## 3 Simulation and Analysis for One-Shot 360-Degree Light Field Capturing  
### Analysis for the Proposed Light Field Capturing System  
Four-dimensional light field information that is expressed as a 2D array form is simulated according to the LFC condition. From the light field image, the depth extraction adopting optical flow method is introduced. Based on these studies, we propose a system for acquiring 360-degree 3D information of object using LFC at a single capture. We choose the simplest structure to achieve our purpose. The proposed system consists of one LFC and a couple of mirrors. The light field information that was obtained by the system depends on the arrangement of viewing angle, mirrors, and objects. With two mirrors and one LFC, three perspectives surround and capture the object, according to their \begin{table}
\begin{tabular}{c c c} \hline
**Optical System** & **Specifications** & **Value** \\ \hline \multirow{3}{*}{Microlens array} & Lens pitch & 38.4 μm \\  & Focal length & 77 μm \\  & Number of microlenses & 501 \(\times\) 501 \\ \hline \multirow{3}{*}{Main lens} & \(f\)-number & 2 \\  & Focal length & 50 mm \\  & Image plane distance (\(a_{1}\)) & 52.08 mm \\ \hline \multirow{3}{*}{Pickup system} & Object distance (\(b_{1}\)) & 1.25 μm \\  & Sensor pitch & 5.5 μm \\ \cline{1-1}  & Total sensor resolution & 3507 \(\times\) 3507 \\ \cline{1-1}  & Lens image resolution & 7 \(\times\) 7 \\ \hline \end{tabular}
\end{table} 
Table 1: Specification for simulation and experiments. Figure 4: Depth extraction example: (**a**) Example of light field image; (**b**) magnified light field image, (**c**) depth extraction results; and, (**d**) comparison of the ground truth and extracted depth maps obtained by InIm method and light field camera (LFC) method. locations and orientations. Since the 3 light field images need to be combined to restore 360-degree information of the object, an analysis of the location and orientation of the optical elements should be preceded. For analytical simplicity, the structure of the proposed system includes the two following assumptions. First, the two mirrors are large enough to reflect a given object. Second, three perspectives have the equal usage of viewing angle on image sensor. This is to ensure that the light field information taken at three viewpoints equally includes the angular information of the object. Figure 5a shows the overall proposed pickup system. The LFC is oriented to the front of object and two mirrors are aligned to compose two additional perspectives, as described above. Therefore, the image sensor in LFC records three perspectives simultaneously. It is supposed that three light field images laid on sensor have same area on sensor. In other words, a third of image sensor is allocated to each perspective horizontally. One of the perspectives uses the field of view (FoV) \(\theta\), when the total FoV of LFC is \(3\theta\), as shown in Figure 5b. Figure 5b only shows left part of the system for less complexity. The point \(S\) is the center of object and the point \(C\) means the center of main lens of LFC where the center of FoV exists. The point \(S^{\prime}\) is an image of the point \(S\) that is reflected by the mirror and the distance between the mirror and the point \(S\) is \(l\). The distance from the point \(S^{\prime}\) to the main lens is represented as \(s\). To make sure three perspectives have the same angle differences, two green dotted lines should form an angle of \(120^{\circ}\), as shown as \(\Omega\) in Figure 5b. The location and orientation of the mirror are determined by two factors, the length of perpendicular line from point \(S\) to point \(C\), represented as \(d\) and the angle between optical axis of LFC and mirror surface, \(\phi\). From geometric analysis, the angle \(\phi\) can be simply calculated as \(\Omega/2\)-\(\theta/2\). The length \(l\) and \(s\) are determined by following equations, Equations (2) and (3).