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Abstract
It is highly challenging for the available glasses-free 3D display to simultaneously possess the advantages of viewing freedom, homogeneous illuminance, high resolution and low crosstalk. This work proposes and demonstrates a directional backlight autostereoscopic display having these advantages with a substantially extended viewing volume and densely packed viewpoints. Low crosstalk and homogeneous illuminance are obtained using dynamically configured directional backlight, realized by a novel system design, in conjunction with viewer’s eye tracking and subsequent backlight control scenario. The autostereoscopy allows the viewers to move around continuously, while the illuminance homogeneity on the screen, high panel resolution and low crosstalk between the left and right eyes are realized, providing high-quality glasses-free 3D display with satisfying viewing experience.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Autostereoscopy [1] has been attracting a great deal of research and industrial attention in recent years [2–4]. While an autostereoscopic display provides convenience for glasses-free virtual 3D viewing experience, several major drawbacks have to be tackled before widespread scientific and commercial applications can be realized. The urgent technical challenges to be overcome include the resolution loss caused by imaging splitting to the left and right eyes, the large glasses-assisted crosstalk [5], the luminance homogeneity and limited viewing zone.
The conventional autostereoscopic display consists of either a lenticular lens array [6–8] or a barrier array [9–12] to deliver different images to different eyes. While these systems have been successful in demonstrating the basic features for glasses-free 3D displays, they are not yet successful in tackling the problems such as reduced resolution, large crosstalk as well as limited viewing volume. Recent years have witnessed an increase of liquid crystal display (LCD) panel resolution, so that the reduction of the resolution can be partially compensated by these 4 K and 8 K panels. The crosstalk can now be better controlled, but it is still not reaching the glasses-assisted 3D display which is less than a few percent [13,14]. Moreover, the viewing zone in a conventional autostereoscopy has not yet reached a satisfactory level, and extending the viewing zone is of paramount importance in autostereoscopy [15–17].
In comparison to lenticular and barrier based autostereoscopy with the schematic shown in Figs. 1(a) and 1(b), a directional backlight autostereoscopy (DB3D) has a fundamentally important advantage that is capable of separating the imaging source with the illumination source, as shown in Fig. 1. The display images of barrier and lenticular based system are originating from the same pixel with backlight, so shift of the images with the viewing position is necessary. But in directional backlight technology, the LCD and the backlight entity consisting of light emitting diode (LED) arrays are spatially separated, leaving a great deal of freedom to optimize LCD illumination. Even temporal synchronization of LCD and backlight is required as shown in Fig. 1(d), but it is not necessary to shift the images with different viewpoints. Left and right views share all the pixels of the image without affecting the color properties.
Fig. 1. Autostereoscopic displays with (a) Barrier, (b) Lenticular lens and (c) Directional backlight. (d) The relationship among the visual effect, LCD signal (displayed images) and LED backlight modulation signal in one frame of directional backlight.
Limited by small viewing volume as well as a number of display defects, a DB3D has not reached the level to satisfy the user’s experience. For example, the viewing zone (also named viewing area, viewing diamond, etc.) is a critical issue for autostereoscopy. However, this issue has not been systematically examined as there has been no well-defined terminology to describe this issue [18–24]. It is known that each lens has only one fixed focal length, therefore, a DB3D is supposed to have only one optimum viewing distance. The basic quality for the display, such as crosstalk, brightness uniformity, is in general not presented within and outside the viewing sweet point. As DB3D illumination is based on the pupil location, eye-tracking technology is commonly used for locating the viewer’s pupil position [22–24]. However, it is likely that there exists a recognition error of the pupil position with the eye tracking images, this uncertainty will give rise to possible deviated backlight illumination, resulting a brightness fluctuation, or high crosstalk, for the display. Overall, achieving a large viewing volume with continuous viewing zone, homogeneous illuminance and low crosstalk is important to high-quality glasses-free 3D display.
