# Super-Resolution Multicomponent Joint-Interferometric Fabry-Perot-Based Technique
## 5 Conclusions  
In this study, we investigated the method of adding a FPI to an interferometric spectroscopic imager to achieve spectral super-resolution. Conventional hyperspectral imaging \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**FPI-\(d\) (cm)** & **FPI-R** & \begin{tabular}{c} **FPI-FWHM** \\ **(cm\({}^{-1}\))** \\ \end{tabular} & \(L\) (cm)** & \begin{tabular}{c} **Resolution** \\ **Improvement** \\ **Multiplier** \\ \end{tabular} & \
\begin{tabular}{c} **Data** \\ **Volume** \\ **Rate** \\ \end{tabular} &
\begin{tabular}{c} **Data** \\ **Utilization** \\ \end{tabular} & **Error (dB)** \\ \hline
0.2 & 95.00\% & 0.0816 & 1.2 & 8.4 \(\times\) 10\({}^{5}\) & 14.57\% & \(-\)27.668 \\  & & 0.7 & 8.7 & 9.8 \(\times\) 10\({}^{5}\) & 12.44\% & \(-\)28.619 \\  & & 0.8 & 7.6 & 1.12 \(\times\) 10\({}^{6}\) & 10.86\% & \(-\)29.650 \\  & & 1.2 & 5.1 & 1.68 \(\times\) 10\({}^{6}\) & 7.29\% & \(-\)31.599 \\  & & 1.8 & 3.4 & 2.52 \(\times\) 10\({}^{6}\) & 5.06\% & \(-\)32.763 \\  & & 2.4 & 2.5 & 3.36 \(\times\) 10\({}^{6}\) & 3.57\% & \(-\)33.426 \\  & & 3.0 & 2.0 & 4.2 \(\times\) 10\({}^{6}\) & 2.86\% & \(-\)33.936 \\ \hline
1 & 93.40\% & & & & & & \(-\)33.232 \\
0.75 & 95.00\% & 0.0217 & 3.0 & 7.7 & 4.2 \(\times\) 10\({}^{6}\) & 11.0\% & \(-\)39.825 \\
0.5 & 96.65\% & & & & & & \(-\)41.6513 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters and results of the RS-HI simulation. systems cannot obtain a continuous spectrum and will eventually lose detailed high-frequency information outside the cutoff frequency. These optical systems can be regarded as low-pass systems of spectral dimension. Here, we showed that the addition of a FPI can achieve a breakthrough in the cut-off frequency of the low-pass system and improve the spectral resolution. The role of the FPI is that the transmission spectrum can be used as a modulated wave to achieve spectrum mixing, and the double-beam interferometer can obtain an interferogram of the spectrum after mixing. It can be viewed as a linear combination of the multiple displacement components of the original interferogram that moves high-frequency interferometric information beyond the maximum OPD into the observable range. Therefore, high-frequency interference information is calculated by constructing a system of linear equations, which is equivalent to increasing the maximal OPD and achieving double-spectral super-resolution. Theoretically, spectral resolution can be improved multiple times based on this idea. Compared to the resampling method, the proposed approach in this paper requires a low level of reflectance for the FPI, no interval change, and less difficulty in spectral reconstruction, and it is more suitable for improving the spectral resolution of interferometric imaging spectrometers. We have introduced the Michelson interferometer as an example, but the proposed method could also be applied to other types of double-beam interferometers. We simulated the method using a high-frequency cosine function, a Gaussian function, and spectral data as the input spectrum. The simulation results show that this method successfully achieves the high-precision recovery of spectral high-frequency information, and that the spectral resolution is significantly improved. The interval and reflectance of the FPI are two important optical parameters in the proposed method. We analyzed the effects of the two parameters on the proposed method, where the interval size determines the magnitude of the spectral resolution, and the reflectance affects the accuracy of the interferogram recovery. Finally, we performed a comparative analysis with related studies. The results show that the MJI-HI is more suitable for the spectral super-resolution of low-resolution interferometric spectrometers, and it has the advantages of high stability, high data utilization, and low cost. The method proposed in this study to improve spectral resolution using the FPI does not provide a complete analysis of the FPI or the optical tolerances of the entire optical system.