Abstract

We demonstrate for the first time (to our knowledge) that an image with high quality can still be obtained in scattering media by applying the second-order correlation of illuminating light field. The effect of multiple scattering on the imaging quality is analyzed both theoretically and experimentally. Potential applications and methods to further improve the imaging quality in scattering media are also discussed.

© 2011 Optical Society of America

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  1. T. S. Mckechnie, J. Opt. Soc. Am. A 8, 346 (1991).
    [CrossRef]
  2. D. A. Raine and J. S. Brenizer, Mater. Eval. 55, 1174 (1997).
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    [CrossRef]
  4. L. V. Wang and H.-I. Wu, Biomedical Optics: Principle and Imaging (Wiley InterScience, 2007).
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef] [PubMed]
  8. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef] [PubMed]
  9. M. D’Angelo and Y. H. Shih, Laser Phys. Lett. 2, 567 (2005).
    [CrossRef]
  10. J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. W. Gong, P. Zhang, X. Shen, and S. Han, http://arxiv.org/abs/0806.3543v2 (2008).
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. R. Hassanein, E. Lehmann, and P. Vontobel, Nucl. Instrum. Methods Phys. Res. A 542, 353 (2005).
    [CrossRef]
  17. P. N. Segrè and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996).
    [CrossRef] [PubMed]
  18. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
    [CrossRef]
  19. K. W. Chan and J. H. Eberly, http://arxiv.org/abs/quant-ph/0404093v2 (2004).
  20. D. F. Walls, Nature 306, 141 (1983).
    [CrossRef]

2009 (1)

Y. Bromberg, O. Katz, and Y. Silbergerg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

2007 (1)

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

2006 (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

2005 (4)

R. Hassanein, E. Lehmann, and P. Vontobel, Nucl. Instrum. Methods Phys. Res. A 542, 353 (2005).
[CrossRef]

D. Zhang, Y. Zhai, L-A. Wu, and X-H. Chen, Opt. Lett. 30, 2354 (2005).
[CrossRef] [PubMed]

M. D’Angelo and Y. H. Shih, Laser Phys. Lett. 2, 567 (2005).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, Phys. Med. Biol. 50, R1 (2005).
[CrossRef] [PubMed]

2004 (2)

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

2002 (1)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

1997 (2)

D. A. Raine and J. S. Brenizer, Mater. Eval. 55, 1174 (1997).

K. P. Maher and J. F. Malone, Contemp. Phys. 38, 131(1997).
[CrossRef]

1996 (1)

P. N. Segrè and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996).
[CrossRef] [PubMed]

1995 (2)

A. Yodh and B. Chance, Phys. Today 48, 34 (1995).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

1991 (1)

1983 (1)

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, Phys. Med. Biol. 50, R1 (2005).
[CrossRef] [PubMed]

Bache, M.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

Boyd, R. W.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

Brambilla, E.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

Brenizer, J. S.

D. A. Raine and J. S. Brenizer, Mater. Eval. 55, 1174 (1997).

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silbergerg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Chan, K. W.

K. W. Chan and J. H. Eberly, http://arxiv.org/abs/quant-ph/0404093v2 (2004).

Chance, B.

A. Yodh and B. Chance, Phys. Today 48, 34 (1995).
[CrossRef]

Chen, X-H.

Cheng, J.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

D’Angelo, M.

M. D’Angelo and Y. H. Shih, Laser Phys. Lett. 2, 567 (2005).
[CrossRef]

Eberly, J. H.

K. W. Chan and J. H. Eberly, http://arxiv.org/abs/quant-ph/0404093v2 (2004).

Ferri, F.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

Gatti, A.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, Phys. Med. Biol. 50, R1 (2005).
[CrossRef] [PubMed]

Gong, W.

W. Gong, P. Zhang, X. Shen, and S. Han, http://arxiv.org/abs/0806.3543v2 (2008).

Han, S.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

W. Gong, P. Zhang, X. Shen, and S. Han, http://arxiv.org/abs/0806.3543v2 (2008).

Hassanein, R.

R. Hassanein, E. Lehmann, and P. Vontobel, Nucl. Instrum. Methods Phys. Res. A 542, 353 (2005).
[CrossRef]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, Phys. Med. Biol. 50, R1 (2005).
[CrossRef] [PubMed]

Katz, O.

Y. Bromberg, O. Katz, and Y. Silbergerg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Lehmann, E.

R. Hassanein, E. Lehmann, and P. Vontobel, Nucl. Instrum. Methods Phys. Res. A 542, 353 (2005).
[CrossRef]

Liu, H.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Liu, Y.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Lugiato, L. A.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

Magatti, D.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

Maher, K. P.

K. P. Maher and J. F. Malone, Contemp. Phys. 38, 131(1997).
[CrossRef]

Malone, J. F.

K. P. Maher and J. F. Malone, Contemp. Phys. 38, 131(1997).
[CrossRef]

Mckechnie, T. S.

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

Pusey, P. N.

P. N. Segrè and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996).
[CrossRef] [PubMed]

Raine, D. A.

D. A. Raine and J. S. Brenizer, Mater. Eval. 55, 1174 (1997).

Segrè, P. N.

P. N. Segrè and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996).
[CrossRef] [PubMed]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

Shen, X.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

W. Gong, P. Zhang, X. Shen, and S. Han, http://arxiv.org/abs/0806.3543v2 (2008).

Shih, Y. H.

M. D’Angelo and Y. H. Shih, Laser Phys. Lett. 2, 567 (2005).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

Silbergerg, Y.

Y. Bromberg, O. Katz, and Y. Silbergerg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

Vontobel, P.

