Abstract

Recently, a two-color quantum ghost imaging configuration was proposed by Karmakar et al. [Phys. Rev. A 81, 033845 (2010)]. By illuminating an object located far away from the source and detector, with a signal beam of long wavelength to avoid absorption of short wavelengths in the atmosphere while a reference beam of short wavelength is detected locally, this imaging configuration can be appropriate for standoff sensing. In practice, the signal beam must propagate through atmosphere in the presence of serious turbulence. We analyzed theoretically the performance of this ghost imaging configuration through turbulence. Based on the Gaussian state source model and extended Huygens–Fresnel integral, a formula is derived to depict the ghost image formed through turbulence of a standoff reflective object. Numerical calculations are also given according to the formula. The results show that the image quality will be degraded by the turbulence, but the resolution can be improved by means of optimizing the wavelengths of the reference and signal beams even when the turbulence is very serious.

© 2014 Optical Society of America

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2013 (6)

Y. P. Yao, R. G. Wan, Y. L. Xue, S. W. Zhang, and T. Y. Zhang, “Positive–negative nonlocal lensless imaging based on statistical optics,” Acta Phys. Sin. 62, 154201 (2013).

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103, 221106 (2013).
[CrossRef]

W. Chen and X. Chen, “Object authentication in computational ghost imaging with the realizations less than 5% of Nyquist limit,” Opt. Lett. 38, 546–548 (2013).
[CrossRef]

J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87, 043810 (2013).
[CrossRef]

Y. P. Yao, R. G. Wan, S. W. Zhang, and T. Y. Zhang, “Effect of turbulence on visibility and signal-to-noise ratio of lensless ghost imaging with thermal light,” Optik 124, 6973–6977 (2013).
[CrossRef]

D. Shi, C. Fan, P. Zhang, H. Shen, J. Zhang, C. Qiao, and Y. Wang, “Two-wavelength ghost imaging through atmospheric turbulence,” Opt. Express 21, 2050–2064 (2013).
[CrossRef]

2012 (2)

R. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100, 131114 (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]

2011 (3)

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

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

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

2010 (3)

C. Li, T. Wang, J. Pu, W. Zhu, and R. Rao, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).
[CrossRef]

S. Karmakar and Y. H. Shih, “Two-color ghost imaging with enhanced angular resolving power,” Phys. Rev. A 81, 033845 (2010).
[CrossRef]

C. Wang, D. Zhang, Y. Bai, and B. Chen, “Ghost imaging for a reflected object with a rough surface,” Phys. Rev. A 82, 063814 (2010).
[CrossRef]

2009 (4)

B. I. Erkmen and J. H. Shapiro, “Signal-to-noise ratio of Gaussian-state ghost imaging,” Phys. Rev. A 79, 023833 (2009).
[CrossRef]

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17, 7916–7921 (2009).
[CrossRef]

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

X. H. Chen, Q. Liu, K. H. Luo, and L. A. Wu, “Lensless ghost imaging with true thermal light,” Opt. Lett. 34, 695–697 (2009).
[CrossRef]

2008 (3)

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

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251 (2008).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

2007 (1)

2005 (4)

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

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

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

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

2003 (1)

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

2001 (2)

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum holography,” Opt. Express 9, 498–505 (2001).
[CrossRef]

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

1995 (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]

1972 (1)

Abouraddy, A. F.

Angelo, M. D.

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

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Bai, Y.

C. Wang, D. Zhang, Y. Bai, and B. Chen, “Ghost imaging for a reflected object with a rough surface,” Phys. Rev. A 82, 063814 (2010).
[CrossRef]

Boyd, R. W.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

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

Brambilla, E.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251 (2008).
[CrossRef]

Cai, Y. J.

Cao, D. Z.

J. Xiong, D. Z. Cao, F. Huang, H. G. Li, X. J. Sun, and K. G. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[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, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

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

Chekhova, M. V.

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Chen, B.

C. Wang, D. Zhang, Y. Bai, and B. Chen, “Ghost imaging for a reflected object with a rough surface,” Phys. Rev. A 82, 063814 (2010).
[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, W.

