Abstract

Classical ghost imaging is a correlation-imaging technique in which the image of the object is found through intensity correlations of light. We analyze three different quality parameters, namely the visibility, the signal-to-noise ratio (SNR), and the contrast-to-noise ratio (CNR), to assess the performance of double- and triple-intensity correlation-imaging setups. The source is a random partially polarized beam of light obeying Gaussian statistics, and the image quality is evaluated as a function of the degree of polarization (DoP). We show that the visibility improves when the DoP and the order of imaging increase, while the SNR behaves oppositely. The CNR is for the most part independent of DoP and the imaging order. The results are important for the development of new imaging devices using partially polarized light.

© 2012 Optical Society of America

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  6. A. Gatti, E. Brambilla, M. Bache, and L. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
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  7. 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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  8. V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77, 043811 (2008).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  35. Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (1)

2011 (5)

T. Shirai, H. Kellock, T. Setälä, and A. T. Friberg, “Visibility in ghost imaging with classical partially polarized electromagnetic beams,” Opt. Lett. 36, 2880–2882 (2011).
[CrossRef]

G. Brida, M. Chekhova, G. Fornaro, M. Genovese, E. Lopaeva, and I. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

T. Shirai, T. Setälä, and A. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801(R) (2011).
[CrossRef]

H. Kellock, T. Setälä, T. Shirai, and A. T. Friberg, “Higher-order ghost imaging with partially polarized classical light,” Proc. SPIE 8171, 81710Q (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 (9)

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

T. Setälä, T. Shirai, and A. T. Friberg, “Fractional Fourier transform in temporal ghost imaging with classical light,” Phys. Rev. A 82, 043813 (2010).
[CrossRef]

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]

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

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, “The impact of light polarization on imaging visibility of nth-order intensity correlation with thermal light,” Opt. Commun. 283, 405–408 (2010).
[CrossRef]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18, 5562–5573 (2010).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2, 405–450 (2010).
[CrossRef]

T. Shirai, T. Setälä, and A. T. Friberg, “Temporal ghost imaging with classical non-stationary pulsed light,” J. Opt. Soc. Am. B 27, 2549–2555 (2010).
[CrossRef]

2009 (4)

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, “High-order thermal ghost imaging,” Opt. Lett. 34, 3343–3345 (2009).
[CrossRef]

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

I. Agafonov, M. Chekhova, T. S. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56, 422–431 (2009).
[CrossRef]

2008 (4)

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77, 043811 (2008).
[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[CrossRef]

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

H.-G. Li, Y.-T. Zhang, D.-Z. Cao, J. Xiong, and K.-G. Wang, “Third-order ghost interference with thermal light,” Chin. Phys. B 17, 4510–4515 (2008).
[CrossRef]

2006 (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

2005 (4)

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

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

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

2004 (3)

T. Setälä, K. Lindfors, M. Kaivola, J. Tervo, and A. T. Friberg, “Intensity fluctuations and degree of polarization in three-dimensional thermal light fields,” Opt. Lett. 29, 2587–2589 (2004).
[CrossRef]

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

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

2002 (1)

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

1995 (2)

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

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

Agafonov, I.

I. Agafonov, M. Chekhova, T. S. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56, 422–431 (2009).
[CrossRef]

Bache, M.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

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

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

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

Bennink, R.

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

Bentley, S.

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

Berchera, I.

G. Brida, M. Chekhova, G. Fornaro, M. Genovese, E. Lopaeva, and I. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Boyd, R.

R. Bennink, S. Bentley, and R. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[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, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18, 5562–5573 (2010).
[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]

Brambilla, E.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

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

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

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

A. Gatti, E. Brambilla, and L. Lugiato, “Quantum imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 251–348.

Brida, G.

G. Brida, M. Chekhova, G. Fornaro, M. Genovese, E. Lopaeva, and I. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Bromberg, Y.

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

Cai, Y.

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Cao, D.-Z.

