The generation of full-parallax and 360-degree three-dimensional (3D) images on a table screen is proposed. The proposed system comprises a small array of high-speed projectors and a rotating screen. Because the screen has a lens function, a large number of viewpoints are generated on a circle when the screen rotates. Thus, 360-degree 3D images having horizontal parallax are generated. Because all projectors are located at different heights from the screen, they generate the viewpoints on a circle at different heights. Therefore, plural viewpoints are aligned in the vertical direction to provide vertical parallax. A prototype display system that employs three high-speed color projectors is constructed.
© 2014 Optical Society of America
Several techniques have been recently proposed to construct 360-degree three-dimensional (3D) displays having a table screen [1–4]. Multiple viewers can be located at any position around the table screen and are allowed face-to-face communication while viewing 3D images. The generation of 3D images on a table screen is suitable for displaying landscape views of 3D objects and scenes. Therefore, they can be used in various applications such as industrial design, city planning, and air traffic control. However, most of them can provide only the horizontal parallax. In this study, we develop a table screen 360-degree 3D display having both horizontal and vertical parallaxes, i.e., full parallax.
The table screen 360-degree 3D displays have been constructed using a high-speed projector system [1, 2], a multi-projection system , and a hybrid system that combines both systems . Figure 1(a) depicts the high-speed projector system, which consists of a high-speed projector and a rotating screen. The high-speed projector projects images onto the rotating screen, which redirects the rays. Screen rotation generates rays in various horizontal directions. Although the system configuration is simple, the high-speed projector usually provides a limited number of colors or gray levels. Therefore, generated 3D images have low color and grayscale representation. Figure 1(b) depicts the multi-projection system, in which a large number of projectors project images onto a common screen. The different projectors emit rays proceeding in different horizontal directions. Because ordinary projectors can be used, this system has good color and grayscale representation. However, the system is large and complicated because a large number of projectors are used. The hybrid system, shown in Fig. 1(c), comprises a small number of high-speed projectors and a rotating screen. The use of multiple projectors improves the color representation because images with different colors can be projected by different projectors. In addition, the hybrid system can reduce the rotation speed of the screen and increase the number of images displayed in the different horizontal directions or number of viewpoints. The required number of projectors is less than that required for the multi-projection system.
Several 360-degree 3D displays having vertical screens have also been proposed. In addition to high-speed [5–9] and multi-projection systems [10, 11], systems employing rotating LED arrays have also been proposed [12–16]. Most of these systems are multi-view displays having only horizontal parallax [6–13]. Some of them are volumetric displays [5, 14–16]. Although volumetric displays provide full-parallax 3D images, they have occlusion issue and can generate 3D images of only diffusive objects because the rays are diffused on the screen. 3D images generated by the multi-view displays are distorted depending on the vertical viewing position, whereas those generated by volumetric displays do not distort. If the table screen 360-degree 3D displays can provide vertical parallax in addition to horizontal parallax, the images generated on the table screen are not distorted and can be viewed from any angle. Although a 2D array of projectors has been used to provide a large number of viewpoints in the horizontal direction, the 2D array of projectors is considered to provide both horizontal and vertical parallaxes [17–19].
Li et al. reported a full-parallax 3D display system with nine horizontal viewpoints and five vertical viewpoints utilizing a square directional diffuser . Based on the 3D display with omnidirectional view , Xia et al. replaced the single-side anisotropic diffusing mirror with a double-side diffusing mirror, featured by different inclinations to generate multiple vertical parallaxes . Moreover, by using the method of light field reconstruction, Xia et al. developed a floating 3D display system with a high-speed projector and a flat light field scanning screen, which could achieve 360-degree viewable horizontal-parallax-only 3D display on the top of the screen . And on this basis a combined screen with multiple tilt angles was utilized to add vertical parallax to this system 
In this study, we propose a technique to provide vertical parallax for the hybrid system used to construct table screen 360-degree 3D displays. Preliminary report of the work presented herein has been published elsewhere . Note that the previous report was limited to initial experimental results and a brief description of the system configuration. In the report, a monochromatic display system was used to show only one 3D image and did not contain any discussion. In contrast, the work presented here describes a color display system and includes additional experimental results. Moreover, the viewpoint generation has been measured to provide correct 3D images. Furthermore, the discussions related to the experimental results have also been provided.
2. Display system
The hybrid system, which combines the high-speed projector and multi-projection systems, was modified to provide vertical parallax for 360-degree 3D images generated on a table screen.