Chen, X.

Chen, X. H.

X. H. Chen, Q. Liu, K. H. Luo, and L. A. Wu, “Lensless ghost imaging with true thermal light,” Opt. Lett. 34, 695–697 (2009).
[CrossRef]

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

Cheng, J.

J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87, 043810 (2013).
[CrossRef]

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17, 7916–7921 (2009).
[CrossRef]

Deacon, K. S.

R. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100, 131114 (2012).
[CrossRef]

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

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

Dixon, P. B.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

Eberly, J. H.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, “Signal-to-noise ratio of Gaussian-state ghost imaging,” Phys. Rev. A 79, 023833 (2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Fan, C.

Gatti, A.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251 (2008).
[CrossRef]

Gong, 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]

Han, S.

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]

Hardy, N. D.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

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

Howell, J. C.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

Howland, G. A.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

Huang, F.

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

Karmakar, S.

S. Karmakar and Y. H. Shih, “Two-color ghost imaging with enhanced angular resolving power,” Phys. Rev. A 81, 033845 (2010).
[CrossRef]

Li, C.

C. Li, T. Wang, J. Pu, W. Zhu, and R. Rao, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).
[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. G.

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

Lin, J.

J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87, 043810 (2013).
[CrossRef]

Liu, Q.

Lugiato, L. A.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251 (2008).
[CrossRef]

Luo, K. H.

Meyers, R.

R. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100, 131114 (2012).
[CrossRef]

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

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

Nasr, M. B.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

O’Sullivan, M. N.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

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

Osche, G. R.

G. R. Osche, Optical Detection Theory for Laser Applications (Wiley-Interscience, 2002).

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]

Pu, J.

C. Li, T. Wang, J. Pu, W. Zhu, and R. Rao, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).
[CrossRef]

Qiao, C.

Rao, R.

C. Li, T. Wang, J. Pu, W. Zhu, and R. Rao, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).
[CrossRef]

Rodenburg, B.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

Saleh, B. E. A.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum holography,” Opt. Express 9, 498–505 (2001).
[CrossRef]

Scarcelli, G.

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

Sergienko, A. V.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum holography,” Opt. Express 9, 498–505 (2001).
[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]

Shapiro, J. H.

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

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Signal-to-noise ratio of Gaussian-state ghost imaging,” Phys. Rev. A 79, 023833 (2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Shen, H.

Shi, D.

Shih, Y. H.

R. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100, 131114 (2012).
[CrossRef]

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

S. Karmakar and Y. H. Shih, “Two-color ghost imaging with enhanced angular resolving power,” Phys. Rev. A 81, 033845 (2010).
[CrossRef]

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

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

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[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]

Simon, D. S.

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (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]

Sun, X. J.

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

Teich, M. C.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum holography,” Opt. Express 9, 498–505 (2001).
[CrossRef]

Valencia, A.

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

Wan, R. G.

Y. P. Yao, R. G. Wan, S. W. Zhang, and T. Y. Zhang, “Effect of turbulence on visibility and signal-to-noise ratio of lensless ghost imaging with thermal light,” Optik 124, 6973–6977 (2013).
[CrossRef]

Y. P. Yao, R. G. Wan, Y. L. Xue, S. W. Zhang, and T. Y. Zhang, “Positive–negative nonlocal lensless imaging based on statistical optics,” Acta Phys. Sin. 62, 154201 (2013).

Wang, C.

C. Wang, D. Zhang, Y. Bai, and B. Chen, “Ghost imaging for a reflected object with a rough surface,” Phys. Rev. A 82, 063814 (2010).
[CrossRef]

Wang, F.

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. G.

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

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

Wang, T.

C. Li, T. Wang, J. Pu, W. Zhu, and R. Rao, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).
[CrossRef]

Wang, Y.

Wu, L. A.

X. H. Chen, Q. Liu, K. H. Luo, and L. A. Wu, “Lensless ghost imaging with true thermal light,” Opt. Lett. 34, 695–697 (2009).
[CrossRef]

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

Xiong, J.

