## 3 Scene Resizing Process (X-Y Axis)  
The conventional InIm display remains the original size of the 3D scene. As the dimension of the display device is fixed, it may be difficult to display a large 3D scene which is over the display capacity. In this section, we propose a scene resizing method to adjust the field-of-view. This method is implemented computationally in the simulated display stage by proportionally resetting (i) the pitch (\(p\)) of the pinhole array, and (ii) the gap between the captured elemental images and the pinhole. The resized field-of-view will match to the specific size of the display device. Figure 3 shows the principle of the scene resizing method in the computationally simulated display process, where a reference plane is set at \(z_{RP}\) from the lenslet array for simulated display. Figure 3a shows the simulated display with the original pickup parameters. The pixel size on the reference plane is denoted by \(s_{1}\). By computationally rescaling the pixel size on the reference plane with a factor of variable \(M_{s}\), the 3D scene size can be adjusted. The position of the rescaled reference plane still locates at \(z_{RP}\), and the rescaled pixel size on the reference plane denoted as \(s_{2}\) is shown in Figure 3b; the expressions for \(s_{1}\) and \(s_{2}\) are as follows:  
\[ \begin{cases}s_{1}=\frac{S_{CCD}}{L_{L}\_resol}\times\frac{z_{RP}}{S_{1}}\\ s_{2}=\frac{S_{CCD}}{L_{L}\_resol}\times\frac{z_{RP}}{S_{2}}\end{cases}  \tag{5}\]  
where \(S_{CCD}\) is the sensor size, \(EL\_resol\) is the resolution of each captured elemental image, \(g_{1}\) is the gap between the sensor and the lenslet array for simulated display with the original pickup parameters. \(g_{2}\) is the gap between the sensor and the pinhole array for simulated display with the scene resizing method. We focus on the same pixels (the green and red pixels shown in Figure 3) in the original reference plane and the new reference plane. Both the green pixel and the red pixel are on the principal optical axis of the corresponding two neighboring lenslets (pinholes). The two principal optical axes are shown in red and green dashed lines, respectively, in Figure 3. The lateral distance between the two pixels is equal to the pitch of the lenslet array (\(p_{1}\)). In order to resize the scene, we update the pitch of the virtual pinhole in the simulated display stage. To avoid nonlinear distortions in this process, the two specific pixels mentioned above should be located on the principal optical axes of the corresponding pinholes. The  
Figure 3: Scene resizing process on the x-y axis. (**a**) With original pickup parameters. (**b**) By field-of-view resizing method in simulated display. new distance between these resized pixels is equal to the pitch of the pinhole array (\(p_{2}\)). The pitch of the two pixels can be calculated as follows:  
\[ \begin{cases}p_{1}=n\times s_{1}\\ p_{2}=n\times s_{2}\end{cases}  \tag{6}\]  
where \(n\) is the pixel number between the two pixels. Using similar triangle geometry, the resized pixel size on the new reference plane can be expressed as follows:  
\[s_{2}=s_{1}\times M_{s}=\frac{S_{CCD}}{EI\_resol}\times\frac{z_{RP}}{g_{1}} \times M_{s} \tag{7}\]  
By combining Equations (5)-(7), the relationship between the gaps in the real pickup stage (\(g_{1}\)) and the field-of-view resizing simulated display stage (\(g_{2}\)) can be calculated. In addition, we are able to obtain the relationship between the original pitch of lenslet array (\(p_{1}\)) in the real pickup process and the pitch of the pinhole array (\(p_{2}\)) in the scene resizing method by the following expression:  
\[ \begin{cases}g_{2}=g_{1}/M_{s}\\ p_{2}=p_{1}\times M_{s}\end{cases}  \tag{8}\]  
Based on Equation (8), by properly setting the gap (g) between the captured elemental images and the pinhole array, and the pitch (\(p\)) of the pinhole array in the simulated display stage, the field-of-view resizing process can be realized.