Open Access
Add to BibSonomy
Abstract
This study proposes a digital implementation of the conventional Mirage, which uses two parabolic mirrors to produce 360-degree three-dimensional (3D) images of real objects placed inside of it. The two mirrors are replaced with multiple light field displays to generate rays emitted from 3D objects in 360 degrees. We propose two techniques for eliminating repeated 3D images produced by the multiple displays, that is, non-tracking and tracking techniques. The former supports multiple viewers, although the 3D image size is limited. The latter can produce large 3D images, although the number of viewers is limited. The display system of the lower half of the light field Mirage was constructed by using four light field displays to verify the proposed techniques.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Three-dimensional (3D) display systems with 360-degree visibility have been expected for the medical and entertainment fields. Such displays are also expected to revolutionize telecommunications via the Internet.
The early 360-degree 3D displays utilized 3D glasses to provide 3D images. One system was proposed that combined a flat-panel 3D display and a hole located above it, and it was called “illusion hole” [1].
Glasses-free 360-degree 3D displays have been developed with time-multiplexing techniques because a large number of rays should be generated in 360-degree directions. A cylindrical display system was developed that contained multiple rotating LED arrays, and it was called “Seelinder” [2,3]. Display systems consisting of a high-speed spatial light modulator (SLM), concave mirror, and scanning mirror were also developed [4,5]. One system, called “Vermeer,” was also developed. It consisted of a high-speed SLM, two parabolic mirrors, and a spinning diffuser [6]. A super multi-view display system was developed that consisted of multiple high-speed SLMs and a rotating screen [7,8]. The above systems utilized mechanical systems to direct rays in 360-degree directions.
Another approach to constructing glasses-free 360-degree 3D displays is to use a large number of video projectors. A display system was developed that contained more than 100 small projectors and a refractive screen, and it was called “fVisiOn” [9–12]. A system that combined a projector array with a reflective screen was also developed [13–15]. These systems require complicated optical systems and special screens.
Because high-resolution flat-panel displays with 4K and 8K resolutions have been developed recently, a single light field display consisting of such a high-resolution display and a lens array have been developed to construct 360-degree 3D displays. Specially designed lenses, such as triplet lenses, have been used for the elemental lenses constituting the lens array to direct rays in 360-degree directions with a small lens aberration [16,17]. The technique of using a catadioptric projection system consisting of one convex mirror and one field lens was also proposed to direct rays in 360-degree directions [18].
In this study, we propose the use of multiple light field displays to construct a glasses-free 360-degree 3D display. The multiple displays are aligned on a circle and are properly inclined to direct rays in 360-degree directions to enable the use of ordinary lens arrays. Preliminary experimental results obtained with the proposed display system were reported in a conference paper [19]. This article proposes two techniques for eliminating the repeated 3D images generated by the multiple displays and also an experimental verification of the two techniques done using four light field displays. Table 1 shows comparisons among the projector array system, the high-resolution flat-panel display system, and the multiple inclined flat-panel display system proposed in this study.
Table 1. Comparisons of techniques for 360-degree 3D display.
2. Theory
2.1 Light field Mirage
Figure 1 shows the original Mirage, which consists of a pair of parabolic mirrors. Rays from a real object placed on the bottom parabolic mirror are reflected twice by the two parabolic mirrors to produce a real image of the object at a hole drilled at the center of the upper parabolic mirror. The real image can be observed from 360 degrees by multiple viewers.
Figure 2 shows the light field Mirage proposed in this study. The two parabolic mirrors of the original Mirage are replaced with multiple flat-panel light-field displays, each consisting of a lens array and a flat-panel display. Rays from the lower displays are transmitted through a half mirror, and rays from the upper displays are reflected by the half mirror to redirect the rays to the top hole. The optical path lengths from the top hole to the upper displays are equal to those to the lower displays. All of the light field displays generate 3D images at the top hole by using the resolution-priority integral imaging technique [19,20]. As shown in Fig. 3, the upper and lower displays are alternatively arranged so that the non-image areas between the upper displays are covered by the image areas of the lower displays, and vice versa. Therefore, the 3D images can be observed from 360 degrees.