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

H.-G. Li, Y.-T. Zhang, D.-Z. Cao, J. Xiong, and K.-G. Wang, “Third-order ghost interference with thermal light,” Chin. Phys. B 17, 4510–4515 (2008).
[CrossRef]

D.-Z. Cao, J. Xiong, and K. 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, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18, 5562–5573 (2010).
[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]

Chekhova, M.

G. Brida, M. Chekhova, G. Fornaro, M. Genovese, E. Lopaeva, and I. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

I. Agafonov, M. Chekhova, T. S. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56, 422–431 (2009).
[CrossRef]

Cheng, J.

D’Angelo, M.

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

Ferri, F.

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

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

Fornaro, G.

G. Brida, M. Chekhova, G. Fornaro, M. Genovese, E. Lopaeva, and I. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Friberg, A.

T. Shirai, T. Setälä, and A. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801(R) (2011).
[CrossRef]

Friberg, A. T.

Gao, L.

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

Gatti, A.

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

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

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

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

A. Gatti, E. Brambilla, and L. Lugiato, “Quantum imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 251–348.

Genovese, M.

G. Brida, M. Chekhova, G. Fornaro, M. Genovese, E. Lopaeva, and I. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Gong, W.

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

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Guan, D.-S.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, “The impact of light polarization on imaging visibility of nth-order intensity correlation with thermal light,” Opt. Commun. 283, 405–408 (2010).
[CrossRef]

Han, S.

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

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]

Iskhakov, T. S.

I. Agafonov, M. Chekhova, T. S. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56, 422–431 (2009).
[CrossRef]

Kaivola, M.

Katz, O.

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

Kellock, H.

Klyshko, D.

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

Korotkova, O.

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

Lajunen, H.

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77, 043811 (2008).
[CrossRef]

Lancis, J.

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77, 043811 (2008).
[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, H.-G.

H.-G. Li, Y.-T. Zhang, D.-Z. Cao, J. Xiong, and K.-G. Wang, “Third-order ghost interference with thermal light,” Chin. Phys. B 17, 4510–4515 (2008).
[CrossRef]

Li, L.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, “The impact of light polarization on imaging visibility of nth-order intensity correlation with thermal light,” Opt. Commun. 283, 405–408 (2010).
[CrossRef]

Lin, L.-F.

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

Lindfors, K.

Liu, H.-C.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, “The impact of light polarization on imaging visibility of nth-order intensity correlation with thermal light,” Opt. Commun. 283, 405–408 (2010).
[CrossRef]

Lopaeva, E.

G. Brida, M. Chekhova, G. Fornaro, M. Genovese, E. Lopaeva, and I. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

Lugiato, L.

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

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

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

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

A. Gatti, E. Brambilla, and L. Lugiato, “Quantum imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 251–348.

Lugiato, L. A.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

Magatti, D.

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

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

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18, 5562–5573 (2010).
[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]

Pittman, T.

T. Pittman, Y. Shih, D. Strekalov, and A. 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]

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]

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.

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

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

Setälä, T.

Shapiro, 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]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2, 405–450 (2010).
[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[CrossRef]

Shen, X.

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

Shih, Y.

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

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

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

Shirai, T.

T. Shirai, H. Kellock, T. Setälä, and A. T. Friberg, “Imaging through an aberrating medium with classical ghost diffraction,” J. Opt. Soc. Am. A 29, 1288–1292 (2012).
[CrossRef]

T. Shirai, T. Setälä, and A. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801(R) (2011).
[CrossRef]

H. Kellock, T. Setälä, T. Shirai, and A. T. Friberg, “Higher-order ghost imaging with partially polarized classical light,” Proc. SPIE 8171, 81710Q (2011).
[CrossRef]

T. Shirai, H. Kellock, T. Setälä, and A. T. Friberg, “Visibility in ghost imaging with classical partially polarized electromagnetic beams,” Opt. Lett. 36, 2880–2882 (2011).
[CrossRef]

T. Setälä, T. Shirai, and A. T. Friberg, “Fractional Fourier transform in temporal ghost imaging with classical light,” Phys. Rev. A 82, 043813 (2010).
[CrossRef]

T. Shirai, T. Setälä, and A. T. Friberg, “Temporal ghost imaging with classical non-stationary pulsed light,” J. Opt. Soc. Am. B 27, 2549–2555 (2010).
[CrossRef]

Silberberg, Y.

