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Abstract
A novel dual-frequency modulated heterodyne quartz-enhanced photoacoustic spectroscopy (DFH-QEPAS) was demonstrated for what we believe to be the first time in this study. In traditional H-QEPAS, the frequency of modulated sinusoidal wave has a frequency difference (Δf) with the resonance frequency (f0) of a quartz tuning fork (QTF). Owing to the resonance characteristic of QTF, it cannot excite QTF to the strongest response. To achieve a stronger response, a sinusoidal wave with a frequency of f0 was added to the modulation wave to compose a dual-frequency modulation. Acetylene (C2H2) was chosen as the target gas to verify the sensor performance. The proposed DFH-QEPAS improved 4.05 times of signal-to-noise ratio (SNR) compared with the traditional H-QEPAS in the same environmental conditions.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Trace gas sensors possess significant potential for applications in medicine, aerospace, and the environment [1–6]. In recent years, the advancement of laser technology has led to rapid growth in trace gas sensors based on laser spectroscopy [7–11]. The photoacoustic effect was initially discovered by Alexander Graham Bell in 1880 [12], serving as the theoretical foundation for photoacoustic spectroscopy (PAS) [13–16]. As a modification of the microphone-based PAS, quartz-enhanced photoacoustic spectroscopy (QEPAS) was first reported in 2002 [17]. Quartz tuning fork (QTF), employed as an acoustic transducer in QEPAS, offers advantages such as low cost, compact size, narrow bandwidth, high Q-factor, and strong noise immunity [18–23]. The gas concentration is typically determined through the second harmonic (2f) signal amplitude during QEPAS measurement which relies on demodulation frequency. Only when the demodulation frequency equals half of the resonance frequency (f0) of QTF does the 2f signal amplitude reach its maximum value [24–26]. Due to the characteristics of QTF, f0 is easily influenced by environmental factors like temperature, gas pressure, and composition [27,28], resulting in a drift of f0 and changes in 2f signal amplitude. Therefore, it is important to calibrate f0 in trace gas monitoring applications. However, the calibration process in QEPAS takes a long time, and the continuous measurement has to be interrupted.
Heterodyne QEPAS (H-QEPAS), also known as beat frequency QEPAS (BF-QEPAS), was first proposed in 2017 [29], enabling fast calibration and continuous measurement simultaneously. In recent research applications, the heterodyne detection approach has not only been confined to H-QEPAS but also expanded to heterodyne PAS (H-PAS) and heterodyne light-induced thermoelastic spectroscopy (H-LITES), demonstrating advantages over traditional PAS and LITES in terms of continuous operation, fast response, and capable calibration [30–32]. Since the first harmonic (1f) signal exhibits maximum amplitude, 1f demodulation is commonly conducted [29–37]. A sinusoidal wave and another high-rate varietal sawtooth are added to constitute a wavelength-modulated signal, which is used to produce an acoustic wave through the photoacoustic effect and scan the corresponding gas-absorption line to get a heterodyne signal. The sinusoidal wave is required to have a frequency difference (Δf) with f0. In the process of laser wavelength gradually approaching and then moving away from the gas-absorption line, the QTF vibrates at f first and subsequently rings down at f0 logarithmically, and the accumulated energy exhausts, which is called the transient response of QTF. According to the demodulation principle of lock-in amplifier, when the generated signal has a Δf with the reference signal, the demodulated signal becomes a sinusoidal wave with a frequency of Δf. By demodulating the electrical signal of QTF at a frequency of f0±Δf, a sinusoidal wave with peak amplitude logarithmically decaying is generated, which constitutes the H-QEPAS signal. The gas concentration, f0, and quality factor (Q) of the QTF can be obtained through the peak amplitude, frequency, and ring-down time of the H-QEPAS signal, respectively. Despite achieving high sensitivity levels, H-QEPAS suffers from suboptimal excitation of QTF due to Δf between modulated frequency and f0.
