Abstract

Sampling number and detection signal-to-noise ratio (SNR) are two major factors influencing imaging quality. Combining the image’s sparsity in the representation basis with the ghost imaging (GI) approach, GI via sparsity constraints (GISC) can nonlocally image the object even when the measurement number is far fewer than the Nyquist criteria required for the conventional GI reconstruction algorithm. The influence of receiving the system’s numerical aperture and detection SNR in the test path to GISC is studied through experiments. It is also shown that the quality of GISC depends on the object’s sparse representation basis.

© 2013 Optical Society of America

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  1. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
    [CrossRef]
  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]
  3. 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]
  4. J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef]
  5. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
    [CrossRef]
  6. M. D’Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
    [CrossRef]
  7. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef]
  8. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
    [CrossRef]
  9. D. Zhang, Y.-H. Zhai, L.-A. Wu, and X.-H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
    [CrossRef]
  10. Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
    [CrossRef]
  11. J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
    [CrossRef]
  12. M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
    [CrossRef]
  13. W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost “pinhole” imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
    [CrossRef]
  14. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
    [CrossRef]
  15. W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” J. Opt. Soc. Am. B 27, 675–678 (2010).
    [CrossRef]
  16. P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
    [CrossRef]
  17. W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36, 394–396 (2011).
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    [CrossRef]
  19. N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
    [CrossRef]
  20. R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
    [CrossRef]
  21. C. Zhang, W. Gong, and S. Han, “Improving imaging resolution of shaking targets by Fourier-transform ghost diffraction,” Appl. Phys. Lett. 102, 021111 (2013).
    [CrossRef]
  22. C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
    [CrossRef]
  23. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
    [CrossRef]
  24. J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37, 1067–1069 (2012).
    [CrossRef]
  25. W. Gong and S. Han, “Multiple-input ghost imaging via sparsity constraints,” J. Opt. Soc. Am. A 29, 1571–1579 (2012).
    [CrossRef]
  26. W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” arXiv:0911.4750 [Quant-ph].
  27. W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
    [CrossRef]
  28. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  29. E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
    [CrossRef]
  30. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [CrossRef]
  31. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
    [CrossRef]
  32. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
    [CrossRef]

2013 (1)

C. Zhang, W. Gong, and S. Han, “Improving imaging resolution of shaking targets by Fourier-transform ghost diffraction,” Appl. Phys. Lett. 102, 021111 (2013).
[CrossRef]

2012 (4)

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37, 1067–1069 (2012).
[CrossRef]

W. Gong and S. Han, “Multiple-input ghost imaging via sparsity constraints,” J. Opt. Soc. Am. A 29, 1571–1579 (2012).
[CrossRef]

W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
[CrossRef]

2011 (4)

W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36, 394–396 (2011).
[CrossRef]

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
[CrossRef]

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

2010 (2)

W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” J. Opt. Soc. Am. B 27, 675–678 (2010).
[CrossRef]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[CrossRef]

2009 (3)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

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

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

2008 (1)

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

2007 (2)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

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

2006 (2)

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

2005 (6)

M. D’Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

D. Zhang, Y.-H. Zhai, L.-A. Wu, and X.-H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
[CrossRef]

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

2004 (2)

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

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]

1995 (2)

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

Bache, M.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[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]

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]

Boyd, R. W.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

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]

Brambilla, E.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Candès, E. J.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

Cao, D.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Chan, K. W. C.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

Chen, M.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

Chen, X.

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Chen, X.-H.

Cheng, J.

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

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

D’Angelo, M.

M. D’Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Deacon, K. S.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

Dixon, P. B.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

Du, J.

Ferri, F.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Figueiredo, M. A. T.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

Gatti, A.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

Gong, W.

C. Zhang, W. Gong, and S. Han, “Improving imaging resolution of shaking targets by Fourier-transform ghost diffraction,” Appl. Phys. Lett. 102, 021111 (2013).
[CrossRef]

J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37, 1067–1069 (2012).
[CrossRef]

W. Gong and S. Han, “Multiple-input ghost imaging via sparsity constraints,” J. Opt. Soc. Am. A 29, 1571–1579 (2012).
[CrossRef]

W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
[CrossRef]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36, 394–396 (2011).
[CrossRef]

W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” J. Opt. Soc. Am. B 27, 675–678 (2010).
[CrossRef]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[CrossRef]

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

W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” arXiv:0911.4750 [Quant-ph].

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Han, S.

C. Zhang, W. Gong, and S. Han, “Improving imaging resolution of shaking targets by Fourier-transform ghost diffraction,” Appl. Phys. Lett. 102, 021111 (2013).
[CrossRef]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
[CrossRef]

W. Gong and S. Han, “Multiple-input ghost imaging via sparsity constraints,” J. Opt. Soc. Am. A 29, 1571–1579 (2012).
[CrossRef]

J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37, 1067–1069 (2012).
[CrossRef]

W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36, 394–396 (2011).
[CrossRef]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[CrossRef]

W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” J. Opt. Soc. Am. B 27, 675–678 (2010).
[CrossRef]

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. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

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

W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” arXiv:0911.4750 [Quant-ph].

Hardy, N. D.

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
[CrossRef]

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

Howell, J. C.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

Howland, G. A.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

Huang, F.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Katz, O.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Klyshko, D. N.