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

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

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

Tervo, J.

Tong, Z.

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

Torres-Company, V.

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77, 043811 (2008).
[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]

Wang, K.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. 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. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

Wang, K.-G.

H.-G. Li, Y.-T. Zhang, D.-Z. Cao, J. Xiong, and K.-G. Wang, “Third-order ghost interference with thermal light,” Chin. Phys. B 17, 4510–4515 (2008).
[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]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Wu, L.-A.

I. Agafonov, M. Chekhova, T. S. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56, 422–431 (2009).
[CrossRef]

Xiong, J.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, “The impact of light polarization on imaging visibility of nth-order intensity correlation with thermal light,” Opt. Commun. 283, 405–408 (2010).
[CrossRef]

H.-G. Li, Y.-T. Zhang, D.-Z. Cao, J. Xiong, and K.-G. Wang, “Third-order ghost interference with thermal light,” Chin. Phys. B 17, 4510–4515 (2008).
[CrossRef]

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. 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. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

Zhang, P.

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

Zhang, S.-H.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, “The impact of light polarization on imaging visibility of nth-order intensity correlation with thermal light,” Opt. Commun. 283, 405–408 (2010).
[CrossRef]

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

Zhang, Y.-T.

H.-G. Li, Y.-T. Zhang, D.-Z. Cao, J. Xiong, and K.-G. Wang, “Third-order ghost interference with thermal light,” Chin. Phys. B 17, 4510–4515 (2008).
[CrossRef]

Zhu, S.-Y.

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[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]

Adv. Opt. Photon. (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. (1)

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

Chin. Phys. B (1)

H.-G. Li, Y.-T. Zhang, D.-Z. Cao, J. Xiong, and K.-G. Wang, “Third-order ghost interference with thermal light,” Chin. Phys. B 17, 4510–4515 (2008).
[CrossRef]

J. Mod. Opt. (2)

I. Agafonov, M. Chekhova, T. S. Iskhakov, and L.-A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56, 422–431 (2009).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

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

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

Opt. Commun. (2)

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, “The impact of light polarization on imaging visibility of nth-order intensity correlation with thermal light,” Opt. Commun. 283, 405–408 (2010).
[CrossRef]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (11)

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

T. Shirai, T. Setälä, and A. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801(R) (2011).
[CrossRef]

G. Brida, M. Chekhova, G. Fornaro, M. Genovese, E. Lopaeva, and I. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A 83, 063807 (2011).
[CrossRef]

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77, 043811 (2008).
[CrossRef]

T. Setälä, T. Shirai, and A. T. Friberg, “Fractional Fourier transform in temporal ghost imaging with classical light,” Phys. Rev. A 82, 043813 (2010).
[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[CrossRef]

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

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

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

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

Phys. Rev. E (1)

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Phys. Rev. Lett. (6)

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

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

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

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

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

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

Proc. SPIE (1)

H. Kellock, T. Setälä, T. Shirai, and A. T. Friberg, “Higher-order ghost imaging with partially polarized classical light,” Proc. SPIE 8171, 81710Q (2011).
[CrossRef]

Other (5)

Y.-C. Liu and L.-M. Kuang, “A theoretical scheme of thermal-light ghost imaging by nth-order intensity correlation,” http://arxiv.org/abs/0903.5015 .

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

A. Gatti, E. Brambilla, and L. Lugiato, “Quantum imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 251–348.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Generic and (b) specific double-intensity correlation-imaging setups. In (a), the source beam [Γ0(r1,r2)] is split into two arms characterized by the kernels K1 and K2. The beam intensities I1 and I2 at the end of the arms are measured and correlated (I1I2). In (b), a laser and a rotating ground glass disk (GD) are used to create a spatially incoherent light beam which then is divided into two arms with a beam splitter (BS). The reference arm has a lens with the focal length f and the test arm contains the object with the transmission function T(r). The propagation distances are denoted by zi, i{a,b,c,d}. The reference arm has a CCD camera to measure the intensity distribution and the test arm includes a bucket detector (BD) which measures the total intensity. An intensity correlation (I1I2) is performed to form an image of the object.

