Fourier transform spectroscopy with bandpass sampling (BPS-FTS) increases the interferogram sampling step and reduces sampling frequency, thereby reducing system implementation difficulty. However, this technology has only been introduced in principle and lacks analysis of the actual system error. In this paper, we present a theoretical analysis of the optical system diffraction effect, derive the bandpass spectrum bandwidth and interferogram sampling step under the influence of the diffraction effect, and conduct modeling and a simulation analysis with and without the diffraction effect. Through simulation, we found that when the diffraction effect was considered, the relative deviation of the recovered spectrum from the input spectrum was 1.30%, and the spectral similarity was 0.9669. However, without considering the diffraction effect, the relative deviation of the recovered spectrum from the input spectrum was 6.23%, and the spectral similarity was only −0.0056. The simulation results demonstrate that the diffraction effect has a significant influence on BPS-FTS interferogram sampling and recovery spectra. The results of this study have reference significance for their technical realization of BPS-FTS.

For traditional Fourier transform (FTS), its integral sampling usually meets the Spectral Modulation Transfer Function (SMTF) criterion. However, for bandpass-sampling Fourier transform spectroscopy (BPS-FTS), based on our analysis, the integral sampling condition derived from the Spectral Modulation Transfer Function (SMTF) is excessively stringent. In other words, the interval of the integral sampling time that fulfills the tolerance requirements for the reconstructed spectrum is very narrow. There are numerous integration sampling time intervals outside this range that still meet the tolerance requirements for the reconstructed spectrum. In this paper, through theoretical modeling, we propose a method based on average |SMTF| as the selection criterion for the integration sampling time. Through simulation analysis, it is evident that the intervals and range of the integral sampling time obtained via this method are more accurate, ensuring the tolerance requirements of the reconstructed spectrum. Under these intervals, when conducting integral sampling on the interferogram, the spectral deviation of the reconstructed spectrum is minimal, and the Spectral Correlation Mapper (SCM) is nearly equal to one. This indicates that compared with the SMTF criterion in traditional FTS, this method is more suitable for the characteristics of BPS-FTS. The analysis in this paper can provide theoretical and simulation support for the implementation of BPS-FTS.

In Bandpass Sampling Fourier Transform Spectroscopy, a comprehensive method for evaluating signal-to-noise ratio (SNR) has not yet been established. This paper employs an energy conservation approach to analyze the relationship of SNR between interferogram and spectra in Bandpass Sampling Time-Modulated Fourier Transform Spectroscopy (BPS-FTS). It systematically presents models for the average SNR of the system interferogram and the average SNR of reconstructed spectra under different parameters. These models are compared with SNR models in traditional Fourier transform spectroscopy (FTS) and are mutually validated through theoretical modeling and simulation analysis. It provides a theoretical basis and simulation verification for the design and implementation of the system.

Fourier-transform imaging spectroscopy (FTIS) faces inherent limitations in spectral resolution due to the maximum optical path difference (OPD) achievable by its interferometer. To overcome this constraint, we propose a novel spectral super-resolution technology integrating a Fabry–Pérot interferometer (FPI) with FTIS, termed multi-component joint interferometric hyperspectral imaging (MJI-HI). This method leverages the FPI to periodically modulate the target spectrum, enabling FTIS to capture a modulated interferogram. By encoding high-frequency spectral interference information into low-frequency interference regions through FPI modulation, an advanced inversion algorithm is developed to reconstruct the encoded high-frequency components, thereby achieving spectral super-resolution. This study analyzes the impact of primary optical errors and tolerance thresholds in the FPI and FTIS on the interferograms and spectral fidelity of MJI-HI, along with proposing algorithmic improvements. Notably, certain errors in the FTIS and FPI exhibit mutual interference. The theoretical framework for error analysis is validated and discussed through numerical simulations, providing critical theoretical support for subsequent instrument development and laying a foundation for advancing novel spectral super-resolution technologies.

A new spectral super-resolution technique was proposed by combining the Fabry–Perot interferometer (FPI) with Temporally and Spatially Modulated Fourier Transform Imaging Spectrometer (TSMFTIS). This study uses the multi-beam interference of the FPI to modulate the target spectrum periodically, and it acquires the modulated interferogram through TSMFTIS. The combined interference of the two techniques overcomes the limitations of the maximum optical path difference (OPD) on spectral resolution. FPI is used to encode high-frequency interference information into low-frequency interference information, proposing an inversion algorithm to recover high-frequency information, studying the impact of FPI optical defects on the system, and proposing targeted improvement algorithms. The simulation results indicate that this method can achieve multi-component joint interference imaging, improving spectral resolution by twofold. This technology offers advantages such as high throughput, stability, simple and compact structure, straightforward principles, high robustness, and low cost. It provides new insights into TSMFTIS spectral super-resolution research.