Auto-stereoscopic displays based on directional backlights with side-glowing polymer optical fiber array module

Optics Communications 459 (2020) 125032

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Auto-stereoscopic displays based on directional backlights with side-glowing polymer optical fiber array module Yong He a , Chaohung Lu b , Chujia Liu a , Feifei Gao a , Zirun Li a , Qiren Zhuang a ,∗ a

College of Information Science and Engineering, Fujian Key Laboratory of Light Propagation and Transformation, Huaqiao University, Xiamen, Fujian 361021, China b TPV Display Technology (Xiamen) Co., Ltd, Xiamen 361101, China

ARTICLE

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Keywords: Auto-stereoscopic display Directional backlights Side-glowing polymer optical fiber Full-resolution

ABSTRACT A compact auto-stereoscopic display based on directional backlights with side-glowing polymer optical fiber (SGPOF) array module is designed and fabricated, to provide better three-dimensional perception with image qualities comparable to that of two-dimensional displays, and to reduce thickness of display. The multiview zones of the SGPOF display is simulated by Tracepro software and experimentally verified. It has been successfully demonstrated by measurement and simulation that the SGPOF display is subject to much lower crosstalk. It is found that the spatial crosstalk coming from adjacent channels is reduced by inserting a grating film as multi-slit diaphragm between the SGPOF array and the cylindrical lens array(CLA),and achieves a crosstalk less than 5% by simulation calculation. In order to effectively improve the coupling efficiency of light to fiber, globular lens in end side of SGPOF is designed, and such scheme is proved to be effective in increasing the coupling efficiency that has raises the .300% times of before. The experimental results show that the luminance uniformity of the SGPOF display is up to 89.3%, the overall crosstalk is shown to be lower than 10%, and minimum achievable crosstalk can be as small as 2.2%. The minimum thickness of SGPOF display is only 18 mm. The full-resolution and low-crosstalk 3D images are realized by using SGPOF array module backlight.

1. Introduction Auto-stereoscopic display technology can achieve stereoscopic effects without requiring the observer to wear special glasses and is regarded as the one of the candidates for future 3D applications [1]. Many techniques are proposed to display parallax images, basically, for creating binocular viewing to provide the perception of depth, different images are sent to the left and right eyes [2]. Which is mainly divided into two types of space or time multiplexing. In the spatial multiplexing, the vertical fringe is manufactured by using the liquid crystal layer and the polarizing coat to form a parallax barrier, and a flat panel liquid crystal display and parallax barriers are coupled precisely. In stereoscopic display mode, the opaque stripes occluded the right eye when the left eye image is displayed, and the viewer could see the 3D images by separating the visual images of the left eye and the right eye [3]. However, the general auto-stereoscopic techniques involving the use of parallax barrier and lenticular 3D techniques now facing serious disadvantages, such as low resolution, low optical efficiency and narrow angle of view. Most importantly, the image resolution is reduced, and the spatial multiplexing display technology cannot provide a full-resolution stereo image [4].

In order to surmount this disadvantage, the auto-stereoscopic display based on time-multiplying directional backlight technology has been proposed due to keeping the original resolution of liquid crystal display unchanged. Among all the technologies in auto-stereoscopic display, the directional backlight is one of vital ones to determine the auto-stereoscopic display quality [5]. In the past decades, various new technologies of directional backlight are proposed, such as a homogeneous free-form directional backlight technique [6]. The technique is to produce a homogeneous secondary emission source using an array of free-form emission surface with a specially tailored light guiding structure, the original resolution parallax images to be drawn on a homogeneous viewing zones. The key is a free-form surface directional backlight technique technology based on LED bars, which generates uniform and stable over a large range backlight modules. The freeform backlight provides the basis for a high quality naked-eye 3D display. However, the free-form emission surface method turns heavily to LEDs for lighting, and large thickness limits the application of free-form emission surface in 3D display. One technology is an autostereoscopic display method of time-multiplexing directional backlight based on COE (cylindrical optical elements) LED array of densely [7].

∗ Corresponding author. E-mail address: [email protected] (Q. Zhuang).

https://doi.org/10.1016/j.optcom.2019.125032 Received 4 September 2019; Received in revised form 22 November 2019; Accepted 27 November 2019 Available online 29 November 2019 0030-4018/© 2019 Published by Elsevier B.V.

