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Abstract
A high-sensitivity differential Helmholtz photoacoustic cell based on multiple reflection was reported, and its performance parameters and gas replacement time were optimized by finite element simulation. To realize the long absorption path of the measured gas, the collimated excitation light was reflected multiple times on the gold-plated wall of the absorption cavity, and the wavelength modulation technology was used to reduce the multiple reflection noise. Additionally, the differential could suppress external co-phase noise and double the photoacoustic signal. When a laser with a central wavelength of 1653 nm was employed as the excitation light source, the minimum detection limit of 177 ppb (signal-to-noise ratio, SNR = 1) for methane was achieved within a detection time of 1 s, and the corresponding normalized noise equivalent absorption coefficient was 4.1×10–10 cm–1WHZ–1/2.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Recently, trace gas detection has been used in the fields of industry, agriculture, national defense and public safety [1–3]. As a detection technology based on spectral analysis, photoacoustic spectroscopy has the advantages of high sensitivity, good selectivity, fast response, and compact modules [4–8], and is widely used in power detection, medical diagnosis, industrial control, atmospheric monitoring and combustion analysis [9–13]. It obtains the gas concentration by detecting the photoacoustic signal generated by the measured gas [14–18].
Methane (CH4) is a colorless, odorless, and combustible, its greenhouse effect is ∼ 25 times that of carbon dioxide [19–21]. Therefore, methane detection is of great significance for industrial safety and environmental protection. Scholars have designed methane sensors using photoacoustic spectroscopy [22–26]. However, photoacoustic spectroscopy is susceptible to environmental noise, gas flow noise, and coherent noise introduced by optical systems [27]. To improve the signal-to-noise ratio (SNR) or signal-to-background noise ratio (SBR) of the detection setup, Scholars have developed various differential techniques to suppress the background noise [28–42].
The differential photoacoustic cell is mainly composed of two identical cavities, and the two microphones detect the photoacoustic signals in each cavity, respectively. The two photoacoustic signals are subtracted and sent to the lock-in amplifier for demodulation, which is called differential. The differential can double the photoacoustic signal and suppress coherent noise. Currently, representative differential photoacoustic cells include differential Helmholtz photoacoustic cells, differential H-type photoacoustic cells, and some variants. A differential photoacoustic cell is based on the principle of reversed-phase resonators. In a specific resonance mode, the sound pressures in the two cavities of the photoacoustic cell have the same amplitude and opposite phase [28].
In this paper, a differential Helmholtz photoacoustic cell (DHPAC) based on multiple reflection was reported, and its various performance parameters were improved by finite element simulation. In the case of smaller volume and less gas consumption, high sensitivity detection of methane was achieved. To increase the absorption path of the measured gas, the excitation light was reflected multiple times on the gold-plated wall of the absorption cavity of the photoacoustic cell. Multiple reflection could effectively improve the intensity of the photoacoustic signal. Additionally, the wavelength modulation technology was employed to suppress the coherent noise. The experimental results showed that when SNR = 1, for methane gas, the photoacoustic cell achieved the minimum detection limit (MDL) of ppb-level and an extremely low normalized noise equivalent absorption coefficient (NNEA) of 10–10 level within a detection time of 1 s.
2. Model and simulation
2.1 Photoacoustic cell model
The model of the conventional differential Helmholtz photoacoustic cell is mainly composed of two identical resonant cavities [27]. To generate the photoacoustic signal, the excitation light passed through the optical windows on both sides of the cavity, and the absorption path of the measured gas was only the length of the cavity.
To excite a larger photoacoustic signal, a high-power excitation light is often used. However, such light sources are usually expensive and bulky. Scholars have designed multi-pass cells to increase the absorption optical path of the measured gas to improve the photoacoustic signal [43,44]. To reduce the volume and complexity of the photoacoustic detection setup, a DHPAC based on multiple reflection was designed, which was composed of two gold-plated cylindrical absorption cavities and a connecting tube, as shown in Fig. 1(a). The collimated light was reflected multiple times on the gold-planted wall of the absorption cavity to achieve the equivalent effect of a high-power light, as shown in Fig. 1(b). When no light beam was emitted from DHPAC, almost all the light energy was absorbed by the cavity. If the intensity modulation technology was used for the light source, strong coherent background noise would be generated. To avoid the influence of such noise on the performance of DHPAC, the wavelength modulation technology would be used in the subsequent experiments.
