Abstract

In this article, the color of ghost imaging (GI) was studied theoretically and experimentally. The theoretical analysis and experimental data show that the color of GI with rotating ground glass plate and computational GI are the same as the light source. If multiwavelength source is used in these schemes, a full color image without distortion can be obtained. In contrast, the color of GI with spatial light modulator as well as that in a quantum system is a superimposed one, depending on the idle and object light beams, and following the principle of light color superposition. Correspondingly, a full color image can also be obtained under the condition of multiwavelength source, but with color distortion existing.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
    [Crossref] [PubMed]
  2. D.-F. Shi, C.-Y. Fan, P.-F. Zhang, H. Shen, J.-H. Zhang, C.-H. Qiao, and Y.-J. Wang, “Two-wavelength ghost imaging through atmospheric turbulence,” Opt. Express 21, 2050–2064 (2013).
    [Crossref] [PubMed]
  3. R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98, 111115 (2011).
    [Crossref]
  4. J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17, 7916–7921 (2009).
    [Crossref] [PubMed]
  5. A.-X. Zhang, Y.-H. He, L.-A. Wu, L.-M. Chen, and B.-B. Wang, “Tabletop X-ray ghost imaging with ultra-low radiation,” Optica 5(4), 374–377 (2018).
    [Crossref]
  6. H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
    [Crossref] [PubMed]
  7. A. Schori and S. Shwartz, X-ray ghost imaging with a laboratory source, Opt. Express 25(13), 14822–14828 (2017).
    [Crossref] [PubMed]
  8. T. B. Pittman, Y. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).
    [Crossref] [PubMed]
  9. A. Valenