Abstract

The effects of misarrangement of elements (elemental lenses and elemental images) that construct three-dimensional (3-D) images in integral photography are presented. If the lens arrays of the capturing system and the display system are not aligned accurately, positional errors of elements may occur, causing the 3-D image to be reconstructed in an incorrect position. The relation between positional errors of elements and the reconstructed image is derived. As a result, it is shown that a 3-D image is separated by local positional errors and blurred by global positional errors. In both local and global positional errors, 3-D images reconstructed far from the lens array are greatly affected.

© 2004 Optical Society of America

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References

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  1. T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1971).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. Y. A. Dudnikov, “On the design of a scheme for producing integral photographs by a combination method,” Sov. J. Opt. Technol. 41, 426–429 (1974).
  8. F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
    [CrossRef]
  9. N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
    [CrossRef]
  10. H.-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]
  11. B. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of the IEEE-LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 491–492.
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. H. Hoshino, F. Okano, H. Isono, I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).
    [CrossRef]
  15. J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).
    [CrossRef]
  16. M. Herzberger, “Light distribution in the optical image,” J. Opt. Soc. Am. 37, 485–493 (1947).
    [CrossRef] [PubMed]
  17. G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (Dover, New York, 2000).

2003 (1)

2002 (1)

B. G. Blundell, A. J. Schwarz, “The classification of volumetric display systems: characteristics and predictability of the image space,” IEEE Trans. Visualiz. Comput. Graphics 8, 66–75 (2002).
[CrossRef]

2001 (1)

1999 (1)

F. Okano, J. Arai, H. Hoshino, 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, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

1974 (1)

Y. A. Dudnikov, “On the design of a scheme for producing integral photographs by a combination method,” Sov. J. Opt. Technol. 41, 426–429 (1974).

1971 (1)

1969 (1)

1968 (1)

1947 (1)

1931 (1)

1908 (1)

M. G. Lippmann, “Épreuves réversibles donnant la sensation du relief,” J. Phys. (Paris) 7, 821–825 (1908).

Arai, J.

J. Arai, H. Hoshino, M. Okui, 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, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

Blundell, B. G.

B. G. Blundell, A. J. Schwarz, “The classification of volumetric display systems: characteristics and predictability of the image space,” IEEE Trans. Visualiz. Comput. Graphics 8, 66–75 (2002).
[CrossRef]

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]

Burckhardt, C. B.

Davies, N.

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

deMontebello, R. L.

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

Doherty, E. T.

Dudnikov, Y. A.

Y. A. Dudnikov, “On the design of a scheme for producing integral photographs by a combination method,” Sov. J. Opt. Technol. 41, 426–429 (1974).

Herzberger, M.

Hoshino, H.

Isono, H.

Ives, H. E.

Javidi, B.

B. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of the IEEE-LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 491–492.

Jung, S.

Korn, G. A.

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (Dover, New York, 2000).

Korn, T. M.

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (Dover, New York, 2000).

Lee, B.

H.-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. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of the IEEE-LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 491–492.

Lippmann, M. G.

M. G. Lippmann, “Épreuves réversibles donnant la sensation du relief,” J. Phys. (Paris) 7, 821–825 (1908).

McCormick, 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]

Min, S.-W.

H.-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. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of the IEEE-LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 491–492.

Okano, F.

Okoshi, T.

Okui, M.

Park, H.-H.

Schwarz, A. J.

B. G. Blundell, A. J. Schwarz, “The classification of volumetric display systems: characteristics and predictability of the image space,” IEEE Trans. Visualiz. Comput. Graphics 8, 66–75 (2002).
[CrossRef]

Yuyama, I.

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

H. Hoshino, F. Okano, H. Isono, I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Visualiz. Comput. Graphics (1)

B. G. Blundell, A. J. Schwarz, “The classification of volumetric display systems: characteristics and predictability of the image space,” IEEE Trans. Visualiz. Comput. Graphics 8, 66–75 (2002).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

J. Phys. (Paris) (1)

M. G. Lippmann, “Épreuves réversibles donnant la sensation du relief,” J. Phys. (Paris) 7, 821–825 (1908).

Opt. Eng. (2)

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

Sov. J. Opt. Technol. (1)

Y. A. Dudnikov, “On the design of a scheme for producing integral photographs by a combination method,” Sov. J. Opt. Technol. 41, 426–429 (1974).

