Abstract

We propose a curved integral imaging system with large depth achieved by the additional use of a large-aperture lens in a conventional large-depth integral imaging system. The additional large-aperture lens provides a multidirectional curvature effect and improves the viewing angle. The proposed system has a simple structure due to the use of well-fabricated, unmodified flat devices. To calculate the proper elemental images for the proposed system, we explain a modified computer-generated pickup technique based on an ABCD matrix and analyze an effective viewing zone in the proposed system. From experiments, we show that the proposed system has an improved viewing angle of more than 7° compared with conventional integral imaging.

© 2006 Optical Society of America

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  1. G. Lippmann, "La photographic integrale," C.R. Acad. Sci. 146, 446-451 (1908).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  22. J.-Y. Son and B. Javidi, "3-Dimensional imaging systems based on multiview images," J. Display Technol. 1, 125-140 (2005).
    [CrossRef]
  23. M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A 22, 597-603 (2005).
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2005 (6)

2004 (5)

2003 (1)

2002 (5)

2001 (2)

1999 (1)

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

1968 (1)

1931 (1)

1908 (1)

G. Lippmann, "La photographic integrale," C.R. Acad. Sci. 146, 446-451 (1908).

Arai, J.

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

Arimoto, H.

Burckhardt, C. B.

Cho, M.

D.-H. Shin, M. Cho, and E.-S. Kim, "Computational implementation of asymmetric integral imaging by use of two crossed lenticular sheets," ETRI J. 27, 289-293 (2005).
[CrossRef]

Choi, H.

Dohi, T.

Hata, N.

Hoshino, H.

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

Ives, H. E.

Iwahara, M.

Jang, J.

Jang, J.-S.

Javidi, B.

J.-Y. Son and B. Javidi, "3-Dimensional imaging systems based on multiview images," J. Display Technol. 1, 125-140 (2005).
[CrossRef]

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A 22, 597-603 (2005).
[CrossRef]

F. Jin, J.-S. Jang, and B. Javidi, "Effects of device resolution on three-dimensional integral imaging," Opt. Lett. 29, 1345-1347 (2004).
[CrossRef] [PubMed]

J. Jang and B. Javidi, "Depth and lateral size control of three-dimensional images in projection integral imaging," Opt. Express 12, 3778-3790 (2004).
[CrossRef] [PubMed]

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).
[CrossRef] [PubMed]

J.-S. Jang, F. Jin, and B. Javidi, "Three-dimensional integral imaging with large depth of focus using real and virtual image fields," Opt. Lett. 28, 1421-1423 (2003).
[CrossRef] [PubMed]

S.-H. Shin and B. Javidi, "Speckle-reduced three-dimensional volume holographic display by use of integral imaging," Appl. Opt. 41, 2644-2649 (2002).
[CrossRef] [PubMed]

J.-S. Jang and B. Javidi, "Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics," Opt. Lett. 27, 324-326 (2002).
[CrossRef]

H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction," Opt. Lett. 26, 157-159 (2001).
[CrossRef]

Jeong, Y.

Jin, F.

Jung, S.

Jung, S. Y.

Kim, E.-S.

D.-H. Shin, M. Cho, and E.-S. Kim, "Computational implementation of asymmetric integral imaging by use of two crossed lenticular sheets," ETRI J. 27, 289-293 (2005).
[CrossRef]

D.-H. Shin, E.-S. Kim, and B. Lee, "Computational reconstruction of three-dimensional objects in integral imaging using lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
[CrossRef]

Kim, Y.

Lee, B.

Liao, H.

Lippmann, G.

G. Lippmann, "La photographic integrale," C.R. Acad. Sci. 146, 446-451 (1908).

Martínez-Corral, M.

Martínez-Cuenca, R.

Min, S.

Min, S.-W.

Okano, F.

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

Park, J.

Park, J.-H.

Pedrotti, F. L.

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice Hall, 1993).

Pedrotti, L. S.

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice Hall, 1993).

Saavedra, G.

Shin, D.-H.

D.-H. Shin, M. Cho, and E.-S. Kim, "Computational implementation of asymmetric integral imaging by use of two crossed lenticular sheets," ETRI J. 27, 289-293 (2005).
[CrossRef]

D.-H. Shin, E.-S. Kim, and B. Lee, "Computational reconstruction of three-dimensional objects in integral imaging using lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
[CrossRef]

Shin, S.-H.