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Optics Communications 459 (2020) 125032

It is suitable for viewing under ambient lighting conditions. And full resolution of the display images can be provided with time-division multiplexing technology. However, the display has complex structure and large volume. Another research including two systems that a lightstrip array backlight and an active slanted LED backlight to implement high efficiency 2D/3D switchable auto-stereoscopic multi-view display [8]. However, such schemes are unsatisfactory because they all have more than 10% crosstalk, which is an uncomfortable 3D image display. In this paper, a compact auto-stereoscopic display based on directional backlights with side-glowing polymer optical fiber (SGPOF) array module is proposed and it has been verified by simulations and experiments. This technique presents the following advantages. First, a SGPOF array module is utilized to reduce display thickness. Second, the SGPOFs lighted up by the way of dynamic time-sharing scan is easier to achieve multi-view display. Third, full resolution is preserved for the images in both the left and right channels. Fourth, an inserting a grating film as multi-slit diaphragm between the SGPOF array and the cylindrical lens array (CLA) are utilized to suppress the crosstalk. The directional backlight with uniform luminance distribution is obtained through the CLA. In addition, we also demonstrate that the proposed backlight system is compact structures, endowed with 2D/3D switchable properties and low crosstalk. This project is undertaken to design a compact auto-stereoscopic displays based on side-glowing polymer optical fiber array module and evaluate its optical performance.

Fig. 1. Schematic show of optical model of the auto-stereoscopic display.

2. Structure and principle 2.1. Directional backlight using SGPOF array It is well known that a large light source does not come to a single focus after a lens for the reason spherical aberration. The spreading of the light source in the image plane becomes increasingly serious for non-paraxial rays, which is typical for a display system where the large viewing angle indicates the light rays with very large intersection angles with the lens axis. As a result, the light intensity distribution will be severely dispersed for a large light source, giving rise to increased crosstalk between the adjacent viewing channels if two parallel planar directional backlight sources are placed for auto-stereoscopic display. Therefore, we propose two methods to relieve the problems. For one thing reducing the aperture of cylindrical lens, for another the SGPOF is employed because it shows a higher luminance and a smaller size. The Directional backlight system is based on the principle of linear light source array illumination auto-stereoscopic display. As illustrated in Fig. 1, it consists of a set of SGPOF, A vertical diffusion film (VDF), a cylindrical lens array (CLA), a high-definition LCD and a polymer dispersed liquid crystal (PDLC) film. The PDLC is placed between the LCD and the CLA to improve the uniformity of light distribution. In 3D mode, the PDLC film stays in transparent state, and the auto-stereoscopic display would provide directional backlighting auto-stereoscopic images, while in 2D mode, all the SGPOFs are turned on and the PDLC film is switched to diffusive state to scatter directional light to form a uniform 2D viewing zone [9]. The LED array of two groups are coupled to two groups of SGPOF, respectively. The SGPOF array is placed at the focal plane of the CLA, each column of the CLA is assigned to two SGPOFs, and SGPOFs of the array are closely spaced in the horizontal, numbered as 1, 2. In this system, the light emitted from LED is modulated by SGPOF and refracted in different directions through the CLA. The refraction angle depends upon the relative position between the SGPOF and the CLA. Standing at a predesigned optimal viewpoint, the left eye will see only the light from number1 SGPOF and the right eye will see another light from number 2. Which are turned on sequentially, and then the refresh rate of 60 Hz. This utilizes a LCD in front of a CLA, presenting a left and a right image refreshing on the 60 Hz single direct-view LCD screen, Left and right images are respectively projected to two exclusive

Fig. 2. Schematic diagram of the light path in the optical system composed of SGPOF array and cylindrical lens.

regions. The eyes of observers stay within these regions, they may see respective images. Generally, these two images should have no intersection, furthermore, full resolution is maintained for the images of each eye. Different images with proper binocular disparity will be perceived by the left and right eye accordingly, then a stereo image is fused in the viewer’s brain. Our current prototype system uses the SGPOF array can make the directional backlight module into the very thin module, which can effectively avoid the problems of large thickness and complicated structure of the time-multiplying directional backlight auto-stereoscopic display. Because the light source is set outside the backlight module, this structure can also avoid the thermal problem of LCD panel caused by the heat dissipation of the light source. 2.2. Design principle of optical system In order to verify the design theory, we need to establish the system model in detail. The optical system is mainly composed of SGPOFs and CLA, as shown in Fig. 2. The LCD panel to the optical field propagation is not considered, as LCD plays little role on light rays deviation [10]. The reference axis is set at the junction of the two cylindrical lenses, where S is the distance from the CLA to the eye of observer, d denote the diameter of SGPOF, f is the focal length of CLA. l denotes the distance from the SGPOF to the center of the cylindrical lens, T and t denote, respectively, the offset of one edge of the object relative to the reference optical axis. Fig. 2 shows the next periodic position of the SGPOF from the same viewpoint is 𝛿ℎ + 𝑡. The SGPOF is imaged by an adjacent column CLA at a distance of 23 𝑃 from the center of curvature to the reference axis. And also the light ray is projected to the same point of view. According to geometry knowledge, Eq. (1) can be obtained: 𝑇 =( 2