Fig. 2.
Fig. 2.

(a) Generic and (b) specific triple-intensity correlation imaging setups. Part (a) is similar to Fig. 1(a) but has three arms instead of two. Likewise, part (b) is analogous to Fig. 1(b) with the exception that there is an additional reference arm which is identical to the first one.

Fig. 3.
Fig. 3.

Qualitative sample realization of a normalized ghost-imaging signal. The object has two transparent regions with a normalized mean signal gmax corresponding to the bright areas of the image. The rest of the object is opaque leading to the signal gmin and the dark areas in the image. The noise levels in the bright and dark areas are characterized by the root-mean-square values rmsmax and rmsmin of the fluctuations, respectively.

Fig. 4.
Fig. 4.

Comparison of the maximum visibility according to the definition by (a) Cao et al. [Eq. (22)] and (b) Gatti et al. [Eq. (24)]. The solid lines correspond to the double-intensity case [Eqs. (25) and (26)], the dashed lines [Eqs. (27) and (28)], and dashed–dotted lines [Eqs. (29) and (30)] are for the general and specific triple-intensity setups, respectively.

Fig. 5.
Fig. 5.

Dependence of the double- and triple-intensity SNRs on the degree of polarization. The solid lines correspond to the extremal SNRs of the second-order ghost-imaging setups shown in Fig. 1. The dashed lines depict the maximum and minimum SNRs of the general third-order correlation imaging arrangement [Fig. 2(a)], while the dashed–dotted lines correspond to the extremal SNR values in the specific triple-intensity ghost-imaging setup [Fig. 2(b)]. The maximum SNRs are plotted in purple and the minimum SNRs in green.

Fig. 6.
Fig. 6.

Dependence of the CNR on the degree of polarization. The solid line is for the double-intensity case [Eq. (39)], while the dashed and dashed–dotted lines correspond to the CNRs of the triple-intensity cases related to Fig. 2(a) [Eq. (41)] and Fig. 2(b) [Eq. (42)], respectively.

Equations (54)

