Due to large flux, wide spectral range, high resolution and many other advantages, Fourier transform infrared spectroscopy has been widely used in the field of atmospheric environment monitoring. Based on the weak infrared interference optical signal characteristic of Fourier transform infrared spectrometer and the tellurium cadmium mercury photoconductive type infrared detector, the characteristics of the interference optical signal of the Fourier transform spectrometer based on the Michelson interference method are analyzed. A kind of weak signal detection circuit taking narrowband filtering method as the core is designed, and the equivalent noise model is established to analyze the noise performance of the circuit. The circuit is simulated by Tina software. Results show that the circuit has constant gain and group delay in the pass band, and the weak interference signal can be amplified without distortion.The designed circuit is applied to the Fourier transform spectrometer, and the atmospheric mid-infrared band spectrum ranging from 400～7000 cm-1 is obtained at room temperature, almost covering the common absorption peak of atmospheric pollutants in the mid-infrared band, which can achieve the identification and measurement of different pollutants.