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

Li, E.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

Li, H.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Liu, H.

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

Liu, Y.

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

Lugiato, L. A.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

Magatti, D.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Meyers, R. E.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

Nowak, R. D.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

O’Sullivan-Hale, C.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

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]

Rodenburg, B.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

Romberg, J. K.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

Scarcelli, G.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Sergienko, A. V.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[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]

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

Shapiro, J. H.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
[CrossRef]

Shen, X.

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[CrossRef]

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. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Shih, Y.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

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

Shih, Y. H.

M. D’Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (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]

Silberberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Simon, D. S.

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[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]

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

Sun, X.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Tao, T.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Wakin, M. B.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

Wang, H.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

Wang, K.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Wei, Q.

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

Wright, S. J.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

Wu, L.

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Wu, L.-A.

Xiong, J.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Xu, W.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

Zhai, Y.

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Zhai, Y.-H.

Zhang, C.

C. Zhang, W. Gong, and S. Han, “Improving imaging resolution of shaking targets by Fourier-transform ghost diffraction,” Appl. Phys. Lett. 102, 021111 (2013).
[CrossRef]

Zhang, D.

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

D. Zhang, Y.-H. Zhai, L.-A. Wu, and X.-H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
[CrossRef]

Zhang, M.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and 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, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[CrossRef]

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

Zhao, C.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

Appl. Phys. Lett. (5)

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

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
[CrossRef]

C. Zhang, W. Gong, and S. Han, “Improving imaging resolution of shaking targets by Fourier-transform ghost diffraction,” Appl. Phys. Lett. 102, 021111 (2013).
[CrossRef]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Commun. Pure Appl. Math. (1)

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

IEEE J. Sel. Top. Signal Process. (1)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

IEEE Signal Process. Mag. (1)

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

IEEE Trans. Inf. Theory (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

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

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

Laser Phys. Lett. (1)

M. D’Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
[CrossRef]

Phys. Rev. A (7)

P. B. Dixon, G. A. Howland, K. W. C. Chan, C. O’Sullivan-Hale, B. Rodenburg, N. D. Hardy, J. H. Shapiro, D. S. Simon, A. V. Sergienko, R. W. Boyd, and J. C. Howell, “Quantum ghost imaging through turbulence,” Phys. Rev. A 83, 051803 (2011).
[CrossRef]

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
[CrossRef]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

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

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (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]

Phys. Rev. Lett. (7)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
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J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
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A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
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F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

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

Other (2)

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W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” arXiv:0911.4750 [Quant-ph].

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of GISC with pseudo-thermal light.

Fig. 2.
Fig. 2.

Experimental reconstruction results of GISC in different N.A. and SNR=40dB, using M=2000 measurements (60% Nyquist rate). (a) N.A.=0.0025 (namely the transmission aperture of the lens in the test path L=2.5mm), (b) N.A.=0.005 (namely L=5.0mm), (c) N.A.=0.01 (namely L=10.0mm), and (d) N.A.=0.02 (namely L=20.0mm).

Fig. 3.
Fig. 3.

Influence of detection SNR in the test path to the quality of GISC, with N.A.=0.02 and M=2000. (a) SNR=5dB, (b) SNR=10dB, (c) SNR=15dB, (d) SNR=20dB, (e) SNR=25dB, and (f) SNR=30dB.

Fig. 4.
Fig. 4.

Performance between the reconstruction fidelity (MSE) and the value N.A. or SNR for GI and GISC reconstruction results. (a) Relationship between N.A. and MSE based on the results obtained in Fig. 2. (b) Relationship between SNR and MSE based on the results achieved in Fig. 3. Black square–solid curve is GI reconstruction results and red circle–dashed curve is corresponding to GISC reconstruction results.

Fig. 5.
Fig. 5.

Dependance of pseudo-thermal GISC on the object’s sparse representation in different detection SNR, with N.A.=0.02 and M=2000 (60% Nyquist rate). (a)–(c) are the object’s sparse representation in Cartesian basis, GISC reconstruction results for SNR=15dB (MSE=0.48) and SNR=40dB (MSE=0.13), respectively; with respect to (a)–(c), (d)–(f) are the object’s sparse representation in 2D-DCT basis, GISC reconstruction results of SNR=15dB (MSE=0.15) and SNR=40dB (MSE=0.021), respectively.

Equations (9)

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Eis(xi)=dx0E0s(x0)hi(xi,x0),i=r,t,
hr(xr,x0)exp{jk2z0(xrx0)2},
1z1+1z2=1f,
ht(xt,x0)dxexp{jk2z0(xx0)2}t(x)sinc[Lλ(xtz2+xz1)],
sinc(x)=sin(πx)πx.
TGISC=|t|2;which minimizes:12BsdxrIrs(xr)|t(xr)|222+τΨ{|t(xr)|2}1,s=1M,
Irs(xr)dx0dx0E0s(x0)[E0s(x0)]*exp{jkz0(x0x0)xr},
Bs=Isignals+Inoisesdxtdx0dx0dxdxt(x)t*(x)E0s(x0)[E0s(x0)]*exp{jkz0(xx0xx0)}×exp{jk2z0(x2x2)}sinc[Lλ(xtz2+xz1)]sinc[Lλ(xtz2+xz1)]+Inoises,
MSE=1Ni[TGI/GISC(xi)T0(xi)]2.

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