# Trace CH\({}_{4}\) Gas Detection Based on an Integrated Spherical Photoacoustic Cell
## 3 Experimental Results and Discussions  
The schematic diagram of the experimental system based on PAS is shown in Figure 7. The system consisted of the SPAC, a near-infrared DFB laser, a high-speed spectrometer, a super luminescent diode (SLD), a circulator, a computer and two mass flow controllers (MFCs). The system used a near-infrared DFB laser with a center wavelength of 1651 nm as the PA excitation source. The laser beam passed through a collimator into the SPAC. The SLD laser was used as the detection source of the fiber-optic acoustic sensor, and the laser was first coupled to the circulator and then propagated into the acoustic sensor. The PA signal deformed the cantilever beam, which in turn caused the F-P (Fabry-Perot) cavity length to change. A LabVIEW-based phase-locked WLI demodulation algorithm based on the high-speed spectrometer was used to demodulate the dynamic cavity length of the acoustic sensor and the magnitude of the gas concentration was obtained. Two MFCs were used to control the concentrations of the CH\({}_{4}\)/N\({}_{2}\) mixture. Because the PA system operated at a non-resonant mode, which avoided the resonant frequency drift due to the temperature change; meanwhile, the experimental procedure was carried out at a constant room temperature and atmospheric pressure--the temperature sensitivity of the SPAC was negligible.  
Figure 6: Acoustic pressure distribution of the SPAC at a frequency of 1290 Hz.  
Figure 7: The PAS experimental system based on the SPAC.  
The two MFCs with \(\pm\)19% error, together with one bottle CH\({}_{4}\)/N\({}_{2}\) gas mixture, and one bottle of pure N\({}_{2}\) used as standard gas, made up the gas mixing system. Five different concentrations of CH\({}_{4}\)/N\({}_{2}\) gas mixture from 50 ppm to 1000 ppm were sequentially passed into the SPAC. The PA signals were measured with the PA cell confined. Figure 8 shows the second harmonic responses of CH\({}_{4}\) gas with the concentrations of 50 ppm, 100 ppm, 200 ppm, 500 ppm, and 1000 ppm, respectively, and Figure 9 shows the linear results of the second harmonic signals to the concentrations of CH\({}_{4}\) gas at the corresponding peak, with a slope value of 0.26 pm/ppm and a fitted R-squared of >0.998, which verifies that this PAS system response shows an approximately linear response to different concentrations of CH\({}_{4}\).  
The background noise of one thousand sample points was obtained by filling the SPAC with pure N\({}_{2}\) gas at an integration time of 10 s, as shown in Figure 10. After calculation, the noise level (1\(\sigma\)) of the background noise was determined to be 0.32 pm. With the sensitivity of 0.26 pm/ppm, the MDL for trace CH\({}_{4}\) detection was calculated to be 1.23 ppm. The Allan-Werle deviation was applied when the SPAC was filled with pure N\({}_{2}\). As shown  
Figure 8: The output of lock-in WLI of CH\({}_{4}\) gas with different concentrations.  
Figure 9: The output PA signals changing with different concentrations of CH\({}_{4}\).  
in Figure 11, the Allan variance was 0.033 pm at an average time of 1000 s. Therefore, the MDL was then estimated to be 126.9 ppb.