## Appendix A  
Figure 11 introduces the derivation of Equation (1). First, Figure 12a conceptually shows the process of extracting the sub-image used for optical flow calculation from the photographed light field image. The proposed method is most commonly used in a variety of applications using lenslet arrays, for example integral photography, integral image, and light field miroscopy. As can be seen from the light field image, there are five microlenses, and seven pixels per lens are assigned on the image sensor. It is assumed that the same shaded pixels have the same brightness, and two pixels of the checkered are corresponding points to each other. Sub-image creation is the process of rearranging the pixels of the lens images that are in the same position relative to the index of the lens to which they belong. Looking at the first sub-image on the far left, we can see that the leftmost pixels of each lens image are gathered together to form the first sub-image. The checkered pixels are each placed at the second pixel of the second sub-image and at the fourth pixel of the central sub-image (fourth). After the sub-images have been extracted, Figure 12b shows the process of finding the corresponding points between the two sub-images and obtaining the distance between them by using the optical flow algorithm. In general, the output of optical flow does not have its own unit, and it is necessary to fit the output value according to the situation to suit the actual situation. In this study, the optical flow values obtained from two sub-images have the pixel width in units, but there still exists area for further development. First, depending on the indices of the sub-images used, which mean their relative positions, the distances of corresponding points become different. Second, the optical flow algorithm can extract the positions of two points with sub-pixel accuracy, although the optical flow value is described as having only integers. For these two reasons, we need to analyze how the output optical flow value has a certain distance in a given situation.  
The final step to derive Equation (1) is shown in Figure 11c, which is a more simplified illustration of Figure 2 in the text. Given the details of the light field camera and the information about the focal plane, we can see the size of the magnified sensor and microlens. The distance between two optical elements can also be obtained, denoted by \(b_{2}-b_{1}\). A variable \(v\) should be considered to get the size of \(D_{OF}\). The variable \(v\) is the distance between the microlenses where the two corresponding points have belonged. From the fact that the position of each pixel in the sub-image is equal to the index of the lens image where it is included before, we can infer that \(v\) is related to the value of optical flow. For example, if the optical flow value is 2, the two pixels come from a lens image with an index difference of 2. Therefore, \(v\) is a value directly related to the optical flow, specifically, \(v=L\cdot OF\), where \(OF\) means the value of optical flow and \(L\) is the pitch of the microlens considering the magnification. On the other hand, \(u\) represents the distance between two pixels on the floated image sensor. The distance between two pixels must be considered--both the distance between the lens images and the positions at which the corresponding pixels lay in the lens images. If the number of pixels allocated to one microlens is \(n\) and the size of the magnified pixel is \(P\), then the distance caused by the optical flow difference is \(P\cdot n\cdot OF\) and the term (\(i_{c}-i\)) related to the index difference of the sub-image is added, where \(i\) represents the index of the sub-image and \(c\) represents center. As a result, by simple geometry, \(D_{OF}\) can be expressed as  
\[D_{OF}=\frac{(b_{2}-b_{1})\cdot(O\cdot L)}{O\cdot P\cdot n+(i_{c}-i)\cdot P-O \cdot L}, \tag{1}\]  
which can be derived to Equation (1) by averaging on horizontal and vertical directions according to indices.