Various suggestions for super multi-view, and visual continuity [25–29], were proposed. Head-tracking, pupil integral imaging, infrared illumination [30–32] are commonly applied to assist pupil locating. In our previous researches, the key issues such as increased field of view and improvement of display quality are optimized with special designed optical configuration and component structures [33–37]. However, the problem to extend the continuous viewing area in a DB3D system needs to be tackled.
This work presents a systematic study to achieve substantially extended continuous viewing zone for autostereoscopy. The simulation of the optical system using ray tracing to analyse the relatedness between the LED backlight array and space illuminance. A 2 mm density super-dense viewpoint design is finished. The continuous and uniform visual effect are realized for both dynamic and static viewing. The low crosstalk and high luminance uniformity are flawlessly kept in hole viewing area, which is verified by the quantitative measurement result. In conjunction with eye tracking scenario, a DB3D system is proposed and demonstrated with sufficient viewing depth for desktop applications, while the low crosswalk and high uniformity are all retained.
2. Continuous viewing zone expansion
As an optical imaging system with LED backlight, lens and pupil of viewer, the location of the light source has to be adjusted based on the location of the viewer. For achieving continuous viewing zone expansion, a ray tracing model [38–41] is applied to guide the design strategy of staggered dense backlight.
2.1 Staggered dense LED backlight
The light source of the system is composed of an array of free-form dense backlight. Figure 2(a) is a brief schematic scheme to show the illuminating system. The Fresnel lens array includes a plurality of lens units, and the lens units are arranged as a concave surface with a definite curvature as shown in Fig. 2(a), which matches with the backlight of free-form to avoid the problem of large incident angle, forming a continuous viewing zone distribution in a viewing region to guarantee the viewing zone a visual effect of uniformity without any dark region [42]. In our system, the lens is contributed as a magnifying glass for the backlight. The density and continuity of backlight controllable units are related to the viewpoints. The non-overlap backlight as Ref. [35] cannot avoid visible luminance change while viewpoints switching.
Fig. 2. (a) Optical path sketch in a DB3D system. The 1-7 denote the 7 backlight units illuminating LCD relate to 7 units Fresnel lens array. (b) The flow chart of numerical simulation. (c) The LEDs overlap arranged in one backlight unit. (d) The experimental set-up of LEDs backlight and longitudinal linear diffuser film (LLDF). (e) The luminance distribution of backlight transmitted through the LLDF. (f) The illuminance contribution of LEDs are combined with a LLDF, and become a staggered dense distribution.
Figure 2(b) describes the flow chart to derive the trajectory of light emitted from each LED in the backlight unit. Fresnel lens structure, material refractive index, and LCD transmission are all taken into account. By simulating the propagation through the optical system, the trajectory and illuminance distribution can be obtained from each backlight entity to the pupil of the viewer.
The configuration modes of LEDs are shown in Fig. 2(c). Each backlight unit consist of 68 columns of LED. With a longitudinal linear diffuser film (LLDF) placed behind the Fresnel lens, the illuminance contributions of LEDs are combined to be a staggered dense backlight, as shown in Fig(e). For each viewing position, with a suitable LED density calculated by the simulation, each eye can receive the luminance contribution from 6 to 9 LEDs as illustrated in Fig. 2(f). It means that the adjustment of viewpoint only needs to change an edge LED which have a weak luminance contribution. For example, the LED “30” of Fig. 2(c) changes to “33”. Another advantage is the crosstalk and luminance uniformity can be optimized by the choice of LED combinations.
The next step to operate the backlight is to find the LED with strongest luminance contribution which is called as “switching on” LED. Surrounding the illumination center of “switching on” LED, the luminance volatility of the visual effect is relatively stable. The “switching on” LED of Fig. 2(c) are LED “30” and “39” for two eyes. Figure 3 shows the simulation results of “switching on” LED serial number in the viewing space from different backlight units based on ray trajectories. Simulation results only show the left half of the display because of the symmetry of the system. The LED serial number is indicated within a unique color shown in the right-hand side bar of the Figs. 3(a) to 3(d). The black circle crossed by horizontal and vertical black lines is the viewpoint at a specific location (0 mm, 900 mm).
