# Super-Resolution Multicomponent Joint-Interferometric Fabry-Perot-Based Technique
## 4 Results and Discussion
### Comparison and Analysis
The central wavelength also varies with the field-of-view angle. To ensure the accurate wavelength of the center of the transmission peak at all levels of the entire field of view, the tuning accuracy of the FPI needs to be controlled on the order of nm. This kind of FPI, with a large interval, a small tuning range, and a very high level of accuracy, is difficult to manufacture and process. A Michelson interferometer requires strict system accuracy, and two interferometers with moving parts will make the whole system less stable. In contrast, the MJJ-HI uses a static FPI, which ensures that the system stability is not greatly affected and reduces both the processing difficulty and the cost of the FPI. As shown in Figure 14b, the RS-HI part of the error comes from the sidelobes of the impulse response of the interferometric spectrometer, and the surrounding sampling points will integrate this part of the sidelobes and thus cause the error, \(S_{\text{(m-1)-d1}}\), and \(S_{\text{m-d1}}\) and \(S_{\text{(m+1)-d1}}\), as shown in the figure, will affect each other. This can lead to pseudo-spectra in parts of the spectrum, with large undulations, resulting in a change in the shape of the spectrum. This problem can be alleviated by apodization and increasing the FSR. However, increasing the FSR leads to an increase in the width of the FPI transmission peak, and a further increase in \(R\) is required to ensure the same spectral resolution. Additionally, increasing the FSR also means that more spectral data between the two sampling points of the FPI will not be used, i.e., the data points outside the shading in Figure 14b, and the data utilization will be further reduced. Therefore, in the FPI spacer design, a trade-off between accuracy and reflectance and data utilization is required to ensure the spectral resolution. In contrast, the RS-HI based on a dispersive imaging spectrometer, the response function of which can be regarded as a rectangular function, does not produce similar errors without considering diffraction. The principle behind the MJJ-HI's super-resolution can be equated to expand the \(L\). Therefore, the super-resolution spectrum is still uniformly sampled, which is more conducive to the processing and application of spectral data. Moreover, the MJJ-HI can obtain twice the super-resolution spectrum using two interferograms \(I_{1}\) and \(I_{2}\), in which there is no data waste. The RS-HI, however, has the problem of non-uniform sampling. This is due to the fact that the tunable FPI changes the interval \(d\); i.e., it changes the FSR, rather than keeping the FSR constant over all of the transmission peak shifts. As shown, Figure 15a-c corresponds to the super-resolution spectra sampled at the long-, medium-, and short-wavelength positions in the measurement spectral range, respectively. In Figure 15b, the FPI sampling range at the mid-wavelength position covers exactly one FSR, while a larger region in the long-wavelength position exists and is not sampled, as in the red-boxed region in Figure 15a. This would result in multiple such regions within the spectrum not being acquired. In addition, sampling more than one FSR at short-wavelength locations can lead to the repeated sampling of the same spectrum, producing meaningless duplicate data. So, the tuning range of the FPI needs to be traded off in terms of spectral coverage and data utilization. Dispersive imaging spectrometers have a much smaller spectral range and lower spectral resolution, and in this regard, the super-resolution method of the RS-HI is more suitable for dispersive imaging spectrometers. We used the atmospheric absorption spectrum in Section 4.1 as the input spectra. The results of the super-resolution of the Michelson interferometer spectra for different _Ls_ were simulated when the RS-HI spectral resolution was consistent with that simulated by the MJI-HI discussed in Section 4.1.