Abstract

Because a three-dimensional (3-D) autostereoscopic image can be seen from a desired viewpoint without the aid of special viewing glasses, integral photography (IP) is an ideal way to create 3-D autostereoscopic images. We have already proposed a real-time IP method that offers 3-D autostereoscopic images of moving objects in real time by use of a microlens array and a high-definition television camera. But there are two problems yet to be resolved: One is pseudoscopic images that show a reversed depth representation. The other is interference between the element images that constitute a 3-D autostereoscopic image. We describe a new gradient-index lense-array method based on real-time IP to overcome these two problems. Experimental results indicating the advantages of this method are shown. These results suggest the possibility of using a gradient-index lens array for real-time IP.

© 1998 Optical Society of America

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References

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  1. T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1971).
  2. H. Higuchi, J. Hamasaki, “Real-time transmission of 3-D images formed by parallax panoramagrams,” Appl. Opt. 17, 3895–3902 (1978).
    [CrossRef] [PubMed]
  3. M. McCormick, “Integral 3D imaging for broadcast,” in Proceedings of the Second International Display Workshops, T. Hatada, ed. (The Institute of Television Engineers of Japan, Hamamatsu, Japan, 1995), 3D-9, pp. 77–80.
  4. F. Okano, H. Hoshino, J. Arai, I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
    [CrossRef] [PubMed]
  5. R. L. DeMontebello, “Wide-angle integral photography—the integram system,” in Three Dimensional Imaging, S. A. Benton, ed., Proc. SPIE120, 73–91 (1977).
    [CrossRef]
  6. D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).
  7. M. Sakamoto, H. Ueshima, M. Fukuyama, M. Toyama, T. Yamada, “Application for multi-aperture system of light-focusing fiber optics,” Electrophotography 12, 12–21 (1973).

1997

1978

1973

M. Sakamoto, H. Ueshima, M. Fukuyama, M. Toyama, T. Yamada, “Application for multi-aperture system of light-focusing fiber optics,” Electrophotography 12, 12–21 (1973).

1964

D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).

Arai, J.

DeMontebello, R. L.

R. L. DeMontebello, “Wide-angle integral photography—the integram system,” in Three Dimensional Imaging, S. A. Benton, ed., Proc. SPIE120, 73–91 (1977).
[CrossRef]

Fukuyama, M.

M. Sakamoto, H. Ueshima, M. Fukuyama, M. Toyama, T. Yamada, “Application for multi-aperture system of light-focusing fiber optics,” Electrophotography 12, 12–21 (1973).

Hamasaki, J.

Higuchi, H.

Hoshino, H.

Marcuse, D.

D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).

McCormick, M.

M. McCormick, “Integral 3D imaging for broadcast,” in Proceedings of the Second International Display Workshops, T. Hatada, ed. (The Institute of Television Engineers of Japan, Hamamatsu, Japan, 1995), 3D-9, pp. 77–80.

Miller, S. E.

D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).

Okano, F.

Okoshi, T.

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1971).

Sakamoto, M.

M. Sakamoto, H. Ueshima, M. Fukuyama, M. Toyama, T. Yamada, “Application for multi-aperture system of light-focusing fiber optics,” Electrophotography 12, 12–21 (1973).

Toyama, M.

M. Sakamoto, H. Ueshima, M. Fukuyama, M. Toyama, T. Yamada, “Application for multi-aperture system of light-focusing fiber optics,” Electrophotography 12, 12–21 (1973).

Ueshima, H.

M. Sakamoto, H. Ueshima, M. Fukuyama, M. Toyama, T. Yamada, “Application for multi-aperture system of light-focusing fiber optics,” Electrophotography 12, 12–21 (1973).

Yamada, T.

M. Sakamoto, H. Ueshima, M. Fukuyama, M. Toyama, T. Yamada, “Application for multi-aperture system of light-focusing fiber optics,” Electrophotography 12, 12–21 (1973).

Yuyama, I.

Appl. Opt.

Bell Sys. Tech. J.

D. Marcuse, S. E. Miller, “Analysis of a tubular gas lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).

Electrophotography

M. Sakamoto, H. Ueshima, M. Fukuyama, M. Toyama, T. Yamada, “Application for multi-aperture system of light-focusing fiber optics,” Electrophotography 12, 12–21 (1973).

Other

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1971).

M. McCormick, “Integral 3D imaging for broadcast,” in Proceedings of the Second International Display Workshops, T. Hatada, ed. (The Institute of Television Engineers of Japan, Hamamatsu, Japan, 1995), 3D-9, pp. 77–80.

R. L. DeMontebello, “Wide-angle integral photography—the integram system,” in Three Dimensional Imaging, S. A. Benton, ed., Proc. SPIE120, 73–91 (1977).
[CrossRef]

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Figures (21)

Fig. 1
Fig. 1

Principle of the real-time IP method: (a) Pickup. (b) Reconstruction.

