This work provides a quantitative evaluation on the uniformity of auto-stereoscopic 3D (AS3D) displays. The single-unit uniformity UM is defined to describe the display quality at different viewing positions, then the overall display quality of an AS3D system is determined by the inter-unit uniformity ŪM. As an example, the uniformity of a directional backlight 3D (DB3D) display is experimentally evaluated. Moreover, a visualized simulation is built to analyze the experimental results and optimize the optical system. By modifying the radiant features of the backlights, the entire uniformity of the DB3D displays can be effectively improved. We foresee this work helps to quantitatively evaluate the uniformity and improve design for any kinds of AS3D display type.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Stereoscopic three-dimensional (S3D) display can create vivid 3D vision on liquid crystal displays (LCDs) by sending parallax images to two eyes. Ways of showing 3D images can be divided into two main categories: one requires aiding goggles to separate the left and right parallax images by time shutters, color filters or polarizers; another is auto-stereoscopic 3D (AS3D) methods  which allow viewers to perceive 3D scenes without the requirement of extra equipment. The most adopted types of AS3D displays are with 3D optical elements such as barrier [2–5], lenticular lens array [6–8] and directional films [9,10]. By blocking or diffracting light emitted from the LCD pixels, all of these technologies allow viewers to easily see parallax images.
Among all the evaluated parameters in AS3D, uniformity is one of vital ones to determine the display quality [11–13]. A uniform screen displays images which remain consistent in terms of clarity, color and brightness at all points within the display area. The brightness contrast of the highest to lowest value is considered as the uniformity value [14–17]:
Generally, a traditional display system with uniform backlight and isotropic display panel can provide high display uniformity; however, light emitting from the AS3D panel will be split into two or more discrete viewing zones at the observing plane, where non-uniformity on the screen occurs when viewing at the gaps between the viewing zones. Therefore, Eq. (1) is not sufficient to describe the uniformity of an AS3D display system. As AS3D displays become popular, a quantitative uniformity evaluation for them should be developed .
In this paper, we present a quantitative method to analyze the display quality and provide uniformity evaluation for AS3D displays. The quantitative method follows two steps: firstly, the whole screen is divided into several display units for independently analysis and a modified uniformity value UM for each single unit based on viewing position xP is taken into consideration; secondly, the inter-uniformity quantitatively evaluates the overall uniformity of the display system.
A reverse ray tracing model from observers’ eyes to the backlight array through the 3D optical element is performed to further analyze the display uniformity in the built directional backlight 3D (DB3D) display [18–20]. By considering the correction from human visual system (HVS), we can accurately visualize the display uniformity which provides us intuitionistic theoretical results to study the uniformity deterioration. Based on the above analysis, we also improve the display quality by modifying the radiant properties of the backlight to give the best uniformity. This optimization assists the design of the display system for better viewing experience.
2. Theoretical model
2.1 Evaluation for uniformity
For an AS3D display with periodic 3D optical elements, a uniform screen has to satisfy two criteria simultaneously:
- 1) The display is uniform corresponding to each unit in the periodic 3D optical element at various viewing positions, which is evaluated by single-unit uniformity UM;
- 2) From a given viewing position, good single-unit uniformity should be maintained among every optical unit, which is evaluated by inter-unit uniformity ŪM.
The inter-unit uniformity is the quantitative value to evaluate the uniformity of AS3D displays. The evaluation is carried out with two steps: The entire display module is first divided into several periodic units corresponding to its real physical structures and the single-unit uniformity UM is then calculated for each unit; the inter-unit uniformity ŪM is obtained by averaging all the individual UM at a specific viewing position.
In our evaluation, a single unit of an AS3D display consists of a period of optical element, a part of LCD panel and a corresponding directional backlight, which is able to produce at least two viewing points. Thus, this unit can be regarded as the minimal display unit to display stereo images. The whole display system can then be separated into M independent units. M is obtained by the period of the optical element P0 and the width of the entire display screen L:
2.2 Visualized simulation
To quantify the display deterioration on uniformity, a visualized simulation based on the reverse ray tracing model is proposed here. In a traditional ray tracing model, the optical intensity distribution on the display screen is obtained by collecting rays from the backlight reaching human eyes. However, the simulation would be either time consuming or inefficient because a large amount of rays are traced from the backlight but few reaches the user’s eyes. Therefore, we use a reverse ray tracing model to effectively increase the simulated accuracy . Rays are traced from an observer’s eye to the backlight array through the 3D optical element . The backlight is considered as the only illuminant device that the viewing angle can be restricted only towards the screen.
