Abstract

An optical depth converter that uses a lens array pair is analyzed theoretically and experimentally. We present a theory of depth conversion and explain the effects of the system parameters in the optical depth converter by using wave-optical analysis. Ray-optical analysis is applied to the investigation of the tendencies of the system parameter effects. We also show that the optical depth converter can be used for the three-dimensional screen in projection-type integral imaging systems.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).
  2. H. E. Ives, “Optical properties of a Lippmann 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. Y. Igarishi, H. Murata, M. Ueda, “3D display system using a computer-generated integral photograph,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
    [CrossRef]
  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. L. Yang, M. McCormick, N. Davies, “Discussion of the optic of a new 3-D imaging system,” Appl. Opt. 27, 4529–4534 (1988).
    [CrossRef] [PubMed]
  8. 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]
  9. 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]
  10. M. C. Forman, N. Davies, M. McCormick, “Continuous parallax in discrete pixilated integral three-dimensional displays,” J. Opt. Soc. Am. A 20, 411–420 (2003).
    [CrossRef]
  11. 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]
  12. B. Lee, S.-W. Min, S. Jung, J.-H. Park, “A three-dimensional display system based on computer-generated integral photography,” J. Soc. 3D Broadcast. Imag. 1, 78–82 (2000).
  13. J.-S. Jang, B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. 42, 1869–1870 (2003).
    [CrossRef]
  14. 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]
  15. B. Lee, S. Jung, J.-H. Park, “Viewing-angle-enhanced integral imaging using lens switching,” Opt. Lett. 27, 818–820 (2002).
    [CrossRef]
  16. H. Choi, J.-H. Park, J. Hong, B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 730–731.
    [CrossRef]
  17. J.-S. Jang, B. Javidi, “Moving array lens technique (MALT) for improved resolution of all-optical three-dimensional projection,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 10–15 (2002).
    [CrossRef]
  18. J.-S. Jang, B. Javidi, “Two-step integral imaging for orthoscopic three-dimensional imaging with improved viewing resolution,” Opt. Eng. 41, 2568–2571 (2002).
    [CrossRef]
  19. Y. Jeong, S. Jung, J.-H. Park, B. Lee, “A reflection-type integral imaging scheme for displaying three-dimensional images,” Opt. Lett. 27, 704–706 (2002).
    [CrossRef]
  20. J.-S. Jang, B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Exp. 12, 1077–1083 (2004), http://www.opticsexpress.org .
    [CrossRef]
  21. H. Liao, M. Iwahara, N. Hata, T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Exp. 12, 1067–1076 (2004), http://www.opticsexpress.org .
    [CrossRef]

2004 (2)

J.-S. Jang, B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Exp. 12, 1077–1083 (2004), http://www.opticsexpress.org .
[CrossRef]

H. Liao, M. Iwahara, N. Hata, T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Exp. 12, 1067–1076 (2004), http://www.opticsexpress.org .
[CrossRef]

2003 (2)

M. C. Forman, N. Davies, M. McCormick, “Continuous parallax in discrete pixilated integral three-dimensional displays,” J. Opt. Soc. Am. A 20, 411–420 (2003).
[CrossRef]

J.-S. Jang, B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. 42, 1869–1870 (2003).
[CrossRef]

2002 (3)

2001 (2)

2000 (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 Broadcast. Imag. 1, 78–82 (2000).

1998 (1)

1997 (1)

1988 (2)

1980 (1)

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

1978 (1)

Y. Igarishi, H. Murata, M. Ueda, “3D display system using a computer-generated integral photograph,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

1968 (1)

1931 (1)

1908 (1)

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

Arai, J.

Burckhardt, C. B.

Choi, H.

H. Choi, J.-H. Park, J. Hong, B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 730–731.
[CrossRef]

Davies, N.

Dohi, T.

H. Liao, M. Iwahara, N. Hata, T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Exp. 12, 1067–1076 (2004), http://www.opticsexpress.org .
[CrossRef]

Forman, M. C.

Hata, N.

H. Liao, M. Iwahara, N. Hata, T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Exp. 12, 1067–1076 (2004), http://www.opticsexpress.org .
[CrossRef]

Hong, J.

H. Choi, J.-H. Park, J. Hong, B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 730–731.
[CrossRef]

Hoshino, H.

Igarishi, Y.

Y. Igarishi, H. Murata, M. Ueda, “3D display system using a computer-generated integral photograph,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

Ives, H. E.

Iwahara, M.

H. Liao, M. Iwahara, N. Hata, T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Exp. 12, 1067–1076 (2004), http://www.opticsexpress.org .
[CrossRef]

Jang, J.-S.

