Abstract

In this paper, we propose a method to three-dimensionally visualize objects in a scattering medium using integral imaging. Our approach is based on a particular use of the interference phenomenon between the ballistic photons getting through the scattering medium and the scattered photons being scattered by the medium. For three-dimensional (3D) sensing of the scattered objects, the synthetic aperture integral imaging system under coherent illumination records the scattered elemental images of the objects. Then, the computational geometrical ray propagation algorithm is applied to the scattered elemental images in order to eliminate the interference patterns between scattered and object beams. The original 3D information of the scattered objects is recovered by multiple imaging channels, each with a unique perspective of the object. We present both simulation and experimental results with virtual and real objects to demonstrate the proposed concepts.

© 2008 Optical Society of America

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    [CrossRef]
  7. H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction," Opt. Lett. 26, 157-159 (2001).
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    [CrossRef] [PubMed]
  9. B. Tavakoli, B. Javidi, and E. Watson, "Three dimensional visualization by photon counting computational Integral Imaging," Opt. Express 16, 4426-4436 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. A. Castro, Y. Frauel, and B. Javidi, "Integral imaging with large depth of field using an asymmetric phase mask," Opt. Express 15, 10266-10273 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. I. Moon and B. Javidi, "Volumetric 3D recognition of biological microorganisms using multivariate statistical method and digital holography," J. Biomed. Opt. 11, 064004 (2006).
    [CrossRef]
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    [CrossRef]
  26. B. Javidi, S. H. Hong, and O. Matoba, "Multidimensional optical sensor and imaging system," Appl. Opt. 45, 2986-2994 (2006).
    [CrossRef] [PubMed]
  27. T. Okoshi, ed., Three-dimensional imaging techniques (Academic, 1976).
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    [CrossRef]
  29. B. Javidi and F. Okano eds, Three dimensional television, video, and display technologies (Springer, 2002).
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    [CrossRef] [PubMed]
  33. P. Réfrégier, ed., Noise theory and application to physics: from fluctuations to information (Springer, 2004).

2008

2007

2006

B. Javidi, S. H. Hong, and O. Matoba, "Multidimensional optical sensor and imaging system," Appl. Opt. 45, 2986-2994 (2006).
[CrossRef] [PubMed]

R. Martinez, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, "Optically-corrected elemental images for undistorted integral image display," Opt. Express 14, 9657-9663 (2006).
[CrossRef]

B. Javidi, I. Moon, and S. Yeom, "Three-dimensional identification of biological microorganism using integral imaging," Opt. Express 14, 12096-12108 (2006).
[CrossRef] [PubMed]

A. Stern and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proceedings of the IEEE 94, 591-607 (2006).
[CrossRef]

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proceedings of IEEE 94, 636-654 (2006).
[CrossRef]

I. Moon and B. Javidi, "Volumetric 3D recognition of biological microorganisms using multivariate statistical method and digital holography," J. Biomed. Opt. 11, 064004 (2006).
[CrossRef]

M. Levoy, "Light fields and computional imaging," IEEE Computer 39, 46-55 (2006).
[CrossRef]

2005

2003

2002

2001

1998

1978

Neal C. Gallagher, "Optimum quantization in digital holography," Appl. Opt. 17, 109-115 (1978).
[CrossRef] [PubMed]

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

1967

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phy. Lett. 11, 77-79 (1967).
[CrossRef]

1931

1908

G. Lippmann, "La photographie intégrale," Compte-Rendus 146, 446-451 (1908).

Abookasis, D.

Arimoto, H.

Baumbach, T.

Castro, A.

Chen, Z.

Frauel, Y.

A. Castro, Y. Frauel, and B. Javidi, "Integral imaging with large depth of field using an asymmetric phase mask," Opt. Express 15, 10266-10273 (2007).
[CrossRef] [PubMed]

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proceedings of IEEE 94, 636-654 (2006).
[CrossRef]

Gallagher, Neal C.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phy. Lett. 11, 77-79 (1967).
[CrossRef]

Hong, S. H.

