Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring

Quartz-enhanced photoacoustic spectroscopy (QEPAS) is a sensitive gas detection technique which requires frequent calibration and has a long response time. Here we report beat frequency (BF) QEPAS that can be used for ultra-sensitive calibration-free trace-gas detection and fast spectral scan applications. The resonance frequency and Q-factor of the quartz tuning fork (QTF) as well as the trace-gas concentration can be obtained simultaneously by detecting the beat frequency signal generated when the transient response signal of the QTF is demodulated at its non-resonance frequency. Hence, BF-QEPAS avoids a calibration process and permits continuous monitoring of a targeted trace gas. Three semiconductor lasers were selected as the excitation source to verify the performance of the BF-QEPAS technique. The BF-QEPAS method is capable of measuring lower trace-gas concentration levels with shorter averaging times as compared to conventional PAS and QEPAS techniques and determines the electrical QTF parameters precisely.

The signals were detected at room temperature and 760 Torr, when the ADM was filled with 2.5 % water vapor. The SNR value corresponding to the 10 ms, 30 ms and 100 ms were not calculated and plotted in (d), as the LIA detection bandwidth was too narrow to detect the perfect BF-QEPAS signal when the LIA time constant was >3 ms. DFB diode laser was used as the excitation source. The modulation frequency and depth of the wavelength was 32,960 Hz and 1 cm -1 , respectively. The time constant and filter slope of the LIA was set at 100 µs and 12 dB, respectively. The signals were detected at room temperature and 760 Torr when the ADM was filled with 2.5 % water vapor. The experiment was carried out with the same system as described in this paper (see Figure. 2) at room temperature and a pressure of 700 Torr.
The DFB quantum cascade laser (DFB-QCL) (AdTech Optics, Inc. Model HHL-14-32) temperature and current were selected to target a CO absorption line located at 2,190.02 cm -1 with a 26.5 mW output power and line-strength of 2.915×10 -19 cm mol -1 . The mid-infrared laser beam was focused by a 50 mm focal length plano-convex CaF 2 lens. The DFB-QCL wavelength was scanned at the rate of 50 cm -1 s -1 by scanning the drive current. A sinusoidal signal with a frequency of 32,640 Hz was applied in order to modulate the DFB-QCL wavelength. The modulation depth was 0.085 cm -1 . The time constant and filter slope of the LIA were set at 3 ms and 12 dB, respectively. interband cascade laser emitting at 3.6 µm. The experiment was carried out with the same system as described in this paper (see Figure. 2) at room temperature and a pressure of 700 Torr.
The DFB interband cascade laser (DFB-ICL) (Nanoplus Nanosystems and Technologies GmbH, S/N: 1485/25-19) temperature and current was selected to target a CH 4 absorption line located at 2,778.64 cm -1 with a 2.3 mW output power and line-strength of 5.241×10 -22 cm mol -1 .
The mid-infrared laser beam was focused by a 30 mm focal length plano-convex CaF 2 lens. The DFB-ICL wavelength was scanned at the rate of 50 cm -1 s -1 by the scanning the drive current. A sinusoidal signal with a frequency of 32,640 Hz was applied in order to modulate the DFB-ICL wavelength. The modulation depth was 0.497 cm -1 . The time constant and filter slope of the LIA were set at 3 ms and 12 dB, respectively. Based on Newton"s law of motion equation when a sinusoidal dither is applied to the laser current at a frequency of f, the QTF response can be expressed as: where h is the step-length and (

Supplementary Note 2: Optimization of the LIA parameters for the BF-QEPAS sensor
The equivalent noise detection bandwidth (ENBW) of the LIA is determined by its time constant and filter slope, which has a direct influence on the signal-to-noise ratio (SNR) of the system.
Unlike traditional QEPAS-based sensors, the ENBW of the LIA in BF-QEPAS based sensor is larger than QTF"s ENBW 2 . However, the large detection bandwidth results in a high background 9 noise. We optimized LIA filter slope and time constant, respectively, in order to obtain a detection bandwidth which does not distort the BE-QEPAS signal and maintains an efficient background noise suppression.
As shown in Supplementary Figure 2, the BF-QEPAS signals increase with a decrease of the LIA filter slope, i.e. the wider LIA ENBW for the same time constant. However, more noise is also detected. For the reported sensor, there was no excessive noise observed when the filter slope decreased from 24 dB to 12 dB. With a further decrease of filter slope, such as 6 dB, the noise increased and became apparent. The LIA time constant was optimized with a similar method. As shown in Supplementary Figure 3, with the same filter slope, the SNR of the BF-QEPAS based sensor increased with the LIA time constant decreasing from 100 ms to 100 µs.
However, a further decrease of the time constant led to the sensor to detect more noise, thereby reducing the sensor"s SNR. We chose 12 dB and 100 µs as the LIA filter slope and time constant, corresponding to a detection bandwidth of ∆f = 1,250 Hz. These experimental results proved that such settings do not distort the line shape of the beat signal and yield the best SNR.
The wavelength scanning rate has a direct influence on the result of the BF-QEPAS based sensor.
As described in this paper, the wavelength scanning rate must be fast enough to induce the transient response of the QTF. Based on the vibrational-translational (V-T) relaxation rate of the targeted trace gas, there is an optimal value for this rate. The results plotted in Supplementary   Figure 4 show three different cases of the wavelength scanning rates. When the wavelength is scanned at 18 cm -1 s -1 , the steady state response affects the beat signal and changes the signal shape. When the wavelength scanning rate is too fast, such as 72 cm -1 s -1 , the signal decreased as the energy absorbed by the gas cannot be effectively transformed to acoustic energy. Hence, the optimal wavelength scanning rate was experimentally determined to be 36 cm -1 s -1 for the detection of water vapor.

Supplementary Note 3: Beat frequency signal analysis
As mentioned in the manuscript section entitled "Theory of BF-QEPAS", the beat frequency signal is generated after a pulsed acoustic wave excited the QTF prongs to vibrate in a short of the linear fitting. Since the larger amplitude contributes to achieving an improved detection limit, a signal analysis was carried out from the first signal peak, except the peak/valley O.

Supplementary Note 4: Performance of BF-QEPAS sensor with three different types of semiconductor lasers
As the BF-QEPAS technique is independent of the excitation wavelength, it was possible to verify the performance of this technique using different kinds of semiconductor lasers. CO and CH 4 were selected as the target gas, respectively. Since CO and CH 4 have a slow V-T relaxation rate, the beat frequency signal is weak when the laser wavelength is scanned rapidly. To obtain a good beat frequency signal, we chose a slower scanning rate and a modulation frequency which