Open Access
Add to BibSonomy
Abstract
A highly sensitive differential Helmholtz photoacoustic sensor with active noise reduction was reported. Coupled to one cavity of the photoacoustic cell, an intensity-modulated excitation light would reflect multiple times to produce photoacoustic signal, and meanwhile cause the solid-state photoacoustic effect forming differential mode noise with the frequency same as the photoacoustic signal, which could not be suppressed by conventional differential technology. Wavelength modulation technology is a splendid method to restrain this effect, which is not suitable for light sources with not adjustable wavelength. To suppress this kind of noise, an intensity-modulated compensation light was coupled to another cavity, whose central wavelength was at the non-absorption line of the measured gas. The compensation light was of the same frequency, phase, and power as the excitation light, by which the solid-state photoacoustic effects were produced to form destructive interference called active noise reduction. The experiment results showed that the active noise reduction significantly improved the signal-to-noise ratio and signal-to-background ratio. Compared with the differential, the differential with active noise reduction improved signal-to- noise ratio by about 1.2 times and signal-to-background ratio by about 9.4 times. When low-power near-infrared lasers were employed as the two light sources, the minimum detection limits for acetylene and methane reached 21 and 200 ppb, respectively.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photoacoustic spectroscopy is an indirect absorption spectroscopy technique. It obtains the gas concentration by detecting the photoacoustic signal generated by the measured gas [1–5]. Due to the advantages of high sensitivity, fast response, and good selectivity [6–10], photoacoustic spectroscopy has been widely used in various gas detection fields [11–17].
The photoacoustic signal value is proportional to the excitation light power [18]. To improve the intensity of the photoacoustic signal, some scholars coated the inner wall of the photoacoustic cell with a reflective film to make the excitation light reflected multiple times [19–23]. The effect of high-power light could be equivalently achieved.
However, the multiple reflection of the light induced a solid-state photoacoustic effect from the photoacoustic cell wall [24], forming noise with the same frequency as the photoacoustic signal (we called it multiple reflection noise, MR-noise), which could be suppressed by the wavelength modulation technology [19]. Unfortunately, some light sources such as light-emitting diodes, laser diodes, and fixed-wavelength lasers could only be intensity-modulated, so MR-noise could not be avoided.
With regard to the active noise reduction in acoustics, it is common to use a microphone to detect noise, and a loudspeaker is employed to generate another noise with the same amplitude and opposite phase. The two kinds of noise form destructive interference [25,26]. However, this method increases the complexity of the sensor and requires corresponding driver circuits.
In this work, a new type of noise compensation method was reported. Based on the differential Helmholtz photoacoustic cell (DHPAC) [27], an intensity-modulated excitation light was coupled to one cavity of the photoacoustic cell and reflected multiple times to produce photoacoustic signal with MR-noise, and an intensity-modulated compensation light was coupled to another cavity and reflected multiple times to produce noise compensation signal (we called it C-noise). The two lights were of the same frequency, phase, and power, except that the central wavelength of the compensation light was at the non-absorption line of the measured gas. So the two kinds of noise (MR-noise and C-noise) form destructive interference, further active noise reduction was achieved by compensation of MR-noise.
Additionally, the differential technology enabled the sensor to double the photoacoustic signal while suppressing incoherent noise. The experimental results showed that the combination of multiple reflection, active noise reduction and differential could effectively increase the photoacoustic signal, reduce the noise, and improve the detection performance.
2. Theories and simulations
2.1 Signal characteristics of differential photoacoustic cell
In the photoacoustic detection, there is the incoherent noise such as gas flow noise and system electromagnetic noise, which affects the detection performance of the photoacoustic sensor [28]. To suppress such noise, scholars have constructed various differential photoacoustic detection sensors [28–32]. Differential photoacoustic cells usually have two cavities of the same size, one as the excitation cavity and the other as the compensation cavity. In a specific resonance mode, the amplitudes of sound waves in the two cavities were the same but the phases were opposite. For the two cavities, the incoherent noise was the common mode signal, while the photoacoustic signal was the differential mode signal. Through the differential, the common mode noise signal could be suppressed, and the differential mode signal could be amplified, thereby improving the detection performance of the photoacoustic sensor. However, the coherent noise generated by the solid-state photoacoustic effect was also the differential mode signal and could not be suppressed by conventional differential technology.