1 𝑅+𝑆 3 𝑅+𝑆 + )( 𝑃 ) − (𝑡 + 𝛿ℎ) 2 2𝑙 2 𝑙

(1)

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Optics Communications 459 (2020) 125032

Apparently, from Eq. (1) the distance 𝛿ℎ between two SGPOFs from the same viewpoint is calculated as: 𝛿ℎ =

𝑙+𝑅+𝑆 𝑃 𝑅+𝑆

(2)

𝑛𝑅 𝑛 − 𝑛0

(3)

𝑑+𝜔 𝑙 = 65 𝑅+𝑆

(4)

𝑓=

Fig. 3. Scattering points distribution schematic of the SGPOF.

According to the conservation of energy: ( ) 𝐾 𝑃0 − 𝐾𝑃0 𝐾𝑃0 = 𝛥𝑥1 𝑏 𝛥𝑥2 𝑏 )] [ ( 𝐾 𝑃0 − 𝐾𝑃0 − 𝐾 𝑃0 − 𝐾𝑃0 = 𝛥𝑥3 𝑏

Where denotes the distance between two adjacent SGPOF, which are tightly connected in our optical system. 𝑛 and 𝑛0 are the air refractive index and refractive index of CLA. These equations can determine the optical structure of the auto-stereoscopic display. The ray-tracing model is the common way of auto-stereoscopic display light intensity distribution [11,12]. In reference [12], an effective method for simulating light intensity distribution is proposed, the equations of output intensity profile can be used to occupy simulation, Eq. (5) gives the eye received intensity profile in that the sum of all light rays from the SGPOF array module through the CLA: 𝑦𝑠 +𝑑

𝐼(y) =

∫ 𝑦𝑠

=⋯=

∫𝜑0

𝑃0 (1 − 𝐾)𝑖 =⋯ 𝛥𝑥𝑖 𝑏

The center distance of scattering points can be obtained by: 𝛥𝑥𝑖 = 𝛥𝑥1 (1 − 𝐾)𝑖−1

(10)

And the constraint condition:

𝜑𝑚

𝑑𝑦

(9)

(5)

𝑑𝜑 cos 𝜑𝛿(𝑌 − 𝐺(𝜑, 𝑦))

tan−1 ((𝑃 ∕2−𝑦)∕(𝑙

𝑁 ∑

− tan−1 ((𝑃 ∕2

Where 𝜑𝑚 = + 𝑅 cos 𝜃)), 𝜑0 = + 𝑦)∕(𝑙 + 𝑅 cos 𝜃)), 𝜑0 and 𝜑𝑚 are the limiting angles of ray tracing, 𝑦𝑠 denotes the position of the starting point of the ray. We can obtain the relation from ray tracing: 𝐺(𝜑, 𝑦) = 𝑦 + (𝑑 + 𝑅 cos(𝜃 + 𝜑)) tan 𝜑 ′

− (𝑆 + 𝑅 − 𝑅 cos(𝜃 + 𝜎)) tan 𝜑

𝑖=1

(6)

𝑥𝑛 =

n ∑

𝛥𝑥𝑖 =

𝑖=1

(11)

n ∑

𝛥𝑥1 (1 − 𝐾)𝑖−1

(12)

𝑖=1

Eqs. (11) and (12) can be seen that the spacing of scattering points is uniquely determined by the scattering point efficiency coefficient, which is related to the depth of the scattering point [15].

cos(𝜃 + 𝜑) = [

(7) 3. Simulation of optical model of the auto-stereoscopic display

According to Snell’s law: 𝜑′ = sin−1 (𝑛 ⋅ sin 𝜃)−(𝜃 + 𝜑)

𝐿 (𝛥𝑥𝑖 ≥ 𝑤) 2

Where 𝑁 is the total number of scattering points and 𝐿 is the length of the SGPOF. The central position coordinates of scattering points can be calculated:

