1D U-Net Enhanced QEPAS Sensor for Trace Water Vapor Detection

Abstract

We report a deep learning-assisted quartz-enhanced photoacoustic spectroscopy (QEPAS) sensor for trace water vapor detection in air. A 1392 nm butterfly-packaged DFB laser is wavelength-modulated at f₀/2, and the QEPAS signal is retrieved by second-harmonic (2f) lock-in demodulation using a commercial quartz tuning fork gas cell. After optimizing the modulation depth to 400 mV, a 1D U-Net denoising network trained with pseudo-clean supervision is applied to the measured 2f traces, yielding an SNR improvement of 2.05× (3.11 dB). Allan deviation analysis indicates a minimum detection limit (MDL) of ~2.21 ppm at an optimum averaging time of ~619 s, corresponding to an ~2.1× improvement compared with the raw output. These results demonstrate that neural-network-based post-processing can improve QEPAS water vapor sensing performance without modifying the optical hardware.

1. Introduction

Photoacoustic spectroscopy (PAS) converts molecular absorption of modulated light into an acoustic response through non-radiative relaxation, enabling selective and sensitive trace-gas sensing with an inherently low optical background. In recent years, PAS has been actively advanced by innovations in resonant architectures and miniaturized transducers, which improve signal build-up and facilitate compact, field-deployable instruments. Representative developments include multi-resonator PAS configurations for sensitivity enhancement, mid-infrared PAS sensors achieving ppb-level performance, non-dispersive schemes using mid-infrared LEDs with differential mode excitation, and emerging broadband implementations such as cavity-enhanced photoacoustic dual-comb spectroscopy and fiber-based optomechanical photoacoustic sensors. These advances highlight PAS as a versatile platform for environmental monitoring, industrial process control, and related applications [1,2,3,4,5,6,7,8].

Quartz-enhanced photoacoustic spectroscopy (QEPAS) is a rapidly growing branch of PAS that replaces the conventional microphone with a quartz tuning fork (QTF) acting as a piezoelectric acoustic-to-electrical transducer. The core advantage arises from the QTF’s extremely high quality factor (Q) and narrowband resonance, which efficiently amplifies the photoacoustic signal at the fork resonance while suppressing broadband ambient noise. In addition, QTFs originate from mature, mass-manufactured timing components, offering excellent consistency and cost-effectiveness. Beyond QEPAS, QTFs have also been explored as miniature optical/infrared detectors and ultra-broadband detectors, indicating the broader utility of quartz devices in spectroscopy and sensing. With the development of custom QTFs, QEPAS is also being pushed toward industrialization and practical packaging [9,10,11,12]. Driven by these strengths, QEPAS has been demonstrated for numerous gas species and realistic measurement scenarios. Examples include near-infrared or mid-infrared QEPAS methane sensing with optimized spectrophone configurations, compact ppb-level NO₂ detection enabled by high-power laser diodes and grooved tuning forks, portable CO monitoring in urban environments, and sub-ppb N₂O sensing based on compact quantum cascade laser modules. QEPAS has also been applied to challenging matrices and applications such as NH₃ impurities in H₂, sarin simulant detection using tailored tuning-fork geometries, rapid field ventilation-rate measurement using an SF₆ sensor, SF₆ matrix studies with T-shaped tuning forks, and continuous real-time monitoring of CO₂ emitted from human skin. Compact atmospheric platforms have further expanded multi-species monitoring capabilities in real environments [13,14,15,16,17,18,19,20,21,22].

To further enhance speed, robustness, and sensitivity, a range of QEPAS and PAS variants have been explored. These include all-optical off-axis QEPAS with dual-wavelength demodulation of out-of-plane vibration modes, swept cavity-enhanced photoacoustic spectroscopy using a QTF, and beat-frequency QEPAS architectures, including optomechanical energy enhancement, to enable fast and sensitive gas sensing under practical constraints [23,24,25,26]. In parallel, quartz-based photothermal/thermoelastic techniques such as quartz-enhanced photothermal spectroscopy and light-induced thermoelastic spectroscopy (LITES) have provided complementary routes to gas detection, leveraging QTF transducers with different excitation/readout modalities and demonstrating high sensitivity with low-frequency or high-frequency forks and multipass configurations [27,28,29,30,31]. Chip-scale photothermal spectroscopy concepts, such as suspended-waveguide enhancement and slow-light enhancement, together with fiber-based Fabry–Pérot photothermal interferometry, further indicate the field’s broader trend toward integrated and miniaturized photothermal/photoacoustic sensing platforms [32,33,34]. Meanwhile, multi-gas optical sensing strategies such as TDM/FDM in TDLAS continue to motivate robust multi-component measurement workflows and signal processing requirements [35]. Alongside hardware advances, algorithmic enhancement has become a cost-effective pathway to improve detection limits without increasing system complexity. Stochastic resonance has been used to improve QEPAS sensitivity in weak-signal regimes, and advanced denoising/decomposition strategies have been reported to enhance QEPAS system performance [36,37]. More recently, deep learning (DL) has shown strong capability in time-series denoising and feature extraction for photoacoustic spectroscopy, including DL-based denoising frameworks and concentration prediction models designed to address correlation degradation [38,39].

