Abstract

Ghost diffraction and ghost imaging are investigated in a lensless imaging system. The evolution process from ghost diffraction to ghost imaging is discussed when the object is moved far away from the source in the test arm. The relation of ghost diffraction and imaging is also studied, and it is found that the visibility of ghost imaging is always better than that of ghost diffraction.

© 2011 Optical Society of America

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  1. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. J. Cheng and S. S. Han, “Incoherent coincidence imaging and its applicability in x-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef] [PubMed]
  8. G. Scarcelli, V. Berardi, and Y. H. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88, 061106 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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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] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2010 (3)

D. S. Simon and A. V. Sergienko, “Odd-order aberration cancellation in correlated-photon imaging,” Phys. Rev. A 82, 023819 (2010).
[CrossRef]

B. Cao and C. Zhang, “Third-order lensless ghost diffraction with classical fully incoherent light,” Opt. Lett. 35, 2091–2093 (2010).
[CrossRef] [PubMed]

N. S. Bisht, E. K. Sharma, and H. C. Kandpal, “The influence of source and object characteristics on coincidence imaging,” J. Opt. 12, 045701 (2010).
[CrossRef]

2009 (6)

I. Vidal, D. P. Caetano, E. J. S. Fonseca, and J. M. Hickmann, “Effects of pseudothermal light source’s transverse size and coherence width in ghost-interference experiments,” Opt. Lett. 34, 1450–1452 (2009).
[CrossRef] [PubMed]

Q. Liu, X. H. Chen, K. H. Luo, W. Wu, and L. A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34, 3343–3345 (2009).
[CrossRef] [PubMed]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Two-color ghost imaging,” Phys. Rev. A 79, 033808 (2009).
[CrossRef]

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ‘pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110(2009).
[CrossRef]

2008 (2)

R. Meyers, K. S. Deacon, and Y. H. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A 77, 041801 (2008).
[CrossRef]

D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. G. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

2007 (2)

Y. F. Bai and S. S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

2006 (1)

G. Scarcelli, V. Berardi, and Y. H. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88, 061106 (2006).
[CrossRef]

2005 (2)

Y. J. Cai and S. Y. Zhu, “Second-order fractional Fourier transform with incoherent radiation,” Opt. Lett. 30, 388–390(2005).
[CrossRef] [PubMed]

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

2004 (3)

J. Cheng and S. S. Han, “Incoherent coincidence imaging and its applicability in x-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Y. Cai and S. Y. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29, 2716–2718 (2004).
[CrossRef] [PubMed]

2002 (1)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

1995 (2)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Bai, Y. F.

Y. F. Bai and S. S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

Berardi, V.

G. Scarcelli, V. Berardi, and Y. H. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88, 061106 (2006).
[CrossRef]

Bisht, N. S.

N. S. Bisht, E. K. Sharma, and H. C. Kandpal, “The influence of source and object characteristics on coincidence imaging,” J. Opt. 12, 045701 (2010).
[CrossRef]

Boyd, R. W.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Two-color ghost imaging,” Phys. Rev. A 79, 033808 (2009).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34, 3343–3345 (2009).
[CrossRef] [PubMed]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Caetano, D. P.

Cai, Y.

Cai, Y. J.

Cao, B.

Cao, D. Z.

D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. G. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

Chan, K. W. C.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Two-color ghost imaging,” Phys. Rev. A 79, 033808 (2009).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34, 3343–3345 (2009).
[CrossRef] [PubMed]

Chen, X. H.

Q. Liu, X. H. Chen, K. H. Luo, W. Wu, and L. A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

Cheng, J.

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

J. Cheng and S. S. Han, “Incoherent coincidence imaging and its applicability in x-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

Deacon, K. S.

R. Meyers, K. S. Deacon, and Y. H. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A 77, 041801 (2008).
[CrossRef]

Fonseca, E. J. S.

Gao, L.

D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. G. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Gatti, A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Gong, W.

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ‘pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110(2009).
[CrossRef]

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

Han, S.

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ‘pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110(2009).
[CrossRef]

Han, S. S.

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Y. F. Bai and S. S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

J. Cheng and S. S. Han, “Incoherent coincidence imaging and its applicability in x-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

Hickmann, J. M.

Huang, D.

Kandpal, H. C.

N. S. Bisht, E. K. Sharma, and H. C. Kandpal, “The influence of source and object characteristics on coincidence imaging,” J. Opt. 12, 045701 (2010).
[CrossRef]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Lin, L. F.

D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. G. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Liu, H. L.

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Liu, Q.

Q. Liu, X. H. Chen, K. H. Luo, W. Wu, and L. A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

Liu, Y. F.

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Lugiato, L. A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Luo, K. H.

Q. Liu, X. H. Chen, K. H. Luo, W. Wu, and L. A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

Meyers, R.

R. Meyers, K. S. Deacon, and Y. H. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A 77, 041801 (2008).
[CrossRef]

O’Sullivan, M. N.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Two-color ghost imaging,” Phys. Rev. A 79, 033808 (2009).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34, 3343–3345 (2009).
[CrossRef] [PubMed]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

Scarcelli, G.

