# Trace CH\({}_{4}\) Gas Detection Based on an Integrated Spherical Photoacoustic Cell
## 1 Introduction  
Trace gas detection plays an important role in environmental atmospheric monitoring, medical clinical diagnosis and industrial control [1, 2, 3]. Photoacoustic (PA) spectroscopy (PAS), which utilizes the PA effect of the gas, is the most common method in trace gas analysis due to its fast reproduction speed, strong selectivity and high sensitivity [4, 5, 6]. The PA effect refers to that when the sample in the PA cell is irradiated by a beam of modulated or pulsed monochromatic light, the absorbed light energy is partially or completely converted into heat in a non-radiative relaxation way, causing the heated volume of the sample to expand to produce pressure waves that extend outward with the center of the light source, and the PA signals can be detected by an acoustic sensor placed in the PA cell [7]. The amplitude of the PA signals generated in the PA cell is proportional to the intensity of the incident light, the sensitivity of the acoustic detector and the PA cell constant [8]. In recent years, many researchers have done a lot of researches in order to optimize the PA system. With the development of laser technology, the near-infrared distributed feedback (DFB) diode laser combined with the erbium-doped fiber amplifier (EDFA) were applied as the excitation source to enhance the PA signals [9, 10]. In 2013, [PERSON] et al. used a mid-infrared quantum cascade laser (QCL) as the excitation source to achieve a minimum detection limit (MDL) of 340 parts per trillion (ppt) and 4 parts per billion (ppb) for carbon monoxide (CO) and nitrous oxide (N\({}_{2}\)O) gases under the optimal data acquisition time of 500 s [11]. In order to further improve the amplitude of PA signal, a high-sensitivity quartztuning fork (QTF) and a fiber-optic acoustic sensor were used to replace the traditional microphone as the acoustic detector [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. In 2002, [PERSON] et al. firstly proposed quartz enhanced photoacoustic spectroscopy (QEPAS) technology. Instead of a gas-filled resonant acoustic cavity, the acoustic energy is accumulated in a high-Q QTF. With the laser output power of 8.44 mW and the working wavelength of 1.53 nm, the MDL of acetylene (C\({}_{2}\)H\({}_{2}\)) gas was 2 parts per million (ppm) [12]. In our previous work, we proposed a low-frequency PA sensor based on a Parylene-C diaphragm for space-limited trace gas detection, the detection limit of C\({}_{2}\)H\({}_{2}\) was 88.4 ppb with a locking integral time of 1 s [13]. Except for the incident light and the acoustic detector, the PA cell has a great impact on the performance of the PAS system. [PERSON] et al. designed a compact differential PA cell consisting of two acoustic resonators [3]. The PAS system has achieved a detection limit of 3.6 ppm with an average time of 1 s. In our previous work, a T-type longitudinal resonant PA cell was developed for trace gas detection [24]. The T-type PA cell possesses a high PA cell constant, a simple manufacturing process and a fast response time. However, at present, the PA cell generally adopted a cylindrical structure [3; 4; 5; 5; 9; 13; 14; 15; 16; 17; 18; 19; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37], and there are few studies on other shapes of PA cells. [PERSON] et al. proposed an ellipsoidal resonant PA cell and concluded that the Q value of the ellipsoidal PA cell could reach 70 through theoretical and simulation analyses [38]. There is also some research about spherical PA cells (SPAC) [39; 40; 41]. [PERSON] et al. proposed that, through theoretical analysis, it was proved that there was no viscous loss in the radial mode of a spherical PA cell; that is, it had a better Q value than the cylindrical PA cell [39]. Afterwards, [PERSON] et al. made a more detailed theoretical analysis of the SPAC on this basis [40]. However, the above studies on the SPAC were lacking in relevant simulation analyses to verify the theoretical results. Furthermore, the PAS system based on the SPAC had a large volume, which was not suitable for on-site measurements.