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Abstract
A wide field of view (FOV) is required to improve the user experience in mobile applications of light-field displays (LFDs). However, the FOV of liquid-crystal-display-based LFDs is narrow owing to the thick gap between the light-direction-control element and the pixel plane. The thin-encapsulated self-emissive displays, such as organic light-emitting diodes (OLEDs), are beneficial for widening the FOV without losing spatial resolution. With OLEDs, a 72-degree FOV, 12-view, 166-ppi LFD with smooth motion parallax is demonstrated. A moiré-free parallax barrier of arctan (1/4) slant angle is used to reconcile the triangular sub-pixel pattern of OLEDs, and further doubles the spatial resolution by aligning sub-pixels into a single column, instead of the conventional two columns. The effects of crosstalk due to the wide slits on the three-dimensional image quality are analyzed.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Three-dimensional (3D) displays deliver 3D images by using various technologies, which process complex high-dimensional data and objects, and provide a sense of depth to the viewer [1]. It is an emerging display technology increasingly adopted in various fields such as automotive, cinema, large-display TV sets, and mobile devices. 3D display is one of the new developments in the display industry, offering a very immersive 3D viewing experience. Thus, 3D displays can bring the new experience of realism and immersion for entertainment, such as 3D movies and 3D gaming.
In various 3D display technologies, light-field display (LFD) technology constructs 3D images by reproducing the light direction and intensity at each pixel on a panel plane [2,3], so the light-field images contain a spatial and angular distribution of light intensity. LFDs are the 3D visualization technology which requires no glasses for viewers to enjoy 3D images. Thus, LFDs are particularly appealing to 3D mobile applications, which are expected to have a huge potential in the next-generation display market. The mobile 3D market is expected to register a compound annual growth rate (CAGR) of 40.6 %, over the forecast period (2021-2026), and 3D gaming accounts for the largest share [4]. Particularly, LFDs as a glasses-free display could be a game changer in mobile game industry [5,6].
In LFDs, multi-view 3D displays can be considered as a special case of LFDs where rays are designed to converge to several viewing points [7]. The horizontal-parallax only (HPO) multi-view LFD is one of the solutions to reduce the infinite ray number into a manageable number [8]. In HPO multi-view displays, the light field is converted into multiple perspective views, each view projecting to a range of viewing zones in the horizontal direction to keep the binocular parallax.
An ideal LFD should project high-resolution 3D images to spatial views with smooth motion parallax over a large field of view (FOV). However, due to the limited resolution of a two-dimensional (2D) display, the spatial resolution, angular resolution and FOV of LFDs require an inevitable trade-off [7]. For example, to build a 3D iPhone with a full-high-definition (Full-HD) 2 K spatial resolution and a 3-degree angular resolution, a 2D display with a 50 K resolution is required for the FOV of 75-degree, which is impossible with the current display technologies. Thus, the FOV is narrowed down to only 15 degrees in commercial mobile 3D displays [9], and it strongly restricts a head movement of viewers to 90 mm horizontally at a viewing distance of 350 mm, meaning the viewer’s head cannot move much, which is extremely harmful to the user experience.
To overcome the narrow FOV of LFDs, various approaches such as eye-tracking [10–12], time-multiplexing [13–15] and multiple projectors [16–19] have been suggested to improve the narrow FOV of LFDs. With LCD displays, which are the main 2D displays for fabricating LFDs, the FOV could be improved up to 120 degrees by using a 35-mm thick backlight, which cannot be used in mobile displays [14]. Fast and accurate eye tracking is still challenging according to user conditions, such as low-light conditions, eyeglasses glare and hair occlusion etc. [20]; time-multiplexed displays require a high refresh rate, precluded by the slow response of LCDs [21]; multiple projectors require a complicated implementation and bulky space. Hence, these methods still have many obstacles to apply for mobile 3D applications, where the spatial resolution plays an important role.