Hong, S. -H.

Hoshino, H.

Hwang, Y. S.

Igarishi, Y.

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

Isono, H.

Ives, H. E.

Javidi, B.

L. Martínez-León and B. Javidi, "Synthetic aperture single-exposure on-axis digital holography," Opt. Express 16, 161-169 (2008).
[CrossRef] [PubMed]

B. Tavakoli, B. Javidi, and E. Watson, "Three dimensional visualization by photon counting computational Integral Imaging," Opt. Express 16, 4426-4436 (2008).
[CrossRef] [PubMed]

Y. S. Hwang, S. -H. Hong, and B. Javidi, "Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging," J. Display Technol. 3, 64-70 (2007).
[CrossRef]

A. Castro, Y. Frauel, and B. Javidi, "Integral imaging with large depth of field using an asymmetric phase mask," Opt. Express 15, 10266-10273 (2007).
[CrossRef] [PubMed]

B. Javidi, S. H. Hong, and O. Matoba, "Multidimensional optical sensor and imaging system," Appl. Opt. 45, 2986-2994 (2006).
[CrossRef] [PubMed]

R. Martinez, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, "Optically-corrected elemental images for undistorted integral image display," Opt. Express 14, 9657-9663 (2006).
[CrossRef]

B. Javidi, I. Moon, and S. Yeom, "Three-dimensional identification of biological microorganism using integral imaging," Opt. Express 14, 12096-12108 (2006).
[CrossRef] [PubMed]

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proceedings of IEEE 94, 636-654 (2006).
[CrossRef]

A. Stern and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proceedings of the IEEE 94, 591-607 (2006).
[CrossRef]

I. Moon and B. Javidi, "Volumetric 3D recognition of biological microorganisms using multivariate statistical method and digital holography," J. Biomed. Opt. 11, 064004 (2006).
[CrossRef]

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools," J. Display Technol. 1, 321- 327 (2005).
[CrossRef]

A. Stern and B. Javidi, "3-D computational synthetic aperture integral imaging (COMPSAII)," Opt. Express 11, 2446-2451 (2003).
[CrossRef] [PubMed]

O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
[CrossRef]

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

Juptner, W.

Kim, M. K.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phy. Lett. 11, 77-79 (1967).
[CrossRef]

Levoy, M.

M. Levoy, "Light fields and computional imaging," IEEE Computer 39, 46-55 (2006).
[CrossRef]

Lippmann, G.

G. Lippmann, "La photographie intégrale," Compte-Rendus 146, 446-451 (1908).

Martinez, R.

Martinez-Corral, M.

Martínez-Corral, M.

Martínez-Cuenca, R.

Martínez-León, L.

Massig, J. H.

Matoba, O.

Moon, I.

I. Moon and B. Javidi, "Volumetric 3D recognition of biological microorganisms using multivariate statistical method and digital holography," J. Biomed. Opt. 11, 064004 (2006).
[CrossRef]

B. Javidi, I. Moon, and S. Yeom, "Three-dimensional identification of biological microorganism using integral imaging," Opt. Express 14, 12096-12108 (2006).
[CrossRef] [PubMed]

Murata, H.

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

Naughton, T.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proceedings of IEEE 94, 636-654 (2006).
[CrossRef]

Okano, F.

Osten, W.

Pons, A.

Rosen, J.

Saavedra, G.

Stern, A.

A. Stern and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proceedings of the IEEE 94, 591-607 (2006).
[CrossRef]

A. Stern and B. Javidi, "3-D computational synthetic aperture integral imaging (COMPSAII)," Opt. Express 11, 2446-2451 (2003).
[CrossRef] [PubMed]

Tahajuerce, E.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proceedings of IEEE 94, 636-654 (2006).
[CrossRef]

Tajahuerce, E.