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

J. Xiong, D. Z. Cao, F. Huang, H. G. Li, X. J. Sun, and K. G. 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]

Xue, Y. L.

Y. P. Yao, R. G. Wan, Y. L. Xue, S. W. Zhang, and T. Y. Zhang, “Positive–negative nonlocal lensless imaging based on statistical optics,” Acta Phys. Sin. 62, 154201 (2013).

Yao, Y. P.

Y. P. Yao, R. G. Wan, Y. L. Xue, S. W. Zhang, and T. Y. Zhang, “Positive–negative nonlocal lensless imaging based on statistical optics,” Acta Phys. Sin. 62, 154201 (2013).

Y. P. Yao, R. G. Wan, S. W. Zhang, and T. Y. Zhang, “Effect of turbulence on visibility and signal-to-noise ratio of lensless ghost imaging with thermal light,” Optik 124, 6973–6977 (2013).
[CrossRef]

Yura, H. T.

Zhai, Y. H.

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

Zhang, D.

C. Wang, D. Zhang, Y. Bai, and B. Chen, “Ghost imaging for a reflected object with a rough surface,” Phys. Rev. A 82, 063814 (2010).
[CrossRef]

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

Zhang, J.

Zhang, P.

Zhang, S. W.

Y. P. Yao, R. G. Wan, Y. L. Xue, S. W. Zhang, and T. Y. Zhang, “Positive–negative nonlocal lensless imaging based on statistical optics,” Acta Phys. Sin. 62, 154201 (2013).

Y. P. Yao, R. G. Wan, S. W. Zhang, and T. Y. Zhang, “Effect of turbulence on visibility and signal-to-noise ratio of lensless ghost imaging with thermal light,” Optik 124, 6973–6977 (2013).
[CrossRef]

Zhang, T. Y.

Y. P. Yao, R. G. Wan, S. W. Zhang, and T. Y. Zhang, “Effect of turbulence on visibility and signal-to-noise ratio of lensless ghost imaging with thermal light,” Optik 124, 6973–6977 (2013).
[CrossRef]

Y. P. Yao, R. G. Wan, Y. L. Xue, S. W. Zhang, and T. Y. Zhang, “Positive–negative nonlocal lensless imaging based on statistical optics,” Acta Phys. Sin. 62, 154201 (2013).

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]

Zhu, W.

C. Li, T. Wang, J. Pu, W. Zhu, and R. Rao, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).
[CrossRef]

Acta Phys. Sin. (1)

Y. P. Yao, R. G. Wan, Y. L. Xue, S. W. Zhang, and T. Y. Zhang, “Positive–negative nonlocal lensless imaging based on statistical optics,” Acta Phys. Sin. 62, 154201 (2013).

Appl. Opt. (1)

Appl. Phys. B (1)

C. Li, T. Wang, J. Pu, W. Zhu, and R. Rao, “Ghost imaging with partially coherent light radiation through turbulent atmosphere,” Appl. Phys. B 99, 599–604 (2010).
[CrossRef]

Appl. Phys. Lett. (4)

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103, 221106 (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]

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

R. Meyers, K. S. Deacon, and Y. H. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100, 131114 (2012).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Optik (1)

Y. P. Yao, R. G. Wan, S. W. Zhang, and T. Y. Zhang, “Effect of turbulence on visibility and signal-to-noise ratio of lensless ghost imaging with thermal light,” Optik 124, 6973–6977 (2013).
[CrossRef]

Phys. Rev. A (12)

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

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

K. W. C. Chan, D. S. Simon, A. V. Sergienko, N. D. Hardy, J. H. Shapiro, P. B. Dixon, G. A. Howland, J. C. Howell, J. H. Eberly, M. N. O’Sullivan, B. Rodenburg, and R. W. Boyd, “Theoretical analysis of quantum ghost imaging through turbulence,” Phys. Rev. A 84, 043807 (2011).
[CrossRef]

S. Karmakar and Y. H. Shih, “Two-color ghost imaging with enhanced angular resolving power,” Phys. Rev. A 81, 033845 (2010).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Signal-to-noise ratio of Gaussian-state ghost imaging,” Phys. Rev. A 79, 023833 (2009).
[CrossRef]

