Dual-Component Beat-Frequency Quartz-Enhanced Photoacoustic Spectroscopy Gas Detection System

Abstract

This study designed and validated a dual-component beat-frequency quartz-enhanced photoacoustic spectroscopy (BF-QEPAS) gas detection system utilizing time-division multiplexing (TDM). By applying TDM to drive distributed feedback lasers, the system achieved the simultaneous detection of acetylene and methane. Its key innovation lies in exploiting the transient response of the quartz tuning fork (QTF) to acquire gas concentrations while concurrently capturing the QTF resonant frequency and quality factor in real-time. Owing to the short beat period and rapid system response, this approach significantly reduces time-delay constraints in time-division measurements, eliminating the need for periodic calibration inherent in conventional methods and preventing detection interruptions. The experimental results demonstrate minimum detection limits of 5.69 ppm for methane and 0.60 ppm for acetylene. Both gases exhibited excellent linear responses over the concentration range of 200 ppm to 4000 ppm, with the R² value for methane being 0.996 and for acetylene being 0.997. The system presents a viable solution for the real-time, calibration-free monitoring of dissolved gases in transformer oil.

1. Introduction

Gas detection, as a continuously evolving technology, has found extensive applications across diverse fields, including petrochemicals, biomedicine, food safety, and environmental monitoring [1,2,3,4,5]. Among various optical sensing-based detection techniques, photoacoustic spectroscopy (PAS) stands out due to its high sensitivity, rapid response, and wide dynamic range [6]. Building upon PAS, quartz-enhanced photoacoustic spectroscopy (QEPAS) has been developed as an alternative method for trace gas photoacoustic detection, with its core concept being the accumulation of acoustic energy within a resonant quartz tuning fork (QTF) transducer. This approach avoids the need for traditional gas-filled photoacoustic cells, thereby eliminating constraints on chamber design imposed by acoustic resonance conditions [7].

Despite the widespread use of QEPAS-based gas sensors, a significant challenge persists. Due to the susceptibility of the QTF’s characteristics to change during actual measurements, periodic calibration of the QTF’s resonant frequency and quality factor is required during gas detection to avoid accuracy degradation caused by resonant frequency and quality factor fluctuations [8,9,10,11,12]. This necessity interrupts continuous, long-term gas monitoring. In 2017, a novel technique termed beat-frequency quartz-enhanced photoacoustic spectroscopy (BF-QEPAS) was introduced for rapid, calibration-free continuous trace gas monitoring. Unlike conventional QEPAS, BF-QEPAS exploits the transient response of the QTF. This generates an electrical signal characterized by an exponentially decaying envelope, enabling the simultaneous determination of both the QTF parameters and the gas concentration [13,14]. This technique has seen widespread application in recent years. In 2022, Li. et al. proposed a calibration-free mid-infrared exhaled breath sensor based on BF-QEPAS for real-time ammonia measurements at the ppb level [15]. In 2024, Ye. et al. developed an optomechanical energy enhanced BF-QEPAS method for fast and sensitive gas sensing [16]. However, existing BF-QEPAS implementations remain primarily limited to single-gas detection, creating a gap for multi-component monitoring applications where time-continuous data is critical.

Gas detection often requires the analysis of gas mixtures, which demands multi-component gas detection techniques capable of distinguishing the concentrations of individual gases. Commonly employed techniques include gas chromatography [17], mass spectrometry [18], electrochemical sensor methods [19], and laser absorption spectroscopy (LAS) [20]. LAS typically utilizes combinations of multiple lasers and detectors to achieve multi-component detection [21,22]. Multi-component sensors often employ multiplexing methods, such as time-division multiplexing (TDM) and frequency-division multiplexing (FDM). In 2018, Zhang et al. proposed a multi-gas QEPAS sensor based on three QTFs with different response frequencies for trace gas detection [23]. This research well demonstrates the gas detection method based on FDM. In 2021, Yu et al. proposed a PAS-based multi-component gas detection system integrating both FDM and TDM, utilizing a resonant photoacoustic cell and a broadband microphone. This system successfully measured the concentrations of four gas components: methane (CH₄), water vapor (H₂O), carbon dioxide (CO₂), and acetylene (C₂H₂) [24]. More recently, in 2024, Qin et al. developed a dual-component gas sensor based on QEPAS and LITES (laser-induced thermoelastic spectroscopy) combined with TDM technology to measure the concentrations of C₂H₂ and CH₄ mixtures [25]. These applications demonstrate the feasibility and convenience of TDM technology.