R. Hassanein, E. Lehmann, and P. Vontobel, Nucl. Instrum. Methods Phys. Res. A 542, 353 (2005).
[CrossRef]

Walls, D. F.

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Wang, L. V.

L. V. Wang and H.-I. Wu, Biomedical Optics: Principle and Imaging (Wiley InterScience, 2007).

Wei, Q.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Wu, H.-I.

L. V. Wang and H.-I. Wu, Biomedical Optics: Principle and Imaging (Wiley InterScience, 2007).

Wu, L-A.

Yodh, A.

A. Yodh and B. Chance, Phys. Today 48, 34 (1995).
[CrossRef]

Zhai, Y.

Zhang, D.

Zhang, M.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Zhang, P.

W. Gong, P. Zhang, X. Shen, and S. Han, http://arxiv.org/abs/0806.3543v2 (2008).

Contemp. Phys. (1)

K. P. Maher and J. F. Malone, Contemp. Phys. 38, 131(1997).
[CrossRef]

J. Mod. Opt. (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

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

Laser Phys. Lett. (1)

M. D’Angelo and Y. H. Shih, Laser Phys. Lett. 2, 567 (2005).
[CrossRef]

Mater. Eval. (1)

D. A. Raine and J. S. Brenizer, Mater. Eval. 55, 1174 (1997).

Nature (1)

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

R. Hassanein, E. Lehmann, and P. Vontobel, Nucl. Instrum. Methods Phys. Res. A 542, 353 (2005).
[CrossRef]

Opt. Lett. (1)

Phys. Med. Biol. (1)

A. P. Gibson, J. C. Hebden, and S. R. Arridge, Phys. Med. Biol. 50, R1 (2005).
[CrossRef] [PubMed]

Phys. Rev. A (3)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silbergerg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Phys. Rev. Lett. (4)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

P. N. Segrè and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996).
[CrossRef] [PubMed]

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

Phys. Today (1)

A. Yodh and B. Chance, Phys. Today 48, 34 (1995).
[CrossRef]

Other (3)

L. V. Wang and H.-I. Wu, Biomedical Optics: Principle and Imaging (Wiley InterScience, 2007).

W. Gong, P. Zhang, X. Shen, and S. Han, http://arxiv.org/abs/0806.3543v2 (2008).

K. W. Chan and J. H. Eberly, http://arxiv.org/abs/quant-ph/0404093v2 (2004).

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Figures (3)

Fig. 1
Fig. 1

(a) Scheme for imaging via the second-order correlation with thermal light in the scattering media. (b) Photograph of a laser beam going through the prepared scattering media.

Fig. 2
Fig. 2

Numerical analytical results of imaging an aperture (“zhong” ring) in different positions of scattering media based on Eqs. (5, 6, 7, 8). (a)  L 1 = 0 mm , L 2 = 40 mm ; (b)  L 1 = 20 mm , L 2 = 20 mm ; (c)  L 1 = 40 mm , L 2 = 0 mm . Images shown in (1)–(3) are the results obtained by conventional imaging, the ghost imaging method (i.e., the test detector was a bucket detector), and the second-order correlation between two paths (the test detector was also a CCD camera), respectively.

Fig. 3
Fig. 3

(I) Horizontal sections of the images when the thermal light from a single slit (silt width a = 0.2 mm ) fixed before the mediums went through different mediums with the scattering thickness L 1 + L 2 = 40 mm . (II) Images of the object obtained when the sample was fixed in different positions of scattering media (averaged 15,000 speckle frames). (a)  L 1 = 0 mm , L 2 = 40 mm ; (b)  L 1 = 20 mm , L 2 = 20 mm ; (c)  L 1 = 40 mm , L 2 = 0 mm . (1) Object; (2) conventional imaging; (3), (4)  images reconstructed by the second-order correlation be tween two paths when the test detector was a bucket detector or a CCD camera with the pixel resolution 6.45 × 6.45 μm , respectively.

Equations (8)

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h ( x , x 0 ) = α h in ( x , x 0 ) + β h sca ( x , x 0 ) ,
h sca ( x , x 0 ) d x P ( x , x 0 ) L A h in ( x , x ) ( L 2 + z 2 ) ,
P ( x , x 0 ) L A = [ 2 π Δ x L A 2 ] 1 / 4 exp { ( x x 0 Δ x L A ) 2 } ,
Δ G ( 2 , 2 ) ( x r , x t ) = | d x 1 d x 2 G ( 1 , 1 ) ( x 1 , x 2 ) × h r * ( x 1 , x r ) h t ( x 2 , x t ) | 2 .
Δ G ( 2 , 2 ) ( x r , x t ) | { α 1 α 2 δ ( x r + x t ) + P ( f 1 f x t , f 1 f x r ) L 2 A × β 1 α 2 } t ( f 1 f x t ) + α 1 β 2 P ( f 1 f x t , f 1 f x r ) L 1 A t ( f 1 f x r ) + β 1 β 2 d x t ( x ) P ( x , f 1 f x r ) L 1 A P ( f 1 f x t , x ) L 2 A | 2 ,
Δ G ( 2 , 2 ) ( x r ) = Δ G ( 2 , 2 ) ( x r , x t ) d x t .
Δ G ( 2 , 2 ) ( x r , x r ) | { α 1 α 2 + α 1 β 2 [ 2 π Δ x L 2 A 2 ] 1 / 4 + β 1 α 2 [ 2 π Δ x L 1 A 2 ] 1 / 4 } t ( f 1 f x r ) + β 1 β 2 C 0 | 2 ,
C 0 = d x t ( x ) P ( x , f 1 f x r ) L 1 A P ( f 1 f x r , x ) L 2 A .

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