Water vapor (H₂O) is among the most abundant molecules in ambient air, making humidity monitoring both a practical necessity and a key factor influencing spectroscopic measurement accuracy. In photoacoustic techniques, H₂O can affect the conversion efficiency through relaxation dynamics and collisional energy transfer, and can also contribute to interference in realistic air measurements [40]. Accordingly, simultaneous atmospheric monitoring of CH₄, N₂O, and H₂O using a single QEPAS sensor, systematic interference studies (including CO₂ and H₂O effects and acoustic noise), and investigations of relaxation dynamics in wet matrices all underscore the importance of robust signal extraction for humidity-related sensing tasks [41,42,43]. This work uses trace water vapor detection as a representative case study and proposes a DL-enhanced QEPAS signal processing approach. Specifically, we employ a 1D U-Net denoising network to enhance QEPAS 2f signals measured with a 1392 nm laser in a commercial gas cell. Recent deep-learning enhancement for photoacoustic sensing has followed two main directions: (i) end-to-end concentration prediction models to mitigate correlation degradation, and (ii) data-driven denoising models (e.g., hybrid CNN–Transformer frameworks) for reconstructing low-SNR 2f signals [44,45,46,47]. In this work, we adopt a complementary strategy by performing trace-to-trace denoising of WMS–2f QEPAS line shapes acquired in a commercial QTF gas cell. Although the gain can be expressed as ~3 dB, it corresponds to a 2.05× increase in linear SNR under our definition (SNR = A/σ), and the ultimate detection capability is further quantified via Allan deviation, showing an ~2.1× MDL/LOD improvement without modifying the optical hardware. The novelty of this work lies in adapting a lightweight 1D U-Net denoiser (encoder–decoder with skip connections) to QEPAS 2f traces and validating the benefit using both short-term SNR and long-term Allan-limited detection limits. The proposed method achieves an SNR improvement of ~3 dB and reaches a minimum detection limit of ~2.21 ppm at an integration time of ~619 s, demonstrating an ~2.1× improvement in the ultimate detection capability compared with the raw output while keeping the hardware unchanged. For context, in optimized QEPAS sensors, incremental hardware refinements often yield modest gains on the order of ~1.3–1.5×, e.g., a 1.37× signal enhancement by introducing a fiber reflector and a 1.4× improvement by shaping the excitation beam into an elliptical profile [46,47].

2. Materials and Methods

A commercial watch-type quartz tuning fork (QTF) (Kaihua Electronics Co., Ltd., Guangzhou, China) was first selected as the acoustic transducer for the QEPAS sensor. Figure 1 shows the microscope image of the QTF, where the laser beam is later aligned to pass through the gap between the prongs. To evaluate the resonant properties of the QTF, an electrical excitation test was performed. A function generator (Tektronix AFG3102, Tektronix, Beaverton, OR, USA) provided sinusoidal signals with identical amplitude but different frequencies to drive the QTF, and the corresponding electrical response was recorded as a function of the excitation frequency. The measured frequency response is shown in Figure 2, from which the resonance frequency is f₀ = 32.758 kHz and the 3-dB bandwidth is Δf = 3.3 Hz. Therefore, the quality factor can be calculated by $Q=f_0/\Delta f=9994$.

Such a high-Q resonator is well suited for QEPAS because it provides high acoustic selectivity and enables efficient conversion of the photoacoustic wave into a detectable electrical signal. In recent photoacoustic research, strategies such as self-calibration have also been proposed to further mitigate system drift and improve robustness for trace-gas sensing [48], and QTF-based schemes have been explored for reconstructing spectral information under challenging modulation/measurement conditions [49]. A recent review focusing on trace photoacoustic sensing for COx detection highlights the importance of long-term stability and advanced signal processing in practical deployments [50]. In addition, conductance-photoacoustic spectroscopy (ConPAS) demonstrates that multi-physics readout can be integrated with a QTF for simultaneous multi-gas analysis, further underscoring the versatility of quartz-based resonant transducers [51].