The applications of multi-component gas detection span an extensive range of scenarios. For example, CH₄ and C₂H₂ are key dissolved gases in transformer oil. Analyzing their composition and concentration allows for the identification of potential internal insulation faults within transformers and an assessment of their severity. Consequently, the real-time monitoring of dissolved gases in oil is crucial for ensuring the reliable operation of power grids [26,27]. In this regard, considerable work and research have recently been conducted. In 2023, Ye et al. proposed a dual-channel off-beam quartz-enhanced photoacoustic spectroscopy sensor system combined with time-division multiplexing technology for detecting methane and acetylene, highlighting the significance of these gas detections. In 2025, Li et al. employed a frequency-division multiplexed fiber-optic photoacoustic sensor to detect dissolved methane and acetylene gases, achieving minimum detectable concentrations of approximately 0.1 μL·L⁻¹ (parts per million) for both gases [28,29]. Therefore, CH₄ and C₂H₂ were selected as the target gases for the system, and corresponding experiments were designed to optimize detection performance.

This paper reports a dual-component BF-QEPAS gas detection system based on TDM technology. The system employs TDM in a BF-QEPAS sensor to simultaneously detect CH₄ and C₂H₂ concentrations under distributed feedback (DFB) laser driver current modulation. Leveraging the BF-QEPAS technique, the system achieves rapid gas concentration measurement while concurrently acquiring the parameter of the QTF, thereby eliminating the need for periodic QTF parameter measurement and calibration inherent in conventional photoacoustic spectroscopy methods, preventing interruptions in gas detection. In terms of measurement speed, the BF-QEPAS method significantly reduces measurement time compared to conventional approaches (e.g., standard QEPAS), owing to its short beat period and rapid system response. The implementation of dual-component gas sensing via TDM of the laser drive signal offers greater operational convenience compared to traditional optical switching control, as it requires no additional control equipment. Furthermore, the system architecture is significantly simplified by utilizing only a single lock-in amplifier. Experimentally, the system successfully detected the concentration of CH₄ and C₂H₂. The minimum detection limits achieved were 5.69 ppm for CH₄ and 0.60 ppm for C₂H₂, with both gases exhibiting excellent linear responses within the concentration range of 200 ppm to 4000 ppm (CH₄:R² = 0.996; C₂H₂:R² = 0.997), validating the superior performance of the system.

2. Selection of Absorption Lines

For multi-component gas detection, it is essential to select appropriate strong absorption lines to avoid cross-interference between the gases. According to the 2020 HITRAN database, the absorption lines of CH₄ and C₂H₂ gases within the wavenumber range of 5800 cm⁻¹ to 6800 cm⁻¹ were simulated, as shown in Figure 1. Through observation and unit conversion, we identified strong, distinct, and non-overlapping absorption lines for C₂H₂ at 1531.59 nm and for CH₄ at 1653.72 nm. These wavelengths were accordingly selected for the lasers.

3. Principle of BF-QEPAS

In photoacoustic gas detection, the QTF exhibits two dynamic response modes. One is the steady-state response, where the QTF is driven by a continuous external force (such as a continuously modulated laser), producing stable vibrations synchronized with the excitation frequency. The other is the transient response, where the QTF is excited by a short-duration external force (such as a pulsed acoustic wave). After the force is removed, the QTF enters a state of free-decay vibration.

The steady-state detection method of traditional QEPAS drives the laser current by superimposing a low-frequency scanning signal (slowly sweeping across the gas absorption peak) and a high-frequency modulation signal. When the QTF output frequency matches the laser modulation frequency, a lock-in amplifier (LIA) is used to demodulate the signal at twice the modulation frequency (2f). The peak amplitude of the demodulated signal corresponds to the gas concentration.

In contrast, the innovative detection method based on the transient response employs a laser scanning waveform with a steep rising edge. This waveform rapidly sweeps to the gas absorption peak, generating a short acoustic pulse that forces the QTF to vibrate at the laser modulation frequency (the transient response phase). After the wavelength moves away from the absorption peak, the acoustic pulse terminates, and the QTF transitions to free vibration (the free-decay phase), oscillating at its inherent resonant frequency f₀.

In the transient response mode of the QTF, driven by the external force, it vibrates at a frequency identical to the modulation frequency. Upon entering the free-decay phase, the QTF vibrates at its own resonant frequency. The frequency of the QTF output signal during the free-decay phase corresponds to the QTF’s resonant frequency, denoted as f₀. The frequency of the input signal f₁ equals f₀. If the frequency of the reference signal is set to f, the beat frequency f_beat of the LIA output signal is the difference between f₀ and f, expressed as

$$f_{\mathrm{beat}}=\left|f_0-f\right|=\Delta f.$$

(1)

By measuring the time interval Δt between two peaks of the beat-frequency signal, Δf can be determined by taking the reciprocal (Δf = 1/Δt). The QTF’s resonant frequency f₀ is then obtained using Equation (3).

$$\Delta f={\displaystyle \frac{1}{\Delta t}}$$

(2)

$$f_0=f\pm {\displaystyle \frac{1}{\Delta t}}$$

(3)

In addition, the Q value of the QTF can also be calculated using the beat frequency signal, and the calculation formula is as follows:

$$\mathrm{Q}=\pi f_0\tau$$

(4)

where $\tau$ is the response time of the system.

