Large-scale autostereoscopic three-dimensional (3D) light-emitting-diode (LED) displays can provide high-quality, even immersive, visual experiences. However, the unique structural characteristics of the LED display panel can enhance moiré effects during parallax generation. We present a novel method for quantitatively characterizing the moiré effect in autostereoscopic 3D-LED displays using a model applying geometrical ray tracing and a brightness distribution stack. An optical diffuser (OD) device for moiré reduction and performance balance is designed and the influence of several key device parameters on moiré pattern features are examined in autostereoscopic 3D-LED displays for the first time. Using the obtained optimal parameters, we assembled an ultra-large moiré-less autostereoscopic 3D-LED display prototype, which was experimentally shown to be capable of reducing moiré fringes without noticeable increase in crosstalk or significant reduction in visual quality. Finally, the effects on the moiré and crosstalk effect of altering key influencing factors were examined.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The finding that binocular visual information occupies approximately 50% of the processing capacity of the human brain  suggests that display systems should evolve toward real-world visual reproduction. As an important step toward this goal, three-dimensional (3D) displays are being increasingly used in various applications [2–4]. Autostereoscopic 3D displays based on binocular disparity are currently the most popular and successfully commercialized 3D display technology and represent the most fruitful avenue toward overcoming some existing shortcomings in such systems [5,6]. Parallax barriers (PBs) and lenticular sheets are widely used in systems that apply binocular disparity to separate left- and right-eye parallax images and reproduce 3D depth perception [7–10]. PBs are technologically mature and cheaper than alternatives and, more importantly, can be easily adapted for experimental use in autostereoscopic 3D-LED displays [11,12]. PB-based autostereoscopic light-emitting diode (LED) displays have singularly good characteristics in terms of high brightness, large visible areas, and simple assembly and disassembly capability that allow for outdoor 3D displays with striking visual properties . However, current PB systems have several problems that require further research , including a susceptibility to the moiré effect, which reduces visual contrast and diminishes 3D visual quality. This effect is commonly caused by interference between light rays passing through two or more periodic layers or repeating structures and was previously exhibited in cathode ray tube (CRT) displays . In autostereoscopic 3D-LED displays, the highly periodic nature of the 2D-LED display panel and one-dimensional PB plate are the primary cause of the appearance of moiré patterns.
Computer simulation can be used to emulate the visual effects of moiré phenomena to aid in the evaluation of the moiré effect in advance. One analytical method for reproducing moiré patterns is based on Fourier transformation, which is applied to model visual perception using a visibility circle in the spectral domain . Other analytical methods for simulating moiré phenomena involve the application of contrast sensitivity function computation to spatial frequencies and human visual response thresholds in autostereoscopic displays . Most moiré-related research has focused on eliminating or at least reducing the moiré effect to achieve moiré-less (reduced-moiré) or moiré-free designs in autostereoscopic displays . Some representative methods concentrate on the optimization of key factors such as the relative angle or gap between periodic layers or repeating structures, the viewing position, or combinations of these. For instance, the simplest method for eliminating horizontal periodic patterns from a color filter is to rotate the display panel by 90° . More accurate extremum angles for moiré minimization in a manner independent of scanning period have been analytically discovered by approximating 3-D displays as four superimposed sine gratings . For a given 3D integral imaging system, the optimal lens array tilt angle for reducing the moiré effect can be found by applying a spatial Fourier transformation [21,22]. Depending on the system, it has been demonstrated that either a non-rational or a rational angle can effectively alleviate the moiré pattern [23,24]. Recent studies have also reported that the amplitude, period and orientation of the moiré patterns in barrier 3D displays can be measured as functions of angle across a wide angular range to within small increments . Other methods involve using optical devices to temporarily or permanently break periodic or repeating structures. For instance, a combination of one or two lenticular lens arrays can be inserted into the front surface of the rear panel of a two-layered 3D display to achieve moiré reduction while suppressing deterioration of the picture quality in the rear liquid crystal panel . Parallax-generation devices with varying periods and slant angles have also been assessed in terms of their abilities to minimize moiré patterns in autostereoscopic displays . Optical low-pass filters, including diffusers and defocusers, have been used for moiré fringe reduction in integral 3D imaging. In such systems, the image on the diffuser’s surface is treated as an integral convolution of the displayed image and its diffusing characteristics . A lenticular diffuser with the appropriate characteristics can also reduce moiré effects in contact-type multi-view 3D imaging systems without significant sacrifice of image quality [29,30].