2.2 Photoacoustic cell simulation
The main parameters of DHPAC shown in Fig. 1(a) were as follows. The radius and height of the cavity were 20 mm and 8 mm, respectively. The length and radius of the connecting tube were 5 mm and 3 mm, respectively. To simulate the photoacoustic effect of the measured gas, the thermoviscous acoustics module of the finite element simulation was used. A cavity was set to a uniform heat source with an amplitude of 1 W/m3 to simulate multiple reflection. The performance of the computer and the time required for the simulation were considered, conventional physics control mesh was employed for division. The simulation results of DHPAC are shown in Fig. 2. Figure 2(a) shows the sound pressure distribution of DHPAC in the Helmholtz resonance mode. The sound pressures of the two cavities had the same amplitude and opposite phase. Figure 2(b) shows the sound frequency characteristic curve of DHPAC. The resonance frequency was 1276 Hz, the sound pressure in one cavity was 2.57×10–3 Pa, and the quality factor was 128.
Fig. 2. Simulation results of DHPAC; (a) sound pressure distribution in the Helmholtz resonance mode, (b) sound frequency characteristic curve
With the above geometric parameters, the resonance frequency of DHPAC was greater than 1 kHz, so the 1/f noise could be well suppressed [45]. However, the sound pressure and quality factor were not optimal. The geometric parameters of DHPAC could be optimized through finite element simulation. The strategy of optimization was to further improve the performance of the photoacoustic cell while ensuring that the resonance frequency was greater than 1 kHz.
The resonance frequency of DHPAC was mainly affected by the cavity size. Therefore, the size of the cavities was optimized firstly. The height of the cavity was fixed at 8 mm. When the cavity radius increased from 15 mm to 25 mm, the change curves of resonance frequency, sound pressure and quality factor are shown in Fig. 3(a). The blue curve represents the resonance frequency (R), the black curve indicates the sound pressure (S), and the red curve is the quality factor (Q). The resonance frequency and quality factor decreased gradually, and the sound pressure showed a maximum value at 19 mm. Therefore, the cavity radius was set to 19 mm.
When the cavity height changed from 5 mm to 15 mm, the resonance frequency and quality factor showed a downward trend, while the sound pressure showed an overall upward trend, as shown in Fig. 3(b). When the cavity height was greater than 9 mm, the upward trend of the sound pressure became slower. The performance and the volume of DHPAC were considered, the height of the cavity was set to 9 mm.
Secondly, the simulation was carried out on the connecting tube. When the tube length increased from 5 mm to 15 mm, the resonance frequency decreased, while the change trend of sound pressure and quality factor was opposite, as shown in Fig. 4(a). When the tube length was 9 mm, the sum of the normalized sound pressure and the normalized quality factor reached the largest, and the resonance frequency was still greater than 1 kHz. When the tube length was greater than 9 mm, although the sound pressure gradually increased, the resonance frequency was lower than 1 kHz, which was inconsistent with the strategy of optimization. Therefore, the optimal length of the tube was set to 9 mm.
According to the principle of the Helmholtz resonator, the radius of the connecting tube should not be too large, otherwise the Helmholtz resonance mode could not be generated [46,47]. Therefore, when the tube radius was not greater than 5 mm was considered during optimization. When the tube radius changed from 2 mm to 5 mm, the resonance frequency, sound pressure and quality factor all increased, as shown in Fig. 4(b). According to the principle of photoacoustic spectroscopy, the photoacoustic signal is inversely proportional to the resonance frequency, and an increase in the resonance frequency would lead to the attenuation of the photoacoustic signal [36]. Although the sound pressure and quality factor of the tube with a radius of 5 mm was higher than the case of 3.8 mm, the former corresponds to a higher resonance frequency, and the latter was closer to the resonance frequency before optimization (1276 Hz), which was convenient for comparison. Therefore, the tube radius was set to 3.8 mm.
For conventional Helmholtz photoacoustic cells, the excitation light passed through a cavity, and the photoacoustic signal in the other cavity was detected. The connecting tube was located in the center of the two cavities [46,47]. However, this structure was not conducive to the replacement of the measured gas in the photoacoustic cell. We speculated that it was more beneficial to gas replacement when the connecting tube was located at the side away from the gas inlet and gas outlet, as shown in Fig. 5(a). The distance from the connecting tube to the center of the cavities (called tube shift) was set from 0 mm to 15 mm, and the simulation results are shown in Fig. 5(b). The resonance frequency gradually decreased, but the sound pressure and quality factor had a maximum value at 12 mm, so the tube shift was set to 12 mm. The influence of the position of the connecting tube on gas replacement would be verified by simulation and experiments later.
