# Trace CH\({}_{4}\) Gas Detection Based on an Integrated Spherical Photoacoustic Cell
## 4 Conclusions  
In summary, we propose an integrated SPAC for trace CH\({}_{4}\) gas detection. The SPAC is divided into two parts, which are coupled to each other through an intermediate thread to form a spherical PA cavity. Formula analysis and numerical calculation are carried out to analyze the acoustic field distribution of the SPAC at resonant and non-resonant modes. From the finite element simulation results, the first-order radial resonant frequency and second-order angular resonant frequency show good agreement with the formula analysis results. A cantilever-based fiber-optic acoustic sensor is used to detect the PA signals based on the WLI phase-locked demodulation algorithm. The integrated SPAC, together with a near-infrared DFB laser and a high-speed spectrometer, makes up a PAS system for trace CH\({}_{4}\) gas detection. Considering the sensitivity and the measurement range of the acoustic sensor, the SPAC works at the non-resonant mode. The reduction in sensitivity caused by the operating frequency in the non-resonant region of the SPAC is fully compensated by the high sensitivity of the acoustic sensor working at the resonant frequency. Different concentrations of CH\({}_{4}\)/N\({}_{2}\) gas mixture are sequentially passed into the SPAC and the experimental results show that the PA signal is proportional to the CH\({}_{4}\) concentration. The linearity of the second harmonic response is measured to be 0.26 pm/ppm. The background noise of one thousand sample points is obtained by filling the SPAC with pure N\({}_{2}\) gas at an integration time of 10 s. Considering the sensitivity of the SPAC, the MDL for trace CH\({}_{4}\) detection is calculated to be 1.23 ppm. The Allan-Werle deviation is applied to make the MDL further decrease to be 126.9 ppb at the average time of 1000 s. Overall, the proposed SPAC has an integrated, miniaturized and all-optical structure, as well as a high  
Figure 11: The Allan–Werle analysis results of the pure N\({}_{2}\) gas.  
Figure 10: The background noises with the SPAC filled with pure N\({}_{2}\) gas.  
sensitivity for trace CH\({}_{4}\) gas detection, which can be used for remote and long-distance trace gas detection.  
Conceptualization, Y.J. and Z.G.; data curation, H.F.; formal analysis, Y.J. and F.S.; funding acquisition, Z.G., K.C., L.M., W.P. and Q.Y.; methodology, H.F. and K.Y.; project administration, W.P.; supervision, L.M.; validation, Z.G.; visualization, K.C.; writing--original draft, Y.J. and H.F.; writing--review and editing, Z.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant numbers 11904045, 61905034, 61705031, and 62075025; China Postdoctoral Science Foundation, grant number 2020M673542; Doctoral Start-Up Foundation of Liaoning Province, grant number 2019-BS-051; Natural Science Foundation of Liaoning Province, grant number 2019-MS-054; Dalian High-Level Talent Innovation Support Plan, grant number 2019 RQ010; Fundamental Research Funds for the Central Universities, grant number DUT20 RC(4)014; State Grid Corporation of China, grant number 521205190014.  
Data Availability Statement: Data sharing not applicable.  
The authors declare no conflict of interest.