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Portable autostereoscopic display based on multi-directional backlight

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Abstract

A multi-directional backlight autostereoscopic display system with high resolution, low crosstalk, and motion parallax is developed in this paper. The proposed multi-directional backlight system is based on the Bragg mismatched reconstruction of volume holographic optical element (VHOE), and includes a set of light sources which are uniformly arrayed along one direction. Each light source produces its corresponding directional lighting to follow the human eye position detected by an eye tracker. Two scenarios are presented to build the multi-directional backlight system. The prism-type backlight system which guides the incident beam with a prism is relatively simple and easy to implement. The waveguide-type one which employs a transflective film to expand the incident light beam within the waveguide and modulate the intensity of the incident beam, is relatively thin and is applicable to large-area display. Two prototypes are built and the effectiveness of the proposed autostereoscopic display system is verified by the experimental results.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

The autostereoscopic display, which allows observers to view three-dimensional (3D) images without wearing auxiliary glasses, offers excellent potential for the next-generation portable display. There are several approaches to achieving autostereoscopic display, such as multi-projector display [13], integral imaging display [47], nano-grating based 3D display [810] and directional backlight 3D display [1115]. The multi-projector display could produce high resolution 3D images with large field of view (FOV) by increasing the number of projectors. However, an accurate calibration is required and a bulky display system cannot be avoided. The integral imaging display and nano-grating based 3D display, which could yield ultra-thin and lightweight display systems, can be applied to portable autostereoscopic display. These two display approaches produce 3D images by dividing the information displayed on the liquid crystal display (LCD) panel to multiple views. Since the amount of pixels of an LCD panel is limited, tradeoffs should be made between spatial resolution and FOV of the integral imaging display and nano-grating based 3D display, and it may be impossible to produce full-resolution 3D images due to the nature of these two display approaches. Moreover, crosstalk cannot be avoided, and it is usually difficult to produce high-performance 3D images with large image depth in these two display approaches. The directional backlight 3D display systems based on time multiplexing technique can produce high resolution 3D images, which could be comparable to two-dimensional (2D) images. This enables the directional backlight 3D display to become a promising approach for autostereoscopic display. Generally, the directional backlight 3D display systems employ a 3D film and an LCD panel to time-sequentially direct full-resolution images to left and right eyes. Ting proposed a full-resolution 3D display for three observers with an inverted trapezoid structure on a multi-user 3D film [13]. Feng employed a sequential beam splitter array to realize a high resolution 3D display with low crosstalk [14]. Hwang developed a time-sequential directional backlight display system with full-resolution images by using volume holographic optical element (VHOE) to replace the conventional 3D film [15]. However, it may be challenging to precisely manipulate the light field and produce multi-directional beams in the time-sequential directional backlight display system. Consequently, high-performance 3D images cannot be guaranteed due to large crosstalk and the lack of motion parallax [16].

This paper presented a time-sequential multi-directional backlight 3D display system with high resolution, low crosstalk, and motion parallax. The key component of the proposed display system is the multi-directional backlight which is based on the Bragg mismatched reconstruction of the VHOE. An LED light source array, which includes a set of LED light sources uniformly arrayed along one direction, is used in the proposed backlight system. An eye tracker detects the current position of the human eye and the corresponding LED source is lit up to produce a directional backlight for that eye position. The rest of this paper is organized as follows. The principle of the proposed system and the recording process of VHOE are introduced in Section 2. The influence of the VHOE orientation on the Bragg mismatched reconstruction is analyzed to guide the fabrication of VHOEs in Section 3. Also in this section, two prototypes are built and the performance of the proposed display system is evaluated. After that, the influence of some key parameters of the proposed display system on the display performance is discussed in Section 4 before we conclude our work in Section 5.

2. Design methodology

2.1. Principle of multi-directional backlight 3D display system

Motion parallax can be realized by changing the retinal images with the eye position in real-time. However, it is not a simple task to achieve motion parallax in the directional backlight 3D display. There are two different ways to achieve the movement of binocular viewpoints. The first one is to mechanically rotate or move the light sources to track the movement of human eyes [17]. The second one is to keep the light source array fixed and then light up the corresponding light source according to the current eye position. To reduce the motion error and achieve high real-time performance, the second method is used in the proposed 3D display system.