Thus, the LFD with a wide FOV, whilst retaining a high spatial resolution is required to be developed for 3D mobile applications. Enlarging the angular resolution was considered to be a promising approach to enhance the FOV from theoretical work [22,23]. To date, however, to the best of our knowledge, there is no experimental work on this approach. The goal in this work is to implement and to characterize the method of enlarging angular resolution for a large FOV in LFDs. In LFDs, the angular resolution is defined as the angular extent of a single view; thus, the FOV is equal to the angular resolution multiplied by the number of views [24,25]. The increasing number of views leads to the reduced spatial resolution because all the pixels are shared by N views, and each view only has 1/N resolution [26], where N is the number of views. It is important to develop the method of enlarging angular resolution for avoiding loss of spatial resolution, i.e., improvement of the FOV of LFDs without losing spatial resolution.
The largest angular resolution occurs as the viewing-zone pitch equal to the interpupillary distance of 65 mm, and it is about 10 degrees/view at the viewing distance of 350 mm. In most cases, the angular resolution depends on the effective gap between the light-direction-control element (LDCE) (e.g., parallax barrier, lenticular lenses) and the pixel plane [22,23,27]. To achieve such a large angular resolution, the effective gap must be as small as 56 $\mathrm{\mu}$m with 10-um sub-pixel pitch. Such a thin effective gap is very difficult to realize LFDs based on liquid-crystal displays (LCDs) [28–33], which have a color-filter with a thickness of about 500 $\mathrm{\mu}$m [34,35]. Compared to LCDs, self-emissive displays, such as organic light-emitting diodes (OLEDs) and micro light-emitting diodes (micro-LEDs), do not require a color filter, so their effective gaps are much thinner than those of LCDs. It is common to stack a polarizer, a waveplate, and a haptic circuit on a self-emissive display for the high contrast ratio and haptic function, and their gap thickness is estimated less than 100 $\mathrm{\mu}$m [36]. Therefore, the FOV can be enhanced by reducing the effective gap with keeping the spatial resolution since no more views are added. Most work on OLED/micro-LED-based LFDs has been performed by using tiled micro displays [24,37], meta-surfaces [38,39], parallax barriers [40] or liquid-crystal (LC) lenticular lenses [41], which demonstrated 34 degrees of FOV at most [24]. On the other hand, the spatial resolution of OLED-based LFDs is only a half of that of LCD-based LFDs owing to the double-column barrier for the special triangular sub-pixel pattern of OLEDs [40].
In our work, a wide FOV LFD with OLEDs is successfully demonstrated for mobile applications. The parallax barrier is attached on the off-the-shelf OLEDs with a thin effective gap of 101.9 $\mathrm{\mu}$m, leading to a 72-degree FOV, 12-view, 166 pixel-per-inch (ppi) HPO multi-view display. The effective gap of 101.9 $\mathrm{\mu}$m was achieved by the thin encapsulation of OLEDs, which is much thinner than $500/1.5 \mbox { (refractive index of glass)} \approx 333$ $\mathrm{\mu}$m of LCDs. Further, the spatial resolution is enhanced by a factor of two by using a zig-zag sub-pixel alignment with a slanted barrier of $\arctan (1/4)$ compared to the use of the conventional parallax barrier with a slant angle of $\arctan (1)$ [40]. As a result, it is found that the zig-zag sub-pixel alignment eliminates the moiré problem arising from the spatial interference of the barrier and the black matrix [42–44]. Although the wide slits on the barrier creates increased crosstalk, it smooths the discrete view transition and improves the continuity of motion parallax. Compared with these OLED-based LFDs [24,37–41], our work points out that the thin-encapsulated OLEDs can provide a wider FOV than the maximum FOV of 34 degrees [24] from these OLED-based LFDs, and the unconventional $\arctan (1/4)$ slanted barrier doubles the spatial resolution and balances the horizontal and vertical resolution drop.
2. System design
2.1 System configuration
In our model system, an HPO multi-view LFD is implemented with the parallax barrier, as seen in Fig. 1. The cost of parallax barrier is much lower than lenticular lenses for prototyping, and it is rapidly fabricated by photoplotting the stripe pattern on a polyethylene terephthalate (PET) film. It comprises of an off-the-shelf OLED display and a slanted parallax barrier. The commercially available 6.7" OLED display that has 3040$\times$1440 resolution and a peak brightness of up to 1200 nits (Samsung model Note 10+) is used in this work. The parallax barrier is an 1D array of multiple slits which confine the rays to specific directions and form 12 beams that are illustrated by the green and orange rays in Fig. 1. The barrier pitch is carefully designed to converge beams from each slit into 12 viewing zones at the viewing distance of 350 mm for mobile applications. The barrier-slit width determines the brightness, and wider slits provide higher brightness because more light can pass through the slits. Here, 1/3 aperture ratio (slit width : barrier pitch) was chosen to obtain a brightness of about 100 nits, which is sufficient with low ambient light [45,46], but may not be sufficient with ambient light of more than 200 lux [47]. It is known that parallax barriers have the brightness-loss problem, which can be resolved with lenticular lenses [48].
