Abstract

When designing a system capable of capturing and displaying 3D moving images in real time by the integral imaging (II) method, one challenge is to eliminate pseudoscopic images. To overcome this problem, we propose a simple system with an array of three convex lenses. First, the lateral magnification of the elemental optics and the expansion of an elemental image is described by geometrical optics, confirming that the elemental optics satisfies the conditions under which pseudoscopic images can be avoided. In using the II method, adjacent elemental images must not overlap, a condition also satisfied by the proposed optical system. Next, an experiment carried out to acquire and display 3D images is described. The real-time system we have constructed comprises an elemental optics array with 54  H×59   V elements, a CCD camera to capture a group of elemental images created by the lens array, and a liquid crystal panel to display these images. The results of the experiment confirm that the system produces orthoscopic images in real time, and thus is effective for real-time application of the II method.

© 2006 Optical Society of America

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References

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    [CrossRef]
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2005 (1)

2004 (1)

2003 (2)

J. Arai, H. Hoshino, M. Okui, and F. Okano, "Effects of focusing on the resolution characteristics of integral photography," J. Opt. Soc. Am. A 20, 996-1004 (2003).
[CrossRef]

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

2000 (1)

1999 (1)

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

1998 (1)

1994 (1)

N. Davies, M. McCormick, and M. Brewin, "Design and analysis of an image transfer system using microlens arrays," Opt. Eng. 33, 3624-3633 (1994).
[CrossRef]

1978 (1)

1968 (1)

1964 (1)

K. Halbach, "Matrix representation of Gaussian optics," Am. J. Phys. 32, 90-108 (1964).
[CrossRef]

1931 (1)

1908 (1)

M. G. Lippmann, "Épreuves réversibles donnant la sensation du relief," J. de Phys. 4, 821-825 (1908).

Arai, J.

J. Arai, H. Hoshino, M. Okui, and F. Okano, "Effects of focusing on the resolution characteristics of integral photography," J. Opt. Soc. Am. A 20, 996-1004 (2003).
[CrossRef]

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, and I. Yuyama, "Gradient-index lens-array method based on real-time integral photography for three-dimensional images," Appl. Opt. 37, 2034-2045 (1998).
[CrossRef]

F. Okano, J. Arai, and H. Hoshino, "Stereoscopic image pickup device and stereoscopic display device," Japan patent 150675 (1998).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Brewin, M.

N. Davies, M. McCormick, and M. Brewin, "Design and analysis of an image transfer system using microlens arrays," Opt. Eng. 33, 3624-3633 (1994).
[CrossRef]

Burckhardt, C. B.

Collier, R. J.

Davies, N.

N. Davies, M. McCormick, and M. Brewin, "Design and analysis of an image transfer system using microlens arrays," Opt. Eng. 33, 3624-3633 (1994).
[CrossRef]

Doherty, E. T.

Esener, S. C.

Firestone, G. C.

Halbach, K.

K. Halbach, "Matrix representation of Gaussian optics," Am. J. Phys. 32, 90-108 (1964).
[CrossRef]

Hamasaki, J.

Hartmann, D. M.

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 2002).

Higuchi, H.

Hoshino, H.

J. Arai, H. Hoshino, M. Okui, and F. Okano, "Effects of focusing on the resolution characteristics of integral photography," J. Opt. Soc. Am. A 20, 996-1004 (2003).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, and I. Yuyama, "Gradient-index lens-array method based on real-time integral photography for three-dimensional images," Appl. Opt. 37, 2034-2045 (1998).
[CrossRef]

F. Okano, J. Arai, and H. Hoshino, "Stereoscopic image pickup device and stereoscopic display device," Japan patent 150675 (1998).

Ives, H. E.

Jang, J.-S.

Javidi, B.

Kibar, O.

Kobayashi, M.

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

Lippmann, M. G.

M. G. Lippmann, "Épreuves réversibles donnant la sensation du relief," J. de Phys. 4, 821-825 (1908).

McCormick, M.

N. Davies, M. McCormick, and M. Brewin, "Design and analysis of an image transfer system using microlens arrays," Opt. Eng. 33, 3624-3633 (1994).
[CrossRef]

Mitani, K.

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

Okano, F.