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

J0=[JxxJxyJyxJyy],
P=J1J2J1+J2.
G(N)(r1,,rN)=I1IN,
g(N)I1INI1IN,
I1IN=i1,,iN{x,y}I1i1INiN,
I1i1INiN=N!Γi1i1̲11̲ΓiNiN̲NN̲,
Γαβ=[ΓxxαβΓxyαβΓyxαβΓyyαβ],
I1I2=trΓ11trΓ22+tr(Γ12Γ21),
I1I2I3=trΓ11trΓ22trΓ33+trΓ33tr(Γ12Γ21)+trΓ22tr(Γ13Γ31)+trΓ11tr(Γ23Γ32)+tr(Γ12Γ23Γ31)+tr(Γ13Γ32Γ21).
Γαβ=J0Γ^αβ,
Γ^αβ=γ0(r1,r2)Kα*(rα,r1)Kβ(rβ,r2)dr1dr2
γ^αβΓ^αβ/Γ^ααΓ^ββ,
g(2)(r1,r2)=1+P2+12|γ^12|2,
K1(r1,r1)=iλζexp{ik2ζ[(r1r1)2zbr12+zar12f]},
K2(r2,r2)=1λ2zazbT(r)exp{ik2[(rr2)2zc+(r2r)2zd]}dr.
Γ^αβ=Kα*(rα,r)Kβ(rβ,r)dr
1f=1zazc+1zb
|Γ^12|2=(zazc)2λ2zb2zd2|T(zazczbr1)|2.
g(3)(r1,r2,r3)=1+P2+12(|γ^12|2+|γ^13|2+|γ^23|2)+3P2+12(γ^12γ^23γ^31),
Γ^12=exp{ik2[1za/fζ(r22r12)]}δ(r1r2),
g(3)(r1,r1,r3)=P2+32+5P2+32|γ^13|2.
VC(N)gmax(N)gmin(N)gmax(N)+gmin(N),
VG(2)=I1I2maxI1I2I1I2max=gmax(2)1gmax(2).
VG(N)I1INmaxI1INminI1INmax=gmax(N)gmin(N)gmax(N).
VC(2)=P2+1P2+5,
VG(2)=P2+1P2+3.
VC(3)=3P2+23P2+4,
VG(3)=3P2+23P2+3.
VC(3)=5P2+37P2+9,
VG(3)=5P2+36P2+4.
noise(I1IN)=I12IN2I1IN2.
SNR(N)I1INnoise(I1IN),
g˜(2N)I12IN2/I12IN2
SNR(N)=g(N)g˜(2N)[g(N)]2
P2+35P4+54P2+21SNR(2)2P4+6P2+5,
SNR(3)=g(3)g˜(6)[g(3)]2
CNR(N)I1INmaxI1INmin12[noisemax2(I1IN)+noisemin2(I1IN)].
CNR(2)=gmax(2)gmin(2)12{g˜max(4)[gmax(2)]2+g˜min(4)[gmin(2)]2},
CNR(2)=P2+13P4+30P2+13.
CNR(3)=gmax(3)gmin(3)12{g˜max(6)[gmax(3)]2+g˜min(6)[gmin(3)]2}.
CNR(3)=12P2+891P6+1827P4+3033P2+577.
CNR(3)=2(5P2+3)48P6+947P4+1602P2+315,
tr(J0n)=J1n+J2n=J1n(1+xn),
(trJ0)n=(J1+J2)n=J1n(1+x)n,
x=1P1+P.
tr(J0n)(trJ0)n=(1+P)n+(1P)n2n,
Γ^αβ=γ(r)Kα*(rα,Rr2)Kβ(rβ,R+r2)drdR.
Γ^αβ=1|1zb/f|2γ(rβrα1zb/f)×exp{ik2ζ[(rβ2rα2)(1zaf)(rβrα)21zb/f]}.
n1,,nm{x,y}An1n21An2n32Anmn1m=tr(A1Am),
Ai=[AxxiAxyiAyxiAyyi]
I12I22=[trΓ11]2[trΓ22]2+tr(Γ11Γ11)[trΓ22]2+[trΓ11]2tr(Γ22Γ22)+tr(Γ11Γ11)tr(Γ22Γ22)+2[tr(Γ12Γ21)]2+2tr(Γ12Γ21Γ12Γ21)+4trΓ11trΓ22tr(Γ12Γ21)+4tr(Γ11Γ12Γ21)trΓ22+4trΓ11tr(Γ12Γ22Γ21)+4tr(Γ11Γ12Γ22Γ21),
g˜(4)=P4+6P2+94+P4+22P2+92|γ^12|2+3P4+10P2+34|γ^12|4,
g˜(6)=18{(P6+9P4+27P2+27)+2(P6+25P4+75P2+27)(|γ^12|2+|γ^23|2+|γ^13|2)+(3P6+19P4+33P2+9)(|γ^12|4+|γ^13|4+|γ^23|4)+2(P6+89P4+139P2+27)×(|γ^12|2|γ^23|2+|γ^12|2|γ^13|2+|γ^13|2|γ^23|2)+2(P6+33P4+27P2+3)|γ^12|2|γ^23|2|γ^31|2cos2(Δϕ123)+4(3P6+51P4+65P2+9)×(|γ^12|2+|γ^23|2+|γ^13|2)|γ^12||γ^23||γ^31|cos(Δϕ123)+4(P6+57P4+171P2+27)|γ^12||γ^23||γ^31|cos(Δϕ123)+2(13P6+117P4+111P2+15)|γ^12|2|γ^23|2|γ^13|2}.
g˜(6)=3P6+39P4+105P2+454+(3P6+111P4+225P2+45)|γ^13|2+15P6+231P4+285P2+452|γ^13|4.

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