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

C. Wang, D. Zhang, Y. Bai, and B. Chen, “Ghost imaging for a reflected object with a rough surface,” Phys. Rev. A 82, 063814 (2010).
[CrossRef]

J. Cheng and J. Lin, “Unified theory of thermal ghost imaging and ghost diffraction through turbulent atmosphere,” Phys. Rev. A 87, 043810 (2013).
[CrossRef]

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

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]

Phys. Rev. Lett. (4)

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

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

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef]

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

Prog. Opt. (1)

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251 (2008).
[CrossRef]

Other (1)

G. R. Osche, Optical Detection Theory for Laser Applications (Wiley-Interscience, 2002).

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Figures (4)

Fig. 1.
Fig. 1.

Klyshko unfolded version of the schematic standoff two-color quantum ghost imaging setup. A SPDC source generates nondegenerate signal and reference beams with central wavelengths λs and λr, respectively. d1, d2, Lo, and Lb are distances from source to lens, source to CCD camera D2, lens to object, and object to bucket detector D1, respectively. ρc, ρf, ρt, and ρb are coordinates on the CCD plane, lens plane, object plane, and bucket detector plane. There exists turbulence in the lens-to-object and object-to-bucket-detector paths.

Fig. 2.
Fig. 2.

(a) Object of a reflective double slit to be imaged; its slit width is 6 cm and slit separation is 12 cm. The reflectivities of the left and right slits are 1 and 0.5, respectively. (b) Normalized cross section ghost image through different levels of turbulence. The image is reversed as the magnification factor is negative.

Fig. 3.
Fig. 3.

Magnification factor as a function of (a) the reference beam wavelength λr with λs=1064nm, and (b) the signal beam wavelength λs with λr=532nm for different turbulence strength levels.

Fig. 4.
Fig. 4.

(a) Point-spread function ΔPSF describing the resolution of the ghost image, and (b) field of view ΔFOV versus λr when λs is fixed at 1064 nm for different turbulence strengths. (c) ΔPSF and (d) ΔFOV versus λs while λr is set to be 532 nm. (e) Point-spread function and (f) field of view plotted corresponding to (c) and (d), respectively, especially when the turbulence is weak.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