In acoustics, if the vibration characteristics of two sound waves are out of phase (with a phase difference of 180°), the vibrations weak or even cancel each other. This phenomenon is called the destructive interference of sound waves [25,26]. The schematic diagram is depicted in Fig. 1.
2.2 Active noise reduction for differential photoacoustic cell
In photoacoustic spectroscopy, the central wavelength of the excitation light is at the strong absorption line of the measured gas to excite the high photoacoustic signal. Because of the low concentration of the measured gas, its absorption of light energy is usually ignored. When excitation light was reflected multiple times in the one cavity of DHPAC, MR-noise of the same frequency as the photoacoustic signal was produced. If the compensation light is reflected multiple times in another cavity, forming C-noise with the opposite phase of MR-noise, the destructive interference generates and the superimposed noise value reduces. To make the photoacoustic signal not be affected, the central wavelength of compensation light should be at the non-absorption line of the measured gas. Since the sound waves in the two cavities of DHPAC have the same amplitude and opposite phase, the phase difference between the excitation light and the compensation light does not need to be 180°, that was, the modulation signals of the two lights only need to be the same.
When random noise is not considered (they usually have little effect), it is assumed that the incoherent noise is denoted as $N^{\prime}$, the sound wave ${S_\textrm{E}}$ in the excitation cavity is:
where ${S_{\textrm{PA}}}$ is the photoacoustic signal in the excitation cavity, ${N_{\textrm{MR}}}$ is MR-noise generated by the excitation light, and $- {N_\textrm{C}}$ is C-noise generated by the compensation light. The sound wave ${S_\textrm{C}}$ in the compensation cavity is:If the compensation light is turned off, ${N_\textrm{C}}$ does not exist, then the differential signal ${S^{\prime}_\textrm{D}}$ is:
${S^{\prime}_\textrm{D}}$ includes not only twice the photoacoustic signal, but also twice the multiple reflection noise produced by solid-state photoacoustic effect. Therefore, the conventional differential technique could only remove incoherent noise, but could not suppress MR-noise. However, MR-noise could be suppressed with the C-noise generated by the compensation light.
2.3 Simulation of active noise reduction
To verify the feasibility of active noise reduction, corresponding simulations were carried out. The schematic model of DHPAC is shown in Fig. 2, and the schematic diagram of the excitation light reflected multiple times in the one cavity of DHPAC is depicted in Fig. 3. Through the finite element simulation, the sound-frequency and phase-frequency characteristics of MR-noise produced by solid-state photoacoustic effect were obtained, as shown in Fig. 4(a) and Fig. 4(b). The differential (mic 1 – mic 2) could not remove MR-noise. Instead, MR-noise was doubled.
Fig. 3. Schematic diagram of the excitation light reflected multiple times in the one cavity of DHPAC.
Fig. 4. Simulation results of MR-noise produced by excitation light. (a) Sound-frequency characteristic curve; (b) Phase-frequency characteristic curve
To simulate the active noise reduction, the compensation light with the same power as the excitation light was added in the simulation, as shown in Fig. 5, and the sound-frequency characteristic curve of the superimposed noise is shown in Fig. 6. The MR-noise was eliminated by the C-noise generated by the compensation light (so the sound pressures of mic 1 and mic 2 were 0), and the superimposed noise was close to zero. Therefore, the derivation in Section 2.2 was verified by the simulation.
Fig. 5. Schematic diagram of the excitation light and compensation light in the two cavities of DHPAC.