Figure 2(a) illustrates the previously proposed hybrid system, which comprises few high-speed projectors and a rotating screen. The system with a reflective screen is shown in the figure. To enable the use of multiple projectors, the lens shift technique is used to superimpose all images generated by multiple projectors onto the rotating screen. The 360-degree 3D image generation is explained in Fig. 2(b), which shows a transmissive screen system for the ease of explanation. The rotating screen has a lens function such that an image of a projection lens is produced in the observation space. The image of the projection lens becomes a viewpoint because an image projected onto the rotating screen can be viewed from this position. Because the lens axis of the screen lens is shifted from the rotation center, the rotation of the screen generates a number of viewpoints on a circle. The use of multiple projectors increases the number of colors and viewpoints and reduces the screen rotation speed. Because the viewpoints are aligned horizontally on circles, the system can provide only horizontal parallax. A vertical diffusion function was added to the rotating screen to increase the vertical viewing zone .
Figure 3(a) illustrates the display system proposed in this study. All projectors are located at different heights from the rotating screen. Thus, the images of the projection lenses are generated at different heights. Therefore, different projectors generate viewpoints on circles at different heights. Because multiple viewpoints are aligned in the vertical direction, vertical parallax is provided. When parallax images are properly prepared corresponding to the positions of the viewpoints and are displayed by rays converging to the viewpoints, 3D images having both horizontal and vertical parallaxes are generated.
As shown in Fig. 3(b), when the distance between the rotating screen and the projector #n is denoted by ln, that between the rotating screen and the circle in which the viewpoints are generated is denoted by ln’, and the focal length of the screen lens is denoted by f, the lens maker’s formula gives the relationship 1/ln + 1/ln’ = 1/f. When the distance between the rotation axis and the lens axis is denoted by r, the radius of the circle on which the viewpoints are generated is given by Rn = (1 + ln’/ln)r. When the rotation axis of the screen is placed at the origin of the coordinate system and the position of the projection lens is denoted by (xp, yp), the circle on which the viewpoints are generated is given by the following equation:
In the previous hybrid system, a vertical diffuser is required to enlarge the vertical viewing zone. In the modified hybrid system proposed in this study, a vertical diffuser is not required when the vertical pitch of the viewpoints is smaller than the pupil diameter. When the vertical pitch of the viewpoints is larger, a vertical diffuser, which appropriately diffuses rays in the vertical direction, should be added to the rotating screen to eliminate the areas in which the images cannot be viewed. The diffusing angle of the vertical diffuser should be appropriately chosen to fill in the vertical gaps between the viewpoints. For smaller values of the diffusing angle, the viewing regions are separated vertically, while for larger values of the diffusing angle, crosstalk appears between the viewpoints.
In this study, multiple projectors were utilized to provide the vertical parallax. In the previous study, this technique was used to increase the number of colors. Therefore, to generate 3D color images, each projector should generate color images. When the projectors use the time-sequential technique to generate color images, R, G, and B images are sequentially displayed to succeeding three viewpoints. The spatial extents of the viewpoints should be continuous along the circle in each color; therefore, the spatial extents of viewpoints should be increased three times.
The hybrid system proposed in this study can be implemented using either reflection or transmission systems, as shown in Fig. 3.
3. Experimental system
The generation of vertical parallax by the proposed technique was verified experimentally. A reflection-type hybrid system was constructed using three high-speed color projectors and a reflective rotating screen.
The high-speed color projector was constructed using a digital micromirror device (DMD) and projection optics. DMD used was the DLP DiscoveryTM 4100 (Texas Instruments, Inc.) with the ALP-4.1 high-speed accessory software package. The resolution was 1,024 × 768, and binary images could be generated with a maximum frame rate of 22,727 Hz. To synchronize the three DMDs, the frame rate was reduced to 22,222 Hz. The projection optics used was the LED Integrated Optical Module (ViALUX GmbH.), which was modified to allow changes in the shift amount of the projection lens. The LED that illuminated DMD was replaced with an RGB-LED to generate color images using the time-sequential technique. The central wavelengths of the R, G, and B LEDs were 625, 525, and 465 nm, respectively.