The experimental system is illustrated in Figure 3. A butterfly-packaged DFB laser (Thorlabs, Inc., Newton, NJ, USA) centered at 1392 nm was used as the excitation source. The laser chip was controlled by a laser driver/temperature controller (CLD1015, Thorlabs, Newton, NJ, USA) that provided both constant-current drive and temperature stabilization. The laser output was collimated and focused between the prongs of the QTF inside a commercially available gas cell.

Two channels of signals were generated by a function generator (Tektronix AFG3102, Tektronix, Beaverton, OR, USA). One channel produced a slow scanning waveform applied to the laser injection current for wavelength tuning across the H₂O absorption feature. The other channel generated a sinusoidal modulation signal at f₀/2, i.e., half of the QTF resonance frequency. In this work, we adopted the f₀/2 detection technique, where the wavelength modulation frequency is set to f₀/2 and the QEPAS signal is demodulated at the second harmonic (2f), resulting in an acoustic response at f₀. The laser beam excites water vapor molecules in the inter-prong region, producing pressure waves that drive the QTF prongs in an anti-symmetric vibration mode. The piezoelectric current from the QTF was converted to voltage by a homemade transimpedance preamplifier, and the amplified signal was then fed into a lock-in amplifier (SR830, Stanford Research Systems, Sunnyvale, CA, USA) for 2f demodulation. The lock-in reference was synchronized with the function generator TTL signal (frequency f₀/2). The lock-in amplifier operated in the 2 V input mode with a 1 s time constant and a 12 dB filter slope. The demodulated data were transferred to a computer via serial communication, and the overall system was controlled using a LabVIEW program(version 2025). Absorption of the wavelength-modulated laser radiation by the target gas produces periodic heating and pressure fluctuations, generating an acoustic wave at the QTF resonance frequency. The pressure waves excite the anti-symmetric flexural vibration of the quartz tuning fork (QTF). Due to the piezoelectric effect of quartz, the prong deflection induces an alternating piezoelectric charge/current on the QTF electrodes. This weak electrical current is converted into a voltage signal using a low-noise preamplifier (transimpedance configuration) and then sent to a lock-in amplifier (SR830, Stanford Research Systems) (Newton, NJ, USA) for 2f demodulation in the WMS–2f scheme. The QEPAS signal plotted in Figure 4 corresponds to the in-phase demodulated output, i.e., the lock-in amplifier X-channel output voltage, recorded synchronously by the LabVIEW program via serial communication. During the scan, the laser injection current was swept by the slow scan waveform, and the corresponding current values (x-axis in Figure 4) were obtained directly from the laser driver current readout (display).

Recent QEPAS studies have shown that detection geometry can significantly affect performance; for example, an off-plane configuration using a commercial QTF was demonstrated to relax optical alignment constraints while maintaining sensitivity [52]. Optical-field enhancement using compact resonant structures has also been reported, such as microfiber knot resonator-augmented QEPAS in the near-infrared [53]. Beyond environmental sensing, photoacoustic sensors have been applied to breath-related and food-related scenarios, where stable operation and strong noise suppression are equally critical [54]. In this context, QTF-based hybrid spectroscopy (e.g., QEPAS combined with conductance spectroscopy) provides a useful framework for multi-gas analysis and system validation [55], while QTF-based LITES systems commonly employ Allan deviation analysis for quantifying long-term stability and minimum detection limits [56].

In our system, the modulation depth was controlled by adjusting the amplitude of the sinusoidal signal applied to the laser driver. As shown in Figure 5, when the modulation depth increased, the normalized 2f signal amplitude first increased, then approached saturation, and finally exhibited a slight variation at larger depths. The optimum modulation depth was found at 400 mV, corresponding to the maximum normalized 2f amplitude, and this value was used for all subsequent measurements. In this work, the effective SNR is calculated as SNR = A/σ, where A is the peak amplitude of the WMS–2f QEPAS signal at the absorption line center and σ is the RMS noise level (1σ standard deviation). The noise level σ is obtained from a noise-only time trace recorded with the laser tuned outside the H₂O absorption line under identical lock-in settings, ensuring a fair comparison.

