## 5 Conclusions  
This study conducts a comprehensive optical error analysis of the spectral super-resolution technology based on the integration of a Fabry-Perot interferometer (FPI) and Fourier-transform imaging spectroscopy (FTIS), referred to as the multi-component joint interferometric imaging spectrometer (MJI-HI). The foundational principle of MJJ-HI is to generate multiple frequency-shifted components on the interferogram through the periodic modulation of the spectrum by the FPI and obtain a joint interferogram via linear superposition. The inversion algorithm establishes a system of linear equations based on the linear relationship between the joint interferogram and the original interferogram, enabling the recovery of high-frequency information carried by these frequency-shifted components that exceed the maximum OPD of the FTIS. However, the presence of certain optical errors disrupts this linear relationship, leading to reduced accuracy in interferogram reconstruction.  
The primary errors in the FPI include optical path errors, non-parallelism errors, surface irregularity errors, and reflectivity variation errors. Based on the analysis results, an OPD calibration algorithm is proposed, and an improved inversion algorithm is developed to address the convolutional errors caused by non-parallelism and surface irregularities in the interferogram. For the FTIS, the main errors include collimation errors, mirror tilt errors, and beam splitter reflectivity variation errors. Based on the analysis results, these errors do not affect the linear relationship of MJJ-HI but may lead to spectral distortion, wavelength shift, and energy reduction in the super-resolved spectra caused by diminished interference intensity. Among these, the tilt errors in the FTIS and the non-parallelism errors in the FPI exhibit mutual influence. This paper provides a detailed analysis of these  
Figure 22: Using \(B_{0}\) = 1 as the input spectrum, the super-resolution spectral results obtained under reflectance variation (**a**) curve 1, (**b**) curve 2, (**c**) curve 3, and (**d**) curve 4 with PV = 2%, 6%, and 10% are shown. Here, \(B_{sup\_PV}\) represents the super-resolution spectra obtained using MJJ-HI under different FPI reflectance error levels.  
interactions and establishes tolerance thresholds through simulation experiments, demonstrating that the impact of these errors on MJI-HI is negligible within the tolerance limits.  
This study comprehensively summarizes the critical technical aspects of MJI-HI, validates the analysis through simulation experiments, and verifies the proposed improved algorithms. It offers detailed theoretical guidance for subsequent experimental development and research on MJI-HI, while also serving as an important theoretical reference for other optical technologies combining FPI and FTIS.  
Conceptualization, Y.Z.; methodology, Y.Z. and Q.L.; software, Y.Z.; validation, Y.Z. and Q.L.; formal analysis, Y.Z., J.W. and Y.T.; investigation, Y.Z., J.S. and X.C.; writing--original draft preparation, Y.Z., Y.L. and Q.L.; writing--review and editing, Y.Z., Y.L. and Q.L.; project administration, Q.L.; funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA28050401) and the National Key Research and Development Program of China (No. 2022 YFB3904800).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflicts of interest.