Abstract

One of the main challenges in three-dimensional integral imaging is its limited depth of field. Such a limitation is imposed by diffraction, among other factors. The easiest way to improve the depth of field is by reducing the numerical aperture of the microlenses. However, such an improvement is obtained at the expense of an important deterioration in the spatial resolution. We propose a technique, which is novel in the context of integral imaging, for improving the depth of field with no deterioration of the spatial resolution. The technique, based on amplitude modulation of the array of phase elements, can substantially improve the figure of merit of the product of depth of the focus and the squared resolution.

© 2004 Optical Society of America

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2003 (5)

2002 (2)

2001 (4)

2000 (1)

1999 (1)

1998 (1)

1997 (1)

1995 (1)

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

1980 (1)

Y. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

1969 (1)

1931 (1)

1908 (1)

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

Andrés, P.

Antipova, E. N.

Y. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Arai, J.

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects on the resolution characteristics of integral photography,” J. Opt. Soc. Am. 20, 996–1004 (2003).
[CrossRef]

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]

Arimoto, H.

Caballero, M. T.

Davies, N.

M. McCormick, N. Davies, “Full natural colour 3D optical models by integral imaging,” in Proceedings of Fourth International Conference on Holographic Systems, Components, and Applications, (Institute of Electrical Engineers, London, 1993), pp. 237–242.

de Montebello, R. L.

R. L. de Montebello, “Wide angle integral-photography: the integram technique,” in Three-Dimensional Imaging, S. A. Benton, ed., Proc. SPIE120, 73–91 (1970).
[CrossRef]

Dudnikov, Y. A.

Y. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Erdman, L.

Gabriel, K. J.

Harashima, H.

Hoshino, H.

Ibáñez-López, C.

Isono, H.

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]

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

Ives, H. E.

Jang, J.-S.

Javidi, B.

Jin, F.

Jung, S.

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, “Computer-generated dynamic three-dimensional display using integral photography adopting Fresnel lenses,” in Algorithms and Systems for Optical Information ProcessingV. B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 9–17 (2001).
[CrossRef]

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.-W. Min, S. Jung, J.-H. Park, “Computer-generated dynamic three-dimensional display using integral photography adopting Fresnel lenses,” in Algorithms and Systems for Optical Information ProcessingV. B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 9–17 (2001).
[CrossRef]

Lippmann, M. G.

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

Martínez-Corral, M.

McCormick, M.

M. McCormick, N. Davies, “Full natural colour 3D optical models by integral imaging,” in Proceedings of Fourth International Conference on Holographic Systems, Components, and Applications, (Institute of Electrical Engineers, London, 1993), pp. 237–242.

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.-W. Min, S. Jung, J.-H. Park, “Computer-generated dynamic three-dimensional display using integral photography adopting Fresnel lenses,” in Algorithms and Systems for Optical Information ProcessingV. B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 9–17 (2001).
[CrossRef]

Motoki, T.

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

Muñoz-Escrivá, L.

Naemura, T.

Okano, F.

Okoshi, T.

T. Okoshi, Three Dimensional Imaging Techniques (Academic, London, 1976).

Okui, M.

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects on the resolution characteristics of integral photography,” J. Opt. Soc. Am. 20, 996–1004 (2003).
[CrossRef]

Park, J.-H.

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, “Computer-generated dynamic three-dimensional display using integral photography adopting Fresnel lenses,” in Algorithms and Systems for Optical Information ProcessingV. B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 9–17 (2001).
[CrossRef]

Rozhkov, B. K.

Y. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Saavedra, G.

Sheppard, C. J. R.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Saulito, Calif., 1986).

Stern, A.

Stokseth, A.

Valyus, N. A.

N. A. Valyus, Stereoscopy (Focal, London, 1966).

Yayuma, I.

Yoshida, T.

Yuyama, I.

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]

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

Zapata-Rodríguez, C. J.

Appl. Opt. (3)

J. Opt. Soc. Am. (3)

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

J. Phys. (Paris) (1)

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

Opt. Express (3)

Opt. Lett. (6)

Proc. IEEE (1)

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

Sov. J. Opt. Technol. (1)

Y. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Other (6)

M. McCormick, N. Davies, “Full natural colour 3D optical models by integral imaging,” in Proceedings of Fourth International Conference on Holographic Systems, Components, and Applications, (Institute of Electrical Engineers, London, 1993), pp. 237–242.

