Abstract

There have already been several analyses about the viewing angle of integral imaging (InIm). However, they can be applied only under the assumption that the original image is merely a single point source and are not suitable for application to an actual condition. We propose an improved analysis based on the actual InIm image, not on a single point source. It is possible to analyze and predict the viewing angle of an InIm system with good accuracy with the new analytic method because almost all the parameters of the InIm system such as the size and focal length of the lens array, image distance, the size and resolution of the image, and the location of the observers are included in this analysis.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  7. J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. B. Lee, S.-W. Min, B. Javidi, “Theoretical analysis for three-dimensional integral imaging systems with double devices,” Appl. Opt. 41, 4856–4865 (2002).
    [CrossRef] [PubMed]
  13. S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Study for wide-viewing integral photography using an aspheric Fresnel-lens array,” Opt. Eng. 41, 2572–2576 (2002).
    [CrossRef]
  14. H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using a dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003), www.opticsexpress.org .
    [CrossRef] [PubMed]
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    [CrossRef]
  16. J.-H. Park, S. Jung, H. Choi, B. Lee, “Integral imaging with multiple image planes using a uniaxial crystal plate,” Opt. Express 11, 1862–1875 (2003), www.opticsexpress.org .
    [CrossRef] [PubMed]

2003

2002

2001

1998

1997

1994

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

1908

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Aggoun, A.

Arai, J.

Brewin, M.

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

Choi, H.

Davies, N.

Erdmann, L.

Gabriel, K. J.

Harashima, H.

Hoshino, H.

Isono, H.

Javidi, B.

Jeong, Y.

Jung, S.

J.-H. Park, S. Jung, H. Choi, B. Lee, “Integral imaging with multiple image planes using a uniaxial crystal plate,” Opt. Express 11, 1862–1875 (2003), www.opticsexpress.org .
[CrossRef] [PubMed]

H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using a dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003), www.opticsexpress.org .
[CrossRef] [PubMed]

B. Lee, S. Jung, J.-H. Park, “Viewing-angle-enhanced integral imaging by lens switching,” Opt. Lett. 27, 818–820 (2002).
[CrossRef]

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

Y. Jeong, S. Jung, J.-H. Park, B. Lee, “Reflection-type integral imaging scheme for displaying three-dimensional images,” Opt. Lett. 27, 704–706 (2002).
[CrossRef]

B. Lee, S. Jung, S.-W. Min, J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. 26, 1481–1482 (2001).
[CrossRef]

J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).
[CrossRef]

S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Three-dimensional display system based on computer-generated integral photography,” in Stereoscopic Displays and Virtual Reality Systems VIII, A. J. Woods, J. O. Merritt, S. A. Benton, eds., Proc. SPIE4297, 187–195 (2001).
[CrossRef]

Lee, B.

H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using a dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003), www.opticsexpress.org .
[CrossRef] [PubMed]

J.-H. Park, S. Jung, H. Choi, B. Lee, “Integral imaging with multiple image planes using a uniaxial crystal plate,” Opt. Express 11, 1862–1875 (2003), www.opticsexpress.org .
[CrossRef] [PubMed]

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

Y. Jeong, S. Jung, J.-H. Park, B. Lee, “Reflection-type integral imaging scheme for displaying three-dimensional images,” Opt. Lett. 27, 704–706 (2002).
[CrossRef]

B. Lee, S.-W. Min, B. Javidi, “Theoretical analysis for three-dimensional integral imaging systems with double devices,” Appl. Opt. 41, 4856–4865 (2002).
[CrossRef] [PubMed]

B. Lee, S. Jung, J.-H. Park, “Viewing-angle-enhanced integral imaging by lens switching,” Opt. Lett. 27, 818–820 (2002).
[CrossRef]

J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).
[CrossRef]

B. Lee, S. Jung, S.-W. Min, J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. 26, 1481–1482 (2001).
[CrossRef]

S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Three-dimensional display system based on computer-generated integral photography,” in Stereoscopic Displays and Virtual Reality Systems VIII, A. J. Woods, J. O. Merritt, S. A. Benton, eds., Proc. SPIE4297, 187–195 (2001).
[CrossRef]

Lippmann, G.

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Manolache, S.

McCormick, M.

Min, S.-W.

Naemura, T.

Okano, F.

Park, J.-H.

H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using a dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003), www.opticsexpress.org .
[CrossRef] [PubMed]

J.-H. Park, S. Jung, H. Choi, B. Lee, “Integral imaging with multiple image planes using a uniaxial crystal plate,” Opt. Express 11, 1862–1875 (2003), www.opticsexpress.org .
[CrossRef] [PubMed]

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

Y. Jeong, S. Jung, J.-H. Park, B. Lee, “Reflection-type integral imaging scheme for displaying three-dimensional images,” Opt. Lett. 27, 704–706 (2002).
[CrossRef]

B. Lee, S. Jung, J.-H. Park, “Viewing-angle-enhanced integral imaging by lens switching,” Opt. Lett. 27, 818–820 (2002).
[CrossRef]

J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).
[CrossRef]

B. Lee, S. Jung, S.-W. Min, J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. 26, 1481–1482 (2001).
[CrossRef]

S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Three-dimensional display system based on computer-generated integral photography,” in Stereoscopic Displays and Virtual Reality Systems VIII, A. J. Woods, J. O. Merritt, S. A. Benton, eds., Proc. SPIE4297, 187–195 (2001).
[CrossRef]

Yoshida, T.

