Abstract

We discuss theoretically the visibility and contrast-to-noise ratio (CNR) of high-order thermal ghost imaging with natural light. Five cases of an object beam and a reference beam with different polarized light are analyzed. Theoretical calculations show that a higher-order N can optimize the ghost imaging in both visibility and CNR in all five cases.

© 2013 Optical Society of America

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  1. T. B. Pittman, Y. Shih, D. V. Strecalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
    [CrossRef]
  2. 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]
  3. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
    [CrossRef]
  4. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef]
  5. J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
    [CrossRef]
  6. L. Basano and P. Ottonello, “A conceptual experiment on single-beam coincidence detection with pseudothermal light,” Opt. Express 15, 12386–12394 (2007).
    [CrossRef]
  7. Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
    [CrossRef]
  8. Y. Cai and S.-Y. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29, 2716–2718 (2004).
    [CrossRef]
  9. I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
    [CrossRef]
  10. Y. Bai and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
    [CrossRef]
  11. L.-H. Ou and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. B 40, 1833–1844 (2007).
    [CrossRef]
  12. 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]
  13. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34, 3343–3345 (2009).
    [CrossRef]
  14. 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]
  15. X.-H. Chen, I. N. Agafonov, K.-H. Luo, Q. Liu, R. Xian, M. V. Chekhova, and L.-A. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett. 35, 1166–1168 (2010).
    [CrossRef]
  16. I. N. Agafonov, M. V. Chekhova, and A. N. Penin, “Multiphoton ghost imaging with classical light,” http://arxiv.org/abs/0911.3718 .
  17. H. Li, J. Shi, Z. Chen, and G. Zeng, “Detailed quality analysis of ideal high-order thermal ghost imaging,” J. Opt. Soc. Am. A 29, 2256–2262 (2012).
    [CrossRef]
  18. 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]
  19. 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]
  20. H. Kellock, T. Setälä, T. Shirai, and A. T. Friberg, “Image quality in double- and triple-intensity ghost imaging with classical partially polarized light,” J. Opt. Soc. Am. A 29, 2459–2467 (2012).
    [CrossRef]
  21. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), pp. 584–586, 340–352.
  22. J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 117–136.

2012 (2)

2011 (1)

2010 (3)

2009 (1)

2008 (2)

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (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]

2007 (3)

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

L.-H. Ou and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. B 40, 1833–1844 (2007).
[CrossRef]

L. Basano and P. Ottonello, “A conceptual experiment on single-beam coincidence detection with pseudothermal light,” Opt. Express 15, 12386–12394 (2007).
[CrossRef]

2005 (4)

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. 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]

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (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 (1)

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 (1)

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

Agafonov, I. N.

X.-H. Chen, I. N. Agafonov, K.-H. Luo, Q. Liu, R. Xian, M. V. Chekhova, and L.-A. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett. 35, 1166–1168 (2010).
[CrossRef]

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

Bache, M.

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

Bai, Y.

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

Basano, L.

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.

Brambilla, E.

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

Cai, Y.

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

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

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. 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.

Chekhova, M. V.

X.-H. Chen, I. N. Agafonov, K.-H. Luo, Q. Liu, R. Xian, M. V. Chekhova, and L.-A. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett. 35, 1166–1168 (2010).
[CrossRef]

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

Chen, X.-H.

Chen, Z.

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]

Ferri, F.

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

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 117–136.

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.

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

Huang, F.

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

Iskhakov, T. S.

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

Kellock, H.

Kuang, L.-M.

L.-H. Ou and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. B 40, 1833–1844 (2007).
[CrossRef]

Li, H.

Li, H.-G.

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

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]

Liu, Q.

Lugiato, L. A.

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

Luo, K.-H.

Magatti, D.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. 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), pp. 584–586, 340–352.

O’Sullivan, M. N.

Ottonello, P.

Ou, L.-H.

L.-H. Ou and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. B 40, 1833–1844 (2007).
[CrossRef]

Penin, A. N.

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

Pittman, T. B.

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

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

Setälä, T.

Shi, J.

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

Shirai, T.

Strecalov, D. V.

T. B. Pittman, Y. Shih, D. V. Strecalov, 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. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[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]

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

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), pp. 584–586, 340–352.

Wu, L.-A.

Xian, R.

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]

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]

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

Zeng, G.

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]

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]

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

J. Opt. Soc. Am. A (2)

J. Phys. B (1)

L.-H. Ou and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. B 40, 1833–1844 (2007).
[CrossRef]

Opt. Commun. (1)

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]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (3)

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

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

T. B. Pittman, Y. Shih, D. V. Strecalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[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. (4)

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]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. 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]

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

Other (3)

I. N. Agafonov, M. V. Chekhova, and A. N. Penin, “Multiphoton ghost imaging with classical light,” http://arxiv.org/abs/0911.3718 .

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), pp. 584–586, 340–352.

J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 117–136.

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Figures (5)

Fig. 1.
Fig. 1.

Scheme of thermal ghost imaging.

Fig. 2.
Fig. 2.

Curves of the maximum visibility in different cases versus order N. n is taken as the integer nearest to N/2. The left three (red) and right three (blue) curves correspond to T=10 and T=50, respectively. The circle, cross, and asterisk refer to case 2, in which the polarization directions of two beams are parallel; case 3, which features a completely polarized object beam and a natural reference beam; and case 5 (and 4), in which we have a completely polarized reference beam and a natural object beam (and the two beams have natural light), respectively.

Fig. 3.
Fig. 3.