N. A. Valyus, Stereoscopy (Focal, London, 1966).

R. L. de Montebello, “Wide angle integral-photography: the integram technique,” in Three-Dimensional Imaging, S. A. Benton, ed., Proc. SPIE120, 73–91 (1970).
[CrossRef]

T. Okoshi, Three Dimensional Imaging Techniques (Academic, London, 1976).

B. Lee, S.-W. Min, S. Jung, J.-H. Park, “Computer-generated dynamic three-dimensional display using integral photography adopting Fresnel lenses,” in Algorithms and Systems for Optical Information ProcessingV. B. Javidi, D. Psaltis, eds., Proc. SPIE4471, 9–17 (2001).
[CrossRef]

A. E. Siegman, Lasers (University Science, Saulito, Calif., 1986).

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Figures (11)

Fig. 1
Fig. 1

Schematic, not to scale, of the capture setup of a 3D integral-imaging system. The points of the surface object O( x , z) out of the reference plane produce blurred images in the aerial pickup plane and therefore on the CCD. In the relay system the field lens collects the rays proceeding from the outermost microlenses, and the camera lens projects the images onto the CCD.

Fig. 2
Fig. 2

Three-dimensional plot of the meridian section of function Hλ 0(r, z) when the pupil of the microlens is a circle of diameter ϕ. The parameters for the calculation are ϕ = 2.0 mm, f = 5.0 mm, λ = 0.5 μm, and a = 100 mm.

Fig. 3
Fig. 3

Schematic, not to scale, of the integral-imaging numerical experiment. The size of the legs of the charts used in our experiments is Δ = 51 μm, which is approximately twice the Rayleigh resolution limit.

Fig. 4
Fig. 4

Two-dimensional elemental images of the tumbling chart captured from nine different views. At any element image we do not show the entire field of view but only a portion of 0.4 mm × 0.4 mm centered at the corresponding optical axis.

Fig. 5
Fig. 5

Enlarged view of the central elemental image in Fig. 4.

Fig. 6
Fig. 6

Three-dimensional plot of the meridian section of function Hλ 0(r, z) when the amplitude transmittance of the microlens is modulated with a binary mask of obscuration ratio δ = 2/2. As in the previous experiment the parameters for the calculation are ϕ = 2.0 mm, f = 5.0 mm, λ = 0.5 μm, and a = 100 mm.

Fig. 7
Fig. 7

Two-dimensional elemental images captured with the amplitude-modulated microlens array. At any element image we do not show the entire field of view but only a portion of 0.4 mm × 0.4 mm centered at the corresponding optical axis.

Fig. 8
Fig. 8

Enlarged view of the central elemental image in Fig. 7. Note that, strictly speaking, the light intensity of these images should be half of that of the images in Fig. 5. This affect does not appear in the figures because they are normalized differently.

Fig. 9
Fig. 9

Cross sections of function H0( x ′, z) corresponding to the nonmodulated lenses and the amplitude-modulated lenses.

Fig. 10
Fig. 10

Enlarged view of the central elemental image obtained by taking into account the polychromatic nature of the illumination: Top, image obtained with the nonmodulated lens; bottom, image obtained with the amplitude-modulated lens.

Fig. 11
Fig. 11

Reconstructed image obtained from the simulated elemental images obtained with, top, the nonmodulated pickup lenslet array and, bottom, the binary-modulated pickup lenslet array.

Equations (13)

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Ox, z=Rxδz-fx,
Hλx; x, z=m expi πλa-z mp-x2  Pzx0exp-i2πx0× x+Mzmp-x-mpλgd2x02,
Pzx0=px0expi πλ1a-z- 1ax02.
Hλx; x, z=P˜zx-Mzxλg2m δx-mp1-Mz.
Iλx= Rxδz-fxHλx; x, zd2xdz= RxHλx; x, z=fxd2x.
Hλx; x, z=Hλx-Mzx; 0, zHλx-Mzx; z.
Iλx= RxHλx-Mzx; z=fxd2x.
Iλ0x= RxHλ0x-Mzx; zd2x,
Hλ0x; z=P˜zxλg2.
Hλ0r, z=0ϕ/2 pr0expi πλzaa-z r02×J02π rr0λgr0dr02.
I0x=0 VλIλ0xdλ,
I0x= RxH0x-Mzx; zd2x,
H0x; z=0 VλHλ0x; zdλ.

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