Fig. 1. The configuration includes an OLED display and an $\arctan (1/4)$-slanted parallax barrier which distributes the sub-pixels into 12 views. The gap is minimized to obtain the wide FOV of 72 degrees. (The schematic is not in scale, and only partial rays are plotted)
Converting 2D displays into multi-view LFDs creates the spatial resolution loss. The slanted barrier not only divides the resolution degradation into both horizontal and vertical directions [49], but also reduces the moiré pattern [50,51]. The slant angle is designed as $\arctan (1/4)$ to align the RGB sub-pixels into a single column, rather than separating RGB into two columns [40], which leads to a 2N-fold resolution loss. Thus, compared to the double-column barrier, the spatial resolution in our work is doubled. Furthermore, for the 12-view LFD, the slant angle of $\arctan (1/4)$ reduces the horizontal resolution of each view by a factor of 3, and the vertical resolution by a factor of 4. Both of the factors are very close to the ideal reducing factor $\sqrt {12}$ [52]. Therefore, the horizontal and vertical resolutions are nearly balanced.
To obtain the largest FOV, the effective gap thickness including the effect of refraction in the gap must be minimized. However, the gap is filled by the encapsulation of the OLED display, including a cover glass, a polarizer, a waveplate, a haptic circuit and the resistive layer. The cover glass is thick and unnecessary in our prototype. After removing the cover glass, the barrier is laminated on the OLED display with liquid optically clear adhesive (LOCA). The total gap thickness includes the thickness of the LOCA. Notice that the printed plane of the barrier is faced downwards to eliminate the substrate thickness of barrier. Finally, the effective gap thickness is reduced into 101.9 $\mathrm{\mu}$m, leading to an FOV of 72 degrees.
2.2 Slanted-barrier design for triangular sub-pixel patterned OLEDs
The OLED display used in our work has a special triangular sub-pixel pattern in Fig. 2(b), where the sub-pixels are inter-wound together; different from the matrix pattern of LCDs in Fig. 2(a), which gives the maximum 3D resolution by the well-aligned matrix pattern. Figure 2(a) shows the slanted-barrier setup for LCDs where the RGB sub-pixels are perfectly aligned at the slant angle of $\arctan (1/3)\approx 18.43$ degrees, and the yellow-framed RGB sub-pixels form a single-view pixel whose width is 1/3 pixel pitch (px), and height is 3 px. Thus, the area of one pixel is 1 $\rm {px}^2$. An N-view display requires N pixels to represent N views; thus, the 3D resolution drops by N-fold. However, for the OLEDs’ triangular sub-pixel pattern, there is no orientation such that RGB sub-pixels are perfectly aligned. Lee et al. [40]] used a 45-degree slanted barrier with two columns to form a single-view pixel framed by the yellow boxes shown in Fig. 2(b).
Fig. 2. (a) The matrix sub-pixel pattern of LCDs is implemented with a slanted barrier of angle $\arctan (1/3)$, and the size of single-view pixel is 1/3 px $\times$ 3 px, which gives the maximum 3D resolution. (b) A conventional 45-degree slanted barrier for the triangular sub-pixel pattern OLEDs and its single-view pixel is 2 px $\times$ 1 px. It requires double the number of pixels, so the resolution loss is doubled over that of LCD-based 3D displays. (c) Our innovative slanted barrier of $\arctan (1/4)$ for the triangular sub-pixel pattern OLEDs shows the size of a single-view pixel is 1/4 px $\times$ 4 px, and it solves the doubling resolution loss of 45-degree slanted barrier in Fig. 2(b).