Where 𝑑, 𝜑′ , 𝜑 and 𝜃 are shown in Fig. 2, cos(𝜃 + 𝜑) is obtained by geometric-optics: tan 𝜑(𝑥 + 𝑑 tan 𝜑) 1 ][− (1 + tan 2𝜑) 𝑅 √ (𝑥 + 𝑑 tan 𝜑) 2 (1 + tan2 𝜑) − ( ) ] + 𝑅

𝛥𝑥𝑖 =

To quantify the display crosstalk on viewing zones, a simplified but reasonable model of SGPOF backlight is built by utilizing the optical software named TracePro. Simulation based calculation of SGPOF optical component is then developed to enhance veracity of the directional backlight source. In our ray tracing model, the optical intensity distribution on the auto-stereoscopic display is obtained by collecting rays from the backlight module reaching human eyes. Table 1 gives the parameters set in the simulation and the simulation detector is placed at the distance of 500 mm from the CLA. Fig. 4 is the luminance and crosstalk distribution of the simulation calculation at the optimal view distance along the horizontal direction x. The SGPOF light radiation is supposed to be a Lambertian distribution. There are 315 sampling points in the figure to form an accurate luminance distribution and crosstalk distribution curves. The normalized luminance is a ratio between noise luminance and maximum luminance. To further confirm that the luminance of left eye and right eye parallax images are separated in space, and the crosstalk distributes in a very tiny area at the boundaries of each view zone. Therefore, the proposed 3D display can limit crosstalk at a lower level. The crosstalk is calculated by [16]:

(8)

2.3. Design of SGPOF In our previous work [13], we have explored the use of lasers to fabricate SGPOF. This method does not seem to be suitable for rapid processing of large size SGPOF. Different from the previous work, here a Hot-processing device is used to fabricate SGPOF, This method improves the machining efficiency and brightness of SGPOF. Our simplified physical model is show in Fig. 3. The light energy is coupled from the white LED source to the SGPOF through an end face of the SGPOF. The light from an LED enters the SGPOF from its one end, and the scattering point extract the light propagating inside the SGPOF. This process generates point light sources homoplastically along the SGPOF. Most of the scattering light will be emitted from the scattering point of the fiber, and the total light flux in the fiber core will be reduced. To make the light emitting uniformly on the SGPOF, the spacing of scattering points in hot-working needs to decrease with the decrease of light flux [14]. The light incident from left side of the SGPOF, 𝑃0 is the input radiation power, 𝑏 is the length of the scattering point in the 𝑌 direction, 𝑤 is the width in the 𝑋 direction. In our model of SGPOF, whose scattering point efficiency coefficient 𝐾 is kept constant along the whole fiber. 𝛥𝑥𝑖 is the central distance between the i scattering point and the 𝑖 − 1 scattering point.

𝐶𝑟𝑜𝑠𝑠𝑡𝑎𝑙𝑘 =

𝐿𝑛𝑜𝑖𝑠𝑒 × 100% 𝐿𝑠𝑖𝑔𝑛𝑎𝑙

(13)

The normalized crosstalk, which equals noise luminance divided by the signal luminance, is no more than 5% in three (A, B, C) viewing zones. 3

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Optics Communications 459 (2020) 125032 Table 1 Parameters set in the simulation. Parameter

Value

Parameter

Value

Quantity of rays Size of POF bars Size of CLA Refractive Index and Abbe coefficient of CLA 𝑑/mm 𝑃 /mm 𝑅/mm

1000000 0.5*5 mm 297.8*5 mm 1.49,57.3 0.5 1.4111 2.2382

Quantity of SGPOFs Columns of CLA Distance from SGPOF to lens Viewing distance S 𝛿ℎ/mm 𝑓 /mm 𝑙/mm

422 211 0 500 mm 1.42185 6 3.7618

Table 2 Related parameters of the POF. Specification

Item Core Material Cladding Material Core Refractive Index Cladding Refractive Index Numerical Aperture Refractive Index Profile Core Diameter Cladding Diameter

Typical value

Unit

Polymethyl-Methacrylate Resin Fluorinated polymer 1.496 1.363 0.5 Step Index 486 500

– – – – – – μm μm

Fig. 4. Simulated intensity profile and crosstalk on the viewing plane for the prototype.

Fig. 6. Schematic drawing of the power of the light coming out of the side and end face.