To the best of our knowledge, neither moiré analysis nor reduction have been studied in the context of autostereoscopic 3D-LED displays. The unique structural characteristics of LED display panels can result in a more serious moiré effect during parallax generation, which makes existing research results not directly applicable and motivates this study. This paper presents a novel quantitative method for removing the moiré effect in autostereoscopic 3D-LED displays through the application of geometrical ray-tracing and a brightness distribution stack. Using this method, an optical diffuser (OD) device for moiré reduction and performance balance was designed. Following a detailed assessment of the key OD device factors influencing moiré pattern suppression, the proposed method was demonstrated through the construction of an experimental prototype of large-scale and moiré-less autostereoscopic 3D-LED display.
2. Quantitative characterization of moiré effect in autostereoscopic 3D-LED displays
The structural characteristics of 2D-LED display panels are quite different from those of other displays in that the emitting pixel sizes and non-emitting areas are both significantly larger. Accordingly, the non-emitting area should be taken into account in conducting moiré analysis. In our study, we looked at a one-dimensional PB that displays repeated parallel lines in which the periodic structures are similar to those of the black matrix in the non-emitting region of a 2D-LED panel. Figure 1(a) shows the light propagation pattern in a PB-based autostereoscopic 3D-LED display. Taking the optimum viewing position of the left eye as an example, the parameters defining light propagation between the 2D-LED panel and the PB can be expressed using geometrical ray tracing as the following formula:Table 1.
Assuming that the zero-order grating slit of the PB is located at the interocular centerline, as shown in Fig. 1(a), the grating slits along the + y-axis direction should be sequentially defined as first-order, second-order, …, m-order, respectively. Using geometrical ray tracing, the rays that emit from the 2D-LED panel and propagate through the lower edges of the m-th and zero-order grating slits are taken into account, which are drawn in red lines in Fig. 1(b) and 1(c). As shown in Fig. 1(b), the y-coordinate distance on the 2D-LED panel will be when observed from the optimum viewing position. If the viewing position deviates to L1, shown in Fig. 1(c), the distance changes to . The difference between the two distances is then given by
From Eq. (2) it can be shown that Δ1 has a linear relationship to m, the order number of the grating slit, indicating that both the visible position and area of the 2D-LED panel will change with viewing position.
At the optimal viewing position, the observer’s left eye will only see the pixel columns of the left-eye image on the 2D-LED display panel through the grating slit. The actual visible area includes a complete column of LED emitting pixels and its corresponding non-emitting area, indicated as the red-colored area in Fig. 1(a). The visible width when viewing through a single grating slit is given by . Although the moiré effect cannot be observed when the LED pixels have a uniform brightness output, the visible area will change with the viewing position. The green region in Fig. 1(a) shows the actual area visible from a viewing position at a distance of L1. Following a similar calculation, the visible width at this position is found to be . Again, the difference between the two visible widths is obtained as
The coordinate origin of the Cartesian coordinate system shown in Fig. 1 is at the intersection of the 2D-LED panel and the interocular centerline. As the y- and z-axes respectively conform and run perpendicular to the 2D-LED display panel, the coordinates of the left eye and the lower and upper edges of the m-th order grating slit are given by (L,-Q/2), (D, mPp-Pe/2), and (D, mPp + Pe/2), respectively. The equation of the straight line passing through (L,-Q/2) and (D, mPp-Pe/2) can then be written as
Along the line corresponding to z = 0 in Eq. (4), the y-values correspond to positions on the 2D-LED panel, and rays from these positions will propagate through the lower edge of the grating slit to the left eye. The position on the 2D-LED display panel corresponding to the lower edge of the m-th grating slit is then given by
To summarize, the visible luminous area/width on an 2D-LED display panel can be calculated from the spacing area between positions yl and yu on the panel. Note that, although this area will inevitably contain LED emitting and non-emitting areas, the visible emitting areas will no longer constitute complete columns of LED emitting pixels. Accordingly, the moiré effect can be quantitatively evaluated as a function of the visible brightness obtained from the combination of emitting and non-emitting areas.
