Abstract

A novel curved computational integral imaging reconstruction (C-CIIR) technique for the virtually curved integral imaging (VCII) system is proposed, and its performances are analyzed. In the C-CIIR model, an additional virtual large-aperture lens is included to provide a multidirectional curving effect in the reconstruction process, and its effect is analyzed in detail by using the ABCD matrix. With this method, resolution-enhanced 3D object images can be computationally reconstructed from the picked-up elemental images of the VCII system. To confirm the feasibility of the proposed model, some experiments are carried out. Experiments revealed that the sampling rate in the VCII system could be kept at a maximum value within some range of the distance z, whereas in the conventional integral imaging system it linearly decreased as the distance z increased. It is also shown that resolutions of the object images reconstructed by the C-CIIR method have been significantly improved compared with those of the conventional CIIR method.

© 2007 Optical Society of America

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References

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2007 (2)

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, "Resolution-enhanced 3D image correlator using computationally reconstructed integral images," Opt. Commun. 276, 72-79 (2007).
[CrossRef]

J.-S. Park, D.-C. Hwang, D.-H. Shin, J.-B. Hyun, J.-K. Lee, H.-H. Kang, and E.-S. Kim, "Recognition of 3D objects by use of computational integral imaging reconstruction," Proc. SPIE 6490, 64901M (2007).
[CrossRef]

2006 (2)

D.-H. Shin, B. Lee, and E.-S. Kim, "Multidirectional curved integral imaging with large depth by additional use of a large-aperture lens," Appl. Opt. 45, 7375-7381 (2006).
[CrossRef] [PubMed]

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, "Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique," Opt. Eng. 45, 117004 (2006).
[CrossRef]

2005 (4)

D.-H. Shin, M. Cho, K.-C. Park, and E.-S. Kim, "Computational technique of volumetric object reconstruction in integral imaging by use of real and virtual image fields," ETRI J. 27, 708-712 (2005).
[CrossRef]

D.-H. Shin, E.-S. Kim, and B. Lee, "Computational reconstruction technique of three-dimensional object in integral imaging using a lenslet array," Jpn. J. Appl. Phys. , Part 1 44, 8016-8018 (2005).
[CrossRef]

D.-H. Shin, M.-J. 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]

Y. Kim, J.-H. Park, S.-W. Min, S. Jung, H. Choi, and B. Lee, "Wide-viewing-angle integral three-dimensional imaging system by curving a screen and a lens array," Appl. Opt. 44, 546-552 (2005).
[CrossRef] [PubMed]

2004 (4)

2003 (1)

2002 (3)

2001 (2)

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]

1968 (1)

1931 (1)

1908 (1)

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

Appl. Opt. (5)

C. R. Acad. Sci. (1)

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

ETRI J. (2)

D.-H. Shin, M. Cho, K.-C. Park, and E.-S. Kim, "Computational technique of volumetric object reconstruction in integral imaging by use of real and virtual image fields," ETRI J. 27, 708-712 (2005).
[CrossRef]

D.-H. Shin, M.-J. 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. Opt. Soc. Am. (2)

Jpn. J. Appl. Phys. (1)

D.-H. Shin, E.-S. Kim, and B. Lee, "Computational reconstruction technique of three-dimensional object in integral imaging using a lenslet array," Jpn. J. Appl. Phys. , Part 1 44, 8016-8018 (2005).
[CrossRef]

Opt. Commun. (1)

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, "Resolution-enhanced 3D image correlator using computationally reconstructed integral images," Opt. Commun. 276, 72-79 (2007).
[CrossRef]

Opt. Eng. (2)

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, "Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique," Opt. Eng. 45, 117004 (2006).
[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 (3)

Opt. Lett. (4)

Proc. SPIE (1)

J.-S. Park, D.-C. Hwang, D.-H. Shin, J.-B. Hyun, J.-K. Lee, H.-H. Kang, and E.-S. Kim, "Recognition of 3D objects by use of computational integral imaging reconstruction," Proc. SPIE 6490, 64901M (2007).
[CrossRef]

Other (2)

D.-C. Hwang, D.-H. Shin, and E.-S. Kim, "Depth extraction by use of a computational integral imaging reconstruction technique," in Proceedings of Asia Display 2007 (Society for Information Display, 2007), Vol. 2, pp. 1961-1966.

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

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Figures (14)

Fig. 1
Fig. 1

(Color online) Schematic of the conventional II system: (a) pickup part, (b) display part.