Fig. 3. (a) The “switching on” LED serial number of unit 1. (b) The “switching on” LED serial number of unit 2. (c) The “switching on” LED serial number of unit 3. (d) The “switching on” LED serial number of unit 4. From (a) to (d), the color bars and numbers represent each “switching on” LED within a unique color and LED serial number, respectively. (e) The spatial coordinate system of calculation. The unit number is match to Fig. 2(a).
In practice, an error between the actual and the ideal position of backlight structure is inevitable, which is magnified by the lens. Therefore, the verification experiment of the actual “switching on” LED was performed. Only one column of LEDs is turned on at one time to compare the practical position with simulated position in the viewing space. A camera is placed in different positions from the LCD, and photos are taken to record the illuminance profile. Figure 4 shows the difference between simulation and experiment with the “switching on” LED of the backlight unit 3 and unit 1. The result clearly indicates that the simulated “switching on” LED are in good agreement with the experiment within 2 mm deviation.
Fig. 4. (a) The difference between simulation and experiment with the “switching on” LED of unit 3. (b) The difference between simulation and experiment with the “switching on” LED of unit 1. The blue line and the red circle represent the experimental and simulated results at 850 mm away from the display, respectively.
2.2 Super-dense viewpoint realization
However, the density is limited and the cost is expensive when we only improved the LED configuration. The interlaced combination of 7 units may further increase the density of viewpoint. As Fig. 3 shows the “switching on” LED number from each column of the backlight unit in the viewing volume, a “reversed” scenario to search an optimal illuminating configuration is applied to locate the “switching on” LED corresponding to the viewer in an optimal viewing location (OVL) in the viewing space. For the viewer at a location given by (x, y, z), the array of the “switching on” LED in each unit is re-traced as (N1, N2, … N7), where Ni describes the ith LED column number in each unit. For example, for the viewer at the viewing space at (0 mm, 0 mm, 850 mm), the column numbers are given by (35, 35, 35, 35, 35, 35, 35).
Accordingly, backlight design only needs to change one or two “switching on” LED to realize the adjustment of viewpoint, as (35, 35, 35, 35, 35, 35, 35) change to (36, 36, 35, 35, 35, 35, 35). The luminance variation can be control in 5%, which can optically eliminate viewpoint adjustment perception in our simulation result.
To verify the accuracy of numerical simulation and to demonstrate effective illumination with the LED array, the depth extension in the viewing zone has been verified. Here we adopt the simulation results at the depth 600 mm, 700 mm, 850 mm, and 1000 mm respectively from the LCD, as shown in the Fig. 5. The convergence of backlight combinations is given by unique colors. Each LED is set to emit 1 million rays which counted at different viewpoints for the convenience of numerical simulation. The final illuminance is normalized for the convenience of display.
Fig. 5. Simulating the illuminance trajectories emanating from different arrays of the “switching on” LED in each unit on the x-z plane. In the figure, (a) the OVL is (100 mm, 0 mm, 600 mm) from the display, and the LED column numbers are given by (11, 13, 16, 19, 22, 25, 29). (b) the OVL is (50 mm, 0 mm, 700 mm) from the display, and the LED column numbers are given by (22, 24, 25, 27, 29, 31, 33). (c) the OVL is (0 mm, 0 mm, 850 mm) from the display, and the LED column numbers are given by (35, 35, 35, 35, 35, 35, 35). (d) the OVL is (0 mm, 0 mm, 1000 mm) from the display, and the LED column numbers are given by (44, 42, 41, 40, 38, 37, 36). Fig. (a) to (d), the color bars represent the normalized illumination of 7 units backlight combinations. And from blue to red, the convergence is from low to high. The number represents the normalized illumination data compared with the initial emission rays. In addition, the center position of the display is (0 mm, 0 mm, 0 mm).
In this way, with a vast number of combinations of the LEDs from different arrays, the viewing distance can be extended from 600 mm, as shown in the Fig. 5(a) to beyond 1000 mm, as shown in the Fig. 5(d). It is hence possible to deliver the backlight LED illuminance to a viewpoint once the locations of the pupil are detected. At different viewing distances, the illuminance trajectory can be controlled to have a well-defined region along the viewing distance with well-separated transverse distribution, which is essential to achieve low crosstalk by avoiding the spatial overlap between left and right eyes.