3. Moiré suppression in autostereoscopic 3D-LED displays
Based on the moiré effect pattern derived from the brightness distribution, an OD device—a short-pass optical filter—is designed to suppress the moiré pattern. Although previous studies have shown that OD devices can reduce the moiré effect without sacrificing visual quality [29,31], such devices have never been assessed in conjunction with autostereoscopic 3D-LED displays, and their key influencing parameters have not been analytically examined. The diffusing performance of an OD device is generally determined by the particle size of the diffusion agent, the relative refractive index between the particles and the substrate, and, most importantly, the clearance distance between the device and the object. Because the relative refractive index is always limited by the material properties of the OD, it is not easy to optimize. However, the other two factors are flexible, particularly for the purposes of experimental verification.
Figure 2 shows a top-view schematic of moiré suppression using an OD device superimposed in front of an autostereoscopic 3D-LED display. The parameter and coordinate settings are the same as those listed in Table 1. Here, the distance between the 2D-LED panel and the OD device is defined as D’, the total number of LED columns is defined as nLED, and the total number of PB slits is defined as mPB. The first LED column above the origin is numbered nLED/2, which is shown in Fig. 2. And the position of the n-th LED column above it is given by
The spatial luminous intensity of a single LED satisfying the Lambertian radiation condition can be expressed as
The luminous direction and intensity of the n-th LED column with respect to the y-axis coordinate position on the OD device yD are expressed respectively as
The luminous intensity produced by the OD at φ, the angle between the incident and emergent rays at position yD, is then given by
Based on the linear propagation properties of light, only a certain region on the OD device can be observed through the upper and lower edges of this slit. The lower and upper edges of this visible area are defined respectively as the y-axis coordinates yl_D(m) and yu_D(m):
The angle between the light emitting and normal directions of the OD device is then
Finally, the total visible brightness distribution through the m-th grating slit is given byEqs. (11) and (16) into Eq. (17) using a pre-determined D'. Equation (17) calculates the visible brightness distribution from each grating slit in the PB-based autostereoscopic LED displays; in other words, it represents a brightness distribution image that comprises a stack of brightness distribution information from the first to the m-th grating slits. Using this brightness distribution image information, the moiré effect can be quantitatively simulated and evaluated.
4. Simulation results
4.1 Key factors influencing the moiré effect
The main parameters used in the simulation and experimental verification are listed in Table 2. Using the scattering theory of Mie , an OD device with an infinitesimal thickness and fabricated from a substrate material of polyethylene terephthalate was simulated. The simulated scattering particles, which were composed of commercially available polymethyl methacrylate, were given a variety of particle diameters and assumed to evenly disperse into the substrate. Figure 3 shows the normalized diffusion function curves for average particle sizes of 20, 25, 30, 35, and 40 μm. It is seen that the diffusing abilities at different average sizes are quite distinct even though the same collimated light is used as an incident source. The wavelength of the incident source is 550 nm. The diffusion angle on full width at half maximum (FWHM) becomes narrower as the particle size increases, corresponding to a weakening diffusing ability as the particle size is increased.
The particle size of the simulated OD device was varied from 20 to 30 and then to 40 μm with D' fixed at 100 mm and the resulting brightness distributions at specific viewing positions were calculated using MATLAB. Figure 4(a) shows the simulated brightness distributions as imaged through different grating slits and observed by the human eye, with vertical moiré fringes apparent in each case. The simulated fringes match the periodic structures of the 2D-LED panel and the PB plate, confirming that they are caused by the moiré effect analyzed in the preceding section. The brightness ratios between bright and dark fringes are indicated by the brightness fluctuation curves in Fig. 4(b). At a particle size of 20 μm, the brightness ratio is particularly low, with the central brightnesses of the dark fringes reaching more than 95% of the brightnesses of the bright fringes, resulting in a uniform brightness distribution and a much less pronounced moiré effect. The fringes become more obvious at an average particle size of 30 μm, where the brightness ratio between the central dark and bright fringes drops to 61%; this ratio decreases to 43% at a particle size of 40 μm. An overall pattern is seen in which the relative brightness of the dark fringes gradually decreases with the particle size, resulting in more conspicuous moiré fringes. This suggests that an OD device with a particle size between 25 and 30 μm can reasonably achieve a moiré-less design for an autostereoscopic 3D-LED display.