Fig. 2
Fig. 2

Example of concavo-convex conversion of an element image.

Fig. 3
Fig. 3

Schematic diagram of an element-image region.

Fig. 4
Fig. 4

Photograph of the interference between element images by the microlenses.

Fig. 5
Fig. 5

Example of the object to be imaged.

Fig. 6
Fig. 6

Structure of the two lens arrays and the two optical barriers: (a) One set of a microlens pair and the optical barriers. (b) Whole set of two microlens arrays and two optical barriers.

Fig. 7
Fig. 7

Schematic diagram of an object and the element images.

Fig. 8
Fig. 8

Geometry of the incident ray and the output ray with a gradient-index lens.

Fig. 9
Fig. 9

Schematic diagram of total reflection.

Fig. 10
Fig. 10

Schematic diagram of the acceptance region of the incident rays and the output rays.

Fig. 11
Fig. 11

Geometry of the interference between element images in a gradient-index lens.

Fig. 12
Fig. 12

Examples of the image-spread ratio Δ′.

Fig. 13
Fig. 13

Schematic diagram of the experimental setup for the measurement of the image-spread ratio Δ′.

Fig. 14
Fig. 14

Comparison of the image-spread ratio Δ′ with a gradient-index lens.

Fig. 15
Fig. 15

Enlarged photograph of element images with θ = 1.178π. The bright part of the photograph represents the interference between element images. Element images can be observed in the dark part of the photograph.

Fig. 16
Fig. 16

Enlarged photograph of element images with θ = 1.5π. Element images can be observed without interference.

Fig. 17
Fig. 17

Schematic diagram of the experimental setup of the real-time IP method with a gradient-index lens array: (a) Pickup. (b) Reconstruction. (c) An expected image from position 1. The letters I and P are overlapped. (d) An expected image from position 2. The letters I and P are separated.

Fig. 18
Fig. 18

Structure of a lens array consisting of gradient-index lenses: (a) Off-set structure. (b) Grid structure.

Fig. 19
Fig. 19

Enlarged photograph of element images on the LCD panel: (a) The letters I and P are overlapped. (b) The letters I and P are separate.

Fig. 20
Fig. 20

Reconstructed 3-D autostereoscopic image. Because the focus is on the 3-D autostereoscopic image the light on the pinholes is out of focus. (a) Photograph from position 1, with the letters I and P overlapping. (b) Photograph from position 2, with the letters I and P separate.

Fig. 21
Fig. 21

Restriction of the inclination of the incident ray.

Tables (2)

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Table 1 Specifications of the Gradient-Index Lenses

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Table 2 Equipment Specifications

Equations (32)

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1 S + 1 S = 1 f M ,
D 2 = 2 f M + f M 2 d M - 2 f M ,
E = - d M - f M d M - 2 f M ,
D 2 2 f ,
E - 1 .
n r = n 0 1 - 1 2   Ar 2 ,
r 2 r 2 = cos   θ 1 n 0 A sin   θ - n 0 A sin   θ cos   θ r 1 r 1 ,
f = 1 n 0 A sin   θ ,
h = 1 n 0 A tan θ 2 ,
L 2 = n 0 L 1 A cos   θ + sin   θ n 0 A n 0 L 1 A sin   θ - cos   θ ,
M = - 1 n 0 A sin   θ L 1 - cot   θ n 0 A ,
θ = A Z ,
sin r 1 n r 1 2 - n r 0 2 1 / 2 .
Y 0 2 r 0 2 - Z 0 2 a 2 = 1 ,
a = r 0 1 tan   Φ max ,
Φ max n 0 A r 0 .
Y 0 2 r 0 2 - Z 0 2 a 2 = 1 .
Δ = r 0 1 + n 0 A L 2 2 1 / 2 - r 0 .
Δ = Δ r 0 + 1 .
sin   ϕ t sin   ϕ ˆ t = n t n ,
sin   θ t sin   θ t + 1 = n t + 1 n t , sin   θ T - 1 sin   θ T = n T n T - 1 ,
sin   θ t sin   θ T = n T n t ,
sin   θ T = 1 .
sin   ϕ t T = n t 2 - n T 2 1 / 2 ,
sin   ϕ t T - 1 = n t 2 - n T - 1 2 1 / 2 <   sin   ϕ t T .
n t n r 1 , n T n r 0 .
lim T sin   ϕ t T = n r 1 2 - n r 0 2 1 / 2 .
r 1 max = n 0 A r 0 1 - r 1 r 0 2 1 / 2 .
r 2 = r 0 sin sin - 1 r 1 r 0 + A Z ,
r 2 max = n 0 A r 0 1 - r 2 r 0 2 1 / 2 .
Y 0 = r 0 1 + n 0 A L 2 2 1 / 2 .
Δ = r 0 1 + n 0 A L 2 2 1 / 2 - r 0 .

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