2.3 Experimental verification of display effect
The extension of the viewing depth for autostereoscopy is experimentally achieved. It is obvious from the Fig. 5 that the viewing depth with each LED combination is limited, hence we have to adopt re-configuration scheme by changing the combination of LED column numbers for the backlight entities to achieve the expansion of depth range. To further confirm the advantages of our scheme, we characterize experimentally the display quality. Two important parameters, the brightness uniformity U and crosstalk rate ($CR$) [33,41], need to be considered. Two mathematical expressions are as follows:
where ${L_{\max }}$ and ${L_{\min }}$ stand for the maximum and minimum brightness on the screen, respectively. ${L_{CR}}$ is the brightness leaked from unintended channel, ${L_{MA}}$ is the brightness presented in the intended channel, ${L_{BA}}$ is the background brightness when all the display pixels are turned off.In the experiment, a camera is applied to record the uniformity of the entire screen at different viewing locations. The brightness distribution is then analyzed with a matlab software. In addition, spectroradiometer is used to measure the brightness directly. This allows to compare the effect of switching between different LED combinations so as to improve the screen uniformity and to minimize the crosstalk.
In this experiment, the illumination scheme is first optimized for a particular distance, for example, at 850 mm away from the LCD. Each column of the backlight units is independently controlled so that the crosstalk is below 3% and homogeneity is better than 90% based on experiments. However, away from 850 mm, the crosstalk increases dramatically and homogeneity deteriorates rapidly, as shown with the dashed black lines in the Fig. 6. To avoid this rapid deterioration, the backlight unit should be controlled in the way predicted by the data shown in the Fig. 3 to achieve an improved viewing distance. The experimental results shown in the Fig. 6 clearly indicate a substantial improvement with the viewpoint dependent backlight switching configuration, shown as the red solid lines in the Fig. 6. It is obvious that a viewer might easily move out of the optimal viewing area for a fixed LED illumination scheme, resulting in a small viewing area and rapidly increased crosstalk. The detailed crosstalk changed within different deviations at (75 mm, 0 mm, 850 mm) are listed in Table 1. These results clearly indicate the necessity and importance of adopting adaptive LED control configuration to achieve the viewing volume and the homogeneity necessary for autostereoscopy. Figure 7(a) shows the photo of the exterior of the 24-inch LCD autostereoscopic display.
Fig. 6. Comparison of the (a) crosstalk and (b) uniformity with optimized control to that without control at the z-axis position from the center of display. Comparison of the (c) crosstalk and (d) uniformity with optimized control to that without control at the x-axis position from the center of display. The black dotted lines represent the effect of the latter and the solid red lines represent the former case. See Visualization 1 and Visualization 2.
Fig. 7. (a) Photo of the exterior of the 24-inch LCD autostereoscopy. The display images viewed at 850 mm and 600 mm are shown in fig. (b) and (c), respectively.
Table 1. Crosstalk changed within different deviations at (75 mm, 0 mm, 850 mm).
Figures 7(b) and 7(c) show the display images viewed at 850 mm and 600 mm, respectively. Results show that the 3D image quality is preserved well, which proves that there is no significant visual difference when the human eye moves between 600 mm and 850 mm away from the display.
Based on the standards of ICDM [43], Fig. 8 shows the results of uniformity and crosstalk values from the experimental measurement. High quality glasses-free 3D with low crosstalk can be visualized in the longitudinal distance at 600 - 1000 mm from the LCD, and horizontal distance can be greater than is ± 270 mm sufficient for a desktop display and the viewing angle range is ± 16.70 degree, analogously. The high quality is manifested with a global crosstalk below 4%, and can reach a value of less than 3% in some areas. Additionally, the brightness uniformity can reach a level of greater than 75%, giving rise to a non-visible homogeneity variation over the entire screen.
