Abstract

Three-dimensional images generated by an integral imaging system suffer from degradations in the form of grid of multiple facets. This multifacet structure breaks the continuity of the observed image and therefore reduces its visual quality. We perform an analysis of this effect and present the guidelines in the design of lenslet imaging parameters for optimization of viewing conditions with respect to the multifacet degradation. We consider the optimization of the system in terms of field of view, observer position and pupil function, lenslet parameters, and type of reconstruction. Numerical tests are presented to verify the theoretical analysis.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. T. Okoshi, “Optimum design and depth resolution of lens-sheat and projection-type three-dimensional displays,” Appl. Opt. 10, 2284–2291 (1971).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).
    [CrossRef]
  13. F. Okano, H. Hoshino, J. Arai, I. Yayuma, “Real time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. A. Stern, B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. 42, 7036–7042 (2003).
    [CrossRef] [PubMed]
  18. J.-S. Jang, B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27, 1144–1146 (2002).
    [CrossRef]
  19. J.-S. Jang, B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27, 324–326 (2002).
    [CrossRef]
  20. J.-S. Jang, B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes,” Opt. Lett. 28, 1924–1926 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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  25. 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]
  26. J. Arai, M. Okui, M. Kobayashi, F. Okano, “Geometrical effects of positional errors in integral photography,” J. Opt. Soc. Am. A 21, 951–958 (2004).
    [CrossRef]
  27. R. Martı́nez-Cuenca, G. Saavedra, M. Martı́nez-Corral, B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express 12, 5237–5242 (2004).
    [CrossRef] [PubMed]
  28. 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]
  29. D. A. Atchinson, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000).
  30. M. P. Keating, Geometric, Physical, and Visual Optics (Butterworth-Heinemann, Oxford, UK, 1988).
  31. An exact calculation would give the reconstructed image as the convolution between O(x)and a properly scaled version of the self-convolution of function H∘(x; 0).Since the study of resolution is not the aim of this paper, the following calculations can be accurately performed by assuming nonsignificant differences between the object and the reconstructed image.

2004 (5)

2003 (6)

2002 (2)

2001 (2)

1998 (2)

1997 (1)

1994 (1)

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

1988 (1)

1980 (1)

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

1971 (1)

1970 (1)

1968 (1)

1931 (1)

1908 (1)

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

Ambs, P.

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

Arai, J.

Atchinson, D. A.

D. A. Atchinson, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000).

Bigue, L.

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

Binet, R.

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

Brewin, M.

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

Burckhardt, C. B.

Caulfield, H. J.

Choi, H.

Colineau, J.

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

Davies, N.

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

N. Davies, M. McCormick, L. Yang, “Three-dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).
[CrossRef] [PubMed]

Dohi, T.

Erdmann, L.

Gabriel, K. J.

Hata, N.

Hoshino, H.

Huignard, J.-P.

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

Isono, H.

Ives, H. E.

Iwahara, M.

Jang, J.-S.

Javidi, B.

J.-S. Jang, B. Javidi, “Three-dimensional integral imaging of micro-objects,” Opt. Lett. 29, 1230–1232 (2004).
[CrossRef] [PubMed]

R. Martı́nez-Cuenca, G. Saavedra, M. Martı́nez-Corral, B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express 12, 5237–5242 (2004).
[CrossRef] [PubMed]

M. Martı́nez-Corral, B. Javidi, R. Martı́nez-Cuenca, G. Saavedra, “Integral imaging with improved depth of field by use of amplitude modulated microlens array,” Appl. Opt. 43, 5806–5813 (2004).
[CrossRef]

J.-S. Jang, B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes,” Opt. Lett. 28, 1924–1926 (2003).
[CrossRef] [PubMed]

A. Stern, B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. 42, 7036–7042 (2003).
[CrossRef] [PubMed]

S. Kishk, B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11, 3528–3541 (2003).
[CrossRef] [PubMed]

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, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27, 1144–1146 (2002).
[CrossRef]

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

Jung, S.

Keating, M. P.

M. P. Keating, Geometric, Physical, and Visual Optics (Butterworth-Heinemann, Oxford, UK, 1988).

Kishk, S.

Kobayashi, M.

Lee, B.

Lehureau, J.-C.

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

Liao, H.

Lippmann, M. G.

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

Marti´nez-Corral, M.

Marti´nez-Cuenca, R.

McCormick, M.

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

N. Davies, M. McCormick, L. Yang, “Three-dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).
[CrossRef] [PubMed]

McMahon, D. H.

Min, S.-W.

Okano, F.

Okoshi, T.

Okui, M.

Park, J.-H.

Saavedra, G.

Smith, G.

D. A. Atchinson, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000).

Stern, A.

Yang, L.

Yayuma, I.

Yuyama, I.

