in this paper. This method significantly expands the dynamic range of DAS by improving the signal-to-noise ratio at small absorbance and reconstructing the distorted spectrum at big absorbance. And also, taking CH4 as an example, an experimental system is established to verify the validity and reliability of the method.
2. Optimized direct absorption spectroscopy method
Compared with the WMS, DAS has the advantage of free calibration and simple circuit structure. It is based on Beer-Lambert's law and can be expressed as [18,19]
where ${I_0}$ is the laser emission intensity, ${I_t}$ is the transmitted laser intensity, $S(T )$ (cm-2· atm-1) is the absorption line intensity at temperature $T$, X is the concentration of gas to be measured, P (atm) is the gas pressure. L (cm), which is usually expressed as the optical path, is the distance that light travels in the gas to be measured. $\phi (\upsilon )$ describing the shape of the gas absorption spectrum is the absorption line-shape function and is related to gas temperature and pressure, $\alpha (\upsilon )$ is the absorption coefficient of the gas to be measured at a specific frequency $\upsilon $.The product $\alpha (\upsilon )L$ is the spectral absorbance, and the line-shape function $\phi (\upsilon )$ is normalized such that $\mathop \smallint \limits_{ - \infty }^\infty \phi (\upsilon )d\upsilon \equiv 1$[20]. The integrated absorbance can be expressed asDuring the measurement process, A can be obtained by integrating the DAS spectrum in the frequency domain. Substituting A into Eq. (2), the gas concentration can be obtained, as shown in Eq. (3),
As described above, the gas concentration can be calculated based on Eq. (3), which is also the theoretical basis of calibration-free DAS. Now to address the issue mentioned in the introduction, it is urgent to develop a new method to meet the needs of wide dynamic concentration range – optimized direct absorption spectroscopy, and the flow chart is shown in Fig. 1.
Fig. 1. Flowchart of the ODAS method. (a)The process of benchmark spectra selection, (b)The process of real-time signal.
In order to obtain accurate spectral measurement results, selecting suitable benchmark spectra for spectral reconstruction is the premise of this method, and the process is shown in Fig. 1(a). Firstly, based on the MATLAB R2020b platform combined with the absorption line intensity of CH4 near 1653.74 nm in the HITRAN database [21], the Vogit absorption function corresponding to m groups of different concentrations are simulated in a concentration-increasing manner. When the pressure and optical path are determined, the simulated absorption spectra corresponding to ${C_1}$, ${C_2}$…${C_m}$ are ${S_{sim\_1}}$, ${S_{sim\_2}}$…${S_{sim\_m}}$, respectively. The simulated spectrum ${S_{sim\_1}}$ corresponding to ${C_1}$ is taken as the first group of benchmark spectra ${S_{bs\_1}}$, and calculate the correlation coefficients between ${S_{bs\_1}}$ and ${S_{sim\_2}}$…${S_{sim\_m}}$ in turn. If the correlation coefficient corresponding to a certain simulated spectrum ${S_{sim\_x}}$ is smaller than the set correlation threshold ${T_{corr}}$, it means that the second group of benchmark spectra should be selected as ${S_{bs\_2}}$ from ${S_{sim\_x}}$…${S_{sim\_m}}$. By analogy, if the correlation coefficient between ${S_{sim\_y}}$ and ${S_{sim\_m}}$ ($y > x$) is smaller than ${T_{corr}}$, it should continue to select the third group of benchmark spectra ${S_{bs\_3}}$. Finally, the correlation coefficients, COEFs, between the simulated spectra and the corresponding benchmark spectrum in each concentration range are all greater than ${T_{corr}}$. And the benchmark spectra are recorded as ${S_{bs\_1}}$, ${S_{bs\_2}}$… ${S_{bs\_n}}$, respectively.