3. Results

To generate controlled water vapor concentrations, a humidifier was used together with nitrogen dilution. By adjusting the mixing ratio, the water vapor concentration was varied, and an electronic hygrometer was used as an independent reference to verify the humidity level. Under the same optimized modulation depth (400 mV), we measured the demodulated 2f QEPAS signals at four water vapor concentrations. Figure 5 shows the resulting 2f line shapes, which exhibit the expected second-harmonic spectral profile. As the water vapor concentration increased, the 2f peak amplitude increased monotonically, confirming the proper system response and linear behavior over the investigated range.

Although lock-in detection effectively suppresses broadband noise, QEPAS signals can still be limited by residual electronic noise, laser-intensity fluctuations, and long-term drift, especially for low signal levels and long averaging times. Here, we implemented a deep-learning denoising method to further improve the QEPAS performance.

The overall workflow is shown in Figure 6. First, a noise-only trace was collected by tuning the laser wavelength outside the water absorption line, so that the recorded signal mainly represented the background noise of the system. Next, the experimentally measured 2f signals were processed by a Savitzky–Golay (SG) smoothing operation to generate a clean-like template (pseudo-clean label). Random noise segments were extracted from the noise-only record and scaled by a factor α, then added to the pseudo-clean label to form synthetic noisy inputs. A 1D U-Net model with encoder–decoder structure and skip connections was trained using the mean squared error (MSE) loss between the network output and the pseudo-clean target. After training, the network was used to denoise experimentally measured 2f traces in real time (offline processing in the current implementation).

The SG-smoothed trace is used here as a clean-like template rather than a perfect physical ground truth. Savitzky–Golay smoothing is a local polynomial least-squares filter commonly used in spectroscopic signal processing, but it may attenuate high-frequency components and introduce boundary artifacts if parameters are not chosen conservatively. To mitigate potential bias, we (i) apply SG smoothing only to construct the pseudo-clean template during training, while the inference is performed directly on raw experimental WMS–2f traces, and (ii) synthesize training inputs by adding randomly sampled and scaled experimentally measured noise-only traces, so that the network learns the statistics of the real instrument noise rather than a deterministic SG operator. Finally, we note that fully label-free/self-supervised denoising (e.g., Noise2Noise/Noise2Void) could further reduce reliance on pseudo-clean targets and is a promising direction for future work.

The denoiser adopts a canonical 1D U-Net encoder–decoder architecture with skip connections. It contains four encoder stages and four decoder stages with a bottleneck; each stage includes two Conv1D layers (kernel size = 3) followed by ReLU activations. Downsampling is performed by max-pooling (pool size = 2, stride = 2), and upsampling is performed by transposed convolution (kernel size = 2, stride = 2). The number of filters is 64, 128, 256, and 512 in the encoder, with 1024 filters at the bottleneck, and then symmetrically decreases in the decoder. A final 1 × 1 Conv1D layer outputs a single denoised trace with a linear activation (regression). The dataset used for training the network contains 6000 paired samples generated following Figure 6. The samples were randomly split into 4800/600/600 for training/validation/testing (80%/10%/10%). The validation set was used to monitor generalization and to select the final model (minimum validation loss), while the test set was reserved for final evaluation only. In this work, each WMS–2f QEPAS trace is represented as a 1D vector with N = 200 sampled points; therefore, the denoiser input and output dimensions are 200 × 1. The noise-only record contains 6000 points, and random noise segments with the same length (N = 200) are extracted and added to the pseudo-clean template to form synthetic noisy inputs.

4. Discussion

Figure 7a compares a representative noise-only trace before and after denoising, showing that the 1D U-net significantly suppresses random fluctuations while preserving the slow baseline behavior. Figure 7b shows the measured 2f signal together with the denoised output. Quantitatively, the RMS noise level decreases from σ_raw = 1.496 μV to σ_DL = 0.650 μV, while the 2f peak amplitude changes from A_raw = 551.585 μV to A_DL = 490.824 μV. Therefore, SNR_raw = A_raw/σ_raw = 368.65 and SNR_DL = A_DL/σ_DL = 754.89, corresponding to an improvement factor of SNR_DL/SNR_raw = 2.05× (i.e., 10log₁₀ (SNR_DL/SNR_raw) = 3.11 dB). These results indicate that deep-learning post-processing can provide a tangible benefit for QEPAS measurements without changing the optical hardware. Notably, the denoised trace in Figure 7b exhibits a modest peak-amplitude scaling (Araw = 551.585 μV versus ADL = 490.824 μV, i.e., ~11% reduction). Such a change is expected for data-driven denoisers and mainly manifests as a multiplicative scale factor. Importantly, this does not alter the monotonic/approximately linear concentration dependence of WMS–2f signals in the weak-absorption regime; instead, it changes the calibration slope. Therefore, for quantitative concentration retrieval, we recommend constructing the concentration–signal calibration curve using the DL-processed outputs (or equivalently applying a constant scale factor obtained from calibration), ensuring unbiased concentration estimates while retaining the improved noise performance and MDL.