We fabricated a fiber array based on 500-μm-diameter POF and fixed it on the supporting plate. The size of the POF array is 350 × 200 mm. The POF used in the experiment are Japanese Eska Mitsubishi POF SK-20, the parameters listed in Table 2. The temperature of the heating plate is set to 130 mm, the contact time between each fiber and the circular inserts is about 0.1s (which is the average result) to change the scattering point efficiency coefficient 𝐾 of the V-shaped scattering point. Fig. 6 shows the white light from the LED enters one end of a POF through lens coupler. Lens coupler is designed for illumination uniformity and effective light utilization of end face of the fiber bundle [17]. The power meter monitor (MOEDL JC2) records the power of the light coming out of the side and other end face. This scattering point efficiency coefficient K is expressed as: 𝐾=

Fig. 5. The schematic diagram of hot-processing device.

𝑃𝑠 × 100% 𝑝𝑒

(14)

Where 𝑃𝑠 is the side-light extraction power, and 𝑝𝑒 denotes the total power. We repeated this measurement of the weight 𝐺 and scattering point efficiency coefficient 𝐾. As shown in Fig. 7, the scattering point efficiency coefficient 𝐾 is almost proportional to the weight 𝐺 Therefore, we can select a desired value for the scattering point efficiency coefficient by choosing the weight of hot-processing device. For increase the brightness of the side light, the SGPOF takes the mode of coupling incident at both ends. The length of the SGPOF is half the height of the 15.6 inch LCD display, about 100 mm. According to Eqs. (9)–(12) and the extreme resolution range of the human eye, the 𝑋1 is set to 0.44 mm. The scattering point efficiency coefficient 𝐾 = 0.2% and the weight 𝐺 ≈ 320 g. The spacing of scattering points and the coordinates of hot-working scattering points are calculated. The distribution of scattering points is shown in Fig. 8(a) and (b).

4. Experimental results and discussion 4.1. Fabrication of SGPOF To obtain the large-scale uniform SGPOF array, we need to explore the scattering point efficiency coefficient 𝐾. A hot-processing device is made, as shown in Fig. 5. The device mainly destroys the POF core– skin interface through a circular inserts, forming a V-shaped scattering point on the surface of the POF. A heat-conducting metal plates are heated using heaters and heat is transmitted to the blades, which for preventing the fiber from breaking and ensuring the integrity of the optical fiber during the machining process. 4

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Optics Communications 459 (2020) 125032

Fig. 9. The SGPOF with sphere-end of deferent shaped.

Fig. 7. Relationship between scattering rate and weight of processing device.

4.2. Improving the coupling efficiency of SGPOF In Fig. 9(a–h), a special shaped-end is produced by burning a gas flame on the end of the SGPOF, thus obtaining a circular-shaped endsurface of the fiber. Under the action of gas heat source, the end face of the fiber is melted and then cooled naturally. owing to the action of the surface tension, the circular spherical end face of various radians will be formed. Therefore, we inferred that the curvature radius of the end face is related to the temperature of the gas heat source and the distance between the fiber and the flame. According to this principle, we can fabricate spherical facets with uniform radians, which replaces the optical coupling lens and increase the coupling efficiency of the light beam. As show in Fig. 10, it is found that the coupling efficiency of the spherical face is 100%–300% times higher than that of the direct coupling efficiency, which is related to the radians of the spherical end face. Fig. 11(a) shows the optical components for compact autostereoscopic display screen, where each optical elements of 345 mm × 194 mm (15.6 inch.) and tight bonding each between optical elements. Fig. 11(b) shows the SGPOF array backlight module without cylindrical lens array, each SGPOF is kept in the specified position. To remove the seam of the hot-processing and the nonuniformity of intensity of the scattering point to be presented, the use of a vertical diffuser film is effective. The diffuser is inserted to blur the seam and nonuniform intensity of the scattering point. In contrast to the state of the SGPOF array backlight module without vertical diffusion film, as seen in Figs. (b, I) and (b, II), the luminance uniformity of backlight module for introducing vertical diffusion film is higher.

Fig. 10. Coupling powers of different end shape of the SGPOF.

4.3. Prototype implementation and test of compact auto-stereoscopic display To verify the effectiveness of the proposed method, we implemented a prototype of the proposed compact auto-stereoscopic display system by assembling the fabricated PDLC and CLA on the backlight mold frame with the LCD screen, and by connecting the assembled display module to the fabricated LED control module and display module. So as to evaluate the stereoscopic effects of auto-stereoscopic display, a crosstalk detector based on rotating detection method is developed. As shown in Fig. 12(a), the image luminance meter (EVERFINE CX-2B) is on the vertical line in the center of the auto-stereoscopic display screen. The auto-stereoscopic display is placed in the object plane (image luminance meter position) and the optimal viewing distance, 500 mm, is located at the image plane with the position determined by the parameter of CLA, which is the comfortable viewing distance for a small panel display system. Fig. 12(b) shows the working process of the experimental setup, the setup maintains the vertical distance (optimal viewing distance 500 mm). The measuring distance 𝑆𝐿 can be obtained by Eq. (15) and the movement distance 𝑆𝑀 can be calculated by Eq. (16). In Fig. 12(c), attention should be paid to making the center vertical line of the backlight coincide with the rotation axis of the rotatable disk when placing the auto-stereoscopic display. Furthermore,

Fig. 8. Graph of the relationship between the lattice spacing of scattering points (a), the coordinates of scattering points (b) and the ordinal number of scattering points.