The structure of the rotating screen, shown in Fig. 4(a), comprises an off-axis Fresnel lens and an aluminum-coated mirror. The diameter of the rotating screen was 300 mm. The focal length and groove pitch of the Fresnel lens were 800 and 0.30 mm, respectively. Because rays passed through the Fresnel lens twice, the effective focal length of the reflective screen was f = 400 mm. The separation between the lens axis and the screen center (rotation axis) was r = 120 mm. A servo motor was used to rotate the screen. The image update signal from the DMD controllers was used to control the servo motor. Figure 4(b) shows a photograph of the reflective rotating screen. The rotation speed was 1,481 rpm, and the frame rate of displayed 3D images was 24.7 fps. Each high-speed projector generated 900 images during each rotation so that 300 viewpoints were generated for each R, G, and B color. To obtain the R, G, and B images, 900 colored parallax images were rendered corresponding to the 900 viewpoints on each circle, and then the R, G, and B images were extracted from them.
Three DMD projectors were used to generate three viewpoints in the vertical direction. Figure 5 shows a photograph of the projector array, and the positions of the three projectors are shown in Fig. 6(a).The heights of the three projectors were l1 = 780 mm, l2 = 840 mm, and l3 = 900 mm. The corresponding heights of the viewpoints were l1’ = 821 mm, l2’ = 764 mm, and l3’ = 720 mm. The calculated radii of the circles in which the viewpoints were generated were R1 = 246 mm, R2 = 229 mm, and R3 = 216 mm, and the corresponding intervals of the viewpoints were 5.2 mm, 4.8 mm, and 4.5 mm. The three circles are shown in Fig. 6(b).
Subsequently, the viewpoint generations were measured, which indicate that the viewpoints are generated on circles located on the planes that are not parallel to the rotating screen. Further investigations on the ray converging points suggest that the rays approximately converge on an identical plane that is inclined toward the rotating screen. A tracing paper attached to a rigid frame was aligned such that the ray converging points are located on the paper. Subsequently, several ray converging points were measured and a circle that fits well with the measured points was determined by the least-squares method. The measured three circles are shown in Fig. 7.The inclination of the circles may have been caused by off-axis aberrations of the Fresnel lens. The measured radii of the circles were R1 = 238 mm, R2 = 224 mm, and R3 = 213 mm. The intervals of the viewpoints for each color of the color image generation were 5.0 mm, 4.7 mm, and 4.5 mm for the circles #1, #2, and #3, respectively. The widths of the light distributions of the viewpoints along the circles were measured, and the average width was 5.6 mm. The inclination of the circles causes the decrease and increase in the vertical intervals of the viewpoints. Especially, the decrease brings about crosstalk between the viewpoints. Thus, the distortion in the viewpoint generations degrades the 3D images. To avoid the image degradation, images displayed by the projectors were rendered by referring to the measured positions of the viewpoints. The parallax images were generated using the computer graphics (CG) software considering the measured positions of the viewpoints as the camera positions used in the CG software. Thus, from each viewpoint, an image having the correct horizontal and vertical parallaxes corresponding to the viewpoint can be observed.
The vertical intervals of the designed positions of the viewpoints were 57 mm and 44 mm. However, the vertical separations were not constant and changed spatially, as shown in Fig. 7. Because the appropriate vertical diffusion was not determined, the vertical diffuser was not used in the experimental system. Therefore, the vertical viewing positions of the experimental system were limited to the viewpoint circles.
The 3D images with vertical parallax produced by the experimental system, shown in Figs. 8, 9, and 10were captured from six different positions indicated by the letters A–F in Fig. 7. The three positions A, B, and C that were located over the negative side of the x-axis had different heights of 774 mm, 699 mm, and 640 mm, respectively. Similarly, the three positions D, E, and F that were located over the positive side of the x-axis had the heights of 712 mm, 699 mm, and 683 mm, respectively. As shown in these photographs, the captured images changed depending on the observation heights. Therefore, the vertical parallax was obtained.
In the photographs captured at the positions A, B, and C shown in Figs. 8–10, the vertical parallax could be observed because of the large vertical intervals of the viewpoints. However, regions with no images existed between the viewpoints, as a vertical diffuser was not used in the experimental system. As evidenced from the photographs captured at positions D, E, and F, the images changed depending on the viewpoints. However, the observed image changes could be ascribed to the horizontal parallax rather than the vertical parallax, as the horizontal intervals were larger than the vertical intervals between the three viewpoints as shown in Fig. 7(b).
In the experimental system, the viewpoints were generated on the inclined circles. We used the Fresnel lens used in our previous system , in which the separation of the rotating axis and the lens axis was r = 200 mm. We found that the circles were inclined with large angles. Thus, the separation r was decreased to 120 mm to decrease the inclination angles. Because the different circles inclined differently, the vertical intervals of viewpoints were not spatially constant. When the interval was large, regions with no image were observed. When the interval was small, the vertical viewing area was limited. Therefore, the inclination of the circles should be reduced to provide constant vertical intervals between viewpoints, and a vertical diffuser with appropriate diffusion should be used to provide continuous viewing area in the vertical direction.