Fig. 8. Test results of crosstalk (Left) and luminance uniformity (Right) of the autostereoscopic display in the viewing zone with dynamically configured backlight modular, z axis shows the central distance from the display, x is the center position of the face.
The detailed parameters are listed in Table 2.
Table 2. Configuration of experiments.
3. DB3D system realization with eye-tracking
Apart from the extended viewing volume, another key factor is the number of viewpoints within the viewing zone. Conventionally, all viewpoints should fall into the center of diamond-shaped viewing area, as described in Ref. [18,19]. In this configuration, however, the viewing area receives contributions from each of the 7 units, or entities, and by the combination of the backlight columns in each entity. In our system, the total number of columns is 68 in each of the 7 units as shown in Fig. 2(c), and there are usually 6 to 9 columns lumped together for homogeneous illumination over the entire screen for one eye. The number of lumped columns to produce a gap between the left and right eyes is 2 to 3. Once the pupil location is probed, the corresponding columns of the LED array should be turned on, based on the data set shown in the Figs. 3 and 4. With this scheme, viewing points at any position can be illuminated with an optimized scenario, which provides a seamless viewing volume that every viewpoint is perfectly illuminated to achieve a desirable homogeneity and low crosstalk. Considering a 2 mm accuracy to locate the pupil of the viewers within the viewing zone, a seamless autostereoscopic display can be visualized.
The same optimized illumination scheme can be extended to other viewing distances. As shown in the Fig. 8, the viewing distance can be extended from less than 600 mm up to over 1000 mm, compared with a viewing distance less than 100 mm with a fixed illumination scheme. Hence the dynamically configured illumination will greatly extend the viewing volume longitudinally, within which the seamless viewing is realized.
It should be mentioned that the configured backlight illumination scheme has to be dynamically adjusted in real time to follow the viewer’s movement, intentionally [44] or non-intentionally. Figure 9 shows the principle of real-time adjustment of viewing zone. In high-speed eye tracking mode (120 Hz), there is an uncertainty to determine the locations of the pupil, as shown in Fig. 9. However, within a certain range of deviation, the display effect can still maintain consistency and luminance uniformity, that is, when the location of human eyes in real-time single frame test is lower than the maximum allowable error, the smooth switching of the viewing zone is realized. The specific implementation of the viewing zone switching scheme is as follows: the pupil position recognized by the eye tracking software will also be changed with the viewer moves. It is the second time the difference between the pupil position tested and the previous position switched exceeds the uncertainty of identification, the viewing zone will be switched.
Fig. 9. The principle of real-time adjustment of viewing zone when the viewer moves. Horizontal axis is the frames of camera used in the eye tracking, and vertical axis shows the pupil x-axis position from the center of display. Red boxes represent different viewing zones. We set the adjustment criterion of viewing zone to ± 4 mm in the viewing space as best design.
It should be mentioned that, there is an uncertainty to determine the locations of the pupil and this uncertainty can set a limit on the ultimate accuracy for eye tracking. Thus, an experiment to test the uncertainty has been conducted. In the experiment, the location of the pupil is recorded by an eye-tracking program when a viewer keeps still for a long time. As shown in the Fig. 10, the uncertainty of eye tracking is ± 2 mm in the viewing space. A higher number of pixel cameras are then advised for eye tracking. The use of eye-tracking in dense viewing zone and our other work on motion prediction [44] to realize the low latency and high accuracy of eye tracking. With the suitable eye-tacking, we finally drive the continuous viewing zone in the DB3D system.
Fig. 10. Pupil position measured by eye tracking software when a viewer keeps still for a long time at (75 mm, 0 mm, 850 mm) away from display. Among of them horizontal axis is frames, and vertical axis is defined as pupil x-axis position from the center of display.
4. Conclusion
A numerical simulation model using ray tracing for a DB3D is proposed and demonstrated. Based on that, we design staggered dense LED backlight and its mode of operation. The simulation is shown to be in good agreement with experimental results.
