High-optical-efficiency integral imaging display based on gradient-aperture pinhole array

Fei Wu; Huan Deng; Da-Hai Li; Qiong-Hua Wang

doi:10.1117/1.OE.52.5.054002

14 May 2013 High-optical-efficiency integral imaging display based on gradient-aperture pinhole array

Fei Wu, Huan Deng, Da-Hai Li, Qiong-Hua Wang

Author Affiliations +

Optical Engineering, Vol. 52, Issue 5, 054002 (May 2013). https://doi.org/10.1117/1.OE.52.5.054002

Abstract

An integral imaging (II) display is proposed which consists of a display panel and a gradient-aperture pinhole array. The gradient-aperture pinhole array is symmetrical in both horizontal and vertical directions. The leftmost and rightmost pinholes are used to fix the horizontal viewing angle, and the uppermost and nethermost pinholes are used to fix the vertical viewing angle. To increase the optical efficiency, the aperture widths of other pinholes are gradually increased from both sides to the middle in the horizontal and vertical directions, respectively. A prototype of the proposed II display is developed. Its horizontal viewing angle is equal to that of the conventional one, while its optical efficiency is higher than that of the conventional one.

1. Introduction

Integral imaging (II) display which presents true three-dimensional (3-D) images with full parallax and continuous viewpoints is regarded as a promising 3-D display.¹ However, it is difficult to realize high resolution, wide viewing angle and large depth display.²^–⁴ To overcome these disadvantages, a number of methods have been proposed.⁵^–⁹ The II display based on a pinhole array has less space and lower cost than that based on a lens array. Moreover, the II display based on a pinhole array is simple in realizing a compact 3-D-2-D convertible display system.¹⁰ An II display using an organic light emitting diode panel as a direct emissive light source is proposed with improved optical efficiency.¹¹ However, low optical efficiency is still one of the problems in the conventional II display using a pinhole array. When the aperture width of the pinhole array is increased, the optical efficiency of the II display is increased, while the crosstalk of the II display is also increased to decrease the viewing angle. We propose an II display using a gradient-aperture pinhole array to overcome the limitation of low optical efficiency. The optical efficiency can be enhanced without loss of the horizontal viewing angle.

2. Structure and Principle

Figure 1 illustrates the structure of the proposed II display. It consists of a display panel and a gradient-aperture pinhole array. Aperture centers of the gradient-aperture pinhole array are located at the centers of the corresponding element images on the display panel. Lights emitted from the elemental image array (EIA) displayed on the display panel are modulated by the gradient-aperture pinhole array, which reconstructs angular distribution of the rays and hence displays the 3-D images.

Fig. 1

Structure of the proposed II display.

Figure 2 shows the structure of the gradient-aperture pinhole array. The gradient-aperture pinhole array is symmetrical in both horizontal and vertical directions. Its aperture widths are gradually increased from both sides to the middle in the horizontal and vertical directions.

Fig. 2

Structure of the gradient-aperture pinhole array.

The principle of the proposed II display is shown in Fig. 3. Suppose that $L$ is the viewing distance between the gradient-aperture pinhole array and the observer, $g$ is the gap between the gradient-aperture pinhole array and the display panel, $p$ is the pitch of the gradient-aperture pinhole array, $D$ is the width of the viewing zone, and $W$ is the aperture width of a conventional pinhole. $M$ and $N$ are the numbers of the elemental images in the horizontal and vertical directions, respectively. $H_{i}$ and $V_{j}$ denote the horizontal and vertical widths of the pinhole which is in the $i$ -th column and $j$ -th row, respectively. $i$ is a positive integer which is greater than or equal to 1 and less than or equal to $M$ , and $j$ is a positive integer which is greater than or equal to 1 and less than or equal to $N$ .

Fig. 3

Principle of the proposed II display.