Plots of the CNR CNR/L as function of order n and (Nn) when T=50. (a) Case 2: the polarization directions of two beams are parallel. (b) Case 3: completely polarized object beam and natural reference beam. (c) Case 4: two beams are completely unpolarized. (d) Case 5: completely polarized reference beam and natural object beam.

Fig. 4.
Fig. 4.

Curves of CNR/L in different cases as a function of order n when Nn=1 and T=50. The black circle, blue triangle, green pentagram, and red asterisk refer to case 2, in which the polarization directions of two beams are parallel; case 3, which features a completely polarized object beam and a natural reference beam; case 4, in which two beams are completely unpolarized; and case 5, in which we have a completely polarized reference beam and a natural object beam, respectively. The solid lines help to show the variation trend of each case.

Fig. 5.
Fig. 5.

Curves of CNR/L in case 4 (two beams are completely unpolarized) as a function of order n when Nn=1. The blue circle, red triangle, black square, green asterisk, and magenta pentagram refer to T=10, 20, 30, 40, 50, respectively. The solid lines help to show the variation trend.

Equations (27)

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

Io=uinTI(uin),
G(n,N)(r)=[uinTI(uin)]n[I(r)]Nn,
V(n,N)G(n,N)(r)maxG(n,N)(r)minG(n,N)(r)max+G(n,N)(r)min.
CNR=G(n,N)(r)maxG(n,N)(r)min12[Δ2G(n,N)(r)max+Δ2G(n,N)(r)min],
Ex(r,t)i^=Ax(r,t)ei[θx(t)2πνt]i^,Ey(r,t)j^=Ay(r,t)ei[θy(t)2πνt]j^,
G(n,N)(r)=[uinTIx(uin)]n[Iy(r)]Nn.
[uinTI(uin)]n=(T+n1)!(T1)!μn,
[I(r)]Nn=(Nn)!μNn,
G(n,N)(r)=(T+n1)!(T1)!(Nn)!μN.
G(n,N)(r)max=(T+N1)!(Nn)!(T+Nn1)!μN,
G(n,N)(r)min=(T+n1)!(Nn)!(T1)!μN.
V(n,N)=12[1+(T+N1)!(T1)!(T+Nn1)!(T+n1)!]1.
CNRL=2[(T+N1)!(Nn)!(T+Nn1)!(T+n1)!(Nn)!(T1)!](T+2N1)!(2N2n)!(T+2N2n1)![(T+N1)!(Nn)!(T+Nn1)!]2+(T+2n1)!(2N2n)!(T1)![(T+n1)!(Nn)!(T1)!]2.
G(n,N)(r)=[uinTIx(uin)]n[Ix(r)+Iy(r)]Nn.
G(n,N)(r)max=k=0NnCNnk(T+n+k1)!(T+k1)!k!(Nnk)!μN=(Nn)!n!(CT+Nn+1CT+n1n+1)μN,
G(n,N)(r)min=k=0NnCNnk(T+n1)!(T1)!k!(Nnk)!μN=(T+n1)!(T1)!(Nn+1)!μN,
V(n,N)=12[1+CT+Nn+1CT+n1n+1(Nn+1)CT+n1n]1.
CNRL=2[(Nn)!n!(CT+Nn+1CT+n1n+1)(T+n1)!(Nn+1)!(T1)!](2N2n)!2n!(CT+2N2n+1CT+2n12n+1)[(Nn)!n!(CT+Nn+1CT+n1n+1)]2+(T+2n1)!(2N2n+1)!(T1)![(T+n1)!(Nn+1)!(T1)!]2.
G(n,N)(r)=[uinT(Ix(uin)+Iy(uin))]n[Ix(r)+Iy(r)]Nn.
G(n,N)(r)max=k=0nm=0NnCNnmCnk(T+k+m1)!m!(T+Nkm1)!(Nnm)!(T+m1)!(T+Nnm1)!μN=(2T+N1)!(2T+Nn1)!(Nn+1)!μN,
G(n,N)(r)min=k=0nm=0NnCNnmCnk(T+k1)!m!(T+nk1)!(Nnm)!(T1)!(T1)!μN=(2T+n1)!(2T1)!(Nn+1)!μN.
V(n,N)=12[1+(2T+N1)!(2T1)!(2T+Nn1)!(2T+n1)!]1.
CNRL=2[(2T+N1)!(Nn+1)!(2T+Nn1)!(2T+n1)!(Nn+1)!(2T1)!](2T+2N1)!(2N2n+1)!(2T+2N2n1)![(2T+N1)!(Nn+1)!(2T+Nn1)!]2+(2T+2n1)!(2N2n+1)!(2T1)![(2T+n1)!(Nn+1)!(2T1)!]2.
G(n,N)(r)=[uinT(Ix(uin)+Iy(uin))]n[Iy(r)]Nn.
G(n,N)(r)max=k=0nCnk(T+k1)!(T1)!(T+Nk1)!(T+Nn1)!(Nn)!μN=(2T+N1)!(2T+Nn1)!(Nn)!μN,
G(n,N)(r)min=k=0nCnk(T+k1)!(T1)!(T+nk1)!(T1)!(Nn)!μN=(2T+n1)!(2T1)!(Nn)!μN.
CNRL=2[(2T+N1)!(Nn)!(2T+Nn1)!(2T+n1)!(Nn)!(2T1)!](2T+2N1)!(2N2n)!(2T+2N2n1)![(2T+N1)!(Nn)!(2T+Nn1)!]2+(2T+2n1)!(2N2n)!(2T1)![(2T+n1)!(Nn)!(2T1)!]2.

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