Another influencing factor is the insertion position of the OD device, which can be defined as the clearance distance D' between the OD device and the 2D-LED display panel. In the simulation model, this distance was set to 60, 100, and 140 mm with the particle size set to 25 μm. Figure 5 shows the brightness distribution and corresponding fluctuation curve for the moiré effect obtained in each case. At D' = 60 mm, the central brightnesses of the dark fringes reach only 42% of the brightnesses of the bright fringes, although a moiré fringe pattern is still clearly observed. At 100 and 140 mm, the brightness ratios increase significantly to 76 and 92%, respectively. These results show that the brightness of the dark fringes gradually increases with the distance between the OD and the 2D-LED panel, resulting in increasing blurring of the moiré fringes; thus, selecting an appropriate clearance distance can effectively suppress the appearance of moiré fringes on the 3D image. Based on the results above, it was determined that a clearance distance approaching 140 mm was most conducive to eliminating the moiré effect in the autostereoscopic 3D-LED display.
4.2 Crosstalk effect simulation results
Although diffusers can be effective in reducing the moiré effect, in most cases they will induce an increased crosstalk effect. It is therefore necessary to determine how the corrective factors discussed above affect the crosstalk levels in the application of an autostereoscopic 3D-LED display. Crosstalk was simulated by using TracePro and represented by the illuminance distribution on a virtual receiving screen. The left- and right-eye illuminance distributions were then obtained by sequentially tracing the corresponding LED-pixel columns.
Figure 6 shows the simulated crosstalk effect for OD devices characterized by differing particle sizes. The illuminance distributions along a horizontal line perceived by left- and right-eye views are represented as solid and dashed curves, respectively. To clearly show the difference between Figs. 6(a)–6(c), gray dotted lines are drawn to represent the average illuminance levels, which are also listed in Table 3. The illuminance fluctuation gradually becomes obvious under the effect of particle size, which will lead to crosstalk change in this system. The crosstalk was evaluated as the ratio of the cross-sectional area to the total areas under the solid and dashed curves [33–35]. In Fig. 6, a certain cross-sectional area has been highlighted in red slant lines, while the corresponding total areas are filled with both red and black slant lines. The cross-sectional area represents the integral sum of the illuminance from the adjacent viewpoints that can be seen in the designated area and cause crosstalk. From both Fig. 6 and Table 3, it can be seen that the crosstalk effect is reduced from 28.76% to 21.23% as the particle size increases from 20 μm to 40 μm. Although the crosstalk value would vary with individual difference and be limited by the moiré level, it has been demonstrated that the crosstalk level can be effectively adjusted with an OD device.
In a similar manner, Fig. 7 shows the crosstalk effect as a function of clearance distance (60, 100, and 140 mm) at an OD device particle size of 25 μm. Table 4 lists the crosstalk level and the average gaps between the maximum and the minimum illuminance. As the clearance distance increases, the cross-sectional areas of the solid and dashed curves occupy a larger proportion of the total area, corresponding to a more serious crosstalk effect. It can be concluded that the crosstalk becomes more serious from 20.41% to 28.31% as the clearance distance increases from 60 mm to 140 mm, with an effect on the moiré pattern that is greater than that on the crosstalk level. These simulation results showing how OD device parameter tuning can be used to optimize moiré and crosstalk performance in an autostereoscopic 3D-LED display were subsequently verified using an experimental prototype, as discussed in the following section.
5. Prototype verification
To validate the simulation results, an ultra-large autostereoscopic 3D-LED display prototype was fabricated. In this section, we discuss the assembly of the LED panel, the fabrication of the large-scale PB and OD device, and the final measurement results.
5.1 Assembly of 2D-LED display panel
Two main LED arrangements are commonly used in 2D-LED display panels. The first is illustrated in Fig. 8(a), which shows a schematic of a triangular structure in which red, green, and blue sub-pixels are positioned at three separate vertexes. The second arrangement is the parallel structure shown in Fig. 8(b). Using the triangular structure in autostereoscopic 3D-LED displays requires a relatively large aperture ratio, resulting in a narrower viewing range and a more serious crosstalk effect. The parallel structure can expand the viewing range while reducing crosstalk and is therefore more suitable for use in autostereoscopic 3D-LED displays. Figures 8(c) and 8(d) show a single LED module and corresponding LED chip imaged using a metallurgical microscope (LV-150N, Nikon). Each LED chip comprises a group of red/green/blue sub-pixels connected by common positive and negative poles. As shown in Fig. 8(e), the LED modules are stitched side-by-side to assemble an ultra-large LED display panel with a visible size of 4,000 mm × 2,300 mm.