Appl. Opt. (9)

D. H. McMahon, H. J. Caulfield, “A technique for producing wide-angle holographic displays,” Appl. Opt. 9, 91–96 (1970).
[CrossRef] [PubMed]

N. Davies, M. McCormick, L. Yang, “Three-dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).
[CrossRef] [PubMed]

F. Okano, H. Hoshino, J. Arai, I. Yayuma, “Real time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
[CrossRef] [PubMed]

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]

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]

L. Erdmann, K. J. Gabriel, “High-resolution digital photography by use of a scanning microlens array,” Appl. Opt. 40, 5592–5599 (2001).
[CrossRef]

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

A. Stern, B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. 42, 7036–7042 (2003).
[CrossRef] [PubMed]

M. Martı́nez-Corral, B. Javidi, R. Martı́nez-Cuenca, G. Saavedra, “Integral imaging with improved depth of field by use of amplitude modulated microlens array,” Appl. Opt. 43, 5806–5813 (2004).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

J. Phys. (Paris) (1)

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

Opt. Eng. (2)

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

Opt. Express (4)

Opt. Lett. (4)

Proc. IEEE (1)

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

Other (5)

S. A. Benton, ed., Selected Papers on Three-Dimensional Displays (SPIE Optical Engineering Press, Bellingham, Wash., 2001).

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

D. A. Atchinson, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000).

M. P. Keating, Geometric, Physical, and Visual Optics (Butterworth-Heinemann, Oxford, UK, 1988).

An exact calculation would give the reconstructed image as the convolution between O(x)and a properly scaled version of the self-convolution of function H∘(x; 0).Since the study of resolution is not the aim of this paper, the following calculations can be accurately performed by assuming nonsignificant differences between the object and the reconstructed image.

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Figures (12)

Fig. 1
Fig. 1

Schematic drawing, not to scale, of the pickup stage of an integral imaging system. Each elemental image has a different perspective of the object. Object points out of the reference plane produce blurred images onto the CCD.

Fig. 2
Fig. 2

Schematic drawing of pseudoscopic real reconstruction. The reconstructed image is depth reversed from the observer point of view. Object points at the reference plane are sharply reconstructed.

Fig. 3
Fig. 3

Schematic drawing of orthoscopic virtual reconstruction. The gap distance is reduced to g v = g - 2 f 2 / ( d - f ) . The reconstructed image and the object have the same size. Object points at the reference plane are sharply reconstructed.

Fig. 4
Fig. 4

Observation of the reconstructed real image. The observed image consists of a rectangular grid of elemental FOVs. Each elemental FOV is observed through a different microlens. The elemental FOVs are centered at points x c ( m ) .

Fig. 5
Fig. 5

Illustration of calculation of the elemental FOV function. (a) When the observer is placed at a distance D 1 = 350   mm from the microlenses, the FOVs have a circle-like shape; (b) when D 2 = 900   mm the FOVs are square like. In both cases we have marked the field of half-illumination (dashed line).

Fig. 6
Fig. 6

Synthetic object used for the numerical experiments.

Fig. 7
Fig. 7

For the case of φ = 0.5 : (a) reconstructed image as seen by the observer when distance is set at D 1 = 350   mm , (b) reconstructed image as seen by the observer when D 2 = 900   mm .

Fig. 8
Fig. 8

Variation with D of spacing between adjacent FOVs (solid curve) and of the FHI. The curves start at the nearest distance of distinct vision. For D < D ϕ the FOVs have circle-like shape. For D > D ϕ they have square-like shape.

Fig. 9
Fig. 9

For the case of φ = 1.0 , the reconstructed image as seen by the observer when set, for example, at D = 350   mm . Note that in this case the visual aspect of the observed image is independent of the value of D.

Fig. 10
Fig. 10

Observation of reconstructed virtual image. The observed image consists of a rectangular grid of elemental FOVs, which are centered at points x c ( m ) .

Fig. 11
Fig. 11

Variation with D of spacing between adjacent FOVs (solid curve) and of the FHI. The curves start at the nearest distance of distinct vision.

Fig. 12
Fig. 12

Reconstructed virtual image as seen by the observer when set at D = 300   mm : (a) the case of square lenslets of φ = 0.5 , (b) the case of square lenslets of φ = 1.0 , and (c) the case of circular lenslets of φ = 1.0 .

Equations (14)

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M p = - Δ / f , where Δ = g - f = f 2 / ( d - f ) .
I ( x ) = R 2 R ( x ) H [ x ;   x ,   z = f ( x ) ] d 2 x ,
H ( x ;   x ,   z ) = H o ( x ;   z )     m δ { x - [ m p ( 1 - M z ) - M z x ] } .
H o ( x ;   z ) = R 2 p ( x o ) exp - i   π z λ d ( d + z )   | x o | 2 × exp - i 2 π x o x λ g d 2 x o 2 .
g v = g - 2 Δ = g - 2   f 2 d - f .
x c ( m ) = D - d r D m p .
E ( x ) = rect x w     circ 2   r ϕ ,
ϕ = d r D   ϕ E , w = D - d r D   Δ L .
D ϕ = d r ϕ E + Δ L Δ L ,
ORI ( x ) = m { O ( x ) E [ x - x c ( m ) ] } .
FHI ( D ) = max { ϕ ,   w } ,
x c ( m ) = D + d v D m p .
ϕ = d v D   ϕ E and w = D + d v D   Δ L ,
D ϕ = d v ϕ E - Δ L Δ L .

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