Fig. 2. Schematic of proposed light field Mirage consisting of multiple upper and lower light field displays and half mirror.
There are overlapping regions between the upper and lower light field displays. The overlapping regions of the adjacent light field displays are not on the same plane. An alpha blending technique should be developed to solve this issue. For the generation of 360-degree 3D images using all light field displays, calibration techniques should be developed to adjust the 3D images generated by all light field displays. Because a technique for handling overlapping regions would be closely related to a calibration technique, the alpha blending technique should be developed with a calibration technique.
The proposed light field Mirage utilizes the resolution-priority integral imaging technique [20,21] because 3D images are generated apart from the screens of the light field displays. In the resolution-priority technique, the lenses of the lens array produce real images of the elemental images displayed on the flat-panel display, and the plane where the real images are produced is called the “central depth plane” (CDP). The CDPs of all of the light field displays are located at the top hole of the light field Mirage. The resolution-priority integral imaging technique can provide higher resolution 3D images than the conventional depth-priority integral imaging technique [22] with which elemental images are imaged at infinity. However, the depth range where 3D images can be observed with small blurring is narrower for the resolution-priority technique than the depth-priority technique.
Flat-panel light-field displays generate repeated 3D images in addition to the desired 3D image because rays emitted from each pixel of the flat-panel display enter into not only the corresponding lens but also the adjacent lenses of the lens array. The generation of the repeated 3D images is a serious problem with the light field Mirage because the light field Mirage consists of multiple light field displays so the desired and repeated 3D images overlap. The repeated images degrade the image quality and the realism of the 360-degree 3D images. This study proposes two techniques for preventing viewers from seeing these repeated 3D images; one utilizes the viewer tracking technique, and the other does not. The two techniques are explained in the following subsections. A technique for combining the Mirage optics and holograms was proposed, that does not generate repeated 3D images [23]. However, an experimental verification of this technique has not been reported.
2.2 Non-tracking technique
With the configuration of flat-panel light-field displays, each lens of the lens array images the corresponding elemental image to produce 3D images. Rays from the elemental images transmitted through the corresponding lenses should be separated from those transmitted through the non-corresponding lenses to prevent repeated 3D images from being seen. The non-tracking technique explained here separates these rays by using the top hole of the light field Mirage.
For each light field display, the images of all elemental images are superimposed one another at the top hole by making the pitch of the elemental images slightly larger than the lens pitch of the lens array as shown in Fig. 4. The 3D images produced by all of the light field displays are also superimposed one another at the top hole by appropriately inclining the light field displays. The size of the hole is made equal to the size of the superimposed images of the elemental images. Consequently, the images of the elemental images generated by the corresponding lenses can pass through the hole, while those generated by the non-corresponding lenses cannot. Thus, the rays producing the repeated 3D images are eliminated by the hole. Different from the tracking technique explained in the next subsection, this technique does not require information on viewer positions.
When the focal length of the lens array is denoted by f, the distance between the lens array and the CDP is denoted by li, and that between the lens array and the pixels of the flat-panel display is denoted by lo, the lens equation provides:
The pitch of the lenses of the lens array is denoted by pl, that of the elemental images is denoted by pe, and the width of the images of the elemental images on the CDP is denoted by wi. The triangle similarity gives two equations:
From the above equations, when the lens array parameters (the lens pitch and focal length) and the distance between the lens array and the top hole are given, the system design parameters (lo, pe, and wi) are calculated using:
Each light field display should be inclined so that the normal line from the center of the screen passes through the center of the top hole, as shown in Fig. 5. When the distance from the central axis of the display system to the center of the screen is denoted by r, the inclination angle is given by α = sin-1 (r/li).
The number of light field displays required to construct the light field Mirage is now considered. As shown in Fig. 6, because the angular width of rays converging to one point on the top hole from one light field display is given by φ = 2 tan-1(wd / 2r) = 2 tan-1(wd / 2li sin α), the required number of displays, denoted by N, is given by the following equation.