5.2 Fabrication of large-area PB and OD device
Ultra-large PB and OD devices were initially fabricated in small rectangular pieces and then stitched into larger-sized assemblies. The OD device was fabricated using injection molding technology with the particle size set based on the simulation results. The one-dimensional PB patterns were prepared using screen printing technology and then bonded onto a glass substrate to achieve large-area stitching. The screen printing technology-based preparation process (Fig. 9) is summarized as follows: (a) a high-stability precision composite screen plate and an ink scraper are installed above a screen printing machine (ATMACE1014, Taiwan); (b) a glass substrate is fixed into a proper position for printing; (c) printing ink (LPR-805, black) is dispersed evenly onto the screen plate; (d) a PB pattern array is printed onto the glass substrate and then allowed to stand for 1 min to enable a specific deformation of the ink; and finally (e) the pattern is cured under a 365 nm UV lamp for 20 min. The final printed pattern is shown in Fig. 9(f).
5.3 Experimental results
The primary parameters used to develop the prototype and the measured results are listed in Table 5. Although the brightness, uniformity, and crosstalk levels could be directly measured, the appearance of the moiré fringes was largely dependent on observation of images by the human eye, particularly with the viewing distance or angle varied. To objectively evaluate the moiré effect, the measuring system shown in Fig. 10(f) was fixed at a specific viewing distance and angle to represent the human-eye observation. It is noted that the moiré effect could not be quantitatively measured by this measuring system that will be updated in our future work.
Figures 10(a) and 10(b) show images produced by the autostereoscopic 3D-LED display prototype without and with the OD device, respectively. The viewing distance, 4,000 mm, deviates from the design optimal distance, and it is seen that moiré fringes occupy the entire display region in the absence of an OD device but are significantly reduced when the specially designed OD device is inserted (Fig. 10(b)). The average width of the dark fringes is also reduced when the OD device is used. It is also seen that image uniformity is significantly improved by the OD device. Overly bright 3D image regions can be observed without the OD device due to the “point-source” LED chips. However, after the OD device is applied, the light will be scattered and evenly distributed, so that the image uniformity can be improved. Although the brightness decrease can be observed with the OD device, it could be overcome by improving the 2D-LED panel (light source) or using lenticular sheets as an alternative [36,37]. As shown in Figs. 10(d) and 10(e), the 3D visual effect is further improved when the viewing distance is set to 5,000 mm, the theoretically optimum value. At this distance, the moiré fringes are nearly eliminated under both bright environment (> 2,000 lux) and dark environment (< 0.2 lux). The remaining moiré fringes could be further reduced by using a slanted PB device or setting a non-rational or rational angle between the PB device and the 2D-LED display panel. These experimental results demonstrate that the moiré effect can be effectively eliminated while achieving favorable 3D visual quality and measurable crosstalk.
6. Analysis and discussion
In the simulation results, vertically aligned moiré fringes occurred as a result of the periodicity of the PB and the non-emitting black matrix between adjacent LEDs. By contrast, the actual 3D images shown in Fig. 10 feature irregular curved or inclined moiré fringes. In the prototype assembly, the LED panels and grating slits were not ideally parallel and the surface roughness was not quite perfect. This potentially caused the LED columns to deviate from their ideal positions when observed through the grating slit, resulting in irregular moiré fringes.
The simulated and experimental results both produced moiré-less image outputs and measurable crosstalk levels at a particle size of 25 μm and a clearance distance of 135 mm. To gain a better understanding of how performance changes as a function of key influencing parameter values, the particle size and clearance distance were varied from 25 to 40 μm and from 30 to 192 mm via simulation, respectively. The changes in how the moiré effect was regulated as a result of this calibration are shown Fig. 11. It is seen that the brightness curves of the dark fringes increase with clearance distance. Because reducing the dark-fringe brightness increases the brightness difference between bright and dark fringes, this results in an enhanced moiré effect. However, the dark-fringe brightness becomes saturated at a clearance distance greater than 140 mm, after which changes in clearance distance do not lead to obvious changes in the visibility of the moiré fringes. By contrast, the diffusion agent particle size has less impact on the moiré effect, and varying the particle size from 25 to 40 μm produces a maximum change dark-fringe brightness of only 29%. It is apparent that reducing the particle diameter of the diffusion agent can, to a certain extent, reduce the visibility of moiré fringes.
