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Multi-view three-dimensional (3-D) displays using directional beam splitter array were proposed to achieve a perfect 3-D perception with low cross-talk. The multi-direction collimated light may project different images to different viewing zones to form the multi-view autostereoscopic display. Furthermore, a high resolution 3-D display can be realized with a sequential beam splitter array and a sequential liquid crystal display. By optimization, the cross-talk of the directional beam splitter backlight system was lowered to 5% to improve the perception of the 3-D displays.
© 2017 Optical Society of America
1. Introduction
The three-dimensional (3-D) displays have attracted great interests because they may achieve perception close to the real life, which include several technologies, such as holographic, stereoscopic, and autostereoscopic displays. Stereoscopic display may achieve perfect 3-D performance and immersive perception, but the audience need to wear auxiliary resulting in the obstacle to free watch [1–6]. Although holographic displays may recover the perfect 3-D images, the recording of a holographic medium is too slow to permit real-time operation [7,8]. Thus, multi-view autostereoscopic display shows its merits of 3-D perception, simple fabrication, and consistency of current two-dimensional display technologies [9–15]. Several kinds of the configurations were applied in the autostereoscopic display which included parallax barrier, lenticular, and directional backlight. The parallax barrier type autostereoscopic display may achieve perfect 3-D perception with low cross-talk, but the luminance loss is the key issue to be solved [16,17]. The lenticular type autostereoscopic display shows high optical efficiency, but the cross-talk is relatively high [18]. And both of the technologies may degrade the resolution of 3-D display because a 3-D pixel is made up of several 2-D pixels according to the multi-view number [19,20]. The directional backlight type autostereoscopic display may keep the same resolution as two-dimensional (2-D) display, but its backlight system is too complex to achieve the multi-view application [21–23]. Currently, David Fattal et al. proposed a full-motion parallax 3-D display technology in view zone of 90 degree by grating type multi-directional backlight. However, the 64-view spatial-multiplexed backlight degraded the resolution and light efficiency due to the aperture ratio of the grating array [24].
In this paper, a multi-view autostereoscopic display using a directional collimated beam splitter backlight was demonstrated. And we proposed two kinds of structures to realize the multi-view autostereoscopic display. One is the spatial multi-view 3-D display and the other is the time sequential 3-D display. The multi-directions collimated light of both structures may project different images to different viewing zones to form the multi-view autostereoscopic display with low cross-talk and high optical efficiency. Furthermore, a high resolution 3-D display can be realized with the sequential directional backlight system.
2. Design principle
According to our previous research, a planar collimated light source (CLS) of high optical efficiency, good uniformity, and narrow viewing cone was demonstrated by utilizing the micro-prism array light guide structure [25]. Figures 1(a) and 1(b) showed the structure and the light path of the collimated backlight. The green laser (λ = 533nm) with uniform light intensity was employed as the collimated light source (CLS). To achieve a high directivity and uniformity emergent light, FWHM of the light source should be less than 5°on both horizontal and vertical directions as the uniformity of the emergent light will be degrade a lot if the conventional LED light source is applied. With this structure, the angular distributions of the collimated backlight may achieve ± 4° of FWHM on both horizontal and vertical directions, as shown in Fig. 1(c).
Fig. 1 The (a) top view and (b) front view structure of the collimated backlight, (c) angular distributions of the collimated backlight.
By integrating the beam splitter array on the top layer of the collimated backlight, a directional beam splitter array can be achieved. Figure 2(a) illustrates the schematic of the proposed 3-D display with directional beam splitter array. The high directional collimated rays of different directions exit from the beam splitter backlight. Among the beam splitter array, the polar angle and azimuthal angle of prism structure in each beam splitter unit were designed separately according to the viewing distance and view number. As the beam splitter unit only changed the direction of rays from the collimated backlight, the rays exit from beam splitter unit pass through one pixel of the LC display and project to a spatial point. As show in Fig. 2(b), rays with image information of N*M pixels projected to the corresponding spatial points to form a 3-D pixel of N*M view 3-D display which may provide both horizontal and vertical direction 3-D perception. Due to the good uniformity and narrow viewing cone of the directional beam splitter array, the multi-view 3-D display may achieve perfect 3-D perception with low cross-talk and large viewing zone. However, the resolution of the multi-view 3-D display degrades a lot as N*M pixels of LC display are needed to form one 3-D pixel.
