Abstract

By adoption of double-device systems, integral imaging can be enhanced in image depth, viewing angle, or image size. Theoretical analyses are done for the double-image-plane integral imaging systems. Both ray optics analysis and wave optics analysis confirm that the double-device integral imaging systems can pick up and display images at two separate image planes. The analysis results are also valuable in the understanding of the conventional integral imaging systems for image positions off the central depth plane.

© 2002 Optical Society of America

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References

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  1. G. Lippmann, “La photographic intégrale,” Comtes-Rendus 146, 446–451 (1908).
  2. H. E. Ives, “Optical properties of a Lippman lenticulated sheet,” J. Opt. Soc. Am. 21, 171–176 (1931).
    [CrossRef]
  3. C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58, 71–76 (1968).
    [CrossRef]
  4. T. Okoshi, “Optimum design and depth resolution of lens-sheet and projection-type three-dimensional displays,” Appl. Opt. 10, 2284–2291 (1971).
    [CrossRef] [PubMed]
  5. T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).
    [CrossRef]
  6. N. Davies, M. McCormick, L. Yang, “3D imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).
    [CrossRef] [PubMed]
  7. F. Okano, H. Hoshino, J. Arai, I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
    [CrossRef] [PubMed]
  8. 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]
  9. J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).
    [CrossRef]
  10. B. Lee, S.-W. Min, S. Jung, J.-H. Park, “A three-dimensional display system based on computer-generated integral photography,” J. Soc. 3D Broadcasting Imaging, 1, 78–82 (2000).
  11. H. Arimoto, B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. 26, 157–159 (2001).
    [CrossRef]
  12. 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]
  13. B. Lee, S. Jung, S.-W. Min, J.-H. Park, “Three-dimensional display using integral photography with dynamically variable image planes,” Opt. Lett. 26, 1481–1482 (2001).
    [CrossRef]
  14. T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).
  15. B. Javidi, F. Okano, eds., Three-Dimensional Television, Video, and Display Technology (Springer-Verlag, Berlin, 2002).
  16. J. S. Jang, B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of non-stationary micro-optics,” Opt. Lett. 27, 324–326 (2002).
    [CrossRef]
  17. J. Ojeda-Castañeda, L. R. Berriel-Valdos, E. L. Montes, “Spatial filter for increasing the depth of focus,” Opt. Lett. 10, 520–522 (1985).
    [CrossRef] [PubMed]
  18. S. Sanyal, A. Ghosh, “High focal depth with a quasi-bifocus birefringent lens,” Appl. Opt. 39, 2321–2325 (2000).
    [CrossRef]
  19. E. Peli, A. Lang, “Appearance of images through a multifocal intracular lens,” J. Opt. Soc. Am. A 18, 302–309 (2001).
    [CrossRef]
  20. B. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, New York, 2001), pp. 491–492.
  21. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

2002 (1)

2001 (4)

2000 (2)

B. Lee, S.-W. Min, S. Jung, J.-H. Park, “A three-dimensional display system based on computer-generated integral photography,” J. Soc. 3D Broadcasting Imaging, 1, 78–82 (2000).

S. Sanyal, A. Ghosh, “High focal depth with a quasi-bifocus birefringent lens,” Appl. Opt. 39, 2321–2325 (2000).
[CrossRef]

1998 (2)

1997 (1)

1988 (1)

1985 (1)

1980 (1)

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).
[CrossRef]

1971 (1)

1968 (1)

1931 (1)

1908 (1)

G. Lippmann, “La photographic intégrale,” Comtes-Rendus 146, 446–451 (1908).

Arai, J.

Arimoto, H.

Berriel-Valdos, L. R.

Burckhardt, C. B.

Davies, N.

Ghosh, A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hoshino, H.

Isono, H.

Ives, H. E.

Jang, J. S.

Javidi, B.

J. S. Jang, B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of non-stationary micro-optics,” Opt. Lett. 27, 324–326 (2002).
[CrossRef]

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

B. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, New York, 2001), pp. 491–492.

Jung, S.