5

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Optics Communications 459 (2020) 125032

Fig. 11. (a) Photograph of the optical components for compact auto-stereoscopic display screen. (b) Photograph of the SGPOF array backlight module, (I) the SGPOF array backlight effect without vertical diffusion film, (II) the SGPOF array backlight effect with vertical diffusion film.

Fig. 12. Configuration of testing system: (a) side-view diagram of luminance distribution measurement in optimal distance, (b) Top view diagram of relationship between movement distance and rotation angle, (c) setup for the entire experiment. Table 3 Luminance measurement.

we introduced a guide rail which is used to calibrate the position of image luminance meter. 500 (mm) cos 𝜃

(15)

𝑆𝑀 = 500 × tan 𝜃(mm)

(16)

𝑆𝐿 =

The obtained SGPOF directional backlight luminance distribution is shown in Fig. 13. It is basically consistent with our simulation results. The brightness of all viewing zones is about 60 cd∕m2 , which is not the maximum brightness of the prototype. The overall crosstalk is shown to be lower than 10%, and minimum achievable crosstalk can be as small as 2.2% in the viewing zones. It is found that the calculated crosstalk is slightly larger than that of the simulation because of the error in the fabrication of optical fiber array in the experiments. Overall, the agreement between the theory and the experiment is good. In order to evaluate the luminance uniformity of the directional backlight, we measured screen luminance of the nine typical areas of the screen as shown in Fig. 14 [18]. According to the image luminance meter EVERFINE CX-2B, with both left image and right image showing the white board. To reduce the measurement error, the sampling points

Option

Value

Sampling point coordinate Average luminance/cd ⋅ m−2 Sampling point coordinate Average luminance/cd ⋅ m−2

P1 95.391 P6 90.948

P2 88.356 P7 88.683

P3 93.489 P8 97.932

P4 92.709 P9 95.124

P5 87.465

are measured many times, the luminance value of 3D mode is recorded in Table 3. The average luminance uniformity M is calculated by Eq. (17) [19]: 𝑀=

𝐿(𝑃𝑖 )min × 100% 𝐿(𝑃𝑗 )max

(17)

Where 𝐿(𝑃𝑖 )min denotes the minimum luminance value of the 𝑖 point and 𝐿(𝑃𝑗 )max denotes the maximum luminance value of the point. According to Table 3, the luminance uniformity of the SGPOF directional backlight is 89.3%. 6

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Optics Communications 459 (2020) 125032

Fig. 15. Photos of images displayed by each viewpoint at different time.

We demonstrate binocular parallax recognizable by using different images (A and B) that corresponds to the left eye and right eye of observer . The binocular parallax is produced at different horizontal positions of the center of the cameras at the viewing zone. Fig. 16 shows the pictures shot at the optimal view distance of the proposed 3D display by NIKON camera D3400. The shooting viewing zones of each picture is labeled on the left side. Pictures in Figs. 16(c)–16(d) are shot in the center-view zone B, the crosstalk are almost invisible across the screen, except for overlaps in certain parts. The pictures Figs. 16(a)–16(b) and 16(e)–16(f) are shot at the viewing zones A and C, respectively. It can be seen that the crosstalk is increased slightly, the increasing crosstalk is caused by the beam expansion of decentered lens. Fig. 16 confirms a clear separation between the left and right images with a crosstalk of much less than 10%, and the crosstalk is acceptable in an entire viewing zones. Therefore, the technology we propose can provide high-quality 3D image display. The moiré pattern is an important issue for auto-stereoscopic display. In our prototype, The SGPOF array backlight module cylindrical lens period and the LCD display pixel period have the significant difference, only slight moiré pattern is produced. [20] In order to improve the performance of the auto-stereoscopic display much further, we will attempt to introduce a pseudo-random arranged color filter array to achieve a reduced moiré pattern [21]. Full-resolution 3D images are important to ensure the resolution of 3D mode and 2D mode. In 3D mode, the PDLC film stays in transparent state, the observers can be achieve directional backlighting auto-stereoscopic images. In 2D mode, all the SGPOFs are turned on and the PDLC film is switched to diffusive state, forming a uniform continuous backlight, which make the backlight lose its directivity. As show in Fig. 17. For 2D and 3D modes, the size and number of pixels are the same. The proposed auto-stereoscopic display achieves twodimensional and three-dimensional compatibility without reducing the resolution. The full-resolution and low-crosstalk 3D images are realized by using SGPOF backlight. It should also be noted that the system developed in this work is compatible with the existing 3D video format based on shutter glasses, thus greatly expanding its applicability. In most traditional multi-view 3D display, special video image format is especially needed. As shown in Fig. 18, the minimum thickness of the SGPOF array module is only 7 mm, and the minimum thickness of the display is 18 mm.