Fig. 2 (a) Schematic of 3-D display with directional collimated beam splitter, (b) spatial multi-view 3-D display, and (c) time sequential 3-D display
To solve the resolution issue of the 3-D display with directional beam splitter array, a time sequential directional beam splitter array was proposed. As shown in Fig. 2(c), the time sequential beam splitter array only turns on the light source, CLS0, at first frame, and the rays may be projected to a spatial point through plane A. Then CLS0 is switched off and CLS1 is turned on at second frame, and the rays may be projected to next spatial point through plane B. After CLS2 and CLS3 are turned on and the rays are projected to other two spatial points through plane C and D sequentially, a cycle of 4-view time sequential 3-D display is completed. Since the rays exit from plane A, B, C, and D pass through same pixel of the time sequential LC display and the LC display shows four view information sequentially on the corresponding four frames, 3-D perception can be achieved without resolution loss. Meanwhile, as the beam splitter unit of time sequential directional beam splitter array only changes the direction of rays from the collimated backlight, the cross-talk of time sequential multi-view 3-D display is very low.
3. Spatial multi-view 3-D display
To investigate the properties of the spatial multi-view 3-D display with the directional beam splitter array, a 9*9 view geometric model for 3-D display was built by the commercial software, Light tools 7.2, which employs the Monte Carlo method [26,27].The material of light guide plate (LGP) is polymethyl methacrylate (PMMA). The dimension of backlight module is 81 mm in length, 81 mm in width and 6 mm in thickness.
Figure 3 shows the cross-section of the 5th horizontal row in the spatial 9*9 view 3-D display simulation. According to the design principle of the directional beam splitter array, the azimuthal angle of 5th row is 0 degree because it is the central row of the beam splitter array. As the view55 is in the center of the directional beam splitter array, the emergent light is perpendicular to the array, there is no prism structure at that position. The adjacent view in the right side of view55 is view56. Then we set the horizontal distance between two adjacent views as 16.25mm, 1/4 of the inter-pupillary distance, and set the viewing distance as 2000mm for a large size 9*9 view 3-D display. As shown in Fig. 4, we can calculate the angle, θ, with the horizontal distance, D and the viewing distance, H. According to the Snell's Law, all the slant angles, α, of the right side prisms can be figured out. As the directional beam splitter array is a symmetric structure, the slant angles of the left side prisms are the same as the right side ones. The different polar angles of nine prism structures of 9*9 view 3-D display are calculated and listed in Table 1.
Table 1. Angle parameters of the 5th row
To investigate the cross-talk of the spatial 9*9 view 3-D display system, the luminance distribution was simulated by the commercial software, Light tools 7.2 (SYNOPSYS) with a collimated light source. And the cross-talk can be calculated by Eq. (2),
Where Imax is the maximum luminance value for a single viewing zone at a specific position, and Imin is the luminance value of the nearest neighboring zone at the same position. As shown in Fig. 5, we may see that there is almost no cross-talk between different views.For easy fabrication, a spatial 2-view prototype was fabricated to demonstrate the 3-D effect as illustrated in Fig. 6(a). The green laser (λ = 532nm) with uniform light intensity was employed as the CLS. And as the 2-view prototype is designed for mobile display, the viewing distance is set as 200 mm, the polar angle of the prism structure is about 19.6°as illustrated in Fig. 6(d). The luminance distribution of the 2-view 3-D display was measured at the viewing distance, 200 mm, by spectroradiometer (CS-2000) for calculating the cross-talk. Three kinds of luminance distributions at the optimized viewing distance (200mm) were illustrate in Fig. 6(b). Imax is the maximum luminance value at view1, Isi-min, Isr-min and Im-min are the luminance value of the ideal simulation, real profile simulation, and measurement data of view2 at the same position respectively. Compared the measurement result with the simulation result of ideal structure and real profile of the microstructure with 5um radius. We may see that the crosstalk of ideal structure is zero, which means two images of the adjacent views can be separated perfectly. The crosstalk of the measurement result is about 5%, which is also lower than tolerable level [20]. The simulation result of the real profile of the microstructure was close to the measurement result which means the luminance distribution difference between the ideal microstructure and the measurement result comes from the fabrication process. However, compare to the simulation result, zero, the measurement cross-talk was a little bit higher. As shown in Fig. 6(d), the ideal micro-prism array can keep the high directional refracted rays without distortion but several factors cause the luminance distribution to be extended. One is the apex scattering of the micro-prism which comes from a deflection with radius of 5μm due to the limitation of fabrication. Besides, surface irregularities and mismatching tolerance in fabrication process also result in the distortion of the ray distribution. Therefore, we may see the light scattering in the experiment because part of refracted rays were diffused by the vertex angle which was not as sharp as the ideal profile of micro-prism.