Lang, A.

Lee, B.

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 using integral photography with dynamically variable image planes,” Opt. Lett. 26, 1481–1482 (2001).
[CrossRef]

B. Lee, S.-W. Min, S. Jung, J.-H. Park, “A three-dimensional display system based on computer-generated integral photography,” J. Soc. 3D Broadcasting Imaging, 1, 78–82 (2000).

B. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, New York, 2001), pp. 491–492.

Lippmann, G.

G. Lippmann, “La photographic intégrale,” Comtes-Rendus 146, 446–451 (1908).

McCormick, M.

Min, S.-W.

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 using integral photography with dynamically variable image planes,” Opt. Lett. 26, 1481–1482 (2001).
[CrossRef]

B. Lee, S.-W. Min, S. Jung, J.-H. Park, “A three-dimensional display system based on computer-generated integral photography,” J. Soc. 3D Broadcasting Imaging, 1, 78–82 (2000).

B. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, New York, 2001), pp. 491–492.

Montes, E. L.

Ojeda-Castañeda, J.

Okano, F.

Okoshi, T.

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).
[CrossRef]

T. Okoshi, “Optimum design and depth resolution of lens-sheet and projection-type three-dimensional displays,” Appl. Opt. 10, 2284–2291 (1971).
[CrossRef] [PubMed]

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

Park, J.-H.

Peli, E.

Sanyal, S.

Yang, L.

Yuyama, I.

Appl. Opt. (6)

Comtes-Rendus (1)

G. Lippmann, “La photographic intégrale,” Comtes-Rendus 146, 446–451 (1908).

J. Opt. Soc. Am. (2)

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

J. Soc. 3D Broadcasting Imaging (1)

B. Lee, S.-W. Min, S. Jung, J.-H. Park, “A three-dimensional display system based on computer-generated integral photography,” J. Soc. 3D Broadcasting Imaging, 1, 78–82 (2000).

Opt. Lett. (4)

Proc. IEEE (1)

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).
[CrossRef]

Other (4)

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

B. Javidi, F. Okano, eds., Three-Dimensional Television, Video, and Display Technology (Springer-Verlag, Berlin, 2002).

B. Javidi, S.-W. Min, B. Lee, “Enhanced 3D color integral imaging using multiple display devices,” in Proceedings of IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, New York, 2001), pp. 491–492.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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Figures (9)

Fig. 1
Fig. 1

Integral imaging system with double devices.

Fig. 2
Fig. 2

Modification of the integral imaging system with double devices for (a) enhanced viewing angle and (b) enlarged image size.

Fig. 3
Fig. 3

Geometry for ray optics analysis for an object in front of the central depth plane.

Fig. 4
Fig. 4

Geometry for ray optics analysis for an object behind the central depth plane.

Fig. 5
Fig. 5

Point-spread functions calculated with Eq. (29) for different values of L (f = 30 mm, ϕ = 5 mm). For different values of L, the values of g are adjusted appropriately.

Fig. 6
Fig. 6

(a) FWHM of the point-spread functions for different values of L as a function of lens diameter ϕ. f = 30 mm. For different values of L, the values of g are adjusted appropriately. (b) Width of the point-spread function calculated with Eq. (30).

Fig. 7
Fig. 7

Point-spread functions for some off-focus cases (L = 0.3 m, ϕ = 5 mm).

Fig. 8
Fig. 8

FWHM of the point-spread functions (for off-focus cases) for different values of L (a) as a function of lens diameter ϕ (b = 50 mm) and (b) as a function of b (ϕ = 5 mm). In all calculations, f = 30 mm is assumed, and for different values of L, the values of g are adjusted appropriately.

Fig. 9
Fig. 9

Simulation result of the integrated images (a) in the conventional integral imaging system and (b) in the integral imaging system represented in Fig. 1.