Figure 1 shows the simulated model by reverse ray tracing method . We first set the human eye in front of the display panel at P = (xP, yP, zP) and the display panel is set at the XoY plane at Z = D, where D is the best viewing distance of the AS3D display. We assume that the 3D optical element (here is a linearly Fresnel lens [5,6], as a minimal unit in a directional backlight 3D (DB3D) display) is attached behind the LCD panel and integrated into the display system, splitting light into several viewing zones. The refractive index of LCD and the air are denoted by nL and nA, respectively.
The reverse ray tracing begins from the observer’s eye at P, with a spatial incident angle (θ, φ) towards Z and Y axes. We consider that a ray r is emitted from the backlight with the beginning position B = (xB, yB, zB) through the crossover point S = (xS, yS, zS) on the screen and finally reaches human eye P. Then S is considered as the distributed coordinate of the optical intensity map and can be obtained by Eq. (5) - (7).
Through LCD panel, the ray reaches the linear Fresnel lens F. It consists of connective saw-tooth units and owns the focal length of f. Therefore, the interface of the lens is regarded as the assemblage of multiple saw-tooth segments, as shown in Fig. 2(a). Thus, the traced ray reaches the surface of ith saw-tooth unit Fi and the function of its interface is given by Eq. (8):Eq. (9) - (11) following the geometrical relationship:
As refraction occurs on both the surface of the saw-tooth and the bottom of the lens, the top view refractive angle θF can be obtained by Snell’s Law Eq. (12).
In Y axes, the incident angle φ maintains during the refraction; so the spatial refractive angle of Z and Y axes is written as (θF, φ).The crossover point on the bottom of the Fresnel lens Fi’ = (xF’, yF’, zF’) can be obtained by Eq. (13) – (15).
Finally, the traced ray reaches the backlight unit which consists of discrete light bars with a specific curved arrangement  (as shown in Fig. 2(b)). Experimentally, each LED bar mounted by a diffuser film can be regarded as a Lambertian illuminant distribution . The equation of the curved arrangement can be expressed by z = G(x) according to the curve in Ref . The point B = (xB, yB, zB) on the backlight unit can be obtained by Eq. (16) – (18).
To obtain the perceived intensity uniformity of the screen, the optical intensity of each ray should be also determined based on the human visual system (HVS) model. We define T0 (B; r) as the vector of each traced ray that reach the backlight B, where |T0| = 1 denotes the rays arriving at the lit backlight, while |T0| = 0 indicates rays reach the parts other than the lighted backlight. Considering that those rays from lit backlight finally reaching a pupil with area ∑ with radius of p and the Gamma correction of the human eye , the normalized perceived optical intensity distribution T on the screen can be obtained by:Eq. (19), (3) and (4), which helps to quantitatively evaluate the uniformity of DB3D displays
3. Results and discussion
To verify the above theory, we compare the experimentally measured and simulated display uniformity of a DB3D display. A seven-period Fresnel lens array (with width of 80 mm for each period) is utilized as the 3D optical element in the DB3D display; each period of the Fresnel lens corresponds to a backlight array consisting of 8 LED bars with specific arrangement to provide multiple viewing zones [21,23–26]. As the main brightness influence comes from adjacent units, three adjacent display units are sufficient for the analysis of the total uniformity. The structure of the system is shown in Fig. 3. The best viewing distance is D = 900 mm and the thickness of the optical element DF + dF = 0.14 mm, with the thicknesses of teeth DF = 0.04mm.
We use a single-lens reflex (SLR) camera to record the perceived intensity distribution at the viewing position P. Figure 4(a) shows the captured result of the detected screen. Considering that viewing zones are provided along X axes, only the normalized value T is calculated for the following evaluation (shown in Fig. 4(b)). The uniformity UM of these three units can be obtained by Eq. (3) and (4). All backlight are turned on and seven viewing positions are tested to research the uniformity performance, respectively.
Figure 5(a) shows the experimental measurements of uniformity in the proposed DB3D display at different viewing positions around the viewing sweet point. When viewing at the sweet point P = (30 mm, 0, 0), the image shows the best uniformity (image D). However, when viewing left or right away from the sweet point, the optical intensity decreases with dark seams. The evaluated values UM of different viewing positions are shown in Fig. 5(b) according to Eq. (19). UM becomes lower when moving close to the sweet point, which means higher uniform can be perceived on the screen. Simulation on the same system shows good fidelity with the experimental results, as compared in Fig. 5(c) and 5(d).