Fig. 13. Illustrations of the crosstalk measurement of the compact auto-stereoscopic display based on SGPOF.

Fig. 14. Sampling position of nine typical areas measurement method.

Table 4 Performance of compact auto-stereoscopic display system. Name

Data

Panel size Resolution in 2D Resolution in 3D Luminance Crosstalk Color temperature Thickness of auto-stereoscopic display

15.6 inch 1366 × 768 1366 × 768 ≥ 45 cd ⋅ m−2 ≤10% 6107 K 18 mm

The experimental results show that the luminance of the whole backlight can reach a high level of uniformity. Finally, we conducted the following experiments on the compact auto-stereoscopic display. The detailed display parameters are summarized in Table 4, the resolution maintains the 1366 × 768 and has a high uniformity. Fig. 15 shows the parallax image displayed by the auto-stereoscopic display at different times. The 𝑥-axis denotes time sequence, while the 𝑦-axis corresponds to the different images received by the observer’s left and right eyes. Actually, for the case that the left SGPOF turns on, only the left viewing-zone for the left image is viewed while the counterpart viewing-zone for the right image is kept to be almost dark, and vice versa. At time 𝑡1 , in the case of right eye, a bright image appears, while the left eye image appears dark due to the backlight in the direction of the time sequence principle. Similarly, at time 𝑡2 , a bright image can be observed in the left eye, while a bright image cannot be seen in the right eye. This indicates a clear separation between the left eye and the right eye, although there is a small crosstalk that the observer can tolerate. At time 𝑡3 , the image is restored to 𝑡1 so that can form a periodic display.

5. Conclusion Full resolution auto-stereoscopic 3D display based on directional backlight with SGPOF array module provides significant improvements in thickness, crosstalk and viewer mode switch compared to conventional auto-stereoscopic 3D displays. One of the more significant findings to emerge from this study is that the thickness of compact auto-stereoscopic display screen is only 18 mm. The second major finding is that the luminance uniformity of the backlight module is up to 89.3%, and the overall crosstalk is shown to be lower than 10%, and minimum achievable crosstalk can be as small as 2.2% in the 7

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Optics Communications 459 (2020) 125032