5. Validation

To quantify the long-term stability and minimum detection limit (MDL), an Allan deviation analysis was performed for both the raw output (Raw) and the deep-learning denoised output (DL), as shown in Figure 8. The Allan deviation decreases with increasing averaging time and reaches an optimum, after which drift contributions become dominant. The DL-processed signal reaches a minimum Allan deviation (ultimate MDL) of ~2.21 ppm at an averaging time of ~619 s. In contrast, the raw output corresponds to ~4.62 ppm at the same averaging time, indicating an ~2.1× improvement in the ultimate detection capability after NN denoising.

The Allan deviation plot is not only a metric for optimum averaging time and ultimate MDL/LOD, but also a diagnostic tool for identifying the dominant noise contributions in QEPAS sensors. In QEPAS systems, the short-averaging-time regime is often limited by approximately white noise contributions associated with the sensor/electronics (e.g., QTF thermal noise and Johnson/electronic noise), while the long-averaging-time regime is typically limited by slow drifts such as laser power instabilities, temperature fluctuations, and mechanical/optical drifts. Consequently, a data-driven denoiser mainly improves performance by suppressing structured and correlated technical noise components in the recorded traces, whereas it cannot eliminate the fundamental random noise floor set by the physical detector and readout chain, nor can it fully remove slow drifts without additional stabilization or referencing. This explains why the achievable improvement is ultimately bounded by the physical noise sources even when post-processing is applied.

In practice, the denoiser is most effective on noise components that are statistically structured and recurrent in the measurement traces (i.e., “learnable” noise), such as correlated baseline fluctuations, periodic electrical pickup (e.g., mains-related components), interference/fringe-like patterns, and other repeatable technical artifacts. These components exhibit temporal correlation or characteristic morphology and can therefore be modeled and suppressed by a data-driven network trained on representative measurements. By contrast, “non-learnable” noise components are dominated by fundamental stochastic noise floors and slow drifts that are not predictable from a single trace without additional physical references. In QEPAS, the ultimate short-term floor is often set by detector/electronics noise such as QTF thermal noise and electronic/Johnson noise, which cannot be removed by post-processing and is commonly diagnosed via Allan deviation analysis. Therefore, deep-learning post-processing primarily reduces structured technical noise, while the achievable improvement is ultimately bounded by the physical noise floor and long-term drift mechanisms.

6. Conclusions

In this work, we developed a QEPAS-based water vapor sensor and demonstrated that deep-learning denoising can provide a practical performance gain without modifying the spectrophone hardware. A tuning-fork-based QEPAS module was characterized and integrated into a WMS–2f detection architecture driven by a 1392 nm DFB laser and a commercial gas cell. The modulation depth was experimentally optimized to maximize the normalized 2f signal amplitude, providing a stable operating point for subsequent humidity measurements. Water vapor 2f spectra were acquired at several concentrations, and a 1D U-Net denoising model (trained under a pseudo-clean supervision framework) was introduced to suppress measurement noise. Although the denoised waveform shows a modest reduction in peak amplitude (i.e., an amplitude scaling), this effect primarily changes the calibration slope and does not affect quantitative concentration retrieval as long as the calibration is performed using the same DL-processed signals (or an equivalent scaling correction is applied). The overall smoothness and baseline fluctuations are significantly improved, leading to a net SNR enhancement of 2.05× (3.11 dB). By evaluating the Allan deviation, the sensor achieved an ultimate MDL of ~2.21 ppm at an averaging time of ~619 s, corresponding to an ~2.1× improvement compared with the raw output. These results confirm that deep-learning-assisted signal processing is an effective route to improve QEPAS humidity sensing performance, and it can be readily extended to other trace-gas targets and real-time implementations with lightweight neural networks.