Other (4)

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

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

B. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of the IEEE-LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 491–492.

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (Dover, New York, 2000).

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Figures (14)

Fig. 1
Fig. 1

Principle of IP. (a) Capturing, (b) display.

Fig. 2
Fig. 2

Principal rays of elemental images and reconstructed image. (a) Capture stage, (b) display stage.

Fig. 3
Fig. 3

Viewing area of IP.

Fig. 4
Fig. 4

Split image caused by a local error. (a) Local error of a lens array for capturing, (b) display of misarranged elemental images.

Fig. 5
Fig. 5

Angle of separation and Nyquist frequency.

Fig. 6
Fig. 6

Ratio of θv to θnyq(Φ(zd1, δ)).

Fig. 7
Fig. 7

Shift of the viewing area caused by the local error in a lens array (a) for capturing, (b) for display.

Fig. 8
Fig. 8

Distribution of the global error.

Fig. 9
Fig. 9

Principal rays from elemental lenses with global error.

Fig. 10
Fig. 10

Examples of the principal-rays spot diagram of a lens array with global error. A point light source located at (zp, xp)=(-150, 0) is assumed as an object. Spreads of the principal rays at zd=-150 (mm) and zd=-94.2 (mm) are calculated. A spread of the principal-rays spot diagram is not the least at the reconstructed image position without global error [in this case, (zd, xd)=(-150, 0)].

Fig. 11
Fig. 11

Principal rays with global errors and their caustic. (a) Elemental lenses from 0 to |h|, (b) elemental lenses from |h| to |mmax|.

Fig. 12
Fig. 12

Position of the plane of least confusion.

Fig. 13
Fig. 13

Example of the relation between the reconstructed image position without global error and its image shift.

Fig. 14
Fig. 14

Example of the image spread at the plane of least confusion.

Equations (30)

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xp=[(mpLp-xp1)/(-zp1)]zp+mpLp,
kmp1=[(mpLp-xp1)/(-zp1)]gp,
kmd1=-kmp1=[(mpLd-xp1)/(-zp1)]gd,
xd=[(-kmd1)/(-gd)]zd+mpLd=-[(mpLd-xp1)/(-zp1)]zd+mpLd.
pLd=apLp,
gd=-bgp,
kmd1=-dkmp1.
xd=adgpzp(d-a)+dgp xp,
zd=abgpzp(d-a)+dgp zp.
θ=2 arctan[wd/(-2gd)].
V=2L tanθ2,
Dp(zd1, δp)=xd1-xd1=[(zd1/gd)-1]δp,
Dd(zd1, δd)=xd1-xd1=[1-(zd1/gd)]δd.
D(zd1, δ)=Dp(zd1, δp)+Dd(zd1, δd)=[(zd1/gd)-1](δp-δd)=[(zd1/gd)-1]δ,
δ=δp-δd.
θv(zd1, |D|)=|D|/(L-zd1),
βnyq=L/2pLd,
θnyq=1/βnyq=2pLd/L.
Φ(zd1, δ)=θv(zd1, |D|)/θnyq.
VLp=-δp(L-gd)/(-gd).
VLd=δd(L-gd)/(-gd).
δG(m)=δGmax[1-ϕ(m)/ϕ(0)],
ϕ(m)=12πexp[-(m/h)2/2],
xd={[-kmd1+δG(m)]/(-gd)}zd+[mpLd+δG(m)].
2δG(m)m2=δGmax1-mh2exp-mh2/2/h2.
xd={[-kmˆd1+δG(mˆ)]/(-gd)}zd+[mˆpLd+δG(mˆ)],
mˆh2exp-mˆh2/2=-gdpLd(zd+1)zp1zd+gd.
VGd(m)=δG(m)(L-gd)/(-gd),
δG(m)Lwd2(L-gd),
VGp(m)=-δG(m)(L-gd)/(-gd),

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