4. Design of Sensor System

The schematic diagram of the experimental setup is shown in Figure 2. The system was designed to operate at standard atmospheric pressure (1 atm) and a constant temperature of 296 K. Two distributed feedback laser diodes DFB-LD-1 (10.63 mW, Wchip) and DFB-LD-2 (10.12 mW, Wuhan 69 Sensing Technology Co., Ltd., Wuhan, China) with 14-pin butterfly packages were employed. Their center wavelengths were 1531.1 nm and 1653.7 nm, respectively. The specific characteristics of the DFB lasers used are detailed in Figure 3. A function generator supplied a composite waveform—comprising a fast sawtooth wave superimposed on a DC signal—to the laser diode controller (Stanford, Santa Clara, CA, USA, LDC501). Simultaneously, it provided the high-frequency sine wave used for modulation and demodulation. The frequency of this sine wave could be adjusted within a range close to the QTF’s resonant frequency. An optical isolator placed after each DFB laser ensured unidirectional laser propagation and prevented optical feedback damage. Standard C₂H₂ gas and CH₄ gas (both balanced in N₂), along with high-purity N₂, were introduced into a gas dilution system (GDS) (Beijing Jinxun Electronics Co., Beijing, China RCS2000-A) via three separate gas channels. This enabled the preparation of various concentration mixtures of C₂H₂ and CH₄. The resulting gas mixture was then flowed through the acoustic detection module (ADM) (Thorlabs, Newton, NJ, USA, model ADM01), which housed the QTF. The laser beam was directed into the ADM. The beat-frequency current signal generated by the photoacoustic excitation from C₂H₂ and CH₄ absorption was subsequently detected using a lock-in amplifier (Zurich Instruments, Zurich, Switzerland H2FLI-50 MHz). Finally, the beat-frequency signal was acquired and transmitted to a computer for data processing and analysis.

5. Experimental Results and Discussion

As mentioned previously, variations in the parameter of the QTF can impact the accuracy of detection data. Therefore, determining the parameter of the QTF is essential. In the experiment, the resonant frequency of the QTF was determined using the heterodyne demodulation method and the Q-factor was obtained through exponential (e-based) fitting. Subsequently, the amplitude of the system output signal was measured at various modulation frequencies near the resonant frequency to identify the modulation frequency yielding the maximum signal amplitude. Finally, the linearity and minimum detection limit of the system were measured using the previously determined optimal modulation frequency, thereby demonstrating the feasibility of the dual-component BF-QEPAS gas detection system.

5.1. Determination of QTF Resonant Frequency via Heterodyne Demodulation

The feasibility of detecting resonance frequencies f₀ is validated using the experimental setup depicted in Figure 2, with C₂H₂ gas serving as the sample gas. As depicted in Figure 4a, the beat-frequency signal over one cycle shows a time interval (Δt) of 0.064 s between two consecutive peaks. The beat frequency Δf was determined using Equation (2), enabling calculation of the resonant frequency f₀ = 12,465.6 Hz via Equation (3). For comparison, the QTF resonant frequency curve was independently measured using the conventional electrical excitation method as shown in Figure 4b, yielding f₀ = 12,465.4 Hz. This traditional approach, however, requires interruption of gas concentration measurements and is time-consuming. Across 10 measurements, we observed that the discrepancy between the two methods was within ±0.5 Hz. The close agreement between the electrically measured f₀ and the heterodyne-demodulated f₀ confirms the validity and reliability of the BF-QEPAS technique. The peak amplitude of the beat-frequency signal is directly proportional to the gas concentration, a relationship that can be derived from the Beer–Lambert law. Therefore, this method enables simultaneous acquisition of both gas concentration and QTF resonant frequency. Moreover, its applicability extends to all resonant-frequency-based sensing targets. Meanwhile, the resonant frequency response curve of the QTF yielded a Q-factor of 7332, while exponential fitting analysis of the beat frequency signal indicated a response time of 0.1861 s. According to Equation (4), the calculated Q-value is 7287 (error < 1% across 10 measurements). This indicates that the system can simultaneously achieve a reasonably accurate Q-factor measurement.

