## 1 Introduction  
Trace gas detection based on infrared absorption spectroscopy is widely applied in exploration geochemistry, medical diagnosis, and industrial analysis fields due to its advantages of high selectivity and high sensitivity [1; 2; 3; 4; 5]. Overlap may occur between adjacent absorption lines since the linewidths of absorption lines are widened by molecular collision, doppler shift, and the measurement instrument [6; 7; 8]. This overlap reduces the accuracy of the system and renders it more susceptible to environmental influences. The number of available absorption lines is limited by the overlap. In previous research, to avoid mutual interference of absorption lines and achieve an accurate measurement, only well-isolated absorption lines with strong absorption were utilized for trace gas measurement [9; 10; 11]. However, it is difficult to avoid overlapping errors in some applications, and overlapping absorption lines are used to increase gas absorption and obtain lower minimum detection limits (MDL) [12; 13; 14; 15]. Consequently, to obtain more usable absorption lines and more accurate retrieved concentrations, a method to correct the interference of overlapping absorption lines is of great significance.  
Multiple methods have been employed for correcting the interference of overlapping absorption lines [16; 17]. Three reference multi-pass cells were utilized to obtain the absorption spectra of standard interferential gases by [PERSON] et al. The interference of the overlap is effectively removed by fitting a linear superposition of the known absorption spectra with the absorption spectrum of the gas mixture detected, and the fitting coefficients were found to be higher than 0.96 [18]. A method of fourth harmonic was introduced by [PERSON] to correct the interference of overlapping absorption lines and achieve accurate measurements of hydrogen sulfide (H\({}_{2}\)S), methane (CH\({}_{4}\)), carbon dioxide (CO\({}_{2}\)), and ammonia (NH\({}_{3}\)) [19]. A direct absorption fitting (DAF) method for the separation of overlapping absorption lines based on a continuous wavelet transform combined with chaos particle swarm optimization was presented by [PERSON] et al., and the fitting coefficient reached 0.99 [20]. However, the accuracy of the reference cell method and the direct fitting method cannot meet the requirements of trace gas measurement. The higher harmonic method has a satisfactory effect on the small absorption line overlap, but cannot separate absorption lines with large overlap. The effect of gas temperature on the overlap is not taken into account in the above methods, which causes large measurement error. It is of great importance to correct this error due to gas temperature and overlap interference.  
In the current work, several approaches were investigated to satisfy the requirements for improving the measurement accuracy of overlapping absorption lines. This paper differs from previous similar studies in the following ways: (a) a 2f-SR approach for correcting the interference of overlapping absorption lines is proposed, (b) a 2f signal restoration method using wavelength modulation spectroscopy based on laser characteristics is described, (c) an approach for obtaining lower detection limits using overlapping absorption lines is proposed, and (d) the novel idea of using overlapping absorption lines to achieve multi-gas detection is explored.