In this study, a novel dual-frequency modulated H-QEPAS (DFH-QEPAS) is reported for the first time. To enhance the response of QTF, a laser wavelength modulation signal consisting of two sinusoidal waves with frequencies of f0 and f0±Δf was employed. The heterodyne signal was acquired by alternately turning on and turning off the sinusoidal wave with a frequency of f0. At first, the response of QTF was the strongest with the modulation frequency of f0, and then removing the sinusoidal modulation, QTF rang down freely with the frequency of f0. With a demodulation frequency of f0±Δf, the DFH-QEPAS signals were acquired. The parameters of laser modulation frequency and current amplitude, laser wavelength-scanning rate, voltage offset, and the detection bandwidth of lock-in amplifier, affecting heterodyne signals, were all optimized. With the same environmental conditions, the signal-to-noise rate (SNR) of the DFH-QEPAS signal was improved 4.05 times compared with H-QEPAS.
2. Experimental setup
The comparison between H-QEPAS and DFH-QEPAS techniques is illustrated in Fig. 1. Compared to the H-QEPAS system, a sinusoidal wave with a frequency of f0 was added additionally to constitute the dual-frequency modulation in the DFH-QEPAS system to enhance the response of QTF. During the wavelength modulation, the varietal sawtooth was absent and the laser central wavelength (λ0) was located constantly at the gas absorption line. The traditional H-QEPAS signal was generated due to the rapid wavelength scanning over the gas-absorption line. While the DFH-QEPAS signal was resulted from the sudden removal of modulation frequency with f0. To ensure the system parameters consistent in signal detection and noise measurement, the modulation frequency of f0±Δf was always present. Demodulating with the same frequency of f0±Δf, the H-QEPAS and DFH-QEPAS signals were received.
The experimental setup for the DFH-QEPAS sensor is shown in Fig. 2. Acetylene (C2H2) was chosen as the target gas to verify the sensor performance. An absorption line located at 6534.37 cm−1 with line strength of 1.21 × 10−20 cm−1/(mol·cm−2) was selected. Due to the largest harmonic amplitude, 1f heterodyne detection was performed. A commercially available QTF with f0 of 32.768 kHz (in vacuum) was utilized as the acoustic detector. Two sinusoidal wave components with frequency of f0 and f0±Δf, respectively, generated by a function generator were composed of the wavelength-modulated signals. The sinusoidal wave with a frequency of f0 existed intermittently to produce heterodyne signals, and the sinusoidal wave with a frequency of f0±Δf existed continuously to ensure consistent excitation. A fiber-coupled, distributed feedback (DFB) diode laser with an emission wavelength of 1530 nm and power of 12.1 mW was chosen as an excitation source. The output laser beam was firstly collimated by a collimator and then transmitted to a lens with a focal length of 40 mm. The lens was used to focus the laser beam and make it pass through the gap of QTF, generating photoacoustic effect. Two windows were equipped on both sides of the gas chamber to ensure laser passing through with low loss. Two microresonators (mRs) with a length of 5 mm and an inside diameter of 0.5 mm were used to enhance the acoustic wave. The power of the laser passing through the gas chamber was detected by a power meter to determine the optical alignment. In the experiments, the power of the laser emitted from the gas chamber was 11.5 mW. Under the effect of piezoelectricity, the vibrations of QTF were converted into an electrical signal. By demodulating the electrical signal with a lock-in amplifier, the gas concentration, f0, and Q of the QTF were inverted.
3. Results and discussions
The traditional H-QEPAS sensor performance was investigated first to make a comparison with this proposed DFH-QEPAS sensor. The system parameters related to the H-QEPAS signal level, such as laser-modulated frequency, modulated current, laser wavelength-scanning rate, and detection bandwidth, were optimized in the experiments. The optimization of laser modulated frequency and modulated current are displayed in Fig. 3. As depicted in Fig. 3(a), the amplitude of H-QEPAS signal was symmetric and centered at the f0 of QTF. During the increasing of Δf, the H-QEPAS signal amplitude was firstly magnified and then diminished, which was determined synergistically by the response of QTF and the interaction between two frequencies. When the Δf arrived at 2.5 Hz, the H-QEPAS signal peak amplitude reached maximum.