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

J. Arai, H. Hoshino, M. Okui, and F. Okano, "Effects of focusing on the resolution characteristics of integral photography," J. Opt. Soc. Am. A 20, 996-1004 (2003).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, and I. Yuyama, "Gradient-index lens-array method based on real-time integral photography for three-dimensional images," Appl. Opt. 37, 2034-2045 (1998).
[CrossRef]

F. Okano, J. Arai, and H. Hoshino, "Stereoscopic image pickup device and stereoscopic display device," Japan patent 150675 (1998).

Okui, M.

J. Arai, H. Hoshino, M. Okui, and F. Okano, "Effects of focusing on the resolution characteristics of integral photography," J. Opt. Soc. Am. A 20, 996-1004 (2003).
[CrossRef]

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

Shimamoto, H.

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

Sugawara, M.

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Yi, A. Y.

Yuyama, I.

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, and I. Yuyama, "Gradient-index lens-array method based on real-time integral photography for three-dimensional images," Appl. Opt. 37, 2034-2045 (1998).
[CrossRef]

Am. J. Phys. (1)

K. Halbach, "Matrix representation of Gaussian optics," Am. J. Phys. 32, 90-108 (1964).
[CrossRef]

Appl. Opt. (4)

J. de Phys. (1)

M. G. Lippmann, "Épreuves réversibles donnant la sensation du relief," J. de Phys. 4, 821-825 (1908).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

N. Davies, M. McCormick, and M. Brewin, "Design and analysis of an image transfer system using microlens arrays," Opt. Eng. 33, 3624-3633 (1994).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

J. Arai, M. Okui, M. Kobayashi, M. Sugawara, K. Mitani, H. Shimamoto, and F. Okano, "Integral three-dimensional television based on super-high-definition video system," in Stereoscopic Displays and Virtual Reality Systems X, A. J. Woods, M. T. Bolas, J. O. Merritt, and S. A. Benton, eds., Proc. SPIE 5006, 49-57 (2003).
[CrossRef]

Other (4)

E. Hecht, Optics (Addison-Wesley, 2002).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

F. Okano, J. Arai, and H. Hoshino, "Stereoscopic image pickup device and stereoscopic display device," Japan patent 150675 (1998).

H. E. Ives, "Optical device," U.S. patent 2,173,003 (12 September 1939).

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Figures (22)

Fig. 1
Fig. 1

Principle of IP method.

Fig. 2
Fig. 2

Reconstruction of the orthoscopic image.

Fig. 3
Fig. 3

Lateral magnification.

Fig. 4
Fig. 4

Capture of elemental images generated by concave lens array.

Fig. 5
Fig. 5

Light path through a radial gradient-index lens.

Fig. 6
Fig. 6

Elemental optics equivalent to radial gradient-index lens with a lens length of 1.5 π / A . (a) Three convex lenses spaced at equal intervals. (b) Thick plano–convex lenses used in place of the three convex lenses in (a). (c) Three convex lenses spaced at unequal intervals. (d) Thick plano-convex lenses used in place of the three convex lenses in (c).

Fig. 7
Fig. 7

Composition of elemental optics array.

Fig. 8
Fig. 8

Ray geometry. (a) Plano–convex lens. (b) Double-convex lens.

Fig. 9
Fig. 9

Ray geometry in the case of an elemental lens.

Fig. 10
Fig. 10

Expanding rays from exit plane.

Fig. 11
Fig. 11

Example of the structure of elemntal optics array: (a) side view. (b) Overview.

Fig. 12
Fig. 12

Stray light inside the optics array: (a) Without aperture array. (b) With aperture array.

Fig. 13
Fig. 13

Change of influence of stray light depending on aperture size.

Fig. 14
Fig. 14

Strength distribution of image created from a point light source.

Fig. 15
Fig. 15

Use of depth-control lens. (a) Depth-control lens with telecentricity. (b) Depth- control lens with small aperture.

Fig. 16
Fig. 16

Object used to capture elemental images.

Fig. 17
Fig. 17

Aperture stop array used in telecentric optics.

Fig. 18
Fig. 18

Example of elemental images acquired by plano–convex lens array: (a) Without the aperture stop array, (b) With the aperture stop array.

Fig. 19
Fig. 19

Example of elemental images acquired by elemental optics array. (a) Without the aperture stop array. (b) With the aperture stop array.

Fig. 20
Fig. 20

(Color online) Elemental images formed on the second focal plane of the lens array by (a) the plano–convex lens array, (b) the elemental optics array.

Fig. 21
Fig. 21

(Color online) Reconstructed images formed from elemental images on the second focal plane of the plano–convex lens array. (a) Left viewpoint, (b) right viewpoint.