Tavakoli, B.

Ueda, M.

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

Watson, E.

Yeom, S.

Yu, L.

Yuyama, I.

Appl. Opt.

Appl. Phy. Lett.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phy. Lett. 11, 77-79 (1967).
[CrossRef]

Compte-Rendus

G. Lippmann, "La photographie intégrale," Compte-Rendus 146, 446-451 (1908).

IEEE Computer

M. Levoy, "Light fields and computional imaging," IEEE Computer 39, 46-55 (2006).
[CrossRef]

J. Biomed. Opt.

I. Moon and B. Javidi, "Volumetric 3D recognition of biological microorganisms using multivariate statistical method and digital holography," J. Biomed. Opt. 11, 064004 (2006).
[CrossRef]

J. Display Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

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

Opt. Express

Opt. Lett.

Proceedings of IEEE

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proceedings of IEEE 94, 636-654 (2006).
[CrossRef]

Proceedings of the IEEE

A. Stern and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proceedings of the IEEE 94, 591-607 (2006).
[CrossRef]

Other

A. P. Sokolov, ed., Autostereoscopy and integral photography by Professor Lippmanns method (Moscow State Univ. Press, 1911).

T. Kreis, ed., Handbook of holographic interferometry (Wiley, 2005).

T. Okoshi, ed., Three-dimensional imaging techniques (Academic, 1976).

B. Javidi and F. Okano eds, Three dimensional television, video, and display technologies (Springer, 2002).

N. Mukhopadhyay, ed., Probability and Statistical Inference (Marcel Dekker, 2000).

P. Réfrégier, ed., Noise theory and application to physics: from fluctuations to information (Springer, 2004).

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Figures (10)

Fig. 1.
Fig. 1.

Computational reconstruction in integral imaging (II).

Fig. 2.
Fig. 2.

A schematic setup of proposed SACII system for 3D visualization of scattered objects.

Fig. 3.
Fig. 3.

Experimental setup for SAII recording and reconstruction.

Fig. 4.
Fig. 4.

The elemental image set generated by computer simulation program. (a) non-scattered elemental images and (b) scattered elemental images.

Fig. 5.
Fig. 5.

The sectional images reconstructed from the elemental image set of Fig. 4 by using the computational SACII algorithm. (a) non-scattered object and (b) scattered object.

Fig. 6.
Fig. 6.

The 3D images reconstructed at different distances by using the computational SACII algorithm. The first elemental images of (a) non-scattered volumetric object and (b) scattered volumetric object were recorded by Autodesk 3DMax© computer program, respectively. The sectional images reconstructed at distance (c) 550mm and (e) 600mm from the non-scattered elemental image set, respectively. The sectional images reconstructed at distance (d) 550mm and (f) 600mm from the scattered elemental image set, respectively.

Fig. 7.
Fig. 7.

The first (a) non-scattered and (b) scattered elemental images.

Fig. 8.
Fig. 8.

The data distributions of the first (a) non-scattered and (b) scattered elemental images in the area marked in white as shown in Fig. 7, where the 500 pixel points was randomly selected over the area.

Fig. 9.
Fig. 9.

The sectional images reconstructed at different distances from the (a) non-scattered and (b) scattered elemental image sets by using the SACII algorithm.

Fig. 10.
Fig. 10.

The data distributions of the (a) original II and (b) restored II data in the area marked in white as shown in Fig. 9, where the 500 pixel points was randomly selected over the area.

Equations (4)

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I ( x , y , z 0 ) = 1 N s i = 0 N i 1 j = 0 N j 1 M E ij ( x + z 0 p x f i , y + z 0 p y f j ) ,
I ( r p ) n ( S 2 + E 2 + 2 S E cos [ ( k s k E ) r p ] ) n ,
I p s ( i ) = I p o + w p ( i ) for i = 1 , . . . , N ,
I = n = 1 N I ( r p ) n N ( S 2 + E 2 ) ,

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