Fig. 3. Optimization of laser modulated frequency and modulated current for H-QEPAS: (a) Amplitude of H-QEPAS signal versus frequency difference; (b) Peak amplitude of H-QEPAS signal versus laser modulation current.
The laser wavelength modulation current has a significant effect on the signal amplitude of the H-QEPAS sensor. Thus, the relationship between laser wavelength modulation current and the peak amplitude of the H-QEPAS signal was investigated, as presented in Fig. 3(b). As the modulation current increased, the peak amplitude firstly rose and subsequently declined. Until the modulation current was equal to 16 mA, the system attained the strongest response.
A fast wavelength-scanning rate results in an intense transient response of QTF. However, too fast a scanning rate makes QTF unable to respond in time, causing a weak signal. Thus, to make the H-QEPAS sensor achieve the best performance, the optimization of the wavelength-scanning rate was conducted, and the results are illustrated in Fig. 4. In this experiment, the wavelength-scanning rate was decided together on the time and amplitude of the variant sawtooth rising edge. It can be seen that the rise time and rise amplitude exhibited optimal values of 342 ms and 420 mV, respectively, making the system achieve the strongest signal amplitude.
Fig. 4. Optimization of laser wavelength-scanning rate for H-QEPAS: (a) Peak amplitude of H-QEPAS signal versus the rise time of variant sawtooth; (b) Peak amplitude of H-QEPAS signal versus the rise amplitude of variant sawtooth.
In H-QEPAS, a certain detection bandwidth is demanded for catching the heterodyne signals. However, a large detection bandwidth causes much noise and deteriorated SNR. Thus, the optimization of detection bandwidth holds significant importance in enhancing the performance of H-QEPAS sensors, and the investigated results are shown in Fig. 5. The SNR reached maximum when the integration time was 8 ms. The detection bandwidth can be calculated by the filter order and the integration time. When the filter order is 3 and the integration time is 8 ms, the corresponding 3-dB detection bandwidth is calculated as 10.61 Hz.
The optimization of DFH-QEPAS signal had also been done in experiments. The Δf between the modulation and demodulation frequency, the modulation depth, the laser voltage offset, and the detection bandwidth all had obvious impacts on the DFH-QEPAS signal. The DFH-QEPAS signal amplitude kept increasing when Δf became smaller, but the heterodyne signal distorted when a small Δf was adopted, preventing analyzing the f0, Q of QTF through the heterodyne signals. To meet the requirement of real-time calibration and achieve a better detection performance, Δf was determined as 8 Hz, as same as the optimized H-QEPAS system. The modulation depth had been optimized in H-QEPAS system as mentioned above. For the same gas-absorption line under the same environmental conditions, the optimum modulation depth was identical for the two methods of H-QEPAS and DFH-QEPAS. Because the 1f detection was applied to the DFH-QEPAS sensor, the maximum peak amplitude was not obtained at gas-absorption line. Thus, in DFH-QEPAS sensor, the laser voltage offset which can change the output wavelength of laser was optimized. The results are displayed in Fig. 6(a). The optimum laser voltage offset was found to be 20 mV. The effect of integration time on the DFH-QEPAS sensor was investigated, as illustrated in Fig. 6(b). For a similar reason, the SNR of DFH-QEPAS sensor firstly improved and then worsened as the integration time increased. The optimal SNR was achieved when filter order was 3 and integration time was 8 ms, which was identical to the H-QEPAS sensor.
Fig. 6. Optimization of laser voltage offset and detection bandwidth at the filter order of 3 for DFH-QEPAS: (a) Peak amplitude of DFH-QEPAS signal versus laser voltage offset; (b) Optimization of detection bandwidth at the filter order of 3 for DFH-QEPAS.