Fig. 6. Sound-frequency characteristic curve of the superimposed noise. (The curves of mic 1 and mic 2 were covered by mic1 – mic 2)
3. Experiments and results
3.1 Absorption lines of acetylene
The performance of DHPAC would be verified using acetylene (C2H2) as the measured gas. Two distributed feedback (DFB) lasers were employed as the excitation light source and the compensation light source, whose central wavelengths were 1532 nm and 1653 nm, respectively. The absorption lines of C2H2 near 1532 nm and 1653 nm were simulated using the HITRAN database [33]. The simulation conditions were 296 K (temperature), 1 atm (pressure), 100 ppm (concentration), and 1 cm (light path). The simulation results of the absorption lines were shown in Fig. 7. The absorption coefficient of C2H2 at 1532.8 nm was about 1 × 10−4 cm−1, while the absorption coefficient near 1653 nm was only about 10−10 orders of magnitude, the difference in absorption coefficients between the two bands was about 4 × 106 times. Therefore, the wavelengths of the excitation light and compensation light were set as 1532.8 nm and 1652.9 nm, respectively.
3.2 Photoacoustic detection setup
With DHPAC as the core unit, a photoacoustic detection setup was built. The schematic diagram is shown in Fig. 8. Since light-emitting diodes, laser diodes, and fixed-wavelength lasers could not suppress MR-noise using wavelength modulation, the DFB lasers (DFB1532nm, DFB1653nm, Tengguang, China) were driven by the intensity modulation to verify that the photoacoustic detection setup was suitable for different light sources.
The signal generator (AFG3102C, Tektronix) generated the intensity modulation signal with a certain frequency, and the signal was divided into two same signals to drive DFB lasers. The temperature and current of the lasers were adjusted, so that the wavelengths of the excitation light and compensation light were 1532.8 nm and 1652.9 nm, and the power of each light was about 7.2 mW. The excitation light and compensation light were collimated and coupled to DHPAC through an optical window (WG61050, Thorlabs).
Two microphones (MPA201, BSWA, China) with a sensitivity of 50 mV/Pa were used to detect the acoustic signal in the cavity. The differential signal (mic 1 – mic 2) was demodulated by lock-in amplifier (SR865A, SRS). The integration time and filter slope were set to 1 s and 12 dB/oct, respectively. The demodulated photoacoustic signal was collected by a data acquisition card (USB3200N, Art technology, China) and uploaded to a personal computer for processing and analysis.
3.3 Photoacoustic detection experiments
To verify the improvement in photoacoustic detection performance by the active noise reduction, corresponding comparative experiments were conducted, including traditional Helmholtz photoacoustic detection, differential Helmholtz photoacoustic detection, and differential Helmholtz photoacoustic detection with active noise reduction.
3.3.1 Traditional Helmholtz photoacoustic detection
For the traditional Helmholtz photoacoustic sensor, the excitation light was coupled to one cavity of the photoacoustic cell, and the acoustic signal in the other cavity was detected (DFB 1 and mic 2). Because of the mechanical errors, the actual resonance frequency deviated from the simulation resonance frequency, it was necessary to obtain the actual resonance frequency through an experiment. The photoacoustic cell was filled with 100 ppm C2H2 (the dilution gas was pure N2). The frequency corresponding to the maximum value of the photoacoustic signal was 1334 Hz. Thus, 1334 Hz was used as the modulation frequency in subsequent experiments.
The photoacoustic signal of 100 ppm C2H2 and noise of pure N2 was recorded, as shown in Fig. 9. The average photoacoustic signal ($Signal$) was about 114.9695 µV, the average noise ($\mu (B )$) and noise standard deviation ($\sigma$) were 7.3807 µV and 0.0495 µV. In the photoacoustic detection, the signal-to-noise ratio ($SNR$) and signal-to-background ratio ($SBR$) were usually used to evaluate the performance of the sensor using Eq. (5) and Eq. (6) [34–39]. Therefore, $SNR$ and $SBR$ of traditional Helmholtz photoacoustic sensor were 2174 and 16.
Fig. 9. Experiment results of traditional Helmholtz photoacoustic sensor. (a) Photoacoustic signal and noise; (b) Noise distribution
3.3.2 Differential Helmholtz photoacoustic detection
For the differential Helmholtz photoacoustic sensor, the excitation light was coupled to one cavity of the photoacoustic cell, and the differential acoustic signal of two cavities was detected (DFB 1 and mic 1 – mic 2). The photoacoustic signal of 100 ppm C2H2 and noise of pure N2 was recorded, as shown in Fig. 10. $Signal$ was about 228.1475 µV, $\mu (B)$ and $\sigma$ were 14.6971 µV and 0.0529 µV. $SNR$ and $SBR$ were 4035 and 16. Therefore, although the differential improved $Signal$, $\mu (B)$ was also amplified, as both signals increased about 2 times, which corresponded to Eq. (4).
