# Super-Resolution Multicomponent Joint-Interferometric Fabry-Perot-Based Technique
## 4 Results and Discussion
### Comparison and Analysis
The interval \(d\) of the FPI in the simulation is 0.2 cm, and the interval scan step is 14 nm, covering the mid-wavelength position FSR is at least 50 scan steps, and for covering the whole spectrum, the number of scan steps is 70. Trigonometric toe-shearing is used to reduce the influence between adjacent sampling  
Figure 14: Schematic diagram of the RS-HI super-resolution principle: (**a**,**d**,**h**) incident spectrum \(B\) and spectrum \(B\)-\(T_{\text{FPI}-d}\) obtained by passing through the FPI with intervals d1, d2, and d3, respectively; (**b**,**e**,**i**) low-resolution spectrum obtained by interferometric spectrometer; (**c**,**f**,**j**) the energy S of the narrow-band spectrum is obtained based on the integration of the low-resolution spectrum; (**k**) the super-resolution spectrum is obtained by combining all of the S according to the central wavelength of the narrow-band spectrum. Figure 15: Sampling of a tunable FPI in (**a**) long-wavelength; (**b**) mid-wavelength; (**c**) short-wavelength ranges. points, ignore the tolerance, and simulate the RS-HI under ideal conditions. The error of the super-resolution spectrum is calculated according to Equation (11). Assuming that \(\alpha\)-fold spectral super-resolution is achieved using \(\beta\) interferograms, the data volume required is defined as \(\beta\times L/l\), and the data utilization rate is \(\alpha/\beta\). The MJI-HI is a two-fold spectral super-resolution using two interferograms, so the data volume is 1.2 \(\times\) 10\({}^{5}\), and the data usage rate is 100%. The maximum optical range \(L\) of the [PERSON] interferometer used is 0.6-3.0 cm, respectively. The simulation results are shown in Table 1. The results show that the error decreases rapidly in the range of \(L\) = 0.6-1.2 cm with the increase of \(L\). This is due to the fact that the impulse-response width of the [PERSON] interferometer decreases, and the mutual influence between adjacent sampling points is reduced. The small variation in errors in the range of \(L\) = 1.2-3 cm indicates that, to achieve the same spectral resolution, an interferometric spectrometer with a smaller optical range could be used, which would have less of an impact on the accuracy, it would significantly reduce the volume of the data to be collected, and it would improve the data utilization. In the same case of a 2-fold super-resolution for the \(L\) = 3.0 cm spectrum, it is slightly higher than the error of the MJI-HI discussed above (\(-\)33.42 dB). However, with this same spectral resolution and close error, the RS-HI collects 35 times more data than the MJI-HI, and the data utilization is lower. This means that the RS-HI is more suitable for the high magnification of spectral super-resolution, and the MJI-HI is more suitable for the low magnification of spectral super-resolution. By increasing the spectral resolution of the FPI to 0.0217 cm\({}^{-1}\), the error of the RS-HI is further reduced. The spectral super-resolution was performed for the same Michelson interferometer, and the spectral resolution was kept around 0.0217 cm\({}^{-1}\) at different intervals \(d\) by adjusting \(R\). The results show that its error rises dramatically as \(d\) approaches \(L\), and the opposite requires a higher reflectivity. This also confirms the need to balance the trade-off between accuracy and \(R\) when designing \(d\) with guaranteed spectral resolution. In summary, compared with the RS-HI, the MJI-HI has greater advantages in FPI parameter requirements, system stability, optical-component processing difficulty, and cost. Based on our analysis of the super-resolution principle, spectral sampling vacancy, low data utilization, and interference between response functions, the RS-HI is more suitable as a dispersive imaging spectrometer, and the MJI-HI is more suitable as an interferometric imaging spectrometer. According to the simulation results, the RS-HI is more suitable for high-magnification spectral super-resolution, and the MJI-HI is more suitable for low-magnification spectral super-resolution.