Based on the above simulation, we are able to analyze the display uniformity of the AS3D display at the sweet point in detail. It is worth noting that even though a small inter-unit uniformity is achieved, it does not yield to a uniform AS3D display if each single-unit uniformity varies too much. The single-unit uniformity of unit 1, 2, and 3 (at sweet points xp = 30 mm) is listed in the first data column (‘original’) in Table 1. It is obvious that UM on the first unit (No. 1) is higher than other units, which indicates a deteriorated uniformity on this unit. The inter-unit uniformity determines the entire uniformity of the display systems. Normally, the luminance difference less than 20% between each unit can be regarded as “uniform” [27,28]. As higher value of the inter-unit uniformity shows a deteriorated display quality in our evaluation, the inter-unit uniformity of the tested three units is not in good performance and the optical features of the DB3D displays should be reconfigured to improve the inter-unit uniformity.
To achieve good uniformity, the light intensity from the curved backlights has to be well directed to the corresponding Fresnel units. The intensity distribution of backlights is determinded by the emitting angle θB of each light source. The LEDs in the proposed system irradiate in a Lambertian distribution which is good symmetric at the normal vector of the light surface with θ0 = 0. However, the curved backlight surfaces are not parallel to the 3D optical element, where the backlights could not uniformly illuminate the entire 3D optical element; and edged defects can be easily seen at the sweet point. Therefore, one way to achieve the reconfiguration is to modify the illuminating directions of each backlight unit as the radiant intensity distribution of the light source matters for this kind of uniformity. To optimize the radiant intensity distribution of backlights, the emitting angle is first expanded because the intensity distribution is usually narrower (general with an angular modulation coefficient k ≥ 1.5) than the ideal Lambertian distribution (with new kcor = 1); then is to change the emitting direction of the normal vector θ0 towards the center of the display unit that to contribute the major illuminance for the 3D optical element while keeping the curved backlight arrangment. Directly rotating the backlight surface is not feasible because it will increase the crosstalk of DB3D displays . The optimized intensity distribution T can be achieved with a modified kernel of cos[kcor·(θB -θ0)] in Eq. (19).
Figure 6 shows the optimizated results on the intenisty distribution. The optical intensity distribution and its display uniformity at the sweet point (P = (30 mm, 0, 0)) are simulated and shown in the 1st row. In Fig. 6, the 1st column is the orginal situation of the backlight with narrow and normal intensity distribution (kcor = 2, θ0 = 0), while 2nd column is the results on with the first step optimization (kcor = 1 and θ0 = 0) and the 3rd column shows the results after optimization (kcor = 1 and θ0 ≠ 0). The 2nd row in Fig. 6 shows the scheme of the radiation of backlight before and after optimization. The intensity distribution and the image captured on the screen are also shown in the 3rd and 4th rows in Fig. 6, respectively. Finally the average UM value can be obtained before and after the optimization, shown in Fig. 6(m). Detailed data has also been listed in Table 1. Moreover, this optimization is also able to increase uniformity beyond the sweet point. Figure 7 compares the inter-unit uniformity at various positions before and after the optimization. It shows that better inter-unit uniformity can be obtained at larger viewing angles through our optimization.
The simulated results show that the optimization can effectively improve the inter-unit uniformity. The 1st step of optimization can quickly reduce the UM value, while the 2nd step of optimization makes the intensity distribution identical, leading to a smaller deviation of UM values from adjecent units. Generally, light shaping is feasible to improve inter-unit uniformity in any type of AS3D display [29–34]. Figure 8 shows the display uniformity of the DB3D before and after optimization in our built system.
This work provides a quantitative evaluation on the uniformity of AS3D displays. A modified uniformity value UM is defined to describe the single-unit uniformity at different viewing positions and the uniformity of the entire AS3D system is determined by inter-unit uniformity ŪM. As an example, the uniformity of a DB3D display is experimentally tested. Moreover, a visualized simulation is built to explain the experimental results and provide solutions to optimize the uniformity quality of the DB3D display. By modifying the radiant features of the backlights, the entire uniformity of the DB3D displays can be effectively improved. We foresee this work helps to quantitatively evaluate the uniformity and improve the design for any kinds of AS3D displays.
National Natural Science Foundation of China (NSFC) (11534017, 11704421); Doctoral Startup National Basic Research Program of Guangdong Province (2015A030310388); Fundamental Research Funds for the Central Universities, 2017 (171gpy20).
We thank Guangzhou Mid Technology Co., Ltd. for helps in electronic design and system assembly.
References and links
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