The area of a single-view pixel is 2 px $\times$ 1 px = 2 $\rm {px}^2$. A doubling of pixel size produces a resolution drop of 2-N fold, leading to the loss of 3D resolution by a factor of two over that of the LCD-based multi-view LFDs. To avoid the doubling of resolution loss, in our work, the RGB sub-pixels are aligned into a single column at the slant angle of $\arctan (1/4)\approx 14.04$ degrees in a zig-zag way; as shown in Fig. 2(c). A single-view pixel framed by the yellow boxes shows the size of 1/4 px $\times$ 4 px = 1 $\rm {px}^2$, and our new design results in a doubling of 3D resolution over Lee’s approach. Further, the zig-zag alignment eliminates the moiré pattern owing to the spatial interference of the periodic black matrix and the barrier [53]. Visualization 1 shows the moiré that occurs with a vertical barrier, and no moiré with the $\arctan (1/4)$ slanted barrier in Visualization 2. Since the vertical barrier interferes with the straight black matrix in the vertical direction, their periods are very close to form the unwanted moiré pattern.
In addition, the small slant angle of 14.04 degrees mitigates the rotation of the 3D image when an observer is moving along the vertical viewing position [54]. In mobile applications, a viewer may change the vertical viewing position significantly, so the slant orientation shall be close to the vertical direction to mitigate the image-rotation problem.
Lastly, in Fig. 2(c), the red and blue sub-pixels deviate a half sub-pixel size from the central line, , and these deviate sub-pixels induce some crosstalk to the neighbor views. However, the crosstalk is moderate because of the relatively low luminance of red and blue sub-pixels comparing to the green [55].
2.3 Optical design of the parallax barrier
In the implementation, the parallax barrier is designed to integrate with the OLED display. The barrier pitch is the most important parameter in the optical design because it eventually determines the viewing distance. Figure 3 shows the side view of the model considered in the work, and it is simplified into a two-view display. In Fig. 3, the barrier is stacked on the gap, and the medium of the gap is regarded as glass with a refractive index of 1.5. The refractive index of medium makes the effective gap $g$ equal to the physical gap $g_0$ divided by n [56,57]. The slits direct the rays from sub-pixels intersecting at the viewing distance $d$, and the barrier pitch $b$ determines the viewing distance $d$. The relationship between the barrier pitch and the viewing distance can be obtained by using the red similar-triangle relation in Fig. 3,
where N is the view number (Two views have been generalized into N views here); $p$ is the single-view pixel pitch; $g$ is the effective gap thickness. Eq. (1) is solved for $d$. Since $p$ and $g$ were fixed when the display was manufactured, $b$ is the only variable. To understand how barrier pitch affects the viewing distance, the differential of $d$ with respect to $b$ is taken, Plug Eq. (1) into Eq. (3), and assume d » g, and the variation of $d$ is estimated by plugging in $d$ = 350 mm; N = 12; $p$ =(pixel pitch)/4$\sim 0.05/4 = 0.0125$ mm given by the display’s nominal pixel size from specification; $b \approx {\rm N}p = 0.15$ mm, given by Eq. (1) simplified with $d>>g$; $g$ is estimated as 0.1 mm as the same order of a thickness of a polarizer, then In mobile applications, $\pm 50$ mm variation of the viewing distance is acceptable; then $\Delta d$ = $\pm 50$ mm, and $\Delta b = \pm 6$ nm from Eq. (5). It means that the variation of $b$ should be less than 6 nm to ensure that the rays are converged approximately at the viewing distance of 350 mm. The search method for $b$ has been included in the Supplement 1.Fig. 3. The optical design for a parallax-barrier display. The red rays show the convergence at the viewing distance, and the blue rays form the viewing zone.