From Fig. 6, the horizontal viewing zone angle for one light field display, denoted by ϕx, is equal to φ, i.e., ϕx = 2 tan-1(wd / 2li sin α). In the same way, the vertical viewing zone angle for one light field display, denoted by ϕy, depends on the height of the lens array denoted by hd, i.e., ϕy = 2 tan-1(hd / 2li). The vertical viewing zone angle of the non-tracking-type light field Mirage is also given by ϕy.
The viewing parameters of the light field Mirage depend on the parameters of the flat-panel displays. The resolution and pixel pitch of the flat-panel displays are represented by X×Y and pp, respectively. The circumferential length of the circularly aligned flat-panel displays is approximated by N X pp, and its radius is given by r = N X pp / 2π. The length between the flat-panel displays and the CDP is li = r/sin α = N X pp / 2π sin α. When the size of the 3D images, denoted by W3D, is considered to be equal to the diameter of the top hole, W3D = pl li / f, when assuming pe ≃ pl and lo ≃ f. Thus, the 3D image size is given by:
The resolution of the 3D images along the diameter of the top hole, denoted by X3D, is equal to the resolution of the elementary images.
The above analysis shows that the 3D resolution X3D can be increased by reducing the pixel pitch pp of the flat-panel displays. The 3D image size W3D can be increased by increasing the horizontal resolution X and the number of flat-panel displays N. These relations are illustrated in Fig. 7.
Fig. 7. Relations between display parameters of light field Mirage and those of flat-panel displays for non-tracking technique: (a) dependence of X3D on pp and (b) dependence of W3D on NX.
2.3 Tracking technique
The tracking technique separates the rays producing the desired 3D image from those producing the repeated 3D images on the viewing plane. In the region where only rays producing the desired 3D image exist, viewers can observe only the desired 3D image as shown in Fig. 8. This correct viewing region can be moved by shifting the positions of the elemental images on the flat-panel displays. Therefore, when the positions of viewers are detected using viewer tracking systems, such as face tracking and eye tracking systems, the correct viewing region is adjusted to the detected viewing position to prevent repeated 3D images from being seen.
To separate rays producing the desired 3D image from those producing the repeated 3D images on the viewing plane, the pitch of the elemental images is properly determined so that rays from all elemental images refracted by the corresponding lenses pass through the correct viewing region.
When the distance between the top hole and the viewing plane is denoted by lv, and the width of the correct viewing region is denoted by wv, the triangle similarity gives:
From Eqs. (1), (10), and (11), the system design parameters (pe and wv) are given by:
When the direction from the viewing position to the screen center of each light field display detected by the viewer tracking system is given by (θx, θy), the elemental images should be shifted by (lo tan θx, lo tan θy) on each light field display, as shown in Fig. 9. If the tracking system also provides the distance to the viewing position lv, the pitch of the elemental images pe should also be changed according to Eq. (12).
The number of light field displays required for the tracking technique is now considered. Because all lenses that are observed by a viewer emit rays proceeding to the viewing position, the screens of all of the light field displays should be connected without a gap in a circle. Because the light field displays are aligned along a circle with a radius of r = li sin α and the horizontal angle corresponding to the width of one light field display is φ = 2 tan-1(wd / 2r), the required number of displays is given by N = 2π / φ = π / tan-1(wd / 2r), which is equal to Eq. (7), as shown in Fig. 10.
The number of allowable viewers depends on the number of the ray directions, the width of the correct viewing region, and the number of the light field displays. Roughly estimated, six displays might support three viewers, and eight displays might support four.
Because the correct viewing zone is the image of the elementary images with the tracking technique, the width and height of the correct viewing zone are equal to wv. Therefore, from Fig. 8, the viewing zone angle both in the horizontal and vertical directions measured from the center of the top hole is given by ϕ = 2 tan-1([wv / 2(lv – li)]. The vertical viewing zone angle of the tracking-type light field Mirage is also given by ϕ.