The sound pressure distribution in the Helmholtz resonance mode of the optimized DHPAC is shown in Fig. 6(a). The tube shift did not affect the opposite phase characteristics. The sound frequency characteristic curve of the optimized DHPAC is shown in Fig. 6(b). The resonance frequency was 1224 Hz, and almost unchanged compared with the case before optimization (1276 Hz). The sound pressure in one cavity was 5.02×10–3 Pa, and the quality factor was 221, which was 195% and 173% of the cases before optimization, respectively. Figure 6(c) is a cross-sectional view of the sound pressure distribution, and the position of the maximum sound pressure was marked in the figure. The sound pressures at the position of the microphones (mic1 and mic 2) were ∼ 93% of the maximum sound pressure. If the microphones were installed at the maximum sound pressure position, there would be interference in the mechanical structure. Therefore, the two microphones were still placed in the middle of the two cavities of DHPAC.
Fig. 6. Simulation results of the optimized DHPAC; (a) sound pressure distribution in the Helmholtz resonance mode, (b) sound frequency characteristic curve; (c) cross-section view of sound pressure distribution
3. Experiments and results
To verify the performance of the optimized DHPAC, CH4 was used as the measured gas. The HITRAN database was simulated to obtain the absorption lines of CH4 in the near-infrared band from 1651.5 nm to 1654.5 nm. The temperature and atmospheric pressure were set to 296 K and 1 atm, respectively. Assuming that in the atmospheric environment, the concentration of methane is ∼ 1 ppm, and the concentrations of water vapor and carbon dioxide are ∼ 1% and 400 ppm, respectively [25]. Their corresponding absorption lines are shown in Fig. 7. CH4 had a high absorption line near 1653.8 nm, while water vapor and carbon dioxide had almost no effect on CH4. Therefore, 1653.8 nm was taken as the excitation line of CH4.
Fig. 7. Absorption lines of CH4, water vapor and carbon dioxide in the near-infrared band from 1651.5 nm to 1654.5 nm.
According to the geometric parameters of the optimized DHPAC, the corresponding mechanical structure was designed, as shown in Fig. 8. A photoacoustic detection setup was built with the optimized DHPAC as the core sensor. Figure 9 shows a schematic diagram of the setup. A distributed feedback laser (1653 nm, Tengguang, China) with an optical power of ∼ 6 mW was used as the excitation light source. The excitation light source was driven by wavelength modulation technology to suppress the coherent noise caused by the absorption of light energy by the optical window and cavity. The two cavities of DHPAC shared an optical window (MgF2, Thorlabs). The excitation light entered the cavity through the optical window, and was reflected multiple times on the gold-planted wall of the absorption cavity to increase the absorption path of the measured gas.
The photoacoustic signals in the two cavities were collected by two microphones (MPA201, BSWA, China) respectively. The differential photoacoustic signal (mic 1 – mic 2) was sent to a lock-in amplifier (SR865A, SRS) for demodulation. The integration time and filter slope of the lock-in amplifier were set to 0.3 s and 12 dB/oct, and the corresponding bandwidth was 0.833 Hz. The demodulated photoacoustic signal was converted into electrical signal by a data acquisition card (USB3200N, ArtDAQ, China), the sampling time was 1 s, and the number of sampling points was 20000.
Due to the influence of machining errors, the actual resonance frequency of the optimized DHPAC had a certain offset compared with the simulated resonance frequency. To obtain the actual resonance frequency and the actual quality factor, it was necessary to change the modulation frequency of the excitation light and fit the photoacoustic signals. The optimized DHPAC was filled with 200 ppm CH4 (diluted with pure nitrogen (N2)) as the measured gas. The laser was driven by intensity modulation technology, and the modulation frequency was increased by 10 Hz each time. The corresponding photoacoustic signals were recorded, as shown in Fig. 10.
Through Lorentz fitting, the actual resonance frequency could be obtained as 1334 Hz, which was only ∼ 10% larger than the simulation. However, the actual quality factor was only 21, and it was much smaller than the simulation result (221). That was because the effects of boundary and thermoviscous losses were not considered in the simulation, and the simulation model was partitioned with a conventional physics control mesh. In fact, the losses and mesh fineness only affect the magnitude of the quality factor without changing its trend. Therefore, it would not affect the parameter optimization of DHPAC. If a higher performance computer was used without considering simulation time, and a finer mesh and the boundary lay were used, the simulated quality factor would be closer to the actual quality factor.