$g$ can be expressed as
Because $d$ = 350 mm, once $b$ and $p$ are measured, then $g$ is calculated by Eq. (6). Moreover, multiplying $g$ by the refractive index n for the gap gives the physical gap size $g_0$.On the other hand, the blue rays in Fig. 3 gives
The viewing-zone pitch $v$ is inverse proportional to the effective gap size $g$, so $v$ gets larger as $g$ gets smaller. Finally, the FOV is given by This equation shows clearly that a smaller gap gives a wider FOV.The barrier-slit width $a$ affects the crosstalk. In Fig. 4(a), when $a$ is infinitesimal, there is no crosstalk between neighboring views though it is impractical in applications due to zero light output. When $a$ is finite, the brightness is proportional to $a$ and the crosstalk between views also occurs. In Fig. 4(b), crosstalk occurs in the overlay regime, and the regime width is approximately equal to $a_0v/p$. Hence, larger $a_0$ leads to more crosstalk. There is a trade-off between the brightness and the crosstalk. Here, $a$ is chosen as $b/3$ to keep the brightness around 1/3 of the 2D brightness; the aperture ratio is 1:3. From Eq. (1) with $d>>g$, $b \approx 12p$, then $a_0 = 4p$. It turns out the overlay regime is $4v$, so there are 4 views overlapped.
Fig. 4. (a) When the barrier-slit width approaches zero, no crosstalk occurs. (b) Increasing the barrier-slit width to $a_0$ increases the overlay regime where crosstalk occurs.
2.4 Implementation
Based on the system design, the implementation follows these steps: A. Remove the cover glass to reduce the gap thickness. B. Measure the pixel and barrier pitch to determine the gap thickness with Eq. (6). C. Measure the thickness of LOCA. D. Include the LOCA in the gap thickness and calculate the effective gap thickness. E. based on the effective gap thickness, calculate the barrier pitch with Eq. (1). F. Fabricate the barrier and laminate it onto the OLEDs. The detail of each step is described in the Supplement 1.
3. Results and discussion
Parameters used in the implementation are summarized in Table 1. The effective gap is only 101.9 $\mathrm{\mu}$m; much thinner than the LCD’s gap of $500/1.5 = 333$ $\mathrm{\mu}$m, and the thin gap widens the FOV to 73.8 degrees given by Eq. (8). In the case of the effective gap thickness of 333 um for the LCDs used, the viewing angle would be only 26 degrees. This result shows clearly that the gap thickness plays an important role in obtaining a wide FOV.
Table 1. The specification and parameters for the OLED light-field display.
In addition, the measured 3D brightness is 26.8 % of the 2D brightness; less than the estimated brightness of 33 % caused by the blockage of the barrier. This is mainly due to the reflection occurring at the interface between the barrier film and the air. Also, the PET substrate of the barrier is not crystal clear (Fig. S5) and consequently leads to some diffusion and scattering.
The 12-view setup is chosen because it gives a large FOV of 73.8 degrees with a 1K spatial resolution. Since the slanted barrier divides the resolution loss into both of the horizontal and vertical directions, the 3D resolution is reduced by 1/3 and 1/4 of the 2D resolution in horizontal and vertical directions, respectively; also, it keeps the 3D resolution nearly equal in both directions. In the implementation, it is difficult to be aware of the existence of barrier because of its thin pitch of 153 $\mathrm{\mu}$m. In Fig. 5, the visual comparison between LFDs with slant angles of $\arctan (1/4)$ and $\arctan (1/1)$ are shown. The slanted barrier of $\arctan (1/4)$ in Fig. 5(a)(b) shows a higher 3D resolution than that of $\arctan (1/1)$ in Fig. 5(c)(d), and the stripes of $\arctan (1/1)$ are clearly observed by eyes because its 3D resolution is only one half of that of $\arctan (1/4)$. The results verify that the 3D resolution of $\arctan (1/4)$ is improved over that of $\arctan (1/1)$. Notice that an even number of views cannot be implemented with $\arctan (1/1)$ barrier [40]; thus, 11 views are implemented for $\arctan (1/1)$, and it slightly improves the 3D resolution of $\arctan (1/1)$.
Fig. 5. (a) The image photo and (b) the close-up for the LFD with $\arctan (1/4)$ slanted barrier. (c) The image photo and (d) the close-up for the LFD with $\arctan (1/1)$ slanted barrier.
The viewing distance is measured as seen in Fig. 6(a). The left and right quarters of pixels in a single view were turned on, and the two beams intersected at around 350 mm. The result shows our barrier pitch provides a right distance for converging rays at the designated viewing distance. Figure 6(b-d) show that the left, central, and right perspectives to demonstrate the horizontal motion parallax where the relative position between petals and the stem changes over perspectives, highlighted in white dash frames. Also, Visualization 3 shows smooth motion parallax with changing perspectives so that the transition among views is continuous, rather than an observable jump.
