# Super-Resolution Multicomponent Joint-Interferometric Fabry-Perot-Based Technique
## 4 Results and Discussion
### Comparison and Analysis  
In previous studies, the resampling super-resolution hyperspectral imager (RS-HI) was proposed [21; 22; 23; 24; 25]. The principle is to add a FPI to perform more detailed sampling within the spectral response of the imaging spectrometer and thus achieve spectral super-resolution. The technique is highly versatile and can be applied to both dispersive imaging spectrometers based on prisms or gratings, as well as interferometric imaging spectrometers [21; 22; 23; 24; 25]. The system structure of the RS-HI applied to the interferometric imaging spectrometer is close to that of Figure 2[21; 23]. However, it uses a tunable FPI, and there are major differences in the principle, system parameters, and applications. Therefore, this section will compare and analyze the MJI-HI and RS-HI. The principle of the RS-HI is as shown in Figure 13[21; 23]. The multiple transmission peaks of the FPI can be used as narrow-band filters to form multiple narrow-band spectra, and Figure 13a,d,h indicates the transmission spectra at different intervals \(d\), respectively. The obtained spectra from the interferometric spectrometer are the impulse responses of these narrow-band spectra, as shaded in Figure 13d,e,i. Integration of the m\({}_{\text{th}}\)-level impulse response yields the energy \(S_{\text{m}}\) of the narrow-band spectrum, as shown in Figure 13c,f,j. The super-resolution spectrum is obtained by changing the interval \(d\) several times and rearranging them according to the central wavelength of the narrow-band spectrum, as shown in Figure 13k. Based on this principle, the RS-HI can more easily achieve high-magnification spectral super-resolution, which is its greatest advantage compared to the MJI-HI. In addition, the RS-HI directly acquires narrow-band spectra between spectral sampling intervals, which is more suitable for dispersive imaging spectrometers, as based on the principle. This will bring great convenience to installation and calibration, etc. MJI-HI mainly processes and calculates the spectrum of a spectrum and is more suitable for interferometric imaging spectrometers. Figure 13: Relationship between the condition number \(\kappa\) and reflectance \(R\) at \(2 nd=2\ L\) and \(2 nd=L\). The transmission spectrum of a FPI vs. reflectance is shown in Figure 12a. The interference intensity is usually defined as \(K=(T_{FPI-MAX}-T_{FPI-MIN})/(T_{FPI-MAX}+T_{FPI-MIN})\), where \(T_{FPI-MAX}\) is the maximum value of \(T_{FPI}(v)\), and \(T_{FPI-MIN}\) is the maximum value of \(T_{FPI}(v)\). When \(K\) is large enough, \(T_{FPI}(v)\) can be viewed as a comb-like transmission spectrum consisting of multiple transmission peaks. Additionally, \(K\) is only related to the fineness \(F\) of FPI, which depends on the reflectivity \(R\). The actual engineering will lead to degradation due to the optical and mechanical tolerances of a FPI. The most fundamental problem of the RS-HI is that the FPI needs to produce transmission peaks with a very narrow width and a stable central wavelength. According to Figure 12a, when the reflectivity can reach more than about 90% and the FPI has a small enough optical tolerance, \(K\) will be high enough to form transmission peaks. According to the results in Section 4.3, the \(R\) of the FPI in the MJJ-HI should be in the range of 20-80%. Excessive reflectance will lead to a greater processing difficulty and a higher cost for the actual design, and it will also reduce the luminous flux significantly, and thus the signal-to-noise ratio, which will weaken the advantage of the multichannel interferometric spectrometer. In addition, the spacing \(d\) of the FPI in the RS-HI is on the order of mm or cm, which is close to the order of the maximum OPD \(L\) of a Michelson interferometer. additionally, the scanning step of \(d\) during the measurement is approximately on the order of nm [21; 23]. To obtain super-resolution spectra, the sampling points need to be aligned according to the central wavelength, which mainly relies on theoretical calculations.