For the tracking technique, the 3D image size depends on the height of the flat-panel displays. Considering the inclination of the displays, the 3D image size is given by:
For the resolution-priority technique, the pixel pitch of the 3D images is given by pp li / lo ≃ pp li / f. The 3D resolution is given by:
Fig. 11. Relations between display parameters of light field Mirage and those of flat-panel displays for tracking technique: (a) dependence of X3D on pp and (b) dependence of W3D and X3D on Y.
3. Experiments
3.1 Experimental system
The proposed two techniques were experimentally verified. Because the difference between the two system configurations for the tracking and non-tracking techniques is the diameter of the top hole, a general experimental system that consisted of multiple light field displays was constructed for both techniques. In this study, only the lower half of the light field Mirage was constructed because the elimination of repeated 3D images can be demonstrated with the system of this half.
The lower half of the system was composed of four light field displays. For the flat-panel displays, liquid-crystal displays (Sharp, LS060R1SX01) with a resolution of 2,560 × 1,440 and a screen size of 6.0 in. were used. For the lens arrays, hexagonal lens arrays with a focal length of 10.0 mm and a lens pitch of 1.98 mm were used. The effective size of the arrays was 100.0 × 74.0 mm2, and there were 58 × 37 lenses that were arranged. Because the array size was smaller than the LCD screen size, the array width caused the screen width of the light field displays wd to be 100 mm. As shown in Fig. 3, the lower left and right corners of the displays were attached to the lower corners of the adjacent displays. The four displays were inclined with an angle of α = 45.0°. The distance from the centers of the screens of the displays to the center of the top hole was li = 119 mm. The distance between the lens array and the LCD screen was lo = 10.7 mm. Acrylic plates were sandwiched between the lens arrays and the LCD panels to maintain this distance. Real images of the elemental images were produced on the CDP with a magnification of 11.2 so that the pixel pitch of the magnified real images was 0.581 mm. The constructed general experimental system is shown in Fig. 12.
The required number of light field displays is N = 5.9 from Eq. (7). Because four displays were used to construct the lower half of the experimental system, which corresponds to eight displays for the full light field Mirage, the experimental system satisfied this requirement.
The generation of elementary images is explained. The elementary images were generated from the observer’s point of view, not the light field display side. First, parallax images seen from multiple camera positions were rendered using computer graphics software. The parallax images are perspective images seen from the cameras. Then, elemental images were synthesized from the parallax images; the ray that emerges from each pixel of the elementary images and passes through the center of the corresponding lens was considered, and cameras were selected in consideration of the distances from the ray. The pixel value is determined by interpolating the corresponding pixel values of the parallax images rendered for the selected cameras. The parallax image rendering was performed by using Blender (blender.org). A pinhole camera model was used. The elementary image synthesis was performed by using a program developed using C++ language (gcc). In this study, the parallax image generation and the elemental image synthesis were performed for each light field display, separately. The arrangements of the cameras are explained in the following subsections, because they are different between the non-tracking and tracking systems.
3.2 Non-tracking technique
The diameter of the top hole used for the non-tracking technique was 24.2 mm from Eq. (6). Figure 13 shows a photograph of the non-tracking-type system. The resolution of the 3D images at the top hole was 41.7 pixels along the diameter of the hole.
Figure 14 shows a 3D image generated when the top hole was removed. The displayed 360-degree 3D image was two interlocked rings. It was captured from directions normal to the screens of the four light field displays; 0°, 90°, 180°, and 270°. 3D images captured from directions obtained by adding ±20° to the four directions are also shown. The desired 3D image was observed with repeated 3D images. It was surrounded by six repeated images because each lens was surrounded by six lenses in the hexagonal lens arrays.
Figure 15(a) shows 360-degree 3D images with the top hole. The repeated 3D images were eliminated successfully by the hole. The magnified 3D images are shown in Fig. 15(b).The calculated viewing zone angle corresponding to one light field display measured from the hole was 61.4°. Therefore, the 3D image could be observed from directions obtained by adding ±20° to the four directions. The 3D images could be observed with both eyes because the 3D image generated by each light field display could be observed with an angle of more than 40°. A video of the 3D image is provided (see Visualization 1). Because of the lack of the upper half system, no image was observed from the viewing zones that should be generated by the light field displays of the upper half system. There was no position where 3D images generated by two different light field displays were observed simultaneously because only the lower half system was constructed.