Extended continuous viewing range is obtained for glasses-free display with dynamically configured backlight switching on configuration which by only changing one or two “switching on” LED to realize the adjustment of viewpoint. The eye tracking accuracy is controlled in ± 4 mm in the viewing space, and the image quality such as crosstalk changed within this deviation is 0.28%. Accordingly, continuous viewing volume and pupils are perfectly matched, hence providing the basis for comfortable viewing. The experimental setup and control scenario are found to be highly effective to obtain a homogeneous and seamless viewing experience for desktop autostereoscopy. The technique will be applicable to various autostereoscopic displays in general.
Funding
Research and Development Plan in Key Areas of Guangdong Province (2019B010152001); National Natural Science Foundation of China (11534017, 61991452); Guangzhou Science and Technology Project (201805010004).
Disclosures
The authors declare no conflicts of interest.
References
1. N. A. Dodgson, “3D without the glasses,” Nature 495(7441), 316–317 (2013). [CrossRef]
2. P. Ferroli, G. Tringali, F. Acerbi, M. Schiariti, M. Broggi, D. Aquino, and G. Broggi, “Advanced 3-dimensional planning in neurosurgery,” Neurosurg. 72(suppl_1), A54–A62 (2013). [CrossRef]
3. N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast. 57(2), 362–371 (2011). [CrossRef]
4. N. A. Dodgson, “Autostereoscopic 3D displays,” Comput. 38(8), 31–36 (2005). [CrossRef]
5. G. Borjigjn and H. Kakeya, “An autostereoscopic display with time-multiplexed directional backlight using a decentered lens array,” in Digital Holography and Three-Dimensional Imaging 2019, OSA Technical Digest (Optical Society of America, 2019), paper W2A.2.
6. C. Y. Chen, T. Y. Hsieh, Q. L. Deng, W. C. Su, and Z. S. Cheng, “Design of a novel symmetric microprism array for dual-view display,” Displays 31(2), 99–103 (2010). [CrossRef]
7. W. X. Zhao, Q. H. Wang, A. H. Wang, and D. H. Li, “Autostereoscopic display based on two-layer lenticular lenses,” Opt. Lett. 35(24), 4127–4129 (2010). [CrossRef]
8. J. H. Lee, Y. H. Ho, K. Y. Chen, H. Y. Lin, J. H. Fang, S. C. Hsu, J. R. Lin, and M. K. Wei, “Efficiency improvement and image quality of organic light-emitting display by attaching cylindrical microlens arrays,” Opt. Express 16(26), 21184–21190 (2008). [CrossRef]
9. G. J. Lv, W. X. Zhao, D. H. Li, and Q. H. Wang, “Polarizer Parallax Barrier 3D Display with High Brightness, Resolution and Low Crosstalk,” J. Disp. Technol. 10(2), 120–124 (2014). [CrossRef]
10. G. J. Lv, Q. H. Wang, W. X. Zhao, and J. Wang, “3D display based on parallax barrier with Multiview zones,” Appl. Opt. 53(7), 1339–1342 (2014). [CrossRef]
11. C. H. Chen, Y. P. Huang, S. C. Chuang, C. L. Wu, H. P. Shieh, W. Mphepö, C. T. Hsieh, and S. C. Hsu, “Liquid crystal panel for high efficiency barrier type autostereoscopic three-dimensional displays,” Appl. Opt. 48(18), 3446–3454 (2009). [CrossRef]
12. H. Yamamoto, M. Kouno, S. Muguruma, Y. Hayasaki, Y. Nagai, Y. Shimizu, and N. Nishida, “Enlargement of viewing area of stereoscopic full-color LED display by use of a parallax barrier,” Appl. Opt. 41(32), 6907–6919 (2002). [CrossRef]