The inclination of the circles where the viewpoints were generated was caused by the field curvature aberration of the Fresnel lens that was used as the screen lens. The field curvature can be reduced when the aspheric surfaces are used as the structures of the Fresnel lens. While using a commercial Fresnel lens, removing the inclination of the circles completely is difficult. Fresnel lenses with aspheric surfaces that are specialized for the screen lens have to be designed.
The generated 3D images had smooth motion parallax along the circles where the viewpoints were generated. The deviations of the viewpoint intervals along the circles were <5%. The average width of the light distributions for the viewpoints was 5.6 mm, which is larger than the intervals of the viewpoints; consequently, the viewpoints were continuously generated along the circles. Note that the average width was 10%–25% larger than the intervals; thus, the crosstalk among the viewpoints was not large. Moreover, the differences between the images displayed to the adjacent viewpoints were small, as 300 viewpoints were generated along the circles; therefore, obvious double images were not observed.
From Figs. 8–10, colors of 3D images changed depending on the vertical viewing positions. As shown in Fig. 4(a), the Fresnel lens comprised many right triangular prisms, most of which were aligned in the same direction because the lens axis was located near the circumference. The dispersion of the prism was large because it was composed of polymethyl methacrylate. The generated viewpoints showed color distribution in the vertical direction; the red component was distributed at a position higher than the blue component. This color distribution problem can be solved by using metal-coated prisms or a low-dispersion material such as glass to construct the prisms. In this study, the color change was not observed along the circles where the viewpoints were generated. Moreover, the color change was temporally stable. Therefore, it is believed that the color change is not caused by the time-multiplexing color generation scheme.
Because the experimental system had only three viewpoints in the vertical direction, the viewing area was very limited. However, in the area in which 3D images could be observed, the shapes of those images showed no distortion regardless of the viewing position. Therefore, 3D objects with large heights could be displayed, as shown in Figs. 8–10. Contrarily, 3D images generated by the previous system were distorted depending on the vertical viewing positions because it had only horizontal parallax, and only low-height objects could be displayed. Such distortion can be solved by combining the eye-tracking mechanism with the display system. When the eye-tracking is accurate and the image generation is sufficiently fast, the latter system may be preferred because the vertical viewing area is larger. The use of the eye tracking system to provide the vertical parallax to 3D displays has been previously proposed and demonstrated in the literatures [7, 8, 19].
In this study, multiple projectors were used to provide vertical parallax. The color images were generated by the time-multiplexing technique. Therefore, the frame rate was decreased to 24.7 fps, which was lower than that of the previous system . Because of this frame rate, a flicker was observable, whereas the color breakup effects were not observable; thus, the flickering effect seems to have hidden the color breakup effects. The use of higher-speed or multiple projectors is required to remove image flickering. Note that the difference among the positions of the R, G, and B viewpoints along the circles might cause color shifts in 3D images. However, the color shifts were not observed because the R, G, and B images were calculated for 900 viewpoints, and not for 300 viewpoints; thus, the color shifts were small
In the experimental system, three projectors were used to verify the generation of the vertical parallax. Note that a maximum of six to eight projectors could be accommodated in the experimental system developed in this study. A typical multi-view display consisted of a liquid-crystal display and a lenticular lens provides five to nine viewpoints, whereas typical horizontal intervals of viewpoints are the interpupillary distance (65 mm in average) or its half. Thus, when the vertical viewpoint interval is equal to the horizontal interval of the typical multi-view displays, approximately six to eight vertical viewpoints provide the viewing area with a height of 195–520 mm.
We proposed a technique to provide vertical parallax for a table screen 360-degree display by using a small array of high-speed projectors. These multiple projectors were used to provide multiple viewpoints in the vertical direction. An experimental system including three DMD projectors, which could generate color images, was constructed to provide three viewpoints in the vertical direction. The generation of the vertical parallax was verified experimentally. However, the off-axis aberrations of the Fresnel lens used as the rotating screen caused distortion in the viewpoint generation in the vertical direction. The chromatic aberration of the Fresnel lens deteriorated the color representation of 3D images.
This study was supported by a Grant-in-Aid for Scientific Research, No. (B) 23360148 from the Japan Society for the Promotion of Science (JSPS). The 3D data of “space shuttle” shown in Fig. 10 was distributed by NASA.
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