J.-S. Jang, B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Exp. 12, 1077–1083 (2004), http://www.opticsexpress.org .
[CrossRef]

J.-S. Jang, B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. 42, 1869–1870 (2003).
[CrossRef]

J.-S. Jang, B. Javidi, “Two-step integral imaging for orthoscopic three-dimensional imaging with improved viewing resolution,” Opt. Eng. 41, 2568–2571 (2002).
[CrossRef]

J.-S. Jang, B. Javidi, “Moving array lens technique (MALT) for improved resolution of all-optical three-dimensional projection,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 10–15 (2002).
[CrossRef]

Javidi, B.

J.-S. Jang, B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Exp. 12, 1077–1083 (2004), http://www.opticsexpress.org .
[CrossRef]

J.-S. Jang, B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. 42, 1869–1870 (2003).
[CrossRef]

J.-S. Jang, B. Javidi, “Two-step integral imaging for orthoscopic three-dimensional imaging with improved viewing resolution,” Opt. Eng. 41, 2568–2571 (2002).
[CrossRef]

J.-S. Jang, B. Javidi, “Moving array lens technique (MALT) for improved resolution of all-optical three-dimensional projection,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 10–15 (2002).
[CrossRef]

Jeong, Y.

Jung, S.

Lee, B.

Y. Jeong, S. Jung, J.-H. Park, B. Lee, “A 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 using 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 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 Broadcast. Imag. 1, 78–82 (2000).

H. Choi, J.-H. Park, J. Hong, B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 730–731.
[CrossRef]

Liao, H.

H. Liao, M. Iwahara, N. Hata, T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Exp. 12, 1067–1076 (2004), http://www.opticsexpress.org .
[CrossRef]

Lippmann, M. G.

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

McCormick, M.

Min, S.-W.

Murata, H.

Y. Igarishi, H. Murata, M. Ueda, “3D display system using a computer-generated integral photograph,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

Okano, F.

Okoshi, T.

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

Park, J.-H.

Y. Jeong, S. Jung, J.-H. Park, B. Lee, “A 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 using lens switching,” Opt. Lett. 27, 818–820 (2002).
[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]

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

H. Choi, J.-H. Park, J. Hong, B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 730–731.
[CrossRef]

Ueda, M.

Y. Igarishi, H. Murata, M. Ueda, “3D display system using a computer-generated integral photograph,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

Yang, L.

Yuyama, I.

Appl. Opt. (5)

C. R. Acad. Sci. (1)

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

J. Opt. Soc. Am. (2)

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

J. Soc. 3D Broadcast. Imag. (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 Broadcast. Imag. 1, 78–82 (2000).

Jpn. J. Appl. Phys. (1)

Y. Igarishi, H. Murata, M. Ueda, “3D display system using a computer-generated integral photograph,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

Opt. Eng. (2)

J.-S. Jang, B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. 42, 1869–1870 (2003).
[CrossRef]

J.-S. Jang, B. Javidi, “Two-step integral imaging for orthoscopic three-dimensional imaging with improved viewing resolution,” Opt. Eng. 41, 2568–2571 (2002).
[CrossRef]

Opt. Exp. (2)

J.-S. Jang, B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Exp. 12, 1077–1083 (2004), http://www.opticsexpress.org .
[CrossRef]

H. Liao, M. Iwahara, N. Hata, T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Exp. 12, 1067–1076 (2004), http://www.opticsexpress.org .
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

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

Other (2)

H. Choi, J.-H. Park, J. Hong, B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 730–731.
[CrossRef]

J.-S. Jang, B. Javidi, “Moving array lens technique (MALT) for improved resolution of all-optical three-dimensional projection,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 10–15 (2002).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

Scheme for the two-step integral imaging system. LA, lens array.

Fig. 2
Fig. 2

Imaging by (a) a pair of convex lenses and (b) a pair of lens arrays.

Fig. 3
Fig. 3

Geometry of the optical depth converter. See text for definitions.

Fig. 4
Fig. 4

Integration plane and focused plane versus position of the object.

Fig. 5
Fig. 5

Optimized gap with respect to the position of the object.

Fig. 6
Fig. 6

Coordinates for the wave-optical analysis.

Fig. 7
Fig. 7

Maximum order of the elemental lens.

Fig. 8
Fig. 8

Intensity profiles for different pitches of the elemental lens.

Fig. 9
Fig. 9

Intensity profiles for different positions of the object.

Fig. 10
Fig. 10

Lateral dispersion for different pitches of the elemental lens.

