The increase in greenhouse gases carbon dioxide and methane can directly lead to changes in the global climate and cause a significant impact on the economies of countries and human life. Methane, as the second-largest greenhouse gas on Earth, has a global warming potential 30 times higher than CO₂over a 100-year period, and its lifespan is approximately 9.1 years. At present, anthropogenic CH₄ emissions primarily originate from numerous point sources. Implementing measures to reduce CH₄ emissions can help decrease the rate of global warming. Therefore, it is crucial to conduct research on monitoring technologies for CH₄ and investigate key carbon emission sources. Hyperspectral satellite remote sensing for detecting greenhouse gases has become a candidate technology for point source detection. It has advantages such as high viewpoint, wide field of view, the ability to achieve dynamic monitoring, obtain more precise and demand-driven information data. Utilizing remote sensing methods to monitor and provide feedback on point source emissions of greenhouse gases like methane plays a crucial role in effectively addressing climate change. Existing payload technologies in China are geared towards large satellite platforms, enabling wide-area coverage with low spatial resolution monitoring. However, traditional methods such as grating spectrometry, Michelson interferometry, and spatial heterodyne are unable to meet the efficient and high-precision monitoring requirements for small-scale anthropogenic emission sources. They struggle to achieve point source detection. Therefore, it is necessary to conduct research on satellite remote sensing carbon monitoring technologies that offer high accuracy and high spatial resolution.The Fabry-Pérot interferometry technique possesses extremely high spectral resolution, capable of discerning minute wavelength differences in the spectrum. The theoretical basis of this technique is the multi-beam equal-inclination interferometry. By using an interference ring, it is possible to directly obtain the spectral information of target light at different incident angles. By collecting the spectral information corresponding to different wavelengths of the target at different positions from multiple consecutive shots, the target spectral curve is obtained. This technique establishes a relationship between CH₄ gas concentration and the depth of spectral curve notches, offering advantages in point source detection with high spectral resolution and high spatial resolution. In CH₄ gas detection, the parameters of the Fabry-Pérot interferometer and the optical filter have a significant impact on detection sensitivity. Properly configuring these parameters is crucial for improving detection accuracy.This paper presents a study on a high spatial resolution method for detecting point sources of methane gas based on the principle of multi-beam interferometric spectral imaging. Firstly, the working principle and detection scheme of the methane gas detector are introduced. The system parameters of the Fabry-Pérot interferometer are designed, and a forward model for methane gas detection is established. Subsequently, the correspondence between interference signals and methane concentration, as well as the influence of instrument parameters on detection sensitivity, are analyzed. In the end, iterative optimization is performed to obtain the optimal values of various optical structural parameters. The results indicate that within the methane detection wavelength range of 1 630~1 675 nm, with a free spectral range of 12.5 nm and a spectral resolution of 0.1 nm, the optimal parameters for the Fabry-Pérot interferometer are a cavity length of 0.08 mm and an intra-cavity reflectance of 97.5%. By using a cutoff filter with a range of (1 630±4) nm ~(1 675±4) nm, the relative change in interference signal corresponding to a 25% concentration variation of the detection source falls within the range of [0.65%, 4.30%], indicating a good detection sensitivity. The research results of this study provide a theoretical basis and technical support for high-precision.