Analysis of Optical Errors in Joint Fabry–Pérot Interferometer–Fourier-Transform Imaging Spectroscopy Interferometric Super-Resolution Systems

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.