Fig. 6 (a) 2-view prototype, (b)luminance distributions of both simulation and experiment 2-view 3-D display and two light spots from the 2-view prototype, (c) the profile of beam splitters array under scanning electron microscope (SEM), and (d) comparison between ideal and real profile of micro structure.
The proposed structure of 2-view 3D display with low crosstalk may cause the black band effect when the user moves the viewing position. It is well known that the 3D perception is trade-off between low crosstalk and weak black band effect. Because the 2-view structure is fit for the small size mobile display whose users are always fit the viewing position, we put the low crosstalk prior to the black band effect to improve the 3D perception and visual fatigue.
Not only the angular distribution, but also the uniformity of backlight is very important to 3-D system. The simulation result of the luminance distribution at the surface of the directional beam splitter array with real profile of the microstructures was illustrated in Fig. 7. For 3-D system, the uniformity of the backlight with beam splitter array is about 97.8%, almost same as the uniformity of the collimated backlight. Therefore, the uniformity of backlight for 3-D system is very good.
We made a simulation for full color system with red light (λ = 633nm), green light (λ = 532nm), and blue light (λ = 440nm) in the 2-view 3-D display. As shown in Fig. 8, the luminance distribution of three kinds of color at the optimized viewing distance (200mm) are almost same, which means the color separations of the proposed structure can be ignored.
4. Time sequential 3-D displays
To investigate the properties of the multi-view 3-D display with time sequential directional beam splitter array, a pyramid structure geometric model, for 2*2 view mobile 3-D display was built and the parameters of the pyramid structure were shown in Fig. 9.
As illustrated in Fig. 2(c), from frame 1 to frame 4, four light sources, CLS0, CLS1, CLS2, and CLS3 will be turned on and the rays may be projected to the designed positions through plane A, B, C, and D sequentially. Since the rays exit from different planes pass through same pixel of the sequential LC display, the image information of four views can be achieved sequentially on designed positions. Therefore, the 3-D perception can be achieved without resolution loss. Because the viewing distance is set as 200 mm, the polar angle of the pyramid structure is about 49.6°,as shown in Fig. 9. To calculate the cross-talk of 2*2 view time sequential 3-D display, the luminance distribution was simulated with the pyramid structure array and four sequential light sources. From Fig. 10, we may see that the cross-talk between the different views is zero resulting in a perfect 3-D perception in both horizontal and vertical directions.
In the proposed time sequential 2*2 view 3-D display system, the conventional 60 Hz should be changed to 240Hz as the frames are quadrupled. In this case, the conventional nematic LC materials may result in severe color breakup. According to the previous research, the color breakup can be well suppressed if the LC response time is less than 1ms [28]. Therefore, fast response LCs such as blue phase LCs [29,30] and optically compensated bend (OCB) mode LCs [28] whose response time is less than 1ms should be adopted in the propose time sequential 2*2 view display to improve the color breakup issue.
5. Conclusion
Multi-view 3-D displays using directional collimated beam splitters were proposed. The multi-direction collimated light may project different images to different viewing zones to form the multi-view 3-D displays. Though limited by the fabrication process, perfect 3-D perception with low cross-talk (5%) can be achieved with the high directional beam splitter arrays. Furthermore, a high resolution multi-view 3-D display can be realized with the sequential collimated beam splitter arrays to improve the resolution loss.
Funding
This work was sponsored by National Basic Research Program of China (2013CB328804), National High Technology Research and Development Program of China (2015AA017001), and NSFC (61275026).
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