The proposed multi-directional backlight 3D display system includes a multi-directional backlight system, an LCD panel, a diffuser with a small circular diffusion angle, and an eye tracker. A desired directional lighting that follows the human eye is produced by the multi-directional backlight according to the feedback of the eye tracker, and is further modulated by the LCD panel to produce a directional image. In order to achieve 3D display, two directional images are sequentially projected to the left and right eyes. The proposed multi-directional backlight system includes an LED light source array, a cylindrical lens, a prism (or a waveguide with an in-coupling prism and a transflective film), a VHOE, and a Fresnel lens, as shown in Fig. 1. A group of LED light sources which can be controlled independently are arrayed along the x-axis direction. The light beam emanating from the LED source is collimated in the z-axis direction by the cylindrical lens, and further diffracted by the VHOE to propagate in the desired direction. Each LED source corresponds to a different direction. The unique Bragg mismatched reconstruction of VHOE allows us to produce a different directional beam by lighting up its corresponding LED source. The proposed multi-directional backlight system can be built upon two different scenarios, as shown in Fig. 1. The first one employs a prism to guide the light beam, and the VHOE is attached to the inclined plane of the prism, as shown in Fig. 1(a). The second one uses a waveguide to direct the light beam, and the VHOE is attached to the bottom of the waveguide, as shown in Fig. 1(b). It should be noted that the transflective film with a particular beam splitting ratio is coated on the bottom of the waveguide before the VHOE is attached. Due to the unique feature of the transflective film, a portion of the light beam incident on the transflective film is transmitted to the VHOE and further extracted from the waveguide, while the remainder continues propagating within the waveguide and repeats the same transmission and reflection process when reaching the transflective film again. The structure of the prism-type multi-directional backlight system is relatively simple and easy to implement. The thickness of the backlight system is determined by the size of the LCD panel. The waveguide-type multi-directional backlight system is much thinner and not limited by the size of the LCD panel. These two scenarios are both implemented in the proposed multi-directional backlight 3D display system.

 figure: Fig. 1.

Fig. 1. Configurations of the proposed multi-directional backlight 3D display, (a) the prism-type 3D display and (b) the waveguide-type 3D display.

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2.2. Recording process of the VHOE

The proposed system has horizontal parallax in the x-axis direction while it does not have vertical parallax in the y-axis direction. To achieve this goal, a directional diffuser is placed in between the mirror and the photopolymer during the recording process of the VHOE, as shown in Fig. 2. After the reference wave and object wave are interfered within a photopolymer, the VHOE is formed by recording the fringe pattern in the material [1822]. When replaying the recorded VHOE with the reference beam, the reconstructed diffused light could be decomposed into a set of plane waves with different propagation directions [23], therefore these multiple plane waves can cover multiple viewpoints in the y-axis direction.

 figure: Fig. 2.

Fig. 2. Schematically diagram of the recording setup for (a) the prism-type VHOE, and (b) the waveguide-type VHOE.

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Figure 2 depicts the recording setup for the prism-type and the waveguide-type VHOEs. The light beam emanating from a green laser is converted into two s-polarized light beams after passing through two half-wave plates (λ/2) and a cube polarization beam splitter (PBS). These two light beams are further collimated and expanded by a spatial filter and a collimating lens. A cylindrical lens and a directional diffuser which diffuses the light rays almost exclusively in one direction are used to generate the reference and object waves, respectively. Subsequently, the interference intensity pattern is recorded on a photopolymer. In the manufacture of the prism-type VHOE shown in Fig. 2(a), a prism is used to direct the reference beam to the photopolymer. Figure 2(b) illustrates the fabrication of the waveguide-type VHOE. A transflective film is coated on the bottom of the waveguide, which is located in between the waveguide and the photopolymer. The reference beam is refracted by an in-coupling prism, and then propagates along the waveguide with an incident angle larger than the critical angle. The travelling light beam within the waveguide is split into transmitted and reflected beams after encountering the transflective film. The transmitted beam strikes the photopolymer to participate in the recording process, while the reflected beam continues propagating within the waveguide and then repeats the above transmission and reflection process when reaching the transflective film again. To ensure that the transmitted beam illuminates the entire photopolymer without overlapping, the footprint width of the incident beam on the bottom of the waveguide should be equal to the propagation period, which is the distance between two bounces of the beam on the bottom of the waveguide.

