## 2 Principle
### Ray Tracing and Pixel Mapping  
The difference between the computational integral imaging and the all-optical integral imaging is that the reconstructed 3D image is synthesized in the computer by using a simulated lens array (or pinhole array, camera array), rather than using a combination of a display device and a lens array. At present, there are two kinds of methods to reconstruct the 3D image in integral imaging [13]. One is to synthesize the pinhole array model by computer and reconstruct the 3D image by ray tracing. The other is to extract and model the depth of the collected 3D information.  
Ray tracing is a fundamental process to generate an elemental image array, as shown in Figure 2a. Any point on the surface of a 3D object is imaged through the lenslet array. Each elemental image represents the imaging mapping of the 3D object through the corresponding optical center. The elemental images record the information of the rays emitted from every point on the surface of a 3D object. Therefore, a ray can be determined by selecting any point in the elemental image array. We can use ray tracing to analyze the recording process of integral imaging.  
Figure 1: The overall approach of our proposed method.  
According to the dual-plane light field parameterization method [46], the imaging range of the lenslet is located behind it, and all of the optical axes of the lenslet are perpendicular to the elemental image array. The optical center of the lenslet corresponds to the elemental image array. Based on geometric optics, from Figure 2a we can derive that  
\[\left\{\begin{array}{l}\frac{u-x}{z}=\frac{s}{s}\\ \frac{v-y}{z}=\frac{t}{g}\end{array}\right. \tag{1}\]  
where \((x,y,z)\) are the coordinates of the ray, it passes through the lenslet array plane \((u,v)\), and imaging on the elemental image arrays is \((s,t)\). Then the light field distribution \((x^{\prime},y^{\prime})\) of the elemental image array can be written as:  
\[\left\{\begin{array}{l}x^{\prime}=u+s(u,x,z)\\ y^{\prime}=v+t(v,y,z)\end{array}\right. \tag{2}\]  
The light field information recorded by integral imaging is:  
\[J=F(u,v,\frac{u-x}{z}\times\text{g},\frac{v-y}{z}\times\text{g}) \tag{3}\]  
Therefore, the recorded \((x^{\prime},y^{\prime})\) is equivalent to \((u,v,s,t)\), and \((u,v,s,t)\) can be reconstructed from \((x^{\prime},y^{\prime})\).  
To reconstruct view images, pixel mapping is used to generate images from different perspectives, as shown in Figure 2b. According to the optical mapping between elemental images and view images [47], parallel rays with the same incident angle (e.g., red or green in Figure 2b) refracted by the lens array will produce corresponding view images at the imaging plane under the corresponding angle. Different angles of light will generate different view images. By using pixel mapping, the pixels with the same viewpoint can be extracted from the elemental image array to reconstruct the view image.  
Parallel light rays with the same incident angle are refracted by the lenslet array and generate view images at corresponding angles on the imaging plane. Different angles of light rays will generate view images from different perspectives. The pixel mapping between elemental image \(E\) and view image \(V\) can be expressed as:  
\[E_{i,j}(x,y)=V_{x,y}(i,j) \tag{4}\]  
where subscript \(i,j\) represent the coordinates of the elemental image, and \((x,y)\) are the pixels in each elemental image. Equation (4) shows that the resolution of the reconstructed view image is equal to the number of elemental images, which means increasing the  
Figure 2: The process of (**a**) ray tracing and (**b**) pixel mapping.  
resolution of view images requires an increase in the number of cameras. For example, a 50 \(\times\) 50 camera array can only reconstruct a 3D image with a resolution of 50 \(\times\) 50. To improve the rendering efficiency, it is necessary to avoid increasing the number of cameras. Therefore, a lite GAN is used to convert the low-resolution 3D image to super-resolution.