Fig. 10. Experiment results of differential Helmholtz photoacoustic sensor. (a) Photoacoustic signal and noise; (b) Noise distribution
3.3.3 Differential Helmholtz photoacoustic detection with active noise reduction
To verify the suppression of MR-noise by the active noise reduction, corresponding experiments were carried out. Different from 3.3.2, excitation light and compensation light were simultaneously coupled to the two cavities of the photoacoustic cell (DFB 1 – DFB 2 and mic 1 – mic 2). The frequency, power, and phase of the two lights were the same. The photoacoustic signal of 100 ppm C2H2 and noise of pure N2 was recorded, as shown in Fig. 11. $Signal$ was about 214.3607 µV, $\mu (B)$ and $\sigma$ were 1.4303 µV and 0.0447 µV. $SNR$ and $SBR$ were 4764 and 150.
Fig. 11. Experiment results of differential Helmholtz photoacoustic sensor with active noise reduction. (a) Photoacoustic signal and noise; (b) Noise distribution
The detection performance of the three sensors is shown in Table 1. Compared with the differential, the differential with active noise reduction reduced $\mu (B)$ by about 90% and $\sigma$ by about 20%. Additionally, the power of the excitation light and compensation light was about 7.2 mW, so MR-noise was not high. When a high-power light source was used, the effect caused by the active noise reduction would be more significant.
Table 1. Comparison of detection performance of three sensors (ANR: active noise reduction)
In summary, it was verified by comparative experiments that the differential Helmholtz photoacoustic sensor with the active noise reduction could effectively amplify the photoacoustic signal while suppressing MR-noise, resulting in improving $SNR$ and $SBR$. In the following experiments, the performance of this sensor would be further analyzed.
3.4 Sensor performance analysis
To further analyze the performance of the sensor and obtain the quality factor Q of the photoacoustic cell, it was necessary to change the modulation frequency around the resonance frequency of 1334 Hz, and record the corresponding photoacoustic signal. When the interval was 10 Hz, the corresponding photoacoustic signal is shown in Fig. 12. The sound-frequency curve was obtained by Lorentz fitting, the coefficient of determination (R2) was 0.994, and full width at half maximum (FWHM) was 63 Hz. Thus, the quality factor Q was about 21. According to Eq. (7) [40], the cell constant ${C_{\textrm{cell}}}$ could be calculated.
where ${S_\textrm{m}}$ was the sensitivity of the microphone, $\alpha$ was the absorption coefficient of C2H2. P was the light power. C was the concentration of C2H2, and $Signal$ was the average photoacoustic signal. So, the cell constant ${C_{\textrm{cell}}}$ was about 10400 Pa·cm/W.According to the principle of photoacoustic spectroscopy, when the absorption of the measured gas was not saturated, there was a linear relationship between the photoacoustic signal and the concentration of the measured gas. To obtain the concentration calibration curve of the sensor, C2H2 (20, 40, 60, 80, and 100 ppm) and pure N2 were sequentially filled into the photoacoustic cell, and the signals were recorded, as shown in Fig. 13. The concentration calibration curve was obtained by linear fitting, and R2 was 0.998, which showed that the sensor had good linearity for different concentrations of C2H2. The fitted equation was y = 2.135x–2.398, so the response capability was 2.135 µV/ppm. The minimum detection limits of C2H2 could be calculated as 21 ppb ($SNR = 1$) and 667 ppb ($SBR = 1$). Compared with the Allan deviation, the results obtained by linear fitting were closer to the actual detection limit of the sensor. Since the integration time of the lock-in amplifier was 1 s and the filter slope was 12 dB/oct, the bandwidth Δf was 0.25 Hz. Thus, the normalized noise equivalent absorption coefficient (NNEA) was 3.2 × 10−10 cm−1WHz−1/2 ($SNR = 1$). NNEA of the recently reported C2H2 sensors was about 10−8∼10−10 orders of magnitude [19,41–49]. The tabularized comparison is shown as Table 2.