Yuyama, I.

Appl. Opt.

C. R. Acad. Sci.

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

J. Opt. Soc. Am. A

Opt. Eng.

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

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

Opt. Express

Opt. Lett.

Other

S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Three-dimensional display system based on computer-generated integral photography,” in Stereoscopic Displays and Virtual Reality Systems VIII, A. J. Woods, J. O. Merritt, S. A. Benton, eds., Proc. SPIE4297, 187–195 (2001).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Viewing angle in the conventional analysis.

Fig. 2
Fig. 2

Parameters of the proposed analysis for (a) real and (b) virtual InIm.

Fig. 3
Fig. 3

Viewing angle for a single elemental lens.

Fig. 4
Fig. 4

Relation between the real image distance b and the viewing angle ratio and the resolution ratio Rreal for a single elemental lens.

Fig. 5
Fig. 5

Relation between the virtual image distance b′ and the viewing angle ratio and the resolution ratio Rvirtual for a single elemental lens.

Fig. 6
Fig. 6

Location of the viewing zone and the overall viewing angle θtotal of an observer who is located at Lo from the lens array.

Fig. 7
Fig. 7

Relation among the real image distance b and the resolution ratio Rreal, total viewing angle ratio θtotal realreference, and the number of the involved lenses N.

Fig. 8
Fig. 8

Relation among the virtual image distance b′ and the resolution ratio Rvirtual, total viewing angle ratio θtotal virtualreference, and the number of the involved lenses N.

Fig. 9
Fig. 9

Experimental results (diamonds) compared with simulated results θtotal by the proposed analysis and θconventional total by the conventional analysis (a) for the real 3D image, (b) for the virtual 3D image.

Fig. 10
Fig. 10

Integrated image with a depth of 70 mm captured in the viewing direction that matches with the maximum viewing angle of the proposed method: (a) integrated real image, (b) integrated virtual image.

Fig. 11
Fig. 11

Integrated image with a depth of 70 mm captured in the viewing direction that matches with the maximum viewing angle of the conventional method: (a) integrated real image, (b) integrated virtual image.

Tables (2)

Tables Icon

Table 1 Experimental Viewing Angle and Simulated Results of θtotal real by the Proposed and θconventional total real by the Conventional Method for a Real Image

Tables Icon

Table 2 Experimental Viewing Angle and Simulated Results of θtotal virtual by the Proposed and θconventional total virtual by the Conventional Method for a Virtual Image

Equations (13)

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θ conventional = 2 arctan ( ρ 2 g ) ,
g = b f b f ,
S elemental image real = g real S subimage rael b = g real ρ ( L o b ) b L o .
θ real = 2 arctan [ 1 2 g real ( ρ S elemental image real ) ] .
θ real = 2 arctan { ρ 2 g real [ 1 g real ( L o b ) b L o ] } = 2 arctan [ ρ ( b L o + b f 2 f L o ) 2 b f L o ] .
θ real = 2 arctan { ρ 2 g real [ 1 R real ( L o b ) L o ] } .
S elemental image virtual = g virtual S subimage virtual b = g virtual ρ ( L o + b ) b L o .
θ virtual = 2 arctan [ 1 2 g virtual ( ρ S elemental image virtual ) ] = 2 arctan { ρ 2 g virtual [ 1 g virtual ( L o + b ) b L o ] } = 2 arctan { ρ ( b + f ) 2 b f [ 1 f b + f ( L o + b ) L o ] } = 2 arctan [ ρ ( L o f ) 2 f L o ] .
R virtual = g virtual b = f b + f .
D = ρ 2 tan ( θ 2 ) ( N 1 ) .
θ total = 2 arctan [ ( L o D ) tan ( θ 2 ) L o ] .
θ total real = 2 arctan [ ( L o D ) tan ( θ real 2 ) L o ] = 2 arctan { 1 L o [ L o ρ 2 tan ( θ real 2 ) ( N 1 ) ] × tan ( θ real 2 ) } = 2 arctan { ρ [ b L o ( N 2 ) b f 2 f L o ] 2 b f L o } .
θ total virtual = 2 arctan [ ( L o D ) tan ( θ virtual 2 ) L o ] = 2 arctan { 1 L o [ L o ρ 2 tan ( θ virtual 2 ) × ( N 1 ) ] tan ( θ virtual 2 ) } = 2 arctan [ ρ ( L o N f ) 2 f L o ] .

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