Fig. 11
Fig. 11

Scheme for the experimental setup. (1), (2), (3), gaps; (i), (ii), (iii), position of screen at 5, 15, and 25 cm, respectively.

Fig. 12
Fig. 12

Experimental results of the optical depth converter: (a) objects, (b) reconstructed image, (c) reconstructed image on the screen. The indications (1), (2), (3), (i), (ii), and (iii) correspond to those in Fig. 11.

Fig. 13
Fig. 13

Lateral dispersion for different positions of the object.

Fig. 14
Fig. 14

Scheme for the projection-type integral imaging system. SLM, spatial light modulator.

Fig. 15
Fig. 15

Experimentally reconstructed image of the projection-type integral imaging system without a diffuser and with an elemental lens pitch of (a) 1 mm and (b) 5 mm.

Fig. 16
Fig. 16

Experimentally reconstructed image of the projection-type integral imaging system with a diffuser located at (a) position A; (b) position B, especially on image “I”; and (c) position B, especially on image “P”. The pitch of the elemental lens is 5 mm. Image “P” is located 5 cm in front of image “I”.

Fig. 17
Fig. 17

Scheme for the projection-type integral imaging system with the optical depth converter (ODC) as the 3D screen. SLM, spatial light modulator.

Fig. 18
Fig. 18

Image of the projection-type integral imaging system with a 3D screen from (a) a center viewpoint, (b) a left-up viewpoint, and (c) a right-down viewpoint.

Tables (1)

Tables Icon

Table 1 Calculated and Measured Viewing Angles

Equations (31)

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

l=d-ffa-df2d-2fa-d-ff=f2/d-2f2a-d-ff/d-2f+d-ffd-2f,
b=afa-f,
h0=1+b/aϕ,
h1=1+d/aϕ.
h2=ϕ-ba ϕ fd-b-f.
L=fd-fa+d.
dl=L=2afa-f,
ULA1x1, y1=ajλexpjkr01x1, y1; ξ, ηr01x1, y1; ξ, η2,
r01x1, y1; ξ, η=r01x1-ξ, y1-η=a1+x1-ξa2+y1-ηa21/2.
ULA1x1, y1=ULA1x1, y1exp-j k2fx1-X1q2+y1-Y1q2,
ULA2x2, y2=djλLA1 ULA1x1, y1×expjkr12x2, y2; x1, y1r12x2, y2; x1, y12dx1dy1,
ULA2x2, y2=ULA2x2, y2exp-j k2fx2-X2q2+y1-Y2q2,
r12x2, y2; x1, y1=r12x2-x1, y2-y1=d1+x2-x1d2+y2-y1d21/2.
hu, v; ξ, η=wjλLA2 ULA2x2, y2×expjkr23u, v; x2, y2r23u, v; x2, y22dx2dy2,
r23u, v; x2, y2=r23u-x2, v-y2=w1+u-x2w2+v-y2w21/2.
r01=a1+x1-ξa2+y1-ηa21/2a2+Ωq0121+Ωq01+x1-ξ2+y1-η22a21+Ωq01,
Ωq01=qϕ/a2.
r01R01=a2+qϕ21/2,
r12=d1+x2-x1d2+y2-y1d21/2d2+Ωqq1221+Ωqq12+x2-x12+y2-y122d21+Ωqq12,
Ωqq12=q-q2d ϕ2,
r12R12=d2+q-q2ϕ21/2,
r23=w1+u-x2w2+v-y2w21/2w2+Ωq2321+Ωq23+u-x22+v-y222w21+Ωq23,
Ωq23=qϕ/w2,
r23R23=w2+qϕ21/2,
hqqu, v; ξ, η=-adwjλ3LA2LA11r012r122r232expjkr01+r12+r23exp-j k2fx1-qϕ2+x2-qϕ2+y12+y22dx1dx2dy1dy2 -adwjλ3R012R122R232expjka2+Ωq0121+Ωq01+d2+Ωqq1221+Ωqq12+w2+Ωq2321+Ωq23×LA1LA2 expjkx1-ξ2+y1-η22a1+Ωq01+x2-x12+y2-y122d1+Ωqq12+u-x22+v-y222w1+Ωq23exp-j k2fx1-qϕ2+x2-qϕ2+y12+y22dx1dy1dx2dy2.
Iu, v=-QmaxQmaxQminQmax |hqqu, v|2,
Qmax=a-f2f.
Qmax=q,
Qmin=q-da-f2af -qaq-a-qda=q  q1.
Iu, v=|h00u, v|2+2 1Qmax |hqqu, v|2.
θ2 arctanQmaxϕa2 arctanϕd.

Metrics