13. E. Lueder, “3D Displays,”, (John Wiley & Sons, Ltd, 2012).
14. S. K. Kim, K. H. Yoon, S. K. Yoon, and H. Ju, “Parallax barrier engineering for image quality improvement in an autostereoscopic 3D display,” Opt. Express 23(10), 13230–13244 (2015). [CrossRef]
15. J. H. Lee, J. Park, D. Nam, S. Y. Choi, D. S. Park, and C. Y. Kim, “Optimal projector configuration design for 300-Mpixel multi-projection 3D display,” Opt. Express 21(22), 26820–26835 (2013). [CrossRef]
16. B. Kim, M. Choi, H. Kim, J. Lim, and S. Kang, “Elimination of flux loss by optimizing the groove angle in modified Fresnel lens to increase illuminance uniformity, color uniformity and flux efficiency in LED illumination,” Opt. Express 17(20), 17916–17927 (2009). [CrossRef]
17. T. Huang, B. Han, X. Zhang, and H. Liao, “High-performance autostereoscopic display based on the lenticular tracking method,” Opt. Express 27(15), 20421–20434 (2019). [CrossRef]
18. N. A. Dodgson, “Analysis of the viewing zone of the Cambridge autostereoscopic display,” Appl. Opt. 35(10), 1705–1710 (1996). [CrossRef]
19. N. A. Dodgson, “Analysis of the viewing zone of multi-view autostereoscopic displays,” Proc. SPIE 4660, 254–265 (2002). [CrossRef]
20. A. Yuuki, S. Uehara, K. Taira, G. Hamagishi, K. Izumi, T. Nomura, K. Mashitani, A. Miyazawa, T. Koike, T. Horikoshi, and H. Ujike, “Viewing Zones of Autostereoscopic Displays and their Measurement Methods,” Proc. 15th IDW, 1111–1114 (2008).
21. A. Yuuki, S. Uehara, K. Taira, G. Hamagishi, K. Izumi, T. Nomura, K. Mashitani, A. Miyazawa, T. Koike, T. Horikoshi, S. Miyazaki, N. Watanabe, Y. Hisatake, and H. Ujike, “Influence of 3-D cross-talk on qualified viewing spaces in two- and multi-view autostereoscopic displays,” J. Soc. Inf. Disp. 18(7), 483–493 (2010). [CrossRef]
22. X. Li, Q. Wu, B. Xiao, X. Liu, C. Xu, X. Li, B. Xu, and Y. Wang, “High-speed and robust infrared-guiding multiuser eye localization system for autostereoscopic display,” Appl. Opt. 59(14), 4199–4208 (2020). [CrossRef]
23. Z. F. Zhuang, L. Zhang, P. Surman, W. T. Song, S. Thibault, X. W. Sun, and Y. J. Zheng, “Addressable spatial light modulators for eye-tracking autostereoscopic three-dimensional display using a scanning laser,” Appl. Opt. 57(16), 4457–4466 (2018). [CrossRef]
24. B. Huang, R. W. Chen, Q. B. Zhou, and W. Xu, “Eye landmarks detection via weakly supervised learning,” Pattern Recogn. 98, 107076 (2020). [CrossRef]
25. Y. Takaki and N. Nago, “Multi-projection of lenticular displays to construct a 256-view super multi-view display,” Opt. Express 18(9), 8824–8835 (2010). [CrossRef]
26. G. Park, J. H. Jung, K. Hong, Y. Kim, Y. H. Kim, S. W. Min, and B. Lee, “Multi-viewer tracking integral imaging system and its viewing zone analysis,” Opt. Express 17(20), 17895–17908 (2009). [CrossRef]
27. L. Seok, P. Juyoung, H. Jingu, K. Byongmin, K. Dongwoo, H. Hyoseok, L. Jinho, C. Yoonsun, C. Kyuhwan, and N. Dongkyung, “Autostereoscopic 3D display using directional subpixel rendering,” Opt. Express 26(16), 20233–20247 (2018). [CrossRef]
28. L. Yang, X. Sang, X. Yu, B. Liu, B. Yan, K. Wang, and C. Yu, “A crosstalk-suppressed dense multi-view light-field display based on real-time light-field pickup and reconstruction,” Opt. Express 26(26), 34412–34427 (2018). [CrossRef]
29. M. K. Kang, H. P. Nguyen, D. Kang, S. G. Park, and S. K. Kim, “Adaptive viewing distance in super multi-view displays using aperiodic 3-D pixel location and dynamic view indices,” Opt. Express 26(16), 20661–20679 (2018). [CrossRef]
30. K. H. Yoon, M. K. Kang, H. Lee, and S. K. Kim, “Autostereoscopic 3D display system with dynamic fusion of the viewing zone under eye tracking: principles, setup, and evaluation,” Appl. Opt. 57(1), A101–A117 (2018). [CrossRef]
31. N. A. Dodgson, “On the number of views required for head-tracked autostereoscopic display,” Proc. SPIE 6055, 60550Q (2006). [CrossRef]
