## 3 Simulation and Analysis for One-Shot 360-Degree Light Field Capturing
### Four-dimensional Light Field Simulation Using Sub-Image Synthesis  
To carry out an optical simulation for an LFC, it is necessary to define the optical elements that characterize the LFC. The 4D light field information to be captured is distributed differently, according to the focal length of the main lens, the focal length and apertures of the MLA, the pixel size of the image sensor, and the overall resolution on light field plane. When the LFC is focused at a certain depth to capture an object, the distance between the MLA and the main lens changes. According to this distance, different magnified image sensor and MLA in space capture objects. The MLA, main lens, image sensor, and the depth of focal plane determine the specifications of the magnified pickup unit. One of methods to make the 2D form of light field is to simulate a sub-image that can be extracted from the target light field. A sub-image can be created by collecting pixels in the same position in each lens image. Before taking a sub-image, the orientations of pixels in rendering software should be determined, according to the specifications of LFC [17]. From the given details of LFC, virtual cameras for sub-images are made in space as the form of Figure 1. The resolution of the camera is same as the number of microlens and the distance between pixels is lens pitch of magnified MLA. From the simulated sub-images, one can restore the light field by relocating pixels of sub-images. The center image of Figure 7a shows one of the light field images by an LFC. A total 49 sub-images, which comprise 7 \(\times\) 7 images in horizontal and vertical direction, are merged to make light field. Resolution of each sub-image is 500 \(\times\) 500. The specifications of the camera used for the simulation are given in Table 1.  
To verify the optical system configuration based on the above analysis, the optical simulations are performed with virtual mirrors, LFCs, and objects. Persistence of Vision Ray Tracer (POV-Ray) software is used to place the 3D information of the object and to make the light field, and the depth extraction method was performed using Matlab software. By using the LFC simulation, light field in the proposed optical capturing system is generated. Figure 6a shows the resultant light field. The specification of MLA and the main lens are also presented in Table 1. The overall condition of pickup system is also the same as the table. However, the focal plane of the main lens is slightly moved back to the camera to represent light field effectively. As shown in the Figure 6a, two additional viewpoint images are taken using a flat mirror. Because the mirror does not have any magnification, the reflected image has a smaller resolution than the front image. As mentioned above, concave mirrors can be an alternative to improve resolution of reflected light field images. With the optical flow algorithm for LFC, the depth information of the simulated light field is also extracted, as shown in Figure 7b. Note that the depth information is normalized to 8-bit information within proper depth range, according to the size of the object. To record the texture information of the light field, digital refocusing technique for LFC is used [10]. As shown in Figure 7c,d, color information of each perspective is demonstrated. Since the resolution of reflected light field has lower resolution than that of center perspective, Figure 6c looks blurry when compared to the Figure 7d. The three pairs of resultant depth map and color information can be projected in virtual space as a form of point cloud having 3D position and color information. To combine the three light field images, the mirrored perspectives should be resized after digital refocusing. The magnification ratio between center and the others are determined by \(s:d\), as shown in the Figure 5b. According to the ratio, the right/left sub-images are resized to have same scale in the results. By binding all point cloud data, the 3D object can be finally reconstructed.