To assess how the key parameters affect crosstalk, the particle size and clearance distance were varied from 25 to 40 μm and from 30 to 180 mm via simulation, respectively. The results shown in Fig. 12 reveal that the crosstalk level increases with clearance distance but decreases with particle size. Increasing the clearance distance results in a higher degree of light scattering that in turn causes an increase in crosstalk. By contrast, increasing the particle size decreases the number of particles per unit area, which reduces the diffusing ability. In Fig. 12, the simulation results of Figs. 6 and 7 and the measured result of the prototype are also marked with square, circular, and pentagram symbols, respectively. It can be found that the measured results have a good agreement with the proposed theoretical approach and simulation.
The above results reveal that both the moiré effect and the crosstalk level are significantly affected by the two key influencing parameters of particle size and clearance distance. In developing a practical system, the particle diameter range of the OD device can be first determined based on simulation and the clearance distance can then be adjusted over small increments to achieve the required display performance. Using the curves in Figs. 11 and 12 for calibration, moiré-less autostereoscopic 3D-LED displays with an acceptable crosstalk level can be fabricated.
Using a model applying geometrical ray tracing and a brightness distribution stack, this paper presented for the first time a quantitatively analytical method for analyzing and controlling the moiré effect in autostereoscopic 3D-LED displays. Based on the modeling, an OD device was specially designed to effectively achieve a balance between moiré and crosstalk level. An ultra-large, moiré-less autostereoscopic 3D-LED display prototype with a visible size of 4,000 mm × 2,300 mm was fabricated and equipped with an OD device characterized by a particle size of 25 μm and a clearance distance of 135 mm. Our experimental results revealed that the prototype provided outstanding performance, with a brightness of 182.5 cd/m2, a uniformity of 82.1%, and a crosstalk level of 25.1%, while significantly reducing the moiré effect. Finally, the regulation of moiré and crosstalk level suppression performance was thoroughly explored by varying the two key influencing factors of particle size and clearance distance. The results of these calibration experiments can provide guidance for further research and have universal applicability to the design and construction of parallax-based autostereoscopic 3D-LED displays.
National Natural Science Foundation of China (61405037); National Key Research and Development Plan (2017YFB0404604); Fujian Science and Technology Key Project (2018H6011); Training Program of Fujian Excellent Talents in University (FETU).
2. E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science 273(5279), 1185–1189 (1996). [CrossRef]
3. B. Javidi and F. Okano, Three-dimensional television, video, and display technologies (Springer, 2002).
4. J. Hong, Y. Kim, H. J. Choi, J. Hahn, J. H. Park, H. Kim, S. W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt. 50(34), H87–H115 (2011). [CrossRef] [PubMed]
6. V. A. Ezhov, “Concept of autostereoscopic full-screen resolution imaging based on a dynamic amplitude parallax barrier with two antiphase liquid-crystal layers,” Opt. Eng. 57(11), 1 (2018). [CrossRef]
8. Y. R. You and S. H. Lee, “Three-dimensional display system using a variable parallax barrier and eye tracking,” Opt. Eng. 50(50), 087401 (2011).
10. X. Sang, X. Gao, X. Yu, S. Xing, Y. Li, and Y. Wu, “Interactive floating full-parallax digital three-dimensional light-field display based on wavefront recomposing,” Opt. Express 26(7), 8883–8889 (2018). [CrossRef] [PubMed]
11. H. Yamamoto, T. Kimura, S. Matsumoto, and S. Suyama, “Viewing-zone control of light-emitting diode panel for stereoscopic display and multiple viewing distances,” J. Disp. Technol. 6(9), 359–366 (2010). [CrossRef]
12. X. Zeng, X. Zhou, T. Guo, L. Yang, E. Chen, and Y. Zhang, “Crosstalk reduction in large-scale autostereoscopic 3D-LED display based on black-stripe occupation ratio,” Opt. Commun. 389, 159–164 (2017). [CrossRef]
13. S. Yang, X. Sang, X. Yu, X. Gao, L. Liu, B. Liu, and L. Yang, “162-inch 3D light field display based on aspheric lens array and holographic functional screen,” Opt. Express 26(25), 33013–33021 (2018). [CrossRef] [PubMed]
14. H. Yamamoto, H. Nishimura, T. Abe, and Y. Hayasaki, “Large stereoscopic LED display by use of parallax barrier of aperture grille type,” Chin. Opt. Lett. 12(6), 21–25 (2014).