Fig. 15. Captured 3D images with top hole for non-tracking technique: (a) observed from 12 directions and (b) magnified 3D images. Refer to Visualization 1 for a video of the 3D image.
The calculated vertical viewing zone angle for the non-tracking-type experimental system was ϕy = 34.4°. Figure 16 shows 3D images captured from the three vertical directions of 35°, 45°, and 55° for four horizontal directions.
Fig. 16. 3D images captured from three vertical directions to show vertical image changes for non-tracking system; they were also captured from four horizontal directions.
The generation of elementary images is explained for the non-tracking system. In the process for rendering parallax images, a rendering screen was placed on the CDP, and a rendering camera array was placed at a position farther from the CDP. The 3D object was located around the top hole, which was where the rendering screen was located, and the parallax images were picked up by using the camera array. The resolution of parallax images was set to the resolution of the elementary images, i.e., 40 × 40. The distance between the camera array and the light field display screen was set to 338 mm (twice li). Because rays diverged from the CDP, the number of cameras had to be larger than the resolution of the elemental images, which was 127 × 104.
3.3 Tracking technique
Although the tracking technique does not require the top hole to remove the repeated 3D images, we included the top hole to allow viewers to observe only the screens of the light field displays. The diameter of the hole was 78 mm, which was the apparent width of the screens of the light field displays observed at a distance of 600 mm from the display screens. A photograph of the tracking-type system is shown in Fig. 17.
The width of the correct viewing region was wv = 114 mm from Eq. (13), which was larger than the average inter-pupil distance of 65 mm. The viewing zone angle corresponding to one light field display measured from the top hole was 18.5°. The pixel pitch on the CDP was 0.581 mm, and the resolution of the 3D images displayed by a single display was 172 × 127. Because the purpose of this experiment was to demonstrate the elimination of repeated 3D images and the movement of the correct viewing regions, no actual eye-tracking system was used. The viewing position was changed virtually in the experiments.
First, 3D images were generated without moving the correct viewing regions. Figure 18 shows the captured 3D images. The 3D objects were two chess pieces: a knight and a pawn. The images were captured from 0°, 90°, 180°, and 270°. They were also captured from directions obtained by adding ±20° to these four directions. The desired 3D images were observed from the four normal directions, and the repeated 3D images were observed from the side directions. The four normal directions were included in the correct viewing regions of the four light field displays, and the side directions were not.
Then, the correct viewing regions were moved in accordance with the virtual viewing positions. Because no actual eye-tracking system was implemented, the simulation results are shown. In this experiment, we assumed that the viewing position was virtually moved in the circular direction with the angles of θx = ±20° and θy = 0°. The elemental images were shifted on the flat-panel displays with the pixel amounts of ±39 in accordance with the viewing directions. Figure 19(a) shows the captured 3D images. The desired 3D images were observed from all 12 directions, and the repeated 3D images were not observed. The magnified 3D images are shown in Fig. 19(b). A video of the 3D image is provided (see Visualization 2). During the movement of the video camera, the 3D images were manually changed corresponding to the camera position to simulate the eye tracking. The average of the measured widths of the correct viewing zones was 114.3 mm, and the 3D images could be observed with both eyes for all 12 directions. There was no position where 3D images generated by two different light field displays were observed simultaneously because only the lower half system was constructed.
Fig. 19. Captured 3D images with viewer tracking: (a) observed from 12 directions, and (b) magnified 3D images. Refer to Visualization 2 for a video of the 3D image.
The calculated vertical viewing zone angle for the tracking-type experimental system was ϕy = 13.5°. Figure 20 shows 3D images captured from the three vertical directions of 40°, 45°, and 50°for four horizontal directions.