G. Scarcelli, V. Berardi, and Y. H. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88, 061106 (2006).
[CrossRef]

Sergienko, A. V.

D. S. Simon and A. V. Sergienko, “Odd-order aberration cancellation in correlated-photon imaging,” Phys. Rev. A 82, 023819 (2010).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Sharma, E. K.

N. S. Bisht, E. K. Sharma, and H. C. Kandpal, “The influence of source and object characteristics on coincidence imaging,” J. Opt. 12, 045701 (2010).
[CrossRef]

Shen, X.

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ‘pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110(2009).
[CrossRef]

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Shih, Y. H.

R. Meyers, K. S. Deacon, and Y. H. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A 77, 041801 (2008).
[CrossRef]

G. Scarcelli, V. Berardi, and Y. H. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88, 061106 (2006).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

Simon, D. S.

D. S. Simon and A. V. Sergienko, “Odd-order aberration cancellation in correlated-photon imaging,” Phys. Rev. A 82, 023819 (2010).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Vidal, I.

Wang, K. G.

D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. G. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

Wei, Q.

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Wu, L. A.

Q. Liu, X. H. Chen, K. H. Luo, W. Wu, and L. A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

Wu, W.

Q. Liu, X. H. Chen, K. H. Luo, W. Wu, and L. A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

Xiong, J.

D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. G. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

Zhang, C.

Zhang, M.

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Zhang, P.

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ‘pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110(2009).
[CrossRef]

Zhang, S. H.

D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. G. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Zhu, S. Y.

Appl. Phys. Lett. (3)

G. Scarcelli, V. Berardi, and Y. H. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88, 061106 (2006).
[CrossRef]

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ‘pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110(2009).
[CrossRef]

D. Z. Cao, J. Xiong, S. H. Zhang, L. F. Lin, L. Gao, and K. G. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

J. Opt. (1)

N. S. Bisht, E. K. Sharma, and H. C. Kandpal, “The influence of source and object characteristics on coincidence imaging,” J. Opt. 12, 045701 (2010).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (9)

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

R. Meyers, K. S. Deacon, and Y. H. Shih, “Ghost-imaging experiment by measuring reflected photons,” Phys. Rev. A 77, 041801 (2008).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Two-color ghost imaging,” Phys. Rev. A 79, 033808 (2009).
[CrossRef]

M. Zhang, Q. Wei, X. Shen, Y. F. Liu, H. L. Liu, J. Cheng, and S. S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Q. Liu, X. H. Chen, K. H. Luo, W. Wu, and L. A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

D. S. Simon and A. V. Sergienko, “Odd-order aberration cancellation in correlated-photon imaging,” Phys. Rev. A 82, 023819 (2010).
[CrossRef]

Y. F. Bai and S. S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Lensless scheme for correlated imaging with incoherent light.

Fig. 2
Fig. 2

Normalized intensity fluctuation correlation versus the position of CCD-2 for different distances from the source to the object.

Fig. 3
Fig. 3

Normalized intensity fluctuation correlation function G ( u 2 ) as a function of u 2 . The parameters are the same as those in Fig. 2 except for different z 1 values.

Fig. 4
Fig. 4

Dependence of the visibility on the transverse size of the source for different z 1 values. Other parameters are the same as those in Fig. 2.

Equations (7)

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G ( 2 ) ( u 1 , u 2 ) = E ( u 1 ) E ( u 2 ) E * ( u 2 ) E * ( u 1 ) = I 1 ( u 1 ) I 2 ( u 2 ) + G ( u 1 , u 2 ) ,
{ I i ( u i ) = Γ ( x 1 , x 2 ) h i ( x 1 , u i ) h i * ( x 2 , u i ) d x 1 d x 2 , G ( u 1 , u 2 ) = Δ I 1 ( u 1 ) Δ I 2 ( u 2 ) = | Γ ( x 1 , x 2 ) h 1 ( x 1 , u 1 ) h 2 * ( x 2 , u 2 ) d x 1 d x 2 | 2 ,
h 1 ( x 1 , u 1 ) = e i k z 1 i λ z 1 exp [ i π λ z 1 ( x x 1 ) 2 ] t ( x ) × e i k z 2 i λ z 2 exp [ i π λ z 2 ( u 1 x ) 2 ] d x ,
h 2 ( x 2 , u 2 ) = e i k z i λ z exp [ i π λ z ( u 2 x 2 ) 2 ] ,
Γ ( x 1 , x 2 ) = G 0 exp ( x 1 2 + x 2 2 4 a 2 ) δ ( x 1 x 2 ) ,
G ( u 1 , u 2 ) = I 0 2 λ 4 z 2 4 | T [ 2 π ( u 1 u 2 ) λ z 2 ] | 2 ,
V = G ( u 1 , u 2 ) G ( 2 ) ( u 1 , u 2 ) ,

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