15. N. Shiramatsu, M. Tanigawa, and S. Iwata, “Practical method for evaluating the visibility of moiré patterns for CRT design,” Proc. SPIE 2408, 255–262 (1995). [CrossRef]
17. R. Liao and R. P. Dong, “A novel analytical method for moiré phenomenon in autostereoscopic displays,” SID Symp. Dig. Tech. Pap. 45(1), 1074–1076 (2015).
18. V. Saveljev and S. K. Kim, “Controlled moiré effect in multiview three-dimensional displays: image quality and image generation,” Opt. Eng. 57(6), 1 (2018). [CrossRef]
19. R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20(2), 57–64 (1999). [CrossRef]
20. V. Saveljev, J. Y. Son, B. Javidi, S. K. Kim, and D. S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. 1(2), 347–353 (2005). [CrossRef]
21. Y. Kim, G. Park, S. W. Cho, J. Jung, B. Lee, Y. Choi, and M. G. Lee, “Integral imaging with reduced color moire pattern by using a slanted lens array,” Proc. SPIE 6803, 68031L (2008). [CrossRef]
22. Y. Kim, G. Park, J. H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt. 48(11), 2178–2187 (2009). [CrossRef] [PubMed]
24. K. Lin, N. Liao, D. Zhao, S. Dong, and Y. Li, “Analysis of moiré minimization in color LED flat-panel display,” Proc. SPIE 9618, 96180K (2015).
25. V. Saveljev and S. K. Kim, “Amplitude, period and orientation of the moiré patterns in barrier 3D displays,” J. Soc. Inf. Disp. 19(2), 81–90 (2018). [CrossRef]
26. K. Oku, Y. Tomizuka, and Y. P. Tanaka, “Analysis and reduction of moiré in two-layered 3D display,” SID Symp. Dig. Tech. Pap. 38(1), 437–440 (2007). [CrossRef]
28. M. Okui, M. Kobayashi, J. Arai, and F. Okano, “Moire fringe reduction by optical filters in integral three-dimensional imaging on a color flat-panel display,” Appl. Opt. 44(21), 4475–4483 (2005). [CrossRef] [PubMed]
29. J. Y. Son, B. R. Lee, M. C. Park, and H. Lee, “Moiré reduction by a diffuser in a multiview 3-D imaging system,” J. Soc. Inf. Disp. 19(12), 873–879 (2011). [CrossRef]
30. J. T. Lien, M. D. Chou, F. C. Lu, C. C. Chang, C. L. Tsou, T. Y. Lin, and C. N. Mo, “Using diffusive adhesives to reduce moiré pattern of autostereoscopic displays,” Proc IDW ’08, 2083–2086 (2008).
31. M. Kawakita, S. Iwasawa, M. Sakai, Y. Haino, M. Sato, and N. Inoue, “3D image quality of 200-inch glasses-free 3D display system,” Proc. SPIE 8288, 82880B (2012). [CrossRef]
32. W. Hergert and T. Wriedt, The Mie theory: basics and applications (Springer, 2012).
33. Information display measurements standard, Version 1.03, (Society for Information Display, http://www.icdm-sid.org/, 2012).
34. X. Zeng, L. Yang, X. Zhou, Y. Zhang, E. Chen, and T. Guo, “Pixel arrangement optimization of two-dimensional light-emitting diode panel for low-crosstalk autostereoscopic light-emitting diode displays,” Opt. Eng. 56(6), 063104 (2017). [CrossRef]
35. S. K. Kim, S. K. Yoon, and K. H. Yoon, “Crosstalk minimization in autostereoscopic multiview 3D display by eye tracking and fusion(overlapping) of viewing zones,” Proc. SPIE 8384, 8384101 (2012).
37. N. A. Dodgson, “Autostereoscopic 3D displays,” Computer 38(8), 31–36 (2005). [CrossRef]