Fig. 20. 3D images captured from three vertical directions to show vertical image changes for tracking system; they were also captured from four horizontal directions.
The generation of elementary images is explained for the tracking system. The process for rendering parallax images for the tracking system is simpler than that for the non-tracking system. A rendering screen was placed on the lens array, and a rendering camera array was placed on the viewing plane. The 3D object was located around the top hole, which was distant from the rendering screen, and the parallax images were picked up by using the camera array. The resolution of parallax images was set to the number of lenses of the lens array. Because hexagonal lens arrays were used, the resolution was set to 174 × 222, which was larger than the number of lenses. The cameras were aligned on an array of 40 × 40, which was equal to the resolution of the elemental images.
4. Discussion
First, the non-tracking technique is discussed. Figures 14 and 15, respectively showing the separation of the desired and repeated 3D images and the elimination of the repeated 3D images, validate the proposed technique.
From Fig. 15, the resolution of the 3D images was not high because it was theoretically equal to that of the elemental images (41.7 pixels along the diameter of the top hole). Although the resolution-priority integral imaging technique [20,21] was used, the elimination of the repeated 3D images limited the resolution of the 3D images. When the depth-priority integral imaging technique [22] was used, the resolution of the 3D images was equal to the number of lenses observed through the top hole, which was 12.2 pixels along the diameter of the top hole. To increase the resolution of the 3D images, the resolution of the elemental images should be increased. In this case, the lens diameter needs to be increased to decrease the number of ray directions. To maintain the number of ray directions, the resolution of the flat-panel displays should be increased.
The size of the 3D images was small as shown in Fig. 15. To increase the size, the magnification of images done by the lens arrays should be increased by reducing the focal length of the arrays. In this case, the pixel pitch on the CDP would increase. To avoid this increase, the resolution of the flat-panel displays should be increased. For example, to obtain 3D images with a diameter of W3D = 100 mm (assuming X3D = 256), Eqs. (8) and (9) require that the focal length of the lens array be f = 182 mm (lens pitch pl = 15.0 mm) and the pixel pitch be pp = 58.6 μm (resolution X = 3,840) when the number of the flat-panel displays is N = 24.
We experimentally confirmed that the desired 3D images could always be seen when the screens of the light field displays were observed through the top hole. When the screens were not observed through the hole, the desired and repeated 3D images could not be seen. Therefore, if the remaining top half of the light field Mirage were to be constructed, 360-degree 3D images would be produced without repeated 3D images being generated. However, when the 3D images were observed at a large angle from the normal of the light field displays and the 3D images were generated by lenses located at the peripheral areas of the lens arrays, the contour of the images looked slightly doubled. Calibrating the lens parameters, such as the focal length, lens pitch, and lens position, could improve the image quality.
Second, the tracking technique is discussed. As shown in Fig. 18, repeated 3D images were observed from several directions without moving the viewing region. With the movement, the desired 3D images were observed instead of the repeated 3D ones as shown in Fig. 19. Therefore, the proposed technique was experimentally verified.
The resolution of the 3D images shown in Fig. 19 for the tracking technique was higher than that shown in Fig. 15 for the non-tracking technique. To increase the resolution of the tracking technique, the screen size of the light field displays should be increased, and the pixel pitch on the CDP should be decreased. To decrease the pixel pitch, the resolution of the flat-panel displays needs to be increased, and the focal length of the lens arrays needs to be increased. The former is costly, and the latter narrows the correct viewing region, resulting in the need for a precise eye-tracking technique.
The size of the 3D images for the tracking system was larger than that for the non-tracking system. To increase the 3D image size, the vertical resolution of the flat-panel displays should be increased as explained in Sec. 2.3. For example, to obtain 3D images with a diameter of W3D = 100 mm (assuming X3D = 256), Eqs. (14) and (15) require that the vertical resolution be Y = 1,080 (pixel pitch pp = 65.5 μm, horizontal resolution X = 1,920) and the focal length and lens pitch of the lens array respectively be f = 47.4 mm and pl = 10.0 mm when the number of the flat-panel displays is N = 10.