The above benchmark spectra selection is the first step of the new method and can be done in advance. Carefully selected benchmark spectra can be directly saved to the computer or microprocessor for subsequent spectral reconstruction, which avoids cumbersome calculations for spectrum fitting and achieves the goal of real-time fast processing. After this, the correlation between the real-time spectrum and the benchmark spectrum must be studied to determine which benchmark spectrum to use for spectral reconstruction. As shown in the first step in Fig. 1(b), two sets of raw signals will be detected by the experimental system, and they are transmitted signal and Fabry-Perot (F-P) signal, respectively. And both are sampled based on sample time series or sample points. In one cycle, the signal is always sampled at equal time intervals. The time to start sampling is t, and the time interval is $\Delta t$. And then the spectrum corresponding to sample time series $[{t,\; \; t + \Delta t,\; \; t + 2\Delta t,\; \; t + 3\Delta t \ldots \; t + n\Delta t} ]\; $ can be obtained. Number the above time series sequentially as a series of sample points starting from 0. In this way, the spectrum corresponding to sample points $[{0,\; 1,\; 2,\; 3 \ldots \; n} ]$ can be obtained. Based on the F-P signal, its frequency range, $\Delta {\upsilon _L}\; $, can be calculated according to Eq. (4)
Among them, N is the number of modes contained in the F-P signal, $\mathrm{\Delta }\nu = 1.5GHz$ is the free spectral range (FSR) of the F-P cavity in the experimental system as described in Part 3.1. Furthermore, as shown in Eq. (5), the wavelength width, $\Delta \lambda $, scanned by the laser can be obtained.
where c is the speed of light, ${\upsilon _0}$ is the central wavenumber of absorption. Since the F-P signal and the transmitted signal are a pair of synchronous trigger acquisition signals, the corresponding wavelength width can be calculated according to the number of modes on the left and right of the absorption peak. The wavelength range obtained can be converted to wavenumber range according to Eq. (6).Record wavenumber range is ${\nu _l} - {\nu _r}$. According to the corresponding relationship among the sample points of F-P signal, the sample points of transmission signal and the wavenumber range above, the conversion relationship between the sample points and the wavenumber in the transmission signal can be obtained by using the second-order polynomial fitting, as shown in Eq. (7).
where ${W_N}$ is the wavenumber corresponding to sample point, $SP$. And A, B and C are coefficients of the second-order polynomial. The spectrum based on the sampling time series or sample points can be converted into a wavenumber-based direct absorption spectrum after the above process. It has to be said that with the increase of concentration, the light intensity is gradually weakened, which will eventually lead to spectral distortion. Therefore, abnormal data will be filtered out before signal correlation study. Calculate the correlation coefficients between the DAS spectrum S and ${S_{bs\_1}}$, ${S_{bs\_2}}$…${S_{bs\_n}}$, which are $COE{F_1}$, $COE{F_2}$… $COE{F_n}$, respectively. Compare and pick out the largest correlation coefficient $COE{F_x}$ and the corresponding benchmark spectrum ${S_{bs\_x}}$.After the above screening, it shows that the DAS spectrum has the best correlation with the benchmark spectrum ${S_{bs\_x}}$ and it is the optimal choice using ${S_{bs\_x}}$ for spectral reconstruction. Next, calculate the coefficient k between ${S_{bs\_x}}$ and S based on least square method, which can represent the scaling factor of measured S relative to simulated ${S_{bs\_x}}$. And the correlation coefficient $COE{F_x}$ represents the weight factor of ${S_{bs\_x}}$ in the reconstructed spectrum. Then it is easy to calculate the weight factor of the original measured S in the reconstructed spectrum is $1 - COE{F_x}$. Therefore, the following spectral reconstruction formula is obtained.
Finally, the concentration corresponding to the reconstructed spectrum ${S_r}$ is calculated.
3. Experimental detail
3.1 Experimental setup
Figure 2 shows the experimental system. The driving circuit on the homemade circuit system controls the distribute feedback (DFB) laser scanning range to be about 6046.12-6047.67 cm-1 (calculated based on F-P signal), which can cover the required absorption line range of CH4 near 1653.74 nm. The light beam emitted by the laser enters the multi-pass cell with 55 cm optical path and F-P interferometer (THORLABS SA200-12B) with free spectral range (FSR) of 1.5 GHz through a 9:1 fiber beam splitter, respectively. It is worth mentioning that the light entering the multi-pass cell is 90% of the total light. It is obvious that the absorption signal is received by the packaged detector inside the cell and sent to the integrated circuit system. Meanwhile, the trigger signal generated by the circuit system will be sent to the data acquisition (DAQ) card to prompt the acquisition of the F-P signal. The transmission signal containing absorption information collected by the circuit system and the F-P signal collected by the DAQ card are sent to the computer for data processing.
3.2 Selection process of the benchmark spectra
Taking CH4 as an example and based on the principle in Part 2, the selection process of benchmark spectra is as follows. Under the specific conditions of 1 atm, 23 °C, and 55 cm optical path, the simulated spectrum with concentration of 0.5 × 104 ppm CH4 is enlarged by 100 times, and compare it with the simulated spectrum of 50 × 104 ppm, which is shown in Fig. 3. It can be concluded that with the increase of concentration, the DAS spectrum does not change linearly, which also proves the necessity of selecting different benchmark spectra according to the concentration range. Based on spectral simulation of CH4, 23 groups of simulated spectra of CH4 gas with different concentrations are obtained, and the corresponding concentration values are shown in Table 1.