3. Model implementation and experimental validations

3.1 VHOE reconstruction model

Efficient wavefront reconstruction can be achieved when the incident reading wave works at or near the Bragg angle. A reconstructed wave which is slightly weakened can be produced when the angular deviation is small. This is called the Bragg mismatched reconstruction [18]. The angular deviation in the proposed system is mainly caused by the marginal light source. However, the reconstructed wave is still affected by the orientation of the VHOE even if the marginal light source satisfies the Bragg mismatched reconstruction condition. Thus, it is necessary to build a VHOE model to analyze the influence of the orientation of VHOE on Bragg mismatched reconstruction [2426]. The VHOE reconstruction model is given in Fig. 3. Here, f is the focal length of the cylindrical lens, d1 denotes the distance between the cylindrical lens and the prism, d2 denotes the half-length of the prism, and α is the tilt angle of the VHOE. The efficient wavefront reconstruction represented by the solid blue lines in Fig. 3 is achieved by the initial reference beam emanating from the on-axis light source. The solid green line shown in Fig. 3 denotes the Bragg mismatched reconstruction produced by the marginal light source. The VHOE is attached to the inclined plane of the prism, and the vertex angle of the prism is changed from 65° to 89°. Since the fabrication principle between prism-type VHOE and waveguide-type VHOE is similar, the prism-type VHOE is taken here as an example. The object wave which has a spread angle only in the y-axis direction could be decomposed into a set of plane waves with different propagation directions, and therefore the fabricated VHOE could be considered as the superposition of multiple gratings recorded by plane waves [23]. Since only one plane wave component which corresponds to one grating in the VHOE can be captured by the human eye when the visual angle of the VHOE is relatively small, it allows us to employ a plane wave instead of the diffused wave. The specifications of the design model are given in Table 1.

 figure: Fig. 3.

Fig. 3. The influence of VHOE orientation on Bragg mismatched construction, (a) geometric layout and (b) side view of the VHOE reconstruction model.

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Tables Icon

Table 1. Specifications of the two models

Since the VHOE in the proposed system is fabricated by non-plane waves, the grating vectors vary continuously over the entire VHOE. By sampling the VHOE at a sufficiently high density, the grating at each sampled point could be considered to be recorded by two plane waves. This allows us to calculate the grating vector at each sampled point on the VHOE and therefore evaluate the diffraction efficiency of the VHOE. We use the Kogelnik’s coupled theory to calculate the diffraction efficiency at each sample point on the VHOE [27]. Figures 4 (a) and 4(b) give the distributions of diffraction efficiency over the entire VHOE when the vertex angle of the prism equals 65° and 73°, respectively. From Fig. 4(a) we observe that the uniformity of the distribution of diffraction efficiency is not that good when the vertex angle equals 65°. In order to quantify the distribution of diffraction efficiency, we let ηcontrast denote the diffraction efficiency contrast which is given by

$${\eta _{contrast}} = 1 - \frac{{{\eta _{min}}}}{{{\eta _{max}}}}, $$
where, the ηmin and ηmax represent the minimum and maximum local diffraction efficiency over the entire VHOE, respectively. A smaller value of ηcontrast indicates a higher uniformity of the distribution of the diffraction efficiency, and higher performance of the VHOE. We also employ ηaverage to denote the average diffraction efficiency. It is obvious that a high value of ηaverage indicates more energy of the reconstructed beam and a high brightness of the display system. It should be mentioned that the reconstructed wave cannot be focused to a point on the image plane due to the fact that the incident light emanating from the marginal light source does not satisfy the Bragg condition, as shown in Fig. 3. The wavefront aberration caused by the Bragg mismatched condition may introduce crosstalk in the system. A large Root-Mean-Square (RMS) spot radius indicates a high crosstalk. Thus, we need to find an optimal tilt angle of the VHOE to obtain a small RMS radius, a high ηaverage, and a low ηcontrast. According to the influence of VHOE orientation given in Figs. 4(c) and 4(f), we know that high brightness and excellent uniformity can be achieved when the tilt angle is greater than 73°. Since the RMS radius monotonically increases, a tilt angle of 73° is chosen to reduce the crosstalk and guide the subsequent experiments on the VHOE fabrication.

 figure: Fig. 4.