With the movement of the viewing region, as shown in Fig. 19, the desired 3D images could always be seen when the screens of the light field displays were observed. Thus, the addition of the upper-half display system will provide 360-degree 3D images. As in the case of the non-tracking technique, the contour of the 3D images was slightly doubled when the 3D images were displayed by the peripheral lenses. Calibration could improve the image quality.
As mentioned above, we experimentally confirmed that the repeated 3D images were eliminated by using the non-tracking and tracking techniques. In the experiments using the lower-half display system, a slight degradation in image quality was observed when viewed from the inclined directions. A calibration technique should be developed when constructing the full system so that 3D images generated by the upper and lower halves are naturally combined. A half mirror is used to combine the upper and lower systems. Anti-reflection coating should be required for the half mirror to avoid the generation of double images. The position of the lower half system should be adjusted considering the refractive index and thickness of the half mirror.
In the experiments, the elementary images were calculated using a PC containing 3-Ghz Intel Core i7-9700 CPU, 16GB of RAM memory, and an nVidia GTX1660 GPU. The calculation time was 2,181 s (2,128 s for the parallax image rendering and 53 s for the elementary image synthesis) for the non-tracking system, and 1,390 s (1,181 s for the parallax image rendering and 209 s for the elementary image synthesis) for the tracking system. In this study, we did not make any effort to increase the calculation speed. Reducing the calculation time is necessary considering the addition of the upper half system and future increases in the resolution of 3D images. The use of multiple PCs and GPUs is a straight forward solution. Because most of the calculation time was consumed for rendering the parallax images, an image interpolation technique for reducing the number of parallax images should be developed. In this study, a large number of cameras were prepared for each light field display to render the parallax images. A technique should be developed that calculates elemental images for all light field displays from parallax images captured from a circularly aligned camera array.
5. Conclusion
This study proposed a light field Mirage that can produce 360-degree 3D images; the upper and lower parabolic mirrors of the conventional Mirage are replaced with multiple light field displays. Two techniques were proposed to eliminate the repeated 3D images generated by the displays, that is, non-tracking and tracking techniques. The lower-half display system, consisting of four light field displays, was constructed to experimentally verify the two techniques.
With the non-tracking technique, the repeated 3D images were successfully eliminated by using a top hole with a diameter of 24.2 mm. The 3D image size was limited by the hole, and the resolution was 41.7 pixels along the diameter of the hole.
With the tracking technique, the observation of repeated 3D images by viewers was successfully avoided by moving the correct viewing regions. The width of the correct regions was 114 mm, and the movement of the correct regions was demonstrated with an angle of ±20°. The resolution of the 3D images given by one light field display was 172 × 127.
In future work, we will complete the light field Mirage by adding the upper half system to the lower half system developed in this study.
Disclosures
The authors declare no conflicts of interest.
References
1. Y. Kitamura, T. Konishi, S. Yamamoto, and F. Kishino, “IllusionHole: An Interactive Stereoscopic Display System for Multiple Users,” J.ITE. 57(10), 1320–1327 (2003). [CrossRef]
2. T. Yendo, N. Kawakami, and S. Tachi, “Seelinder: the cylindrical lightfield display.” in Proceedings of ACM SIGGRAPH 2005 on Emerging technologies. 2005. 16-es.
3. T. Yendo, T. Fujii, M. Tanimoto, and M. P. Tehrani, “The Seelinder: Cylindrical 3D display viewable from 360 degrees,” J. Vis. Commun. Image Represent. 21(5-6), 586–594 (2010). [CrossRef]
4. D. Miyazaki, N. Akasaka, K. Okoda, Y. Maeda, and T. Mukai, “Floating three-dimensional display viewable from 360 degrees,” Proc. SPIE 8288, 82881H (2012). [CrossRef]
5. D. Miyazaki, G. Miyazaki, Y. Maeda, and T. Mukai, “Floated integral imaging display viewable from surrounding area,” in Imaging and Applied Optics 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper DW2B.5.