32. P. Surman, I. Sexton, K. Hopf, R. Bates, and W. Lee, “Head tracked 3D displays,” Springer LNCS 4105, 769–776 (2006).
33. H. Fan, X. Wang, S. Liang, K. Li, R. Jian, Y. Zhou, J. Wang, and J. Zhou, “Quantitative measurement of global crosstalk for 3D display,” J. Soc. Inf. Disp. 24(5), 323–329 (2016). [CrossRef]
34. J. Wang, H. Liang, H. Fan, Y. Zhou, P. Krebs, J. Su, Y. Deng, and J. Zhou, “High-quality autostereoscopic display with spatial and sequential hybrid control,” Appl. Opt. 52(35), 8549–8553 (2013). [CrossRef]
35. H. Fan, Y. Zhou, J. Wang, H. Liang, P. Krebs, J. Su, D. Lin, K. Li, and J. Zhou, “Full Resolution, Low Crosstalk, and Wide Viewing Angle Auto-Stereoscopic Display with a Hybrid Spatial-Temporal Control Using Free-Form Surface Backlight Unit,” J. Display Technol. 11(7), 620–624 (2015). [CrossRef]
36. Y. Zhou, P. Krebs, H. Fan, H. Liang, J. Su, J. Wang, and J. Zhou, “Quantitative measurement and control of optical Moiré pattern in an autostereoscopic liquid crystal display system,” Appl. Opt. 54(6), 1521–1527 (2015). [CrossRef]
37. P. Krebs, H. Liang, H. Fan, A. Zhang, Y. Zhou, and J. Chen, “Homogeneous free-form directional backlight for 3d display,” Opt. Commun. 397, 112–117 (2017). [CrossRef]
38. Y. Chang, L. Tang, and C. Yin, “Efficient simulation of intensity profile of light through subpixel-matched lenticular lens array for auto-stereoscopic liquid crystal,” Appl. Opt. 52(1), A356–359 (2013). [CrossRef]
39. S. M. Jung, H. Kang, B. Y. Lee, and I. B. Kang, “Numerical Simulation of the Displayed Image on the Entire Screen of Autostereoscopic Displays,” Opt. Express 23(6), 7842–7855 (2015). [CrossRef]
40. H. Liang, S. An, J. Wang, Y. Zhou, H. Fan, P. Krebs, and J. Zhou, “Optimizing time-multiplexing auto-stereoscopic displays with a genetic algorithm,” J. Disp. Technol. 10(8), 695–699 (2014). [CrossRef]
41. J. He, Q. Zhang, J. Wang, J. Zhou, and H. Liang, “Investigation on quantitative uniformity evaluation for directional backlight auto-stereoscopic displays,” Opt. Express 26(8), 9398–9408 (2018). [CrossRef]
42. Y. Zhou, J. Zhou, H. Fan, K. Li, H. Chen, and Y. Xu, “Directional backlight stereoscopic display device,” U.S. Patent, 9,946,087[P]. (2018).
43. J. M. J. C. D. G. L. R. R. Ed Kelley and J. Miseli, “Information display measurements standard,” SID Definitions and Standards Committee, ICDM, 1475 S. Bascom Ave., Ste. 114, Campbell, CA 95008-4006., version 1.03 Edition (June 2012).
44. H. Zhang, M. Chen, X. Li, K. Li, X. Chen, J. Wang, H. Liang, J. Zhou, W. Liang, H. Fan, R. Ding, S. Wang, and D. Deng, “Overcoming latency with motion prediction in directional autostereoscopic displays,” J. Soc. Inf. Disp. 28(3), 252–261 (2020). [CrossRef]