Fig. 3. Nonlinearity of the simulated spectra corresponding to different concentrations. (a)Simulated spectra and (b)Residual.
Table 1. Concentrations corresponding to 23 groups of simulated spectra
The pink dots in Fig. 4 are the correlation coefficients when only the first simulated spectrum is selected as the benchmark. As the concentration increases, the correlation of the simulated spectrum gradually weakens, which also leads to an increase of the error during spectral reconstruction. The threshold of correlation coefficient is determined to be ${T_{corr}}$=0.99995. As the specific steps proposed in Part 2, another benchmark spectrum should be selected in the simulated spectra whose correlation coefficient are smaller than ${T_{corr}}$. Finally, among the 23 groups of simulated spectra corresponding to different concentrations, three groups of benchmark spectra are selected, and their corresponding concentrations are 0.5 × 104 ppm, 20 × 104 ppm, 75 × 104 ppm, which are marked with the star points in Fig. 4. These three groups of benchmark spectra are also corresponded to the different concentration ranges marked in Fig. 4, respectively. In each concentration range, it can be observed that the correlation coefficients between benchmark spectrum and the remaining simulated spectra are all greater than ${T_{corr}}$, which meets the threshold requirement. The experimental results obtained in Part 4 are all based on these three groups of benchmark spectra. It is worth noting that the above 23 concentration values in Table 1 don’t strictly follow the concentration gradient at equal interval.
4. Result and discussion
The measured F-P signal and transmission signal are shown in Fig. 5(a)(b), respectively. The wavenumber range scanned by the laser can be calculated with the assistance of the FSR parameters of F-P interferometer and the quantity of modes based on the steps in Part 2. It can be known from Fig. 5(a) that there are 31 cavity modes in total, and it can be calculated that the scanning wavelength width is about 0.4239 nm based on Eq. (4) and Eq. (5). In addition, the time series of the transmission signal can be converted to wavenumbers by taking the central wavelength of the absorption line as the standard. Therefore, the DAS spectrum can be obtained, which is shown in Fig. 5(c).
Fig. 5. Measured signal and converted DAS spectrum. (a)F-P signal, (b)Transmission signal, (c)DAS spectrum.
The discussion of spectral reconstruction by the ODAS method can be divided into two different cases. Adopting appropriate algorithms to eliminate or reduce the influence of kinds of noise in spectral signal has always been the focus of researchers [17,22–24]. The experimental and simulated spectrum of CH4 with concentration of 0.5 × 104 ppm are shown in Fig. 6 (a), respectively. It is clearly shown in the illustration in Fig. 6(a) that the random noise level in the experimental spectrums is 0.003. And meanwhile the peak value of the DAS spectrum is about 0.1 and the maximum value of the residual in Fig. 6(c) is 0.004. It can be easily calculated the relative error of peak value will reach 4%, so the concentration calculated based on the raw absorption signal will be inaccurate. In contrast, the reconstructed spectrum obtained by the ODAS method reduces the residual level to 0.00001 and the relative error of peak value to 0.01%, as shown in Fig. 6 (b)(d).
Fig. 6. Spectra and residual with small absorbance of 0.5 × 104 ppm CH4. (a)Simulated spectrum and experimental spectrum and (c)Residual, (b)Simulated spectrum and reconstructed spectrum and (d)Residual.
In addition to the problem that measured spectrum is affected by noise mentioned above, the problem of spectral distortion is more difficult to solve when measuring large absorbance, which even will cause the traditional concentration inversion algorithm to fail completely. According to the specific steps of ODAS proposed in Part 2, when measuring large absorbance with concentration of 50 × 104 ppm CH4, the reconstructed spectrum and its residual with simulated spectrum are shown in Fig. 7(b) and (d), respectively. The maximum residual in reconstructed spectrum is 0.07, and the peak value of absorption in Fig. 7(b) is about 10. According to the calculation method similar to Fig. 6, the relative error is approximately 0.7%, which greatly improves the reliability and credibility when measuring large absorbance. In comparison, it is impossible for traditional DAS method to complete concentration calculation due to spectral distortion, which is shown in Fig. 7(a) and (c).
Fig. 7. Spectra and residual with large absorbance of 50 × 104 ppm CH4. (a)Simulated spectrum and experimental spectrum and (c)Residual, (b)Simulated spectrum and reconstructed spectrum and (d)Residual.