Table 2. Tabularized comparison of C2H2 sensors and reported in this work. (PAC: photoacoustic cell; MDL: minimum detection limit)
4. Discussion
According to the experiment results, MR-noise after active noise reduction was greatly reduced, which improved $SNR$ and $SBR$ of the sensor. Although some literature only use $SNR$ to evaluate the performance of photoacoustic sensors, $SBR$ was also an important evaluation criterion, especially in the case of high background noise caused by high-power light sources.
The light sources used in this work were a C2H2 detection laser (1532 nm) and a methane (CH4) detection laser (1653 nm). The absorption lines of CH4 near 1653 nm and 1532 nm were shown in Fig. 14. The absorption coefficient at 1653.7 nm and 1531.5 nm was about 3.8 × 10−5 cm−1 and 1 × 10−10 cm−1. When 1653 nm laser was used as the excitation light and 1532 nm was used as the compensation light, high sensitivity detection of CH4 was also achieved. The experiment results showed that the minimum detection limits reached 200 ppb ($SNR = 1$) and 3 ppm ($SBR = 1$), and the NNEA was 1.1 × 10−9 cm−1WHz−1/2 ($SNR = 1$). The detection performance was close to the case achieved using the wavelength modulation technique in the previous work (177 ppb, 4.1 × 10−10 cm−1WHZ−1/2 $SNR = 1$) [27].
5. Conclusion
A new type of noise compensation method was designed, and the feasibility of the method was verified through theoretical derivation, simulation analysis and comparative experiments. For light sources with fixed wavelengths, active noise reduction proposed in this work was applicable. For C2H2, the sensor exhibited good linearity, and a high value of cell constant. When $SNR = 1$, the minimum detection limit and NNEA of the C2H2 were 21 ppb and 3.2 × 10−10 cm−1WHz−1/2 respectively. For CH4, the two performance parameters were 200 ppb and 1.1 × 10−9 cm−1WHz−1/2 respectively, which were close to the effect of wavelength modulation.
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.
References
1. Z. Gong, T. Gao, L. Mei, K. Chen, Y. Chen, B. Zhang, W. Peng, and Q. Yu, “Ppb-level detection of methane based on an optimized T-type photoacoustic cell and a NIR diode laser,” Photoacoustics 21, 100216 (2021). [CrossRef]
2. Y. Ma, Y. He, Y. Tong, X. Yu, and F. K. Tittel, “Quartz-tuning-fork enhanced photothermal spectroscopy for ultra-high sensitive trace gas detection,” Opt. Express 26(24), 32103–32110 (2018). [CrossRef]
3. X. Yin, L. Dong, H. Zheng, X. Liu, H. Wu, Y. Yang, W. Ma, L. Zhang, W. Yin, L. Xiao, and S. Jia, “Impact of humidity on quartz-enhanced photoacoustic spectroscopy based CO detection using a Near-IR telecommunication diode laser,” Sensors 16(2), 162 (2016). [CrossRef]
4. H. Lin, H. Zheng, B. A. Z. Montano, H. Wu, M. Giglio, A. Sampaolo, P. Patimisco, W. Zhu, Y. Zhong, L. Dong, R. Kan, J. Yu, and V. Spagnolo, “Ppb-level gas detection using on-beam quartz-enhanced photoacoustic spectroscopy based on a 28 kHz tuning fork,” Photoacoustics 25, 100321 (2022). [CrossRef]
5. Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuator B 247, 290–295 (2017). [CrossRef]
6. Y. Ma, Y. Hu, S. Qiao, Z. Lang, X. Liu, and Y. He, “Quartz tuning forks resonance frequency matching for laser spectroscopy sensing,” Photoacoustics 25, 100329 (2022). [CrossRef]