Fig. 2
Fig. 2

(Color online) Conceptual diagram of image reconstruction on the output plane of z = L using the CIIR method.

Fig. 3
Fig. 3

(Color online) Conceptual diagram of the conventional and curved II systems: (a) conventional II system, (b) curved II system.

Fig. 4
Fig. 4

(Color online) Conceptual diagram of the VCII system: (a) pickup process, (b) display process.

Fig. 5
Fig. 5

(Color online) Pickup and C-CIIR-based display processes of the VCII system.

Fig. 6
Fig. 6

(Color online) Schematics of CIIR models: (a) conventional CIIR model, (b) proposed C-CIIR model.

Fig. 7
Fig. 7

(Color online) Schematics for analysis of moving of pixel positions as the distance z changes in the (a) conventional II system, (b) VCII system.

Fig. 8
Fig. 8

(Color online) Sampling rate dependences on the distance z of the conventional II and VCII systems.

Fig. 9
Fig. 9

(Color online) Experimental setup for computational pickup and C-CIIR-based reconstruction.

Fig. 10
Fig. 10

(Color online) Object images and their line intensity profiles, reconstructed by the conventional CIIR technique at (a) 36   mm , (b) 72   mm , and (c) 108   mm and reconstructed by the proposed C-CIIR technique at (d) 36   mm , (e) 72   mm , and (f) 108   mm , respectively.

Fig. 11
Fig. 11

(Color online) Enlarged image of object images reconstructed by the conventional CIIR technique at (a) 36   mm , (b) 72   mm , and (c) 108   mm and reconstructed by the proposed C-CIIR technique at (d) 36   mm , (e) 72   mm , and (f) 108   mm , respectively.

Fig. 12
Fig. 12

(Color online) Experimental setup for optical pickup of the VCII system.

Fig. 13
Fig. 13

(Color online) EIAs captured by the conventional II system at (a) 36   mm and (c) 72   mm , and by the VCII system at (b) 36   mm and (d) 72   mm .

Fig. 14
Fig. 14

(Color online) Object images reconstructed using the conventional CIIR technique at (a) 36   mm , (b) 72   mm , and reconstructed using the proposed C-CIIR technique at (c) 36   mm , (d) and their line intensity profiles at the distance of (e) 36   mm and (f) 72   mm , respectively.

Tables (1)

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Table 1 Abbreviations Used

Equations (16)

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[ H n x k x ( z = g ) H n y k y ( z = g ) A n x k x ( z = g ) A n y k y ( z = g ) ] = [ k x P + n x d k y P + n y d n x d g n y d g ] ,
[ H n x k x ( 0 ) H n y k y ( 0 ) A n x k x ( 0 ) A n y k y ( 0 ) ] = [ k x P k y P n x d g n y d g ] .
T = [ 1 z 0 1 ] [ 1 0 1 / f 1 ] .
[ H n x k x ( z ) H n y k y ( z ) ] = [ k x P ( 1 z f ) z n x d g k y P ( 1 z f ) z n y d g ] .
[ 0 < k x V x , 0 < k y V y N x 2 < n x N x 2 , N y 2 < n y N y 2 ] ,
X n x k x ( z ) = k x P z n x d g ,
Y n y k y ( z ) = k y P z n y d g .
O n x n y k x k y ( z ) = { 1 , ( 0 , 0 ) < ( X n x k x ( z ) , Y n y k y ( z ) ) ( V x N x , V y N y ) 0 , otherwise .
R = k x = 1 V x k y = 1 V y n x = N x / 2 N x / 2 n y = N y / 2 N y / 2 O n x n y k x k y ( z ) ,
S R = R V x N x V y N y × 100 ( % ) .
[ 0 < k x V x , 0 < k y V y N x 2 < n x N x 2 , N y 2 < n y N y 2 ] ,
H n x k x ( z ) = k x P ( 1 z f ) z n x d g ,
H n y k y ( z ) = k y P ( 1 z f ) z n y d g .
Q n x n y k x k y ( z ) = { 1 , ( ( 0 , 0 ) < ( H n x k x ( z ) , H n y k y ( z ) ) ( V x N x , V y N y ) ) 0 , otherwise .
R VCII = k x = 1 V x k y = 1 V y n x = N x / 2 N x / 2 n y = N y / 2 N y / 2 Q n x n y k x k y ( z ) ,
S R = R VCII V x N x V y N y × 100 ( % ) .

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