## 3 Experimental Setups  
Water vapor was the main interference gas in the CH\({}_{4}\) absorption spectroscopy during the near-infrared band. In order to evaluate the effect on the CH\({}_{4}\), the absorption spectroscopy of CH\({}_{4}\) in the 1.653-1.655 \(\upmu\)m band were simulated by the HITRAN database. Simulation parameters were as follows: the temperature of 298 K, the pressure of 101 kPa, the path length of 10.8 m, the CH\({}_{4}\) concentration of 1000 ppm, and the water vapor concentration of 10,000 ppm. The simulation results are shown in Figure 1. Although water vapor also exhibited some absorption features in the 1.653-1.655 \(\upmu\)m band, the interference effect on the CH\({}_{4}\) absorption spectroscopy was minimal. It could be concluded that the effect of water vapor on the absorption intensity of CH\({}_{4}\) was negligible. Therefore, 1.6537 \(\upmu\)m was chosen as the center absorption wavelength for CH\({}_{4}\) in this paper. The structure of the CH4 sensor with a compact gas cavity based on OA-ICOS is shown in Figure 2. The sensor consists of an optical part, an electrical part, and a gas path part. The sensor can support two measurement modes: DA-OA-ICOS and WM-OA-ICOS. In the optical part, a DFB laser with a center wavelength of 1.6537 um was used as the light source. The laser provided a stable light source with high single mode output characteristics. The light beam was collimated by a collimator before entering an optical resonance cavity. The optical noise of the system could be reduced by adjusting the position of the collimator. The optical resonance cavity consisted of two high reflection mirrors (band of 1450-1670 nm, curvature radius of 20 cm, reflectivity \(>99\%\)), which enabled multiple reflections of the beam inside the cavity. Based on the required optical path, the cavity length was designed to be 7 cm by MATLAB r2019b program. An effective optical path length of 10.8 m with a cavity volume of 8.9 mL was obtained, satisfying the design requirements of compact sensor. The output beam enhanced by the optical resonance cavity was focused by the lens (focal length of 6 cm) onto an InGaAs amplified detector. In the electrical part, different scanning signals were generated by a signal generator for DA-OA-ICOS, WM-OA-ICOS and white noise perturbation. The white noise perturbations  
Figure 1: Absorption spectroscopy of CH4 with 1000 ppm and water vapor with 10,000 ppm in the 1.653–1.655 μm band. Figure 2: Schematic structure of the CH4 sensor with small gas cavity based on OA-ICOS. were generated by the broadband random noise from the signal generator. The special customized narrowband RF noise source was not required. (1) The random broadband white noise could more efficiently integrate various noise sources due to the randomness of the spectra, and the cavity mode noise was dispersed. Under low signal intensity, the randomness of broadband white noise contributed to prevent the accumulation of noisy signals at specific frequencies. The RF narrowband white noise tended to excessive focus on the noise within a limited frequency range, thus affecting the measurement accuracy and stability. (2) Since the broadband white noise provided the richer frequency component, the automatic compensation of baseline noise was improved to enhance baseline stability. The RF narrowband white noise only covered a specific frequency band, which made it difficult to cope with various frequency interferences, resulting in baseline drift or instability. (3) The random broadband white noise could suppress the effect of external environmental noise by introducing signals in multiple frequency bands, thereby increasing the robustness of the system. The RF narrowband white noise might be interfered with the specific frequency bands, resulting in the system more susceptible to high-frequency noise. The DFB laser was precisely controlled by a laser temperature controller and a current driver simultaneously.