7. Z. Lang, S. Qiao, and Y. Ma, “Acoustic microresonator based in-plane quartz-enhanced photoacoustic spectroscopy sensor with a line interaction mode,” Opt. Lett. 47(6), 1295–1298 (2022). [CrossRef]
8. H. Zheng, Y. Liu, H. Lin, R. Kan, P. Patimisco, A. Sampaolo, M. Giglio, W. Zhu, J. Yu, F. K. Tittel, V. Spagnolo, and Z. Chen, “Sub-ppb-level CH4 detection by exploiting a low-noise differential photoacoustic resonator with a room-temperature interband cascade laser,” Opt. Express 28(13), 19446–19456 (2020). [CrossRef]
9. Y. Ma, Y. Hu, S. Qiao, Y. He, and F. K. Tittel, “Trace gas sensing based on multi-quartz-enhanced photothermal spectroscopy,” Photoacoustics 20, 100206 (2020). [CrossRef]
10. Z. Gong, K. Chen, Y. Yang, X. Zhou, and Q. Yu, “Photoacoustic spectroscopy based multi-gas detection using high-sensitivity fiber-optic low-frequency acoustic sensor,” Sens. Actuators, B 260, 357–363 (2018). [CrossRef]
11. Y. Yun, W. Chen, Y. Wan, and C. Pan, “Photoacoustic detection of dissolved gases in transformer oil,” Eur. Trans. Electr. Power 18(6), 562–576 (2008). [CrossRef]
12. X. Yin, H. Wu, L. Dong, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Ppb-level photoacoustic sensor system for saturation-free CO detection of SF6 decomposition by use of a 10 W fiber-amplified near-infrared diode laser,” Sens. Actuators, B 282(1), 567–573 (2019). [CrossRef]
13. Z. Lang, S. Qiao, Y. He, and Y. Ma, “Quartz tuning fork-based demodulation of an acoustic signal induced by photo-thermo-elastic energy conversion,” Photoacoustics 22, 100272 (2021). [CrossRef]
14. X. Yin, H. Wu, L. Dong, B. Li, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Ppb-Level SO2 photoacoustic sensors with a suppressed absorption-desorption effect by using a 7.41 µm external-cavity quantum cascade laser,” ACS Sens. 5(2), 549–556 (2020). [CrossRef]
15. S. D. Russo, A. Sampaolo, P. Patimisco, G. Menduni, M. Giglio, C. Hoelzl, V. M. N. Passaro, H. Wu, L. Dong, and V. Spagnolo, “Quartz-enhanced photoacoustic spectroscopy exploiting low-frequency tuning forks as a tool to measure the vibrational relaxation rate in gas species,” Photoacoustics 21, 100227 (2021). [CrossRef]
16. C. Popa, M. Petrus, and A. M. Bratu, “Effect of wearing surgical face masks on gas detection from respiration using photoacoustic spectroscopy,” Molecules 27(11), 3618 (2022). [CrossRef]
17. C. Popa, M. Petrus, and A. M. Bratu, “Alfalfa (medicago sativa) sprouts respiratory responses to cadmium stress using IR LPAS,” Molecules 27(6), 1891 (2022). [CrossRef]
18. J. Rouxel, J. G. Coutard, S. Gidon, O. Lartigue, S. Nicoletti, B. Parvitte, R. Vallon, V. Zéninari, and A. Glière, “Miniaturized differential Helmholtz resonators for photoacoustic trace gas detection,” Sens. Actuators, B 236, 1104–1110 (2016). [CrossRef]
19. K. Chen, B. Zhang, S. Liu, F. Jin, M. Guo, Y. Chen, and Q. Yu, “Highly sensitive photoacoustic gas sensor based on multiple reflections on the cell wall,” Sens. Actuators, A 290, 119–124 (2019). [CrossRef]
20. T. Yang, W. Chen, Z. Zhang, J. Lei, F. Wan, and R. Song, “Multiple reflections enhanced fiber-optic photoacoustic sensor for gas micro-leakage,” Opt. Express 29(2), 2142–2152 (2021). [CrossRef]