Fig. 22
Fig. 22

(Color online) Reconstructed images formed from elemental images on the second focal plane of the elemental optics array. (a) Left viewpoint. (b) Right viewpoint. (c) Upper viewpoint. (d) Lower viewpoint.

Tables (1)

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Table 1 Specification of the Lens Array

Equations (38)

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M L = f / ( f + s o ) ,
[ u 2 h 2 ] = S 1 [ u 1 h 1 ] ,
S 1 = [ 1 Φ 1 / n 1 n 1 d 1 / n 2 1 d 1 Φ 1 / n 2 ] ,
Φ 1 = ( n 2 n 1 ) / r 1 .
d 1 = n 2 r 1 / ( n 2 n 1 ) .
[ u 4 h 4 ] = S 2 [ u 3 h 3 ] ,
S 2 = [ 1 d 2 Φ 4 / n 2 { Φ 3 + Φ 4 ( 1 d 2 Φ 3 / n 2 ) } / n 1 n 1 d 2 / n 2 1 d 2 Φ 3 / n 2 ] ,
Φ 3 = ( n 2 n 1 ) / r 3 ,
Φ 4 = ( n 1 n 2 ) / r 4 .
[ u 4 h 4 ] = S [ u 1 h 1 ] ,
S = S 2 [ 1 0 0 1 ] S 1 = [ ( 1 d 2 Φ 4 n 2 ) d 1 { Φ 3 + Φ 4 ( 1 d 2 Φ 3 / n 2 ) } n 2 n 1 { d 2 + d 1 ( 1 d 2 Φ 3 / n 2 ) } n 2 1 n 1 [ Φ 1 ( 1 d 2 Φ 4 n 2 ) + ( 1 d 1 Φ 1 n 2 ) { Φ 3 + Φ 4 ( 1 d 2 Φ 3 n 2 ) } ] d 2 Φ 1 n 2 + ( 1 d 2 Φ 3 n 2 ) ( 1 d 1 Φ 1 n 2 ) ] .
S = [ 1 n 1 / Φ 1 Φ 1 / n 1 2 ] .
δ 1 = 2 r 1 n 1 / ( n 2 n 1 ) ,
δ 2 = 3 r 1 n 1 / ( n 2 n 1 ) ,
f = n 1 / Φ 1 = n 1 r 1 / ( n 2 n 1 ) < 0 ( f o r 0 < r 1 , n 1 = 1 < n 2 ) ,
y = u 4 min z + h 4 = ( w h 4 ) ( n 1 n 2 ) z / 2 r 1 n 1 + h 4 ,
Q 1 z = 2 r 1 n 1 / ( n 2 n 1 ) ,
Q 1 y = w .
y = u 4 max z + h 4 = ( w h 4 ) ( n 1 n 2 ) z / 2 r 1 n 1 + h 4 ,
Q 2 z = 2 r 1 n 1 / ( n 2 n 1 ) ,
Q 2 y = w .
β = C h 12 / h 11 ,
ϕ 1 ( w + 2 h 1 ) < u 1 < ϕ 1 ( w + 2 h 1 ) .
z 01 = ( a w ) / { 2 ϕ 1 ( w a ) } .
β = 0.
z 02 = w / { ϕ 1 ( w a / 2 ) } .
β = 2 z 0 2 ϕ 1 2 ( a w ) + z 0 ϕ 1 ( a 2 w ) 4 ( z 0 ϕ 1 + 1 ) w z 0 ϕ 1 .
z 03 = 1 / ϕ 1 .
β = 1 2 + 1 2 z 0 ϕ 1 .
z 04 = 1 / 3 ϕ 1 .
β = 0.
β = w ( 1 + 3 z 0 ϕ 1 ) 2 w z 0 ϕ 1 .
z 06 = ( a ϕ 1 w ) + ( w a ϕ 1 ) 2 + 2 w a ϕ 1 2 w ϕ 1 .
β = ( 2 z 0 ϕ 1 ) 2 ( a z 0 w ) + ϕ 1 ( a 2 w z 0 ) 4 w z 0 ϕ 1 ( z 0 ϕ 1 + 1 ) .
β = 0.
γ = sin [ π w 2 z ^ 0 2 λ f 2 ] / π w 2 z ^ 0 2 λ f 2 ,
z ^ 0 = | f f ( z 0 + δ 1 ) f + z 0 + δ 1 | .
D < f d < w δ 1 ,

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