Therefore, it can be seen from the above two aspects that ODAS method can not only complete the reconstruction of the spectrum with low signal-to-noise ratio but also the distorted spectrum with large absorbance based on benchmark spectrum. Next, the important work is examining the errors and linearity of the ODAS method by detecting groups of CH4 with different concentrations, and comparing the results with DAS method. In this part, it will be divided into two cases of small absorbance and big absorbance for experimental demonstration, which are shown in Fig. 8(a)(c) and (b)(d), respectively. The pink and purple points in Fig. 8 are results of measuring concentration and absolute error based on DAS and ODAS method, respectively. It can be seen from Fig. 8(a)(c) that in the case of small absorbance with concentration below 1000 ppm, the maximum error obtained by DAS is 39.3 ppm, which is double greater than 16.8 ppm obtained by ODAS. The more pronounced effect is reflected in the measurement of big absorbance, as shown in Fig. 8(b)(d). Due to the distortion of the measured spectrum, the error of DAS reaches an astonishing value of 31.18 × 104 ppm when measuring 75 × 104 ppm, and the corresponding relative error is 41.6%. It can be concluded that the traditional DAS method has been unable to deal with this kind of distorted spectrum. However, the ODAS method based on the reconstruction of spectrum can still obtain accurate results. Even measuring large absorbance of 75 × 104 ppm, the absolute error is 1.81 × 104 ppm.
Fig. 8. Inverted concentrations and errors based on DAS and ODAS method. (a)Inverted concentrations and (c)Errors of small absorbance, (b)Inverted concentrations and (d)Errors of large absorbance.
Here, we also compare and analyze the performance in wide range measurement presented in this paper and other literature, as shown in Table 2. Using WMS method can only achieve the measurement of 3 orders of magnitude in [25]. And it can be seen from Table 2 that the ODAS method proposed in this paper fulfills the measurement range that is equivalent to that of the literature [12]. In contrast, the ODAS method has lower hardware complexity, demonstrating the superiority of the method.
Table 2. Comparison of performance in wide range measurement presented in this paper and other literature
Last but not least, temperature and pressure have an effect on the intensity and broadening of gas absorption spectrum. This is also the focus of our research. In the actual application, there are two ways to reduce or eliminate the influence of temperature and pressure. The first one is to maintain the temperature and pressure based on the corresponding control system during measurement [26]. The second one is to measure the temperature and pressure in site while measuring concentration, and then correct the concentration based on the temperature and pressure [12]. The focus of this paper is mainly on a novel method that can realize gas concentration wide range measurement, so the peripheral system of temperature and pressure is not described. In order to explain the applicability of the method, we analyzed it from the following two aspects. If the ODAS method is used in the TDLAS system where the temperature and pressure are maintained, the influence of temperature and pressure on concentration does not need to be considered. In another situation, spectral reconstruction can also be accomplished by selecting benchmark spectra among simulated spectra under gradient temperature and gradient pressure. Therefore, it can be seen that for the above two cases, the novel method can always fulfill spectral reconstruction and obtain good measurement results.
5. Conclusion
In this paper, the optimized direct absorption spectroscopy method is developed for in situ wide-range gas measurement. Signal correlation for determination of benchmark spectrum, spectral reconstruction for small and big absorbance are combined to establish the new method to fulfill wide-range measurement. As well, in this paper, CH4 is taken as an example for experimental verification. With the assistance of the new method, on-line accurate detection of CH4 in wide dynamic range is realized, whether for small absorbance of 100 ppm or big absorbance of 75 × 104 ppm, which is impossible to realize with traditional DAS method. With the new method, the reconstructed spectrum is able to reduce the relative error by two orders of magnitude. When measuring small absorbance and big absorbance, the degree of linear relationship for measurements are both 0.997, which demonstrates the validity and uniformity of the ODAS method in measuring small and big absorbance. The maximum error with measuring 75 × 104 ppm of CH4 is 1.81 × 104 ppm, and the corresponding relative error is 2.4%. In addition, only three sets of simulated spectrums are selected as benchmarks in this paper. If more benchmark spectra, smaller measurement errors will be obtained. Given all of that, the new method has the advantages of simple calculation and online processing. It is expected that it will be more appropriate for wide-range detection of gases in many fields and has broad application prospects.
Funding
National Key Research and Development Program of China (2021YFB3201904, 2022YFB3207601); National Natural Science Foundation of China (11874364, 41877311, 42005107); Hefei Institutes of Physical Science, Chinese Academy of Sciences (YZJJ2022QN02).
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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