## 3 Simulation and Analysis for One-Shot 360-Degree Light Field Capturing
### Analysis for the Proposed Light Field Capturing System
\[l=\frac{\sin\theta}{2\cos\left(\frac{\Omega+\phi}{2}\right)}d, \tag{2}\]  
\[s=2l\sin\varphi+d. \tag{3}\]  
To simultaneously capture images in \(S\) and \(S^{\prime}\), it is necessary to analyze where the focal plane of the light field camera is located. When a regular camera focuses on a specific position, the depth of field is determined based on the specification of the camera, and the information of the object can be acquired without blur in that range. On the other hand, in the case of the light field camera, the size of blur according to the distance behaves in the opposite manner to blurring mechanism of the regular camera. The blur made by light field camera appears to be small in most areas, except the near the focal plane, and the size of blur is bounded to that of the microlens in the focal plane. Analysis of blur for light field camera has been done in several researches [10; 11; 13]. Based on this previous research, the  
Figure 5: (**a**) Proposed light field pickup system and (**b**) geometrical figure for analysis on the proposed system. blur radius of microlens is calculated according to the distance to various focal planes, which is shown in Figure 6a. The focal lengths of the main lens and the MLA are 50 mm and 0.12 mm, respectively. When the focal plane moves away from the camera, the image of the microlens becomes thick in space, and therefore, the light field information of the object that is placed near the focal plane may not be captured properly. This suggests that the method of finding the optimal focal point depends on the position of the object. According to Equations (2) and (3), the position of the mirror image can be shown in Figure 6b,c depending on the position of the object. When the object is relatively close to camera, for example, 200 mm in Figure 6b, the space that is suffered by blur is small enough to be between points \(S\) and \(S^{\prime}\). In this case, the depth of the object can be obtained properly, except when the peak of the blur covers one of the two images. However, the farther away from the peak of the blur, the greater the number of repetitions of a point on the light field image, which leads to the possibility that both of the perspectives will invade their respective regions. Therefore, in the case of Figure 6b, it is desirable that the peak be located between two objects. When the object distance is relatively large, as is the case of Figure 6c, it is impossible to place a focal plane between two objects because the width of the peak is too thick. In this case, the peak should be placed on either side of the two objects. However, as the distance from the camera increases, the number of pixels that are used for recording per unit distance decreases, which is shown as pixel per millimeter (ppm) in Figure 6b. Therefore, to record two objects in similar quality, it is desirable that the near object undergoes a larger blur. Consequently, in the case of Figure 6c, the focal point of the camera should be in front of the object. Meanwhile, the comparison between black solid lines in Figure 6b,c shows the tradeoff between the size of the photographic object and the amount of information per unit length of the recorded light field. Therefore, it should be placed at a distance from the camera that achieves the highest resolution, depending on the size of the given object. Meanwhile, mirrors having a specific curvature can be used in the proposed capturing system. Since the mirrors in our system does not magnify images, the reflected images are located beyond mirror and occupy smaller portion of the image sensor, as compared to the center perspective light field image. To enhance light field resolution on the sensor, a pair of optical elements that magnify an object can be used, such as concave mirrors. When one uses concave mirrors to the proposed system, the location and orientation of the mirrors are determined by the distance between main lens and the object, like plane mirrors.