21. B. Zhang, K. Chen, Y. Chen, B. Yang, M. Guo, H. Deng, F. Ma, F. Zhu, Z. Gong, W. Peng, and Q. Yu, “High-sensitivity photoacoustic gas detector by employing multi-pass cell and fiber-optic microphone,” Opt. Express 28(5), 6618–6630 (2020). [CrossRef]
22. Z. Li, G. Si, Z. Ning, J. Liu, Y. Fang, B. Si, Z. Cheng, and C. Yang, “Highly sensitive sphere-tube coupled photoacoustic cell suitable for detection of a variety of trace gases: NO2 as an example,” Sensors 22(1), 281 (2021). [CrossRef]
23. Y. Jiao, H. Fan, Z. Gong, K. Yang, F. Shen, K. Chen, L. Mei, W. Peng, and Q. Yu, “Trace CH4 gas detection based on an integrated spherical photoacoustic cell,” Appl. Sci. 11(11), 4997 (2021). [CrossRef]
24. A. Rosencwaig and G. Allan, “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47(1), 64–69 (1976). [CrossRef]
25. N. George and G. Panda, “Advances in active noise control: A survey, with emphasis on recent nonlinear techniques,” Signal Process 93(2), 363–377 (2013). [CrossRef]
26. Y. Kajikawa, W. Gan, and S. M. Kuo, “Recent advances on active noise control: open issues and innovative applications,” APSIPA. Trans. Signal. 1(1), e3 (2012). [CrossRef]
27. Z. Li, J. Liu, G. Si, Z. Ning, and Y. Fang, “Design of a high-sensitivity differential Helmholtz photoacoustic cell and its application in methane detection,” Opt. Express 30(16), 28984–28996 (2022). [CrossRef]
28. I. Sherstov and L. Chetvergova, “Experimental researches of acoustical modes of various types of resonant photo-acoustic detectors,” Opt. Commun. 462, 125184 (2020). [CrossRef]
29. J. M. Rey and M. W. Sigrist, “New differential mode excitation photoacoustic scheme for near-infrared water vapour sensing,” Sens. Actuators, B 135(1), 161–165 (2008). [CrossRef]
30. M. Suchenek, “Photoacoustic cell with digital differential detection,” Int. J. Thermophys 36(9), 2351–2355 (2015). [CrossRef]
31. A. Glière, J. Rouxel, B. Parvitte, S. Boutami, and V. Zéninari, “A coupled model for the simulation of miniaturized and integrated photoacoustic gas detector,” Int. J. Thermophys 34(11), 2119–2135 (2013). [CrossRef]
32. S. Alahmari, X. Kang, and M. Hippler, “Diode laser photoacoustic spectroscopy of CO2, H2S and O2 in a differential Helmholtz resonator for trace gas analysis in the biosciences and petrochemistry,” Anal. Bioanal. Chem. 411(17), 3777–3787 (2019). [CrossRef]
33. L. S. Rothman, D. Jacquemart, A. Barbe, D. C. Benner, M. Birk, L. R. Brown, M. R. Carleer, C. Chackerian Jr, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, J.-M. Flaud, R. R. Gamache, A. Goldman, J.-M. Hartmann, K. W. Jucks, A. G. Maki, J.-Y. Mandin, S. T. Massie, J. Orphal, A. Perrin, C. P. Rinsland, M. A. H. Smith, J. Tennyson, R. N. Tolchenov, R. A. Toth, J. V. Auwera, P. Varanasi, and G. Wagner, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 96(2), 139–204 (2005). [CrossRef]
34. J. P. Besson, S. Schilt, and L. Thévenaz, “Multi-gas sensing based on photoacoustic spectroscopy using tunable laser diodes,” Spectrochim. Acta, Part A 60(14), 3449–3456 (2004). [CrossRef]
35. X. Yin, L. Dong, H. Wu, H. Zheng, W. Ma, L. Zhang, W. Yin, S. Jia, and F. K. Tittel, “Sub-ppb nitrogen dioxide detection with a large linear dynamic range by use of a differential photoacoustic cell and a 3.5 W blue multimode diode laser,” Sens. Actuators, B 247, 329–335 (2017). [CrossRef]