When the light source is driven by wavelength modulation technology, the modulation frequency should be half of the resonance frequency (667 Hz). To verify that DHPAC could double the photoacoustic signal and suppress coherent noise. The photoacoustic cell was filled with 200 ppm CH4, and the photoacoustic signals detected in the differential (mic 1 – mic 2) and non-differential (mic 1) modes were obtained respectively, as shown in Fig. 11. The differential photoacoustic signal was approximately twice that of the non-differential photoacoustic signal. Meanwhile, to verify the ability of DHPAC to suppress coherent noise, pure N2 was filled into the photoacoustic cell. The standard deviation of the noise in the non-differential mode was 0.0734 µV, while the standard deviation of the noise in the differential mode was 0.0371 µV. Differential reduced noise floating by ∼ 50%. Therefore, the advantage of differential detection was verified.
To further verify the performance of the photoacoustic detection setup, the optimized DHPAC was filled with 160 ppm, 120 ppm, 80 ppm, 40 ppm CH4, respectively, and the corresponding second harmonic signals within 1 s are shown in Fig. 12(a). In the theory of photoacoustic spectroscopy, when the absorption of the measured gas is not saturated, the photoacoustic signal is proportional to the concentration. The photoacoustic signal amplitudes of CH4 and the average noise signal of pure N2 were fitted with a linear equation, and the concentration calibration curve was obtained, as shown in Fig. 12(b). The goodness of fit (R2) of the curve was 0.997, indicating that the setup had high accuracy. The standard deviation of the noise signal was 0.0371 µV with pure N2, therefore, MDL for CH4 was ∼ 177 ppb (SNR = 1) and 531 ppb (SNR = 3). The optical power of the laser used in this paper was 6 mW, so NNEA was calculated to be 4.1×10–10 cm–1WHZ–1/2 (SNR = 1). Recently, the reported NNEA of photoacoustic detection setups for CH4 was ∼ 10–7 to 10–10 level [48–57].
Fig. 12. (a) Second harmonic signals of different concentrations CH4 and pure N2 and (b) concentration calibration curve.
To verify the influence of tube shift on the gas replacement time, the corresponding simulation was carried out. A reactive flow module and a diluted matter module were used to simulate the gas replacement. The concentration of the measured gas was set to 1 mol/m3, and the flow rate was set to 200 mL/min. Figure 13 shows the distribution of the measured gas in DHPAC at 10 s. To facilitate observation and understanding, we used a cross-sectional view to show the gas replacement situation. The gas replacement speed after optimization was much faster than the case before optimization. Therefore, the gas replacement could be completed while using the less measured gas when the tube shift was 12 mm.
To analyze the gas replacement time, the optimized DHPAC was filled with 200 ppm CH4, and then filled with pure N2 at a flow rate of 200 mL/min. The corresponding photoacoustic signals were recorded, as shown in Fig. 14. When the time was 10 s, the photoacoustic signal was close to 0, indicating that the gas was almost displaced, which corresponded to the simulation result in Fig. 13(b). When the time was 20 s, the photoacoustic signal did not change again, so the gas replacement time was 20 s, and the consumption was ∼ 67 mL.
4. Conclusion
A differential Helmholtz photoacoustic cell was developed, and the performance parameters were improved through finite element simulation. Different from conventional differential Helmholtz photoacoustic cells and differential H-type photoacoustic cells, the excitation light could be reflected multiple times on the gold-planted wall of the photoacoustic cell to increase the absorption path of the measured gas. When a low-power distributed feedback laser was used as the excitation light source, the ppb-level MDL of CH4 could be achieved within 1 s, and NNEA was only 10–10 level (SNR = 1). Additionally, due to the shift of connecting tube, the gas replacement time was much less, which could be completed in 20 s with a flow rate of 200 mL/min. The center wavelength of the excitation light source used in this paper was located in the near-infrared band with weak absorption. For most gases, the absorption coefficient in the mid-infrared band is larger. Theoretically, if a mid-infrared laser with higher optical power was employed, sub-ppb level detection could be achieved. Simultaneously, since the collimated excitation light still had a certain divergence angle, the light energy would be dissipated after multiple reflection. Therefore, the inner wall of the absorption cavity could be processed into an elliptical surface with a certain radian, which would re-converge the reflected light beams and further increase the times of reflections. This work provides a reference for the design and optimization of high-sensitivity photoacoustic cells.
Funding
National Natural Science Foundation of China (61875207); Scientific Instrument Developing Project of the Chinese Academy of Sciences (YJKYYQ20190050); Anhui Science Foundation for Distinguished Youth Scholars (1908085J23).
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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