# Single-Lens Imaging Spectral Restoration Method Based on Gradient Prior Information Optimization
## 5 Experiment  
According to the imaging principle of a single-lens system, the object distance is generally required to be greater than twice the focal length of the system. This way, the obtained image is a reduced real image. In order to reduce the length of the imaging system, \begin{table}
\begin{tabular}{c c c c} \hline
**Method** & **Feature Points** & **SCC** & **SMSE** \\ \hline MTV & A & 0.7655 & 0.0169 \\ B & 0.2804 & 0.0931 \\ \hline Ours & A & 0.9748 & 0.0092 \\ B & 0.8248 & 0.0350 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of spectral quality. Figure 6: Restored spectral data. in this study, we chose the following lens parameters: diameter of 30 mm, focal length of 60 mm @ 587.6 nm, and N-BK7 material. The detector parameters were 1024 \(\times\) 1024 pixels with a sensor size of 12.7 mm \(\times\) 12.7 mm. The PSF measurement system was set up as shown in Figure 7. In the experiment, a monochromator was used to illuminate a pinhole, and a CCD was used to capture an image of the pinhole. By moving the CCD, the pinhole's clearest image was obtained, which represents the in-focus PSF for that spectral band. Then, by adjusting the wavelength, PSFs at different degrees of defocus for other spectral bands relative to this band were obtained. Through this method, in-focus and defocused PSFs for different spectral bands were obtained. As shown in Figure 8a, the setup for the PSF measurement experiment consisted of a pinhole with a diameter of 0.1 mm. The CCD exposure time for all measurements was set to 16.69 ms, as shown in Figure 8b. In this study, PSFs for the spectral range of 0.520 \(\upmu\)m to 0.590 \(\upmu\)m were measured with a sampling interval of 0.010 \(\upmu\)m, as shown in Figure 9. The experimental setup is shown in Figure 10. A monochromator was used as a single-wavelength light source, and an LED (light-emitting diode) was used as a polychromatic light source. The object distance was set to 42.5 cm. When using the polychromatic light source, the center brightness of the LED was considered to be too high, resulting in an overexposed center region and relatively dark image edges. To address this, a mirror was used to reflect the light, making the entire light source more uniform. The object captured in the images is the uppercase letter \"E\". Figure 11 shows the experimental restoration results for the spectral range from 0.520 \(\upmu\)m to 0.590 \(\upmu\)m, where (a) to (h) represent the experimental results for different wavelengths. From left to right are the acquired original image, the captured image, the MTV-restored image, and the image restored using the algorithm proposed in this study. Figure 8: Experimental setup for PSF measurement. (**a**) Experimental setup; (**b**)schematic of the pinhole. Figure 7: PSF measurement system. Figure 11: _Cont._  
Figure 10: Experimental setup of the imaging system. Figure 9: PSFs at different positions. Figure 6:0 _Cont._  
From a comparison of the restoration results, it can be observed that the spectral restoration quality of the algorithm proposed in this study is superior to that of the MTV algorithm. For point A, the restored spectrum using the algorithm in this study and the MTV-restored spectrum both exhibit the same trend as the original spectrum, but the similarity of the algorithm in this study is higher. For point B, the MTV algorithm's restored spectrum is completely distorted, while the restored spectrum using the algorithm proposed in this study shows a high similarity to the original spectrum. An evaluation of the quality of the restored spectral data is shown in Figure 6:1 \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Feature Points** & **SCC** & **SMSE** \\ \hline \multirow{2}{*}{MTV} & A & 0.6432 & 0.0059 \\  & B & 0.0580 & 0.0060 \\ \hline \multirow{2}{*}{Ours} & A & 0.7142 & 0.0032 \\  & B & 0.9851 & 0.0042 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of quality evaluation of experimental restored spectra. Figure 13: Experimental spectral restoration results.