Fig. 4. The influence of VHOE orientation on Bragg mismatched reconstruction for (a-c) the large size VHOE and (d-f) the small size VHOE. The diffraction efficiency distributions for (a) the large size VHOE with tilt angle of 65°, (b) the large size VHOE with tilt angle of 73°, (d) the small size VHOE with tilt angle of 65°, and (e) the small size VHOE with tilt angle of 73°. The average diffraction efficiency, diffraction efficiency contrast, and RMS radius at different tilt angles for (c) the large size VHOE and (f) the small size VHOE.

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3.2 Prism-type multi-directional backlight 3D display system

Figure 2(a) depicts the recording setup for the prism-type VHOE. We use a customized prism (length = 68mm, width = 40mm, and height = 20mm) with an apex angle of 73.6°, and a photopolymer film (Geola Digital, UAB) is laminated on the inclined plane of the prism. The reference beam after refraction by a cylindrical lens (Thorlabs LJ1125L2) with a focal length of 40mm illuminates the photopolymer film. The object beam has a spread angle of 60° in the y-axis direction and 1° in the x-axis direction after it passes through a directional diffuser (Luminit). The optical power density of the reference and object wave equals 0.256 mW/cm2. After exposure, the VHOE is bleached for about 2 minutes under a UV lamp. The diffraction efficiency of the fabricated VHOE is defined by [15]

$$\eta = \frac{{{P_{diff}}}}{{{P_{diff}} + {P_{trans}}}}, $$
where, Pdiff and Ptrans denote the power density of the diffracted and transmitted beam, respectively. The diffraction efficiency of the fabricated VHOE is approximately 70.53%.

After the VHOE is constructed, we build the prism-type multi-directional backlight system. The LED light source array (Everlight, 16-213/GHC-YR1S1/3T) includes 25 LED sources uniformly arranged along the x-axis direction, and the interval between every two neighboring LEDs equals 2mm. The fabricated VHOE is attached to the inclined plane of the prism, as shown in Fig. 5(a). A diffuser (not shown in Fig. 5(a)) with a small circular diffusion angle of 3.5° is placed in front of the Fresnel lens to improve the illumination uniformity. Figures 5(b) and 5(c) give the images captured on the diffuser when the central and marginal LED light sources are lit up, respectively. The uniformity of the irradiance distribution on the diffuser is defined by [28,29]

$$U = 1 - \frac{{{I_{max}} - {I_{min}}}}{{{I_{max}} + {I_{min}}}}, $$
where, Imax and Imin represent the maximum and minimum irradiance, respectively. Obviously, a larger value of U indicates a higher uniformity. According to the recorded irradiance distributions given in Figs. 5(b) and 5(c), we know that U = 82.79% and 81.55%, indicating a good display performance at both the central and marginal viewing zones.

 figure: Fig. 5.

Fig. 5. Experimental verification of the prism-type multi-directional backlight system. (a) Prototype of the prism-type multi-directional backlight. The irradiance distributions on the diffuser illuminated by (b) the central and (c) the marginal LED light sources, respectively. (d) The normalized intensity distributions at seven viewing zones.

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The crosstalk between two eyes is a critical factor that affects the performance of the 3D display system and is given by [30,31]

$$Crosstalk = \frac{{{I_{noise}}}}{{{I_{signal}}}}, $$
where, Isignal denote the intensity of outgoing light beam produced by the current desired light source, and Inoise is the light intensity of outgoing light beam produced by the other light sources. A Chroma Meter (CL-200) is placed on the observation plane which is placed at 300 mm to the left of the Fresnel lens to measure the intensity distribution of every directional lighting. Figure 5(d) depicts the normalized intensity distributions at 7 viewing zones produced by the proposed backlight system with a 3.5° diffuser. The average and maximum binocular crosstalk of the prism-type 3D display system equals 2.75% and 4.1%, respectively, which are less than the threshold value of 5% [30]. It is worth mentioning that the interval between each two neighboring LED light sources does not introduce a black band effect because there are overlapping areas between the 25 viewing zones.

An LCD panel (sharp LCY-131402B) is used here to modulate the multi-directional backlight, and an eye tracker is employed to track the movement of the human eye. The FOV of the display system equals 32°. From this experimental result, we know the angular bandwidth is relatively large, which is a unique feature of the proposed system. This is due to the fact that the LED light sources are arrayed in the sagittal plane, this arrangement means the azimuthal angle of each incident light beam is different, and the decay in diffraction efficiency is slow when the incident light beam changes in azimuthal angle [32]. Figure 6 shows the captured images at five different viewing zones at a view distance of 300mm. These high-quality images indicate an excellent performance of the proposed multi-directional backlight 3D display system.

 figure: Fig. 6.

