## 2 Resolution-Improved Near-Virtual-Image-Mode Light-Field Display  
Here, we explain the proposed technique to adopt the resolution-priority technique for enhancing the resolution of 3D images generated by the light-field display using the near-virtual-image mode. The resolution-priority technique increases the resolution of the 3D images by reducing the magnification of the elementary images from infinity to several dozen, enabling more than one pixel to be observed through each lens [18; 19]. The low magnification of the virtual pixel images in the near-virtual-image-mode light-field display enables each aperture to transmit plural virtual pixel images. In this case, because the aperture width is smaller than the lens pitch, black regions are generated between the plural virtual pixel images corresponding to each lens. Thus, the lenses are also used to image the apertures to virtually increase the aperture width. It is known that the resolution-priority technique decreases the depth resolution of 3D images due to ray divergence. As a result, we analyzed the ray divergence of the resolution-improved near-virtual-image-mode display. Figure 1 shows the schematic of the resolution-improved light-field display with the near-virtual-image mode. The light-field display consists of a flat-panel display, a lens array, and an aperture array. The gap between the lens array and pixels of the flat-panel display, denoted by \(g_{p}\), is made smaller than the focal length of the lens array, denoted by \(f\), to enlarge the viewing zone--although the gap is nearly equal to the focal length of the conventional lens-array-type light-field displays. In this case, the pixels are imaged as virtual images behind the flat-panel display. The aperture array is used to allow several virtual pixel images to be seen through each lens in the lens array as well as reduce the crosstalk. Because the width of the virtual pixel images exceeds that of the physical pixels, the width of the aperture is made larger than that of conventional aperture-array-type light-field displays, which allows only one physical pixel to be observed through each aperture of the aperture array. Thus, the light efficiency of the near-virtual-image mode is higher than that of the conventional aperture-array-type light-field display. The utilization of an aperture array reduces the aberrations of the lens array, enabling an efficient increase in the viewing zone. The proposed technique improves the resolution by reducing the magnification of the virtual pixel images, thereby increasing the number of observable virtual pixel images through each lens described in Figure 1a. From the Gauss lens law, the distance between the lens array and the virtual image plane of the pixels becomes \(g^{\prime}{}_{p}=fg_{p}/(f-g_{p})\). The magnification of the pixels is given by  
\[M_{p}=g^{\prime}{}_{p}/g_{p}=f/\big{(}f-g_{p}\big{)}. \tag{1}\]  
Assuming \(p\) and \(q\) denote the lens pitch of the lens array and pixel pitch, respectively, the number of virtual pixel images observed through each lens is given by \(n\times n\), where \(n=p/(M_{p}q)\). In the original near-virtual-image-mode light-field display, only one virtual pixel image was observed through a single lens. The 3D resolution of the proposed technique is increased by \(n\times n\) times compared with that of the original near-virtual-image-mode light-field display. The plural virtual pixel images observed through one lens and those observed through an adjacent lens should be connected smoothly. However, the aperture width cannot be made equal to the lens pitch because the apertures suppress the aberrations of the lens array. In this study, we eliminated the gaps between the virtual pixel images by imaging the apertures virtually, increasing the aperture width. Figure 1b depicts the generation of the virtual image of the aperture.