## 2 Methodology
### Generation of the Virtual Degraded Image
#### 2.1.2 Generation of the Point Spread Function  
In this section, we outline our methodology for generating the PSF of the UDC panel, combining both optical experiments and numerical simulations. Our goal is to validate the consistency between these two approaches, thereby offering a comprehensive understanding of the optical behavior of UDC panels and ensuring the accuracy of the simulation model for replicating degradation phenomena. To begin, we designed a simplified UDC panel structure based on a commercial smartphone panel, focusing on the essential pattern structures that affect light behavior, such as transparent and opaque regions (see Figure 3a). For the optical experiment, we fabricated a simplified UDC panel pattern by laser etching on chrome-coated glass (see Figure 3b). This setup allowed us to conduct experiments to observe how light behaves as it passes through the panel. Concurrently, we digitally recreated the UDC panel structure at a resolution of 1024 (H) \(\times\) 1024 (V) pixels with a pixel size of 2.544 \(\upmu\)m for use in numerical simulations. Here, we utilized the ASM to simulate the PSF of the UDC panel, as explained previously. The experimental and simulation conditions are illustrated in Figure 4. To capture the PSF, we placed the image plane at the focal point of the lens, positioning the pinhole (point source) 300 mm away. The image distance was calculated using the lens formula:  
\[\frac{1}{f}=\frac{1}{D_{o}}+\frac{1}{D_{i}}, \tag{4}\]  
where \(D_{o}\) is the object distance and \(D_{i}\) is the image distance. Consequently, the image sensor was placed 3.439 mm behind a lens with a focal length of 3.4 mm. In this setup, the  
Figure 3: Mimicking the UDC panel structure for the experiment: (**a**) observed image from a commercial smartphone and (**b**) fabricated UDC panel pattern. point source \(u(x,\ y,\ 0)\) first propagates 300 mm using the ASM before interacting with the UDC panel, which is represented by the transfer function \(UDC(x,\ y)\). The field then passes through the lens, described by its pupil function \(P(x,\ y)\) and a quadratic phase factor, and propagates an additional 3.4 mm to the CCD plane using the ASM. This sequence of transformations effectively models the optical behavior of the UDC system and enables precise observation of the PSF formation. Both the numerical simulation and the optical experiment confirmed the PSF formation by the UDC panel within the designated optical imaging system, as shown in Figure 4.  
For the experiment, we measured PSF fields at wavelengths of 634 nm, 551 nm, and 445 nm and then simulated the corresponding PSF fields under identical conditions. By comparing the simulated and experimental PSF fields, we assessed their alignment. After validating the consistency between the results of the numerical simulation and the optical experiment for each monochromatic PSF field, we extended this method to simulate PSFs for all wavelengths. Building on this, we describe the generation of a three-channel (3 ch) PSF for the UDC. The 3 ch PSF, denoted as \(k\), is calculated as follows:  
\[k(x,y)=\sum_{\lambda}\gamma_{c}(\lambda)\cdot k_{\lambda}(x,y),\ \ \ c=\{R,G,B\}. \tag{5}\]  
Here, \(\gamma_{c}\) represents the camera spectral sensitivity for each color channel R, G, and B, and \(k_{\lambda}\) is the PSF field for each wavelength [30; 31; 32; 33]. The calibrated camera spectral sensitivity \(\gamma_{c}\) and the simulated 3 ch PSF \(k\) are shown in Figures 5a and 5b, respectively. Figure 4: Setup for the simulation and optical experiment to observe PSF fields generated by the UDC panel. Deep Neural Network Approach Based on Hybrid Frequency-Spatial Domain Learning for Image Restoration  
In this study, we adopted a conditional generative adversarial network (cGAN) for image restoration, as cGANs have demonstrated remarkable effectiveness in generating realistic and high-quality images [34; 35; 36; 37; 38; 39]. A cGAN model comprises two main components: a generator and a discriminator network.