Fig. 6. Images captured at five viewing zones of the prism-type 3D display. We use a “dice” model with royalty-free license from http://www.cgtrader.com.

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3.3 Waveguide-type multi-directional backlight 3D display system

The cylindrical lens and the directional diffuser used above are also employed in the optical recording setup for the waveguide-type VHOE. After the cylindrical reference wave is constructed, the light beam passes through the in-coupling prism and propagates within the waveguide with an incident angle of 73°. The thickness of the waveguide equals 3mm. Then, a portion of incident light beam is transmitted to the photopolymer by the transflective film coated at the bottom of the waveguide. Since the ratio between reflection and transmission of the transflective film is constant, the power intensity of the transmitted beam decreases with the propagation period. The fabricated VHOE may have different diffraction efficiency and inevitably generate a nonuniform outgoing beam. In order to produce the outgoing diffracted beam with a uniform intensity distribution, the pre-exposure method, which is realized by illuminating the photopolymer with a light beam before the recording process of a VHOE, is used here to control diffraction efficiency of the VHOE [33]. Two propagation periods are considered when recording the VHOE in the experiment for simplicity. The pre-exposure method is employed for sub-VHOE in the first propagation period to adjust its diffraction efficiency. The intensity ratio between the object and reference waves is set to be 1 in order to achieve an optimal diffraction efficiency of the sub-VHOE in the second propagation period.

Figure 7 gives the experimental fabrication process of the VHOE. We place a shelter in front of the first propagation period to block out the object wave in the pre-exposure process. It should be noted that the pre-exposure process does not affect the sub-VHOE recording in the second propagation period. After the pre-exposure process, the shelter is removed to initialize the sub-VHOE recording in the first propagation period, while the sub-VHOE in the second propagation period is still under recording. The power of the outgoing light beam from the sub-VHOEs in the first and second propagation periods is measured after UV bleaching. The power difference between these two outgoing light beams is quantified by the relative power error δ, which is defined by

$$\delta \textrm{ } = \textrm{ }\frac{{{P_1} - {P_2}}}{{{P_2}}} \times 100\%, $$
where, P1 and P2 respectively represent the power of the outgoing light beams from the first and second propagation periods. A smaller value of δ indicates less power difference between the two outgoing light beams. Figure 7(c) depicts the relationship between the pre-exposure time and the relative power error δ. From this figure we choose an optimal pre-exposure time and record the waveguide-type VHOE with a pre-exposure time of 1.15s. The diffraction efficiency of the waveguide-type VHOE is 67.6%.

 figure: Fig. 7.

Fig. 7. Fabrication of the waveguide-type VHOE. (a) Pre-exposure process, (b) recording process, and (c) relative power error at different pre-exposure times.

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After the waveguide-type VHOE is fabricated, we built the waveguide-type multi-directional backlight system. The LED light source array (Togaled, TJ-S2016G05YK-A3) is used here which includes 7 LED sources uniformly arrayed along the x-axis direction, and the interval between two neighboring LED sources is equal to 6mm. The fabricated VHOE is laminated on the backside of the waveguide, as shown in Fig. 8(a). The 3.5° diffuser which is not shown in Fig. 8(a) is also placed in front of the Fresnel lens to improve the illumination uniformity. Figures 8(b) and 8(c) give the irradiance distributions on the diffuser when the central and marginal LED light sources are turned on, respectively. From these two figures we know that the irradiance uniformity equals 76% and 68.64%. We also calculate the crosstalk of this system. The normalized intensity distributions at 7 viewing zones are depicted in Fig. 8(d). The average binocular crosstalk equals 5.55%. The overlapping area between each two neighboring viewing zones shown in Fig. 8(d) also indicates the black band effect can be avoided.

 figure: Fig. 8.

Fig. 8. Experimental verification of the waveguide-type multi-directional backlight system. (a) Prototype of the waveguide-type multi-directional backlight. The irradiance distributions on the diffuser produced by (b) the central LED light source and (c) the marginal LED light source. (d) The normalized intensity distributions at 7 viewing zones.

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We also built the prototype of the waveguide-type 3D display system which includes the same LCD panel and eye tracker used in the prism-type multi-directional 3D display system. The FOV of the display system equals 27°. Figure 9 gives the images captured at five different viewing zones at a view distance of 300mm. These high-quality images also indicate an excellent performance of the proposed waveguide-type multi-directional 3D display system.

 figure: Fig. 9.