6. A. Butler, O. Hilliges, S. Izadi, S. Hodges, D. Kim, and D. Kong, “Vermeer: direct interaction with a 360° Viewable 3D Display,” Proc.UIST’11, 569–576(2011).
7. Y. Takaki and S. Uchida, “Table screen 360-degree three-dimensional display using a small array of high-speed projectors,” Opt. Express 20(8), 8848–8861 (2012). [CrossRef]
8. S. Uchida and Y. Takaki, “360-degree three-dimensional table-screen display using small array of high-speed projectors,” Proc. SPIE 8288, 82880D (2012). [CrossRef]
9. S. Yoshida, M. Kawakita, and H. Ando, “Light-field generation by several screen types for glasses-free tabletop 3D display,” in Proceedings of 2011 3DTV Conference on The True Vision-Capture, Transmission and Display of 3D Video (IEEE, 2011) pp. 1–4.
10. S. Yoshida, “fVisiOn: glasses-free tabletop 3-D display–its design concept and prototype–,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DTuA1.
11. S. Yoshida, “fVisiOn: 360-degree viewable glasses-free tabletop 3D display composed of conical screen and modular projector arrays,” Opt. Express 24(12), 13194–13203 (2016). [CrossRef]
12. S. Yoshida, “Virtual multiplication of light sources for a 360°-viewable tabletop 3D display,” Opt. Express 28(22), 32517–32528 (2020). [CrossRef]
13. M. Makiguchi, T. Kawakami, M. Sasai, and H. Takada, “Smooth motion parallax glassless 3D screen system using linear blending of viewing zones and spatially imaged iris plane,” in Proceedings of SID Symposium Digest of Technical Papers, Vol. 48(1), (Wiley, 2017), pp. 903–906.
14. M. Makiguchi, H. Takada, T. Fukiage, and S. Nishida, “Reducing image quality variation with motion parallax for glassless 3D screens using linear blending technology,” in Proceedings of SID Symposium Digest of Technical Papers, Vol. 49(1), (Wiley, 2018), pp. 251–254.
15. M. Makiguchi, H. Takada, T. Kawakami, and M. Sasai, “360-degree tabletop type 3D screen system using linear blending of viewing zones and spatially imaged iris plane,” in Proceedings of SID Symposium Digest of Technical Papers, Vol. 50(1), (Wiley, 2019), pp. 585–588.
16. X. Yu, S. Xinzhu, X. Gao, Y. Binbin, C. Duo, L. Boyang, L. Li, G. Chao, and P. Wang, “360-degree tabletop 3D light-field display with ring-shaped viewing range based on aspheric conical lens array,” Opt. Express 27(19), 26738–26748 (2019). [CrossRef]
17. X. Gao, X. Sang, X. Yu, W. Zhang, B. Yan, and C. Yu, “360° light field 3D display system based on a triplet lenses array and holographic functional screen,” Chin. Opt. Lett. 15(12), 121201 (2017). [CrossRef]
18. A. Ö. Yöntem, K. Li, and D. Chu, “Reciprocal 360-deg 3D light-field image acquisition and display system [Invited],” J. Opt. Soc. Am. A36(2), A77–A87 (2019). [CrossRef]
19. Y. Momonoi, K. Yamamoto, and Y. Takaki, “Proposal for light field Mirage,” presented at the 26th International Display Workshops (IDW‘19), Japan, 28 Nov. 2019.
20. J.-S. Jang, F. Jin, and B. Javidi, “Thee-dimensional integral imaging with large depth of focus by real and virtual image fields,” Opt. Lett. 28(16), 1421–1423 (2003). [CrossRef]
21. F. Jin, J.-S. Jang, and B. Javidi, “Effects of device resolution on three-demensional integral imaging,” Opt. Lett. 29(12), 1345–1347 (2004). [CrossRef]
22. H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15(8), 2059–2065 (1998). [CrossRef]
23. L. Onural, “Design of a 360-degree holographic 3D video display using commonly available display panels and a paraboloid mirror,” Proc. SPIE 10126, 101260I (2017). [CrossRef]