As shown in Fig. 3, we can see that when $L$ is constant, the viewing angle of the proposed II display is only determined by $D$ . When the gradient-aperture pinhole array and the display panel are fixed, $D$ is only determined by the solid lines emitted from the leftmost and rightmost pinholes. Therefore, the horizontal viewing angle of the proposed II display is only determined by the solid lines emitted from the leftmost and rightmost pinholes. When the horizontal viewing angle of the proposed II display is equal to that of the conventional II display, the relationship between $H_{1}$ and $W$ can be determined as

Eq. (1)

H_{1} = W .

Points A and B are the points on the left and right edges of the viewing zone, respectively. The dotted lines emitted from the pinholes whose aperture widths are increased in the left half of the gradient-aperture pinhole array converge on Point B, and the dashed lines emitted from the pinholes whose aperture widths are increased in the right half of the gradient-aperture pinhole array converge on Point A. According to the position of each pinhole in horizontal direction, its horizontal width is increased to increase the optical efficiency of the proposed II display.

H_{i}

is given by a simple geometric calculation as follows:

Eq. (2)

{\begin{cases} H_{i} = H_{1} + \frac{2 g p}{L + g} (i - 1) & 1 \leq i \leq \frac{M}{2} \\ H_{i} = H_{1} + \frac{2 g p}{L + g} (M - i) & \frac{M}{2} < i \leq M \end{cases} .

The horizontal viewing angle of the proposed II display

θ_{H}

is expressed as

Eq. (3)

θ_{H} = 2 arc \tan [\frac{p - H_{1}}{2 g} - \frac{(M - 1) p}{2 L}] .

Suppose that

H_{MAX}

and

V_{MAX}

are the horizontal and vertical widths of the central pinhole, respectively. To obtain maximum optical efficiency, the relationship between

H_{MAX}

and

V_{MAX}

can be obtained as

Eq. (4)

H_{MAX} = V_{MAX} .

In a similar way,

V_{j}

is deduced as

Eq. (5)

{\begin{cases} V_{j} = V_{MAX} - \frac{2 g p}{L + g} [ceil (\frac{N}{2}) - j] & 1 \leq j \leq \frac{N}{2} \\ V_{j} = V_{MAX} - \frac{2 g p}{L + g} [j - floor (\frac{N}{2}) - 1] & \frac{N}{2} < j \leq N \end{cases} .

The vertical viewing angle of the proposed II display

θ_{V}

is shown as

Eq. (6)

θ_{V} = 2 \arctan [\frac{p - V_{1}}{2 g} - \frac{(N - 1) p}{2 L}] .

The optical efficiency of the conventional II display

φ

is expressed as

Eq. (7)

φ = \frac{W^{2}}{p^{2}} .

The optical efficiency of the proposed II display

φ^{'}

is also shown as

Eq. (8)

φ^{'} = \sum_{i = 1}^{M} \sum_{j = 1}^{N} \frac{H_{i} V_{j}}{M N p^{2}} .

As mentioned above, the horizontal viewing angle and optical efficiency of the conventional II display are related to $W$ . As shown in Eqs. (2), (3), (5), and (8), the horizontal viewing angle of the proposed II display is related to $H_{1}$ , which is equal to $W$ , while the optical efficiency of the proposed II display is related to $H_{i}$ and $V_{j}$ , which are greater than or equal to $W$ . Therefore, when the horizontal viewing angle of the proposed II display is equal to that of the conventional one, the optical efficiency of the proposed II display is higher than that of the conventional one.

3. Experiments and Results

We developed a prototype of the proposed and conventional II displays. For accuracy in our experiment, a back light unit and a film were combined as the display panel. The display panel was used to generate the EIAs of the proposed and conventional II displays. Another film was used as the gradient-aperture and conventional pinhole arrays. The specifications of the proposed II display prototype are shown in Table 1.

Table 1

Specifications of the proposed II display prototype.

Specifications	$H_{1}$	$V_{1}$	$H_{MAX}$	$p$	$g$	$L$	$M$	$N$
Values	0.06 mm	0.14 mm	0.25 mm	1.27 mm	3.6 mm	720 mm	32	20

The EIAs of the proposed and conventional II displays were generated using a computer.¹² Each EIA of a 3-D scene “SC” consists of $32 \times 20$ elemental images, and each elemental image has $60 \times 60 pixels$ .