The proposed DFH-QEPAS sensor is an improvement of the traditional H-QEPAS sensor. A comparison of the detection performance between these two methods was performed. The H-QEPAS and DFH-QEPAS signals with the respective optimal system parameters were recorded, which are shown in Fig. 7(a), and (b), respectively. In identical environmental conditions, the peak amplitude of signals obtained by H-QEPAS and DFH-QEPAS sensors were 134.93 µV and 347.65 µV, respectively. Due to the strongest excitation by a sinusoidal wave with frequency of f0, a 2.57 times larger peak amplitude can be acquired based on the DFH-QEPAS method. The noise was determined at the regions where the decays were finished, as presented by the green dashed line in Fig. 7. In comparison, the DFH-QEPAS system had a lower noise level. This is because when λ0 is located nearly at the gas-absorption line, the frequency of power variation caused by laser modulation is two times the modulation frequency. Due to 1f demodulation, the power variation is filtered by a lock-in amplifier. The corresponding SNRs were calculated as 262.03 and 1061.75, respectively, for H-QEPAS and DFH-QEPAS techniques. Compared with H-QEPAS, the DFH-QEPAS method had a 4.05 times improvement in SNR. The minimum detection limit (MDL) for C2H2 measurement was determined as 18.84 ppm. In addition, owing to no longer need to complete wavelength-scanning in DFH-QEPAS, the process for the system parameter optimization is easier than H-QEPAS.
Fig. 7. The comparison of H-QEPAS and DFH-QEPAS signals: (a) Optimized H-QEPAS signal; (b) Optimized DFH-QEPAS signal.
For examining the concentration response of such a DFH-QEPAS sensor, the peak amplitudes of signals were detected when C2H2 concentrations were varied from 0 to 20000 ppm, and the results are displayed in Fig. 8(a). Applying the linear fitting to the peak values, the calculated R-square value was equal to 0.995, indicating the DFH-QEPAS sensor exhibited an excellent linear response to C2H2 concentrations. The long-term stability of such a DFH-QEPAS sensor was estimated with an Allan deviation analysis. The results are illustrated in Fig. 8(b). The data was measured for more than two hours with the gas chamber filled with pure N2. When the Average time began from 1 s to 1000 s, the Allan deviation continued to decrease. The span was 3 orders of magnitude, implying the DFH-QEPAS sensor had good stability.
Fig. 8. The performance of DFH-QEPAS sensor: (a) Concentration response of DFH-QEPAS sensor; (b) Allan deviation of DFH-QEPAS sensor.
4. Conclusions
In conclusion, a DFH-QEPAS sensor was demonstrated for the first time. In the DFH-QEPAS technique, the laser wavelength modulation signals are composed of two sinusoidal waves with frequencies of f0 and f0±Δf, alternately turning on and turning off the sinusoidal wave with the frequency of f0 to complete signal detection. Compared with the traditional H-QEPAS sensor, the excitation response of QTF in DFH-QEPAS is significantly improved under the modulation frequency of f0. The system parameters affecting heterodyne signals were all optimized in experiments. For investigating the performance improvement of the DFH-QEPAS sensor over H-QEPAS, the DFH-QEPAS and H-QEPAS signals were detected at the same environmental conditions. The results indicated that compared with H-QEPAS, the DFH-QEPAS sensor had a 4.05 times improvement in SNR for C2H2 detection. The concentration response and long-term stability of the DFH-QEPAS sensor had been validated with excellent performance.
Funding
National Natural Science Foundation of China (62022032, 62335006, 62275065, 61875047); Key Laboratory of Opto-Electronic Information Acquisition and Manipulation (Anhui University), Ministry of Education (OEIAM202202); Fundamental Research Funds for the Central Universities (HIT.OCEF.2023011).
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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