Fig. 9. Images captured at five viewing zones of the waveguide-type 3D display. We use a “dice” model with royalty-free license from http://www.cgtrader.com.

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4. Discussions

4.1 Uniformity

As mentioned above, we use a diffuser with a small circular diffusion angle to improve the uniformity of the multi-directional backlight display. When the marginal LED is lit up, some outgoing light rays would slightly deviate from the corresponding viewing direction due to the Bragg mismatch. When the human eye moves to the corresponding viewing position, only a part of the displayed image can be captured, as shown in Fig. 10. This issue can be well addressed by using a diffuser with a small diffusion angle. The maximum deviation angle which is the maximum angle from between the corresponding viewing direction and the direction of the outgoing light ray equals 1.44°. A 3.5° circular angle diffuser is used to spread the light beam so that the human eye can capture the entire image. Although the footprint of the outgoing beam on the observation plane at each viewing zone increases slightly due to the scattering property of the diffuser, the uniformity of the backlight system can be dramatically improved, as shown in Figs. 5 and 8. Moreover, the nonuniformity caused by errors during fabricating the VHOE can also be eliminated by the use of a diffuser.

 figure: Fig. 10.

Fig. 10. Images captured on the observation plane at (a) 5mm to the left of the corresponding viewing position, (b) the corresponding viewing position, and (c) 5mm to the right of the corresponding viewing position.

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4.2 Crosstalk

Crosstalk is mainly caused by the incomplete separation of footprints of the outgoing beams on the observation plane, and therefore the footprint width needs to be controlled in the proposed autostereoscopic display system. In addition to the influence of the diffuser, the footprint width is also determined by the Bragg mismatch condition and the source size. Since the Bragg mismatched reconstruction is employed to achieve multiple directional outgoing beams, it is necessary to analyze the influence of source size on crosstalk. The LED light sources with small size are employed in the proposed prism-type multi-directional backlight, and therefore low crosstalk 3D images are achieved. However, these LED light sources which have relatively low power cannot meet the requirement of the waveguide-type system. Inevitably, a larger size of high-power LED light source yields a large footprint size of the outgoing beam and a larger crosstalk, as shown in Subsection 3.2. We also employed a laser diode (LD) source instead of the LED sources in the waveguide-type system, as shown in Fig. 11(a). The LD source is placed on a linear translation stage and moved with an interval of 6mm along the x-axis direction. The normalized intensity distributions for the LD source in different positions are depicted in Fig. 11(b). The value of average crosstalk is reduced to 2.41% due to the small étendue of the LD source. However, interference fringes cannot be avoided due to the nature of an LD source. The micro-LEDs which have high brightness and small étendue could also be used to reduce the crosstalk, and the performance of the proposed system could be further improved with the increase of brightness of micro-LED source.

 figure: Fig. 11.

Fig. 11. Experimental verification of the waveguide-type multi-directional backlight system with LD source. (a) Prototype of the waveguide-type multi-directional backlight with LD source, (b) normalized intensity distributions at 7 viewing zones.

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4.3 Fabrication of large-area VHOEs and full-color display

As mentioned above, the proposed waveguide-type configuration can be applied to create large-area and ultra-thin backlight systems. A key step in fabricating large-area VHOEs is to design a special transflective film. In order to achieve a high uniformity of the transmitted light beam, the transmittance of the transflective film should be elaborately tailored according to the propagation of light within the waveguide. After the special transflective film is obtained, the fabrication of large-area VHOEs becomes relatively simple and no pre-exposure processing is required.

It is of great interest to mention that the proposed method can also be applied to design full-color multi-directional backlight systems. Due to the high wavelength selectivity of VHOEs, the incident light whose wavelength deviates greatly from the recording wavelength will be transmitted without diffraction [34]. This allows us to fabricate red, green, and blue VHOEs separately with the proposed fabrication method. After stacking the red, green, and blue VHOEs together in the multi-directional backlight 3D display system, full-color 3D perception can be achieved. If chromatic dispersion takes place in the display system, it can be suppressed by pre-processing the displayed images and pre-designing the VHOEs.