5.2. Modulation Frequency Optimization

With the modulation amplitude fixed at 0.4 V, we investigated the effect of modulation frequency on the output signal amplitude. As shown in Figure 5, we observe that the signal amplitude initially increases and then decreases as the deviation between the modulation frequency and the resonant frequency of the QTF (f₀) widens. This phenomenon can be attributed to two factors governing the amplitude of the BF-QEPAS signal. First, the QTF’s response to the acoustic wave frequency—which equals the laser modulation frequency—is optimal when the laser modulation frequency f approaches the QTF’s resonant frequency f₀, making the QTF more easily excited into vibration. Second, Δf plays a critical role: a smaller Δf results in a longer interval between two constructive interferences. The longer this interval, the more vibrational energy the QTF dissipates during this period. These two factors work in concert, leading to a maximum modulation frequency response within a certain range near the QTF’s resonant frequency. Multiple experiments were conducted using C₂H₂ and CH₄ as sample gases. The experimental results demonstrated that both gases exhibited relatively high beat signal amplitudes at a modulation frequency of 12,450 Hz.

5.3. System Linearity Analysis

Based on prior experiments, the system modulation frequency was fixed at 12,450 Hz with a constant modulation amplitude of 0.4 V. We first configured CH₄ gas at concentrations ranging from 200 to 3000 ppm, and a C₂H₂ gas range from 200 to 4000 ppm using the GDS. These calibrated mixtures were sequentially introduced into the ADM. Beat frequency signals from CH₄ and C₂H₂ at various concentrations were detected individually. Portions of these data are presented in the multi-color curves of Figure 6.

Experimental data confirmed that the beat-frequency signal amplitude is a linear function of gas concentration, exhibiting excellent linearity. Figure 7a displays the linear relationship and corresponding parameters for CH₄ gas, yielding a coefficient of determination (R²) of 0.996. Figure 7b shows the linear function for C₂H₂ gas, with an R² value of 0.997, indicating outstanding linear responses for both gases.

Following this, simultaneous detection of CH₄ and C₂H₂ was performed using the system. As depicted in Figure 8, the TDM signal waveform features a 1 s composite cycle comprising a 100 ms rapid sawtooth wave followed by a DC segment. Crucially, within each second-long cycle, only one laser emits a pulsed signal to perform gas detection, thereby achieving true time-division multiplexing.

Figure 9 presents the beat-frequency detection signal for a gas mixture containing 2700 ppm CH₄ and 400 ppm C₂H₂. The signal amplitude of CH₄ was measured to be 0.01253 V, and the signal amplitude of C₂H₂ was 0.0177 V. The signal intensities closely align with the linear calibration curves established previously, demonstrating the feasibility and reliability of the TDM system.

Subsequently, pure nitrogen was introduced into the ADM to characterize the noise of the system. The output signal was continuously monitored for minutes under this N₂ environment to establish the noise baseline, yielding a 1σ noise level of 0.0264 mV. Figure 10 shows an excerpt of the recorded noise data. Based on this characterization, the system’s minimum detection limits were calculated as 5.69 ppm for CH₄ and 0.60 ppm for C₂H₂.

The conversion of Allan deviation data, calculated for long-term-averaged noise in pure N₂, yielded the system’s detection limits. Figure 11 displays the Allan deviation for CH₄ and C₂H₂, from which minimum detection limits of 13.59 ppb (CH₄) and 1.425 ppb (C₂H₂) were determined at an averaging time of 170 s. This analysis validates that the minimum detection limit is proportional to 1/√t (t = lock-in integration time).

6. Conclusions

This study successfully designed and validated a dual-component BF-QEPAS gas detection system based on TDM. By integrating beat-frequency quartz-enhanced photoacoustic spectroscopy technology with the TDM method, the system achieved the highly sensitive and rapid detection of CH₄ and C₂H₂. Owing to its short beat period and fast system response, the BF-QEPAS method significantly reduces the time delay inherent in time-division measurements. Simultaneously, it overcomes the issue of gas detection interruption caused by periodic calibration of the QTF parameter in traditional quartz-enhanced photoacoustic spectroscopy techniques. The experimental results demonstrated excellent linear response across a concentration range of 200 ppm to 4000 ppm, with the R² value for CH₄ being 0.996 and for C₂H₂ being 0.997. The minimum detection limit for CH₄ reached 5.69 ppm and that for C₂H₂ reached 0.60 ppm.

The successful development of this system provides an effective technical means for the real-time monitoring of dissolved gases in transformer oil, holding significant importance for power grid fault warning and operational reliability. Future research could further optimize system performance, extend it to the detection of more gas components, and explore its application potential in areas such as environmental monitoring and industrial safety.