# Four-Channel Polarimetric-Spectral Intensity Modulation Imager
## 3 Effectiveness Validation for the FCPS Scheme
### The Effectiveness of the FCPS  
In this section, the following simulations are carried out to prove the effectiveness of the FCPS. The data demodulation results of the FCPS are compared with those of the traditional channel filtering method. According to Section 3.1, the parameters of the system matrix calibrated for the FCPS are shown in Figure 6, where Figure 6a-d represent the matrix calibration parameters of the four channels, respectively.  
The simulated input Stokes spectra for the simulation are shown in Figure 7. It is a 30\({}^{\circ}\) line polarized light.  
\[DOLP=\frac{\sqrt{S_{1}^{2}+S_{2}^{2}+S_{3}^{2}}}{S_{0}^{2}}=1 \tag{31}\]  
The simulated spectra are input, and four modulated simulation curves are obtained through Equation (1), as shown in Figure 8. It can be seen from Figure 8 that each channel is modulated well. Using calibrated system matrix, the reconstructed Stokes spectra are obtained and shown in Figure 9.  
Figure 6: The calibrated system matrix. (**a**) The first channel’s system matrix calibration parameters. (**b**) The second channel’s system matrix calibration parameters. (**c**) The third channel’s system matrix calibration parameters. (**d**) The fourth channel’s system matrix calibration parameters.  
Figure 7: The input Stokes spectra.  
In Figure 9, the two lines overlap in Figure 9a-c, indicating that the reconstructed \(S_{0}\), \(S_{1}\), and \(S_{2}\) are well. In Figure 9d, although the two curves do not overlap perfectly, the maximum error is less than \(5\times 10^{-13}\), and the average error is \(1.5\times 10^{-16}\), which proves the accuracy of the reproduction.  
To compare the accuracy of this method, the Stokes vector is demodulated using the traditional channel filter Fourier transform (CFFT), and the simulation conditions are the same as the first channel. [PERSON]'s [18] calibration method is utilized to demodulate the data during demodulation. The simulated modulation curve is shown in Figure 10. The demodulated Stokes vector is shown in Figure 11.  
Figure 8: The simulated modulated spectra. (**a**) R3, R4, and P1 modulation spectra; (**b–d**) the modulation spectra through R1, R2, P2, P3, and P4, respectively.  
Figure 9: Reconstructed full Stokes spectra. (**a**) The red line shows the reconstructed \(S_{0}\) and the green line shows the input simulation \(S_{0}\); (**b**) the red line shows the reconstructed \(S_{1}\) and the green line shows the input simulation \(S_{1}\); (**c**) the red line shows the reconstructed \(S_{2}\) and the green line shows the input simulation \(S_{2}\); (**d**) the red line shows the reconstructed \(S_{3}\) and the green line shows the input simulation \(S_{3}\).  
As shown in Figure 11, the middle part of the spectra obtained by the channel filter data demodulation method coincides well with the input spectrum, while the edge part has jitter. Comparing Figures 9 and 11, it can be seen that the effect of the FCPS is better. The edge data of demodulation and the simulation input data well coincide, indicating that this method has a better effect.  
The root mean square error (RMSE) of the FCPS and CFFT is calculated to prove the accuracy of the method. Due to the serious edge jitter of the CFFT, the edge part is discarded when calculating the RMSE. The RMSE is listed in Table 1, where the PMSE of the FCPS is much smaller than that of the CFFT.  
Figure 11: The reconstructed full Stokes spectra obtained using the traditional channel filter Fourier transform. (**a**) The red line shows the reconstructed \(S_{0}\) and the blue line shows the input simulation \(S_{0}\); (**b**) the red line shows the reconstructed \(S_{1}\) and the blue line shows the input simulation \(S_{1}\); (**c**) the red line shows the reconstructed \(S_{2}\) and the blue line shows the input simulation \(S_{2}\); (**d**) the red line shows the reconstructed \(S_{3}\) and the blue line shows the input simulation \(S_{3}\).  
Figure 10: The simulated modulated spectra.