5. Conclusion

In summary, a time-sequential autostereoscopic display which generates full-resolution and low crosstalk 3D images with motion parallax is proposed in this paper. The multi-directional backlight system based on the Bragg mismatched reconstruction of the VHOE produces the desired directional lighting to follow the human eye position detected by the eye tracker. The multi-directional backlight can be realized in two scenarios. The prism-type backlight, in which the VHOE is laminated on the inclined plane of the prism to diffract the incident light beam, is relatively simple and easy to implement. The waveguide-type backlight employs a transflective film located between the waveguide and the VHOE to expand the incident light beam within the waveguide and modulate its intensity. The waveguide-type backlight system is relatively thin and can be applied to ultra-thin and large-area display systems. Two high-performance autostereoscopic display systems are built and high resolution images with low crosstalk and motion parallax can be observed at each viewing zone. Since the high resolution 3D images are achieved by the temporal multiplexing, the frame rate inevitably decreases to half (left/right eyes), and it is further reduced with the increase of the number of the observers. An LCD panel with higher refresh rate could alleviate the influence caused by frame rate decrease. Although a monochromatic autostereoscopic 3D display is demonstrated here, the proposed autostereoscopic 3D display system can also be applied to full-color display.

Funding

National Key Research and Development Program of China (2021YFB2802200).

Disclosures

The authors declare that there are no conflicts of interest related to this paper.

Data Availability

No data were generated or analyzed in the presented research.

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Data Availability

No data were generated or analyzed in the presented research.

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Figures (11)

Fig. 1.
Fig. 1. Configurations of the proposed multi-directional backlight 3D display, (a) the prism-type 3D display and (b) the waveguide-type 3D display.
Fig. 2.
Fig. 2. Schematically diagram of the recording setup for (a) the prism-type VHOE, and (b) the waveguide-type VHOE.
Fig. 3.
Fig. 3. The influence of VHOE orientation on Bragg mismatched construction, (a) geometric layout and (b) side view of the VHOE reconstruction model.
Fig. 4.
Fig. 4. The influence of VHOE orientation on Bragg mismatched reconstruction for (a-c) the large size VHOE and (d-f) the small size VHOE. The diffraction efficiency distributions for (a) the large size VHOE with tilt angle of 65°, (b) the large size VHOE with tilt angle of 73°, (d) the small size VHOE with tilt angle of 65°, and (e) the small size VHOE with tilt angle of 73°. The average diffraction efficiency, diffraction efficiency contrast, and RMS radius at different tilt angles for (c) the large size VHOE and (f) the small size VHOE.
Fig. 5.
Fig. 5. Experimental verification of the prism-type multi-directional backlight system. (a) Prototype of the prism-type multi-directional backlight. The irradiance distributions on the diffuser illuminated by (b) the central and (c) the marginal LED light sources, respectively. (d) The normalized intensity distributions at seven viewing zones.
Fig. 6.
Fig. 6. Images captured at five viewing zones of the prism-type 3D display. We use a “dice” model with royalty-free license from http://www.cgtrader.com.
Fig. 7.
Fig. 7. Fabrication of the waveguide-type VHOE. (a) Pre-exposure process, (b) recording process, and (c) relative power error at different pre-exposure times.
Fig. 8.
Fig. 8. Experimental verification of the waveguide-type multi-directional backlight system. (a) Prototype of the waveguide-type multi-directional backlight. The irradiance distributions on the diffuser produced by (b) the central LED light source and (c) the marginal LED light source. (d) The normalized intensity distributions at 7 viewing zones.
Fig. 9.
Fig. 9. Images captured at five viewing zones of the waveguide-type 3D display. We use a “dice” model with royalty-free license from http://www.cgtrader.com.
Fig. 10.
Fig. 10. Images captured on the observation plane at (a) 5mm to the left of the corresponding viewing position, (b) the corresponding viewing position, and (c) 5mm to the right of the corresponding viewing position.
Fig. 11.
Fig. 11. Experimental verification of the waveguide-type multi-directional backlight system with LD source. (a) Prototype of the waveguide-type multi-directional backlight with LD source, (b) normalized intensity distributions at 7 viewing zones.

Tables (1)

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Table 1. Specifications of the two models

Equations (5)

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η c o n t r a s t = 1 η m i n η m a x ,
η = P d i f f P d i f f + P t r a n s ,
U = 1 I m a x I m i n I m a x + I m i n ,
C r o s s t a l k = I n o i s e I s i g n a l ,
δ   =   P 1 P 2 P 2 × 100 % ,
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