# Signal-to-Noise Ratio Analysis of Bandpass Sampling Time-Modulated Fourier Transform Spectroscopy
); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (W.L)  
[PERSON]  
1 Aerospace Information Research Institute, Chinese Academy of Sciences, No. 9 Dengzhuang South Road,  
Haidian District, Beijing 100094, China; [EMAIL_ADDRESS] (X.C. ); [EMAIL_ADDRESS] (Z.T. ); [EMAIL_ADDRESS] (J.W. ); [EMAIL_ADDRESS] (N.Z. ); [EMAIL_ADDRESS] (Y.T. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (W.L)  
[PERSON]  
1 Aerospace Information Research Institute, Chinese Academy of Sciences, No. 9 Dengzhuang South Road,  
Haidian District, Beijing 100094, China; [EMAIL_ADDRESS] (X.C. ); [EMAIL_ADDRESS] (Z.T. ); [EMAIL_ADDRESS] (J.W. ); [EMAIL_ADDRESS] (N.Z. ); [EMAIL_ADDRESS] (Y.T. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (W.L)  
[PERSON]  
1 Aerospace Information Research Institute, Chinese Academy of Sciences, No. 9 Dengzhuang South Road,  
Haidian District, Beijing 100094, China; [EMAIL_ADDRESS] (X.C. ); [EMAIL_ADDRESS] (Z.T. ); [EMAIL_ADDRESS] (J.W. ); [EMAIL_ADDRESS] (N.Z. ); [EMAIL_ADDRESS] (Y.T. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (W.L)  
[PERSON]  
1 Aerospace Information Research Institute, Chinese Academy of Sciences, No. 9 Dengzhuang South Road,  
Haidian District, Beijing 100094, China; [EMAIL_ADDRESS] (X.C. ); [EMAIL_ADDRESS] (Z.T. ); [EMAIL_ADDRESS] (J.W. ); [EMAIL_ADDRESS] (N.Z. ); [EMAIL_ADDRESS] (Y.T. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (W.L)  
[PERSON]  
1 Aerospace Information Research Institute, Chinese Academy of Sciences, No. 9 Dengzhuang South Road,  
Haidian District, Beijing 100094, China; [EMAIL_ADDRESS] (X.C. ); [EMAIL_ADDRESS] (Z.T. ); [EMAIL_ADDRESS] (J.W. ); [EMAIL_ADDRESS] (N.Z. ); [EMAIL_ADDRESS] (Y.T. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (J.S. )environmental adaptability of FTS. This new type of broadband high-resolution FTS, namely BPS-FTS, has the characteristics of a small number of sampling points along the optical path difference and a large sampling interval, which can reduce the requirements for the sampling frequency of the moving mirror and increase the stability of the system. Therefore, BPS-FTS technology has been widely studied, and different types of principle schemes have been proposed. In FTS, the data obtained are modulated interferograms, requiring data reconstruction to obtain the desired spectra [1; 2; 3; 4; 5]. Therefore, the signal-to-noise ratio (SNR) of FTS includes the SNR of the interferogram and the SNR of the reconstructed spectrum [6]. For FTS, the SNR of the interferogram can evaluate the quality of the instrument's output signal. However, in practical applications, users are typically more concerned about the SNR of the reconstructed spectra; hence, evaluating the SNR of the reconstructed spectra holds greater practical significance. In view of the importance of SNR, the SNR analysis method of FTS has been widely studied, and a variety of SNR estimation methods have also been proposed. For example, the correspondence between the interferogram at the zero optical path difference (OPD) and the reconstructed spectrum is used to deduce the correspondence among the local interferogram SNR, the spectra SNR, and the number of interferogram sampling points [6; 7; 8]. However, this derivation is not rigorous because the interferogram is a modulated signal, the signal at each point is different, and the noise is approximately the same. Therefore, the SNR of the interferogram at each point is different. The SNR at zero OPD is the largest [6] and cannot represent the SNR of the entire interferogram and the reconstructed spectrum. Another method is to directly perform a Fourier transform on the interferogram noise to obtain the noise in the reconstructed spectrum and calculate the SNR of the reconstructed spectrum [6].