Corresponding to the aperture widths of the gradient-aperture pinhole array, the horizontal and vertical viewing angles of the proposed II display are both 16 deg. The 3-D images reconstructed by the proposed II display viewed from different angles are shown in Fig. 4.

Fig. 4

3-D images reconstructed by the proposed II display prototype.

We also developed a conventional II display prototype. The aperture width of each pinhole is 0.06 mm. Therefore, the horizontal and vertical viewing angles of the conventional II display prototype are 16 deg and 17 deg, respectively. The 3-D images which are reconstructed through the conventional II display prototype are captured at different angles, as shown Fig. 5. The orthoscopic images are seen within 8 deg to the left and right in the proposed and conventional II displays. Although the vertical viewing angle of the proposed II display is slightly decreased, it is equal to the horizontal one. For the proposed II display prototype, the full white luminance of the 3-D images is $40.6 cd / m^{2}$ . The full white luminance of the 3-D images reconstructed by the conventional II display prototype is $5.1 cd / m^{2}$ . Therefore, the optical efficiency of the proposed II display is about seven times higher than that of the conventional II display.

Fig. 5

3-D images reconstructed by the conventional II display prototype.

The experimental results prove that the optical efficiency of the proposed II display is higher than the conventional one, and the horizontal viewing angle of the proposed II display is equal to that of the conventional one.

4. Conclusions

An II display using a gradient-aperture pinhole array is proposed. The aperture widths of the gradient-aperture pinhole array are gradually increased from both sides to the middle in the horizontal and vertical directions. A prototype of the proposed II display is developed. Its optical efficiency is higher than that of the conventional one, while its viewing angle is the same as that of the conventional one. It could be a practical solution of high-luminance 3-D displays.

Acknowledgments

The work is supported by the NSFC under Grant Nos. 61225022 and 61036008, the “973” Program under Grant No. 2013CB328802, and the “863” Program under Grant Nos. 2012AA011901 and 2012AA03A301.

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Biography

Fei Wu is working toward his PhD degree in optical engineering from the School of Electronics and Information Engineering, Sichuan University, China. His recent research interest is information display technologies including 3-D displays.

Huan Deng is a lecturer of optical engineering at the school of Electronic and Information Engineering, Sichuan University, China. She has published 10 papers. She is a member of the Society for Information Display. Her recent research interest is information display technologies including 3-D displays.

Da-Hai Li is a professor of optics at the School of Electronics and Information Engineering, Sichuan University, China. He received his MS degree from the University of Electronic Science and Technology of China in 1996 and his PhD degree from Sichuan University in 2002, respectively. He has published more than 30 papers. His recent research interests include optics and optoelectronics, especially display technologies and optical measurements.

Qiong-Hua Wang is a professor of optics at the School of Electronics and Information Engineering, Sichuan University, China. She was a post-doctoral research fellow in the School of Optics/CREOL, University of Central Florida, in 2001–2004. She received her MS and PhD degrees from the University of Electronic Science and Technology of China (UESTC) in 1995 and 2001, respectively. She worked at UESTC in 1995–2001, and at Philips Mobile Display Systems, Philips Shanghai, in 2004. She has published 170 papers on display devices and systems. She holds five US patents and 21 Chinese patents. She is a senior member of the Society for Information display. Her recent research interests include optics and optoelectronics, especial display technologies.

CC BY: © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Fei Wu, Huan Deng, Da-Hai Li, and Qiong-Hua Wang "High-optical-efficiency integral imaging display based on gradient-aperture pinhole array," Optical Engineering 52(5), 054002 (14 May 2013). https://doi.org/10.1117/1.OE.52.5.054002

Published: 14 May 2013

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KEYWORDS

Integral imaging

Prototyping

1.

Introduction

2.

Structure and Principle