viewing zones, which can provide comfortable 3D visions. This study has shown that the coupled way with globular lens in end side of SGPOF is used to increase the coupling efficiency between LED and SGPOF. It is found that the coupling efficiency is 300% times higher than that of the direct coupling efficiency. In future work, we will consider following aspects: (1) Evaluating and improving the color gamut of the prototype; (2) Optimizing the CLA and improving the SGPOF position to reduce crosstalk of the display; (3) Using a larger number of SGPOF and high speed LCD screen together to realize more viewing zones. (4)Compressing the divergence angle of the LEDs to obtain the beam with small divergence angle to increase the optical coupling efficiency, so as to improve the luminance of the 3D prototype. CRediT authorship contribution statement Yong He: Conceptualization, Methodology, Writing - original draft. Chaohung Lu: Data curation, Software. Chujia Liu: Formal analysis, Investigation. Feifei Gao: Methodology. Zirun Li: Validation. Qiren Zhuang: Writing - review & editing, Funding acquisition. Acknowledgment This work was supported by the Key Program of Fujian Provincial Department of Science and Technology, China. [grant numbers: 2016H6016]. References [1] W. Yen, F. Chen, W. Chen, J. Liou, C. Tsai, Enhance Light Efficiency for Slim Light-Strip Array Backlight on Autostereoscopic Display, 2012, http://dx.doi.org/ 10.1109/3DTV.2012.6365474. [2] G.J. Lv, B.C. Zhao, F. Wu, W.X. Zhao, Y.Z. Yang, Q.H. Wang, Autostereoscopic 3D display with high brightness and low crosstalk, Appl. Opt. 56 (10) (2017) 2792–2795, http://dx.doi.org/10.1364/AO.56.002792. [3] W. Zhao, Q. Wang, D. Li, Y. Tao, Pixel arrangement of autostereoscopic liquid crystal displays based on parallax barriers, Mol. Cryst. Liq. Cryst. 1 (05) (2009) 67–72, http://dx.doi.org/10.1080/15421400903048305. [4] H. Fan, Y. Zhou, J. Wang, H. Liang, P. Krebs, J. Su, D. Lin, K. Li, 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. Disp. Technol. 11 (7) (2015) 620–624, http://dx.doi.org/10.1109/JDT.2015.2425432. [5] J. Liou, K. Lee, J. Huang, Low crosstalk multi-view tracking 3-D display of synchro-signal LED scanning backlight system, 7 (8) (2011) 411–419. http: //dx.doi.org/10.1109/JDT.2011.2134830. [6] J. He, Q. Zhang, J. Wang, J. Zhou, H. Liang, Investigation on quantitative uniformity evaluation for directional backlight auto-stereoscopic displays, Opt. Express 26 (8) (2018) 93–98, http://dx.doi.org/10.1364/OE.26.009398. [7] Z. Zhuang, L. Zhang, P. Surman, S. Guo, B. Cao, Y. Zheng, X.W. Sun, Directional view method for a time-sequential autostereoscopic display with full resolution, 55 (28) (2016) 7847–7854. http://dx.doi.org/10.1364/AO.55.007847. [8] J. Liou, C. Yang, F. Chen, Dynamic LED backlight 2D/3D switchable autostereoscopic multi-view display, J. Disp. Technol. 10 (8) (2014) 629–634, http://dx.doi.org/10.1109/JDT.2014.2307691. [9] H. Chen, H. Liang, Q. Zhang, J. He, J. Zhou, J. Li, J. Wang, T.H. Lin, I.C. Khoo, P-69: Studies on 2D/3D switchable autostereoscopic display with spatial and sequential hybrid control using PDLC films, 47 (1) (2016) 1395–1398. http://dx.doi.org/10.1002/sdtp.10939. [10] K. Li, H. Fan, J. Wang, Y. Xu, J. Zhou, Y. Zhou, Visual effect of a linear Fresnel lens illuminated with a directional backlight, 33 (6) (2016) 1155–1159. http://dx.doi.org/10.1364/JOSAA.33.00115. [11] Y. Chang, L. Tang, C. Yin, Efficient simulation of intensity profile of light through subpixel-matched lenticular lens array for two- and four-view auto-stereoscopic liquid-crystal display, 52 (1) (2013) A356. http://dx.doi.org/10.1364/AO.52. 00A356. [12] H. Liang, S. An, J. Wang, Y. Zhou, H. Fan, P. Krebs, J. Zhou, Optimizing time-multiplexing auto-stereoscopic displays with a genetic algorithm, J. Disp. Technol. 10 (8) (2014) 695–699, http://dx.doi.org/10.1109/JDT.2014.2314138. [13] H. Yong, L. Zirun, G. Feifei, L. Chujia, Q. Yu, Z. Qiren, Side-glowing optical fiber as directional backlight in autostereoscopic display, 45 (11) (2018) 202-211. http://dx.doi.org/10.3788/cjl201845.1106003. [14] J. Spigulis, D. Pfafrods, M. Stafeckis, W. Jelinska-Platace, Glowing Optical Fiber Designs and Parameters, 1997, http://dx.doi.org/10.1117/12.266542. [15] Y. Okuda, K. Onoda, I. Fujieda, Laser backlight unit based on a leaky optical fiber, 51 (7) (2012) 74001. http://dx.doi.org/10.1117/1.OE.51.7.074001.

Fig. 16. Demonstrated photographs of the proposed SGPOF-based directional backlight with the LCD panel at the positions of the left and right eyes: 16(a)–16(b), 16(c)–16(d) and 16(e)–16(f) Pictures shot in the positions of the left and right eyes in viewing zone A,B and C, respectively.

Fig. 17. Intuitional image in 2D mode (a) Outside viewing zones without PDLC, (b) Inside viewing zones without PDLC (c) Outside viewing zones with PDLC, (d) Inside viewing zones without PDLC.

Fig. 18. Thicknesses of the SGPOF array module (a) and the 3D display (b).

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