36. G. Liang, H. Liu, A. H. Kung, A. Mohacsi, A. Miklos, and P. Hess, “Photoacoustic trace detection of methane using compact solid-state lasers,” J. Phys. Chem. A 104(45), 10179–10183 (2000). [CrossRef]
37. J. G. Coutard, A. Berthelot, A. Glière, H. Lhermet, B. Scherer, T. Strahl, A. Teulle, and T. Verdot, “Micro PA detector: pushing the limits of mid IR photoacoustic spectroscopy integrated on silicon,” Silicon Photonics XV. International Society for Optics and Photonics 1128513, 37 (2020). [CrossRef]
38. A. Miklós and P. Hess, “Application of acoustic resonators in photoacoustic trace gas analysis and metrology,” Rev. Sci. Instrum. 72(4), 1937–1955 (2001). [CrossRef]
39. Z. Bozóki, Á. Mohácsi, G. Szabó, Z. Bor, M. Erdélyi, W. Chen, and F. K. Tittel, “Near-Infrared Diode Laser Based Spectroscopic Detection of Ammonia: A Comparative Study of Photoacoustic and Direct Optical Absorption Methods,” Appl. Spectrosc. 56(6), 715–719 (2002). [CrossRef]
40. J. Li, W. Chen, and B. Yu, “Recent progress on infrared photoacoustic spectroscopy techniques,” Appl. Spectrosc. Rev. 46(6), 440–471 (2011). [CrossRef]
41. C. Zhang, Y. Yang, Y. Tan, H. Ho, and W. Jin, “All-optical fiber photoacoustic gas sensor with double resonant enhancement,” IEEE Photonics Technol. Lett. 30(20), 1752–1755 (2018). [CrossRef]
42. Y. Ma, S. Qiao, Y. He, Y. Li, Z. Zhang, X. Yu, and F. K. Tittel, “Highly sensitive acetylene detection based on multi-pass retro-reflection-cavity-enhanced photoacoustic spectroscopy and a fiber amplified diode laser,” Opt. Express 27(10), 14163–14172 (2019). [CrossRef]
43. C. Zhang, Q. Wang, H. Pan, F. Pian, Z. Li, and P. Shan, “Highly sensitive multi-pass enhanced photoacoustic cell based on three spot-ring structure (TSR-MPC),” Infrared Phys. Techn. 118, 103880 (2021). [CrossRef]
44. H. Pan, Q. Wang, C. Zhang, Z. Li, P. Shan, and Z. Ma, “High-sensitivity acetylene detection system using ellipsoid multi-pass cell (EMPC) based on the opposite dual optical source,” Infrared Phys. Technol. 118, 103874 (2021). [CrossRef]
45. Z. Gong, K. Chen, Y. Chen, L. Mei, and Q. Yu, “Integration of T-type half-open photoacoustic cell and fiber-optic acoustic sensor for trace gas detection,” Opt. Express 27(13), 18222–18231 (2019). [CrossRef]
46. L. Liu, H. Huan, W. Li, A. Mandelis, Y. Wang, L. Chang, X. Zhang, X. Yin, Y. Wu, and X. Shao, “Highly sensitive broadband differential infrared photoacoustic spectroscopy with wavelet denoising algorithm for trace gas detection,” Photoacoustics 21, 100228 (2021). [CrossRef]
47. Q. Zhang, J. Chang, Z. Cong, Y. Feng, Z. Wang, and J. Sun, “Scanned-wavelength intra-cavity QEPAS sensor with injection seeding technique for C2H2 detection,” Opt. Laser. Technol. 120, 105751 (2019). [CrossRef]
48. Z. Gong, Y. Chen, T. Gao, K. Chen, Y. Jiao, M. Guo, B. Zhang, S. Liu, L. Mei, W. Peng, and Q. Yu, “Parylene-C diaphragm-based low-frequency photoacoustic sensor for space-limited trace gas detection,” Opt. Laser. Eng. 134, 106288 (2020). [CrossRef]
49. Y. Ma, Y. He, L. Zhang, X. Yu, J. Zhang, R. Sun, and F. K. Tittel, “Ultra-high sensitive acetylene detection using quartz-enhanced photoacoustic spectroscopy with a fiber amplified diode laser and a 30.72 kHz quartz tuning fork,” Appl. Phys. Lett. 110(3), 031107 (2017). [CrossRef]