Fig. 6. (a) Two beams from the left and right edges intersected at around 350 mm, matching the designated viewing distance. (b-d) Comparing the left, central, and right perspectives for the OLED light-field display, the relative positions of the petals and the stem are changing with different perspectives, thus demonstrating the motion parallax.
To investigate the FOV and crosstalk, the angular luminance distribution of the light field is shown in Fig. 7(a), which is measured by the luminance meter (SR-LEDW, Topcon Inc.) at the viewing distance of 350 mm. From Eq. (8), the FOV is defined as the viewing angle enclosing the 12 viewing zones, which is 72 degrees, as marked in Fig. 7(a); very close to our calculated viewing angle of 73.8 degrees from Eq. (8). It indicates that the implementation matches our optical design.
Fig. 7. (a) The light-field distribution indicates the viewing range is 72 degrees, marked by red dashed lines. The black dashed lines are the angular location of two eyes based on the interpupillary distance of 65 mm, and the overlapping views are circled: Four views are overlapped in each eye. (b) Depth and blur vs. disparity is plotted, and the limited disparity of $\pm$ 10 px is marked by the red dashed lines.
Crosstalk (xtalk) is an important parameter in evaluating a light-field display, and it is calculated by [58]:
Fig. 8. The 3D images of various disparity from 5 px to 20 px, and the vertical edges get more blurred with increasing disparity. Once the disparity is beyond 10 px, the blur becomes ghosting.
Our prototype LFD with a parallax barrier suffers from brightness loss and crosstalk, which are the downsides of parallax barriers. Replacing with lenticular lenses can not only recover the 3D brightness to nearly the level of 2D brightness, but also reduce the crosstalk to an estimated low crosstalk of 30 % owing to the shared red and blue sub-pixels from adjacent views. Because the brightness of red and blue sub-pixels occupies 30 % of the brightness of white pixels, the shared red and blue sub-pixels from adjacent views can contribute up to 30 % crosstalk. In our future work, the parallax barrier will be replaced by lenticular lenses to improve the brightness and reduce the crosstalk.
For a multi-view LFD, the FOV is widened with the increase of viewing-zone pitch, which arises from the reduction of the gap between the LDCE and the pixel plane. Compared to LCDs, self-emissive displays, such as OLEDs and Micro-LEDs, provide the thin-gap advantage to further widen the FOV. In this work, the viewing-zone pitch has been increased to 43.8 mm. In theory, it can be broadened to the interpupillary distance of 65 mm. Then, the effective gap must be further reduced from 101.9 $\mathrm{\mu}$m to 68.6 $\mathrm{\mu}$m, leading to the maximum theoretical FOV of 96 degrees for 12 views. This will rely on reducing the adhesive, or embedding the LDCE below other layers, such as the polarizer, waveplate, and haptic circuits, etc.
4. Conclusion
With the optimized optical design, the 12-view, 72-degree FOV, and 166-ppi LFD based on a triangular sub-pixel patterned OLED display is demonstrated, and its effective gap is 101.9 $\mathrm{\mu}$m; only about one third of that of the LCDs. A moiré-free slanted parallax barrier with a slant angle of $\arctan (1/4)$ is used to reconcile the special triangular sub-pixel pattern of OLEDs, and the 3D resolution is double that of the previous approach that uses 45-degree barrier. It is found that the large crosstalk produces from the wide slits on the parallax barrier, and the blur depends on the disparity. To avoid intolerable ghosting, the disparity should be confined to a reasonable range. OLED is adapted in this work because of the only commercially available self-emissive displays. Micro-LEDs as another self-emissive display format, which are not commercially available now, could provide the similar or better performance due to superior properties, such as ultrahigh resolution of 8500-ppi [65], fast response time of ns [66], high luminance of $10^7$ nits [66,67] and power saving [66]. Thus, adapting a thin encapsulated self-emissive display, such as OLEDs/Micro-LEDs, can open the way toward a wide FOV LFD.
Funding
Fundamental and Applied Research Fund of Guangdong Province (2021B1515130001); Shenzhen Science and Technology Innovation Program (JCYJ20190812141803608, KQTD20170810110313773).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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