Son, J.-Y.

Yuyama, I.

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

Appl. Opt. (3)

C.R. Acad. Sci. (1)

G. Lippmann, "La photographic integrale," C.R. Acad. Sci. 146, 446-451 (1908).

ETRI J. (1)

D.-H. Shin, M. Cho, and E.-S. Kim, "Computational implementation of asymmetric integral imaging by use of two crossed lenticular sheets," ETRI J. 27, 289-293 (2005).
[CrossRef]

J. Display Technol. (1)

J. Opt. Soc. Am. (2)

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

Jpn. J. Appl. Phys. (1)

D.-H. Shin, E.-S. Kim, and B. Lee, "Computational reconstruction of three-dimensional objects in integral imaging using lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
[CrossRef]

Opt. Eng. (2)

S.-W. Min, S. Jung, J.-H. Park, and B. Lee, "Study for wide-viewing integral photography using an aspheric Fresnel-lens array," Opt. Eng. 41, 2572-2576 (2002).
[CrossRef]

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

Opt. Express (4)

Opt. Lett. (7)

Other (1)

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice Hall, 1993).

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Figures (10)

Fig. 1
Fig. 1

(Color online) (a) Curved LDII system designed by use of curved devices. (b) Curvature-effect LDII system designed by use of flat devices and a large-aperture lens. (c) Viewing zone of the curved LDII system. (d) Viewing zone of the curvature-effect LDII system.

Fig. 2
Fig. 2

(Color online) Ray formation in the curvature-effect LDII system for the pixels of (a) n = 0 and (b) n 0 .

Fig. 3
Fig. 3

(Color online) EVZs in (a) a conventional LDII system and (b) a curvature-effect LDII system.

Fig. 4
Fig. 4

(Color online) Optical setup.

Fig. 5
Fig. 5

(Color online) Comparison between calculated viewing range (lines) and the measured viewing range (squares, curvature-effect LDII; circles, conventional LDII). (a) Horizontal direction. (b) Vertical direction.

Fig. 6
Fig. 6

(Color online) Experimental setup for measuring the EVZ of the proposed system.

Fig. 7
Fig. 7

Synthesized elemental images: (a) curvature-effect LDII system and (b) conventional LDII system.

Fig. 8
Fig. 8

(Color online) Reconstructed images captured by a CCD camera at (a) 10   cm and (b) 20   cm .

Fig. 9
Fig. 9

Reconstructed images from different viewing angles.

Fig. 10
Fig. 10

(Color online) Side viewing zone in (a) conventional LDII system and (b) curvature-effect LDII system.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

[ H n k ( z = 0 ) A n k ( z = 0 ) ] = [ k p + n d n d / g ]
[ H n k ( g ) A n k ( g ) ] = [ k p n d / g ] .
T = [ 1 z g 0 1 ] [ 1 0 1 / f L 1 ] .
H n k ( z ) = k p ( 1 z g f L ) ( z g ) n d g .
v c ( z ) = H ( N 1 ) / 2 ( K 1 ) / 2 ( z ) H ( N 1 ) / 2 ( K 1 ) / 2 ( z )
= ( K 1 ) p + ( z g ) ( N 1 ) d g
K p + ( z g ) p g for   z > z c .
v r ( z ) = H ( N 1 ) / 2 ( K 1 ) / 2 ( z ) H ( N 1 ) / 2 ( K 1 ) / 2 ( z )
= ( K 1 ) p ( 1 z g f L ) + ( z g ) ( N 1 ) d g   if   z r < z < f L K p ( 1 z g f L ) + ( z g ) p g ,
v r ( z ) = H ( N 1 ) / 2 ( K 1 ) / 2 ( z ) H ( N 1 ) / 2 ( K 1 ) / 2 ( z )
= ( K 1 ) p ( 1 z g f L ) + ( z g ) ( N 1 ) d g   if   f L z K p ( 1 z g f L ) + ( z g ) p g .
θ c ( z ) = 2 tan - 1 [ v c ( z ) 2 ( z z c ) ] for   z > z c ,
θ r ( z ) = 2 tan - 1 [ v r ( z ) 2 ( z z r ) ] for   z > z r ,

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