Equations (47)

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R=fRdisL-f,
ψ=2 arctanϕ/2g,
1g+1L=1f,
L-b:q+12ϕ=b:x1,
x1=bq+12ϕL-b.
x2=bq-12ϕL-b.
L-b:q-12ϕ+xb1=b:x1-xb1,
xb1=bϕ/L.
xb2=bϕ/L,
S=2bϕ/L.
x1=bq+12ϕL+b,
x2=bq-12ϕL+b,
xb1=bϕ/L,
xb2=bϕ/L,
h1u, v; ξ, η=1λ2Lg-- Px, yexp-j 2πλ×ξL+ugx+ηL+vgydxdy,
Px, y=rectx/ϕrecty/ϕ.
h1u, v; ξ, η=h1u-ξ˜, v-η˜ =1λ2Lg-- Px, yexp-j 2πλg×u-ξ˜x+v-η˜ydxdy,
ξ˜=M1ξ, η˜=M1η,
M1=-g/L.
h1u, v; ξ, η=h1u-ξ˜, v-η˜=ϕ2λ2Lg×sincϕλgu-ξ˜sincϕλgv-η˜.
I1u, v=-- h1u-ξ˜, v-η˜2 Igξ˜, η˜dξ˜dη˜,
Igξ˜, η˜=1|M1|2 Ioξ˜M1, η˜M1=1|M1|2 Ioξ, η.
IPξ, η=-- h2ξ-ũ, η-v˜2I1gũ, v˜dũdv˜,
ũ=M2u, v˜=M2v,
M2=-L/g,
I1gũ, v˜=1|M2|2 I1ũM2, v˜M2=1|M2|2 I1u, v,
h2ξ, η; u, v=h2ξ-ũ, η-v˜ =1λ2gL-- Px, y×exp-j 2πλLξ-ũx+η-v˜ydxdy.
h2ξ, η; u, v=h2ξ-ũ, η-v˜ =ϕ2λ2gLsincϕλLξ-ũ×sincϕλLη-v˜.
IPξ, η=---- h2ξ-M2u, η-M2v2×h1u-M1ξ, v-M1η2×Ioξ, ηdudvdξdη =M12---- h2ξ-ũ, η-v˜2×h1M1ũ-ξ, M1×v˜-η2 Ioξ, ηdũdv˜dξdη.
S=4λL/ϕ,
h3u, v; ξ, η=h3u-ξ˜, v-η˜ =1λ2L-bg-- Px, y×expj πλ1L-b+1g-1f×x2+y2exp-j 2πλgu-ξ˜×x+v-η˜ydxdy,
ξ˜=M3ξ, η˜=M3η,
M3=-gL-b.
1L+b+1g-1f=1L+b-1L
h4ξ, η; u, v=h4ξ-ũ, η-v˜=1λ2gL-b-- Px, y×expj πλ1g+1L-b-1f×x2+y2exp-j 2πλL-b×ξ-ũx+η-v˜ydxdy,
ũ=M4u, v˜=M4v,
M4=-L-bg.
IAξ, η=---- h4ξ-M4u, η-M4v2×h3u-M3ξ, v-M3η×2 Ioξ, ηdudvdξdη =M32---- h4ξ-ũ, η-v˜2×h3M3ũ-ξ, M3×v˜-η2Ioξ, ηdũdv˜dξdη.
h3u, v; ξ, η=h3u-ξ˜, v-η˜=-ϕ2Lλgbsincϕfxsincϕfy exp-j πλLL-bbfx2+fy2,
fx=u-ξ˜λg, fy=v-η˜λg.
sincϕfxexp-2.04ϕ2fx2,
h3u-ξ˜, v-η˜2exp-u-ξ˜2+v-η˜2×4.08ϕ2L2L-b2g2λ2L2L-b2+b2ϕ4,
h4ξ-ũ, η-v˜2exp-ξ-ũ2+η-v˜2×4.08ϕ2L2λ2L2L-b2+b2ϕ4.
IAξ, ηexp-2.04ϕ2L2λ2L2L-b2+b2ϕ4ξ2+η2,
S=1.17λ2L2L-b2+b2ϕ41/2ϕL.
S=1.17λL/ϕ,
S=1.17bϕ/L.

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