E^c(ρc,t1)=dρrE^r(ρr,t1d2/c)H(kr,d2,ρc,ρr),
E^t(ρt,t2)=dρsdρfE^s[ρs,t2(d1+Lo)/c]H(ks,d1,ρf,ρs)L(ρf)H(ks,Lo,ρt,ρf)eψo(ρt,ρf),
eψm*(ρj1,ρk1)eψm(ρj2,ρk2)=e(|ρj1ρj2|2+(ρj1ρj2)·(ρk1ρk2)+|ρk1ρk2|2)/2ρm2,
T*(ρt)T(ρt)=λs2O(ρt)δ(ρtρt).
C^(ρp)=1TITI/2TI/2dti^p(tτd)i^b(t)=q2η2Apdτ1dτ2Abdρbhc(tτdτ1)hb(tτ2)×E^c(ρp,τ1)E^T(ρb,τ2)E^c(ρp,τ1)E^T(ρb,τ2),
E^c(ρp,τ1)E^T(ρb,τ2)E^c(ρp,τ1)E^T(ρb,τ2)=dρtdρtT*(ρt)T(ρt)eψb*(ρb,ρt)eψb(ρb,ρt)H*(ks,Lb,ρb,ρt)H(ks,Lb,ρb,ρt)×E^c(ρp,τ1)E^t(ρt,τ2Lb/c)E^c(ρp,τ1)E^t(ρt,τ2Lb/c)=1Lb2dρtO(ρt)E^c(ρp,τ1)E^t(ρt,τ2Lb/c)E^c(ρp,τ1)E^t(ρt,τ2Lb/c).
C^(ρp)=q2η2ApAbLb2dτ1dτ2dρthc(tτdτ1)hb(tτ2)O(ρt)dρrdρrdρsdρsdρfdρfE^r(ρr,τ1τr)E^s(ρs,τ2τs)E^r(ρr,τ1τr)E^s(ρs,τ2τs)×H*(kr,d2,ρp,ρr)H(kr,d2,ρp,ρr)H*(ks,d1,ρf,ρs)H(ks,d1,ρf,ρs)L*(ρf)×L(ρf)H*(ks,Lo,ρt,ρf)H(ks,Lo,ρt,ρf)eψo*(ρt,ρf)eψo(ρt,ρf),
E^r(ρr,τ1τr)E^s(ρs,τ2τs)E^r(ρr,τ1τr)E^s(ρs,τ2τs)=E^r(ρr,τ1τr)E^s(ρs,τ2τs)E^r(ρr,τ1τr)E^s(ρs,τ2τs)+E^r(ρr,τ1τr)E^r(ρr,τ1τr)E^s(ρs,τ2τs)E^s(ρs,τ2τs)+E^r(ρr,τ1τr)E^s(ρs,τ2τs)E^s(ρs,τ2τs)E^r(ρr,τ1τr).
E^K(ρ1,t1)E^K(ρ2,t2)=2Pπa02e|ρ1|2+|ρ2|2a02e|ρ1ρ2|22ρ02e(t1t2)22T02
E^s(ρ1,t1)Er(ρ2,t2)=0,
E^s(ρ1,t1)Er(ρ2,t2)=2Pπa02e|ρ1|2+|ρ2|2a02e|ρ1ρ2|22ρ02e(t1t2)22T02.
C^(ρp)=P2ks4kr2q2η2ApAb16π5a04d12Lo2Lb2d22dτ1dτ2h(tτdτ1)h(tτ2)dρtO(ρt)×{exp([(τ1τr)(τ2τs)]2T02)θμα2+γ2exp((mρtρp)2ΔPSF2)exp(ρt2ΔFOV2)+υκσexp[υ(δ*+δ+2(αβ)γ2κ)ξ2ρt22(αβ)φ2ρp2σ]},
1ΔPSF2=θφ2(A+B2μεγ2β2α2+γ2),m=iμξγβ[Dεα+iγ(μεγ2β2α2+γ2B)Cεαiγ(μεγ2β2α2+γ2A)]φ(A+B2μεγ2β2α2+γ2)1ΔFOV2=m2ΔPSF2+μξ2(C+D2ε)2θμεγ2β2α2+γ2·(μξγβ)2α2+γ2(Dε)(Cε)θB(μξγβ)2(α+iγ)2(Dε)2θA(μξγβ)2(αiγ)2(Cε)2,α=1/a02+1/2ρ02,β=1/2ρ02,γ=ks/2d1,δ=1/2ρD2+iks/2f,ε=1/2ρo2,ξ=ks/2Lo,φ=kr/2d2,C=D*=δ*+ε+iξ+iγ+γ2α+iγ,A=B*=αβ2α+iγ+μDγ2β2(α+iγ)2+iφ,E=F*=δ*+ε+iξ+iγ+(αiγ)γ2α2+γ2β2,μ1=CDε2,θ1=ABμ2ε2γ4β4(α2+γ2)2,υ1=EF(ε+βγ2α2+γ2β2)2,κ=α2+γ2β2,σ=α2+φ2β2.
C^(ρp)=P2ks4kr2q2η2ApAb16π5a04d12Lo2Lb2d22dρtO(ρt)×{ΩBT04exp((τdτs+τr)2T02+16/ΩB2)θμα2+γ2exp((mρtρp)2ΔPSF2)exp(ρt2ΔFOV2)+υκσexp[υ(δ*+δ+2(αβ)γ2κ)ξ2ρt22(αβ)φ2ρp2σ]}.
G(ρp)=P2ks4kr2q2η2ApAb16π5a04d12Lo2Lb2d22dρtO(ρt){ΩBT04θμα2+γ2exp((mρtρp)2ΔPSF2)exp(ρt2ΔFOV2)+υκσexp[υ(δ*+δ+2(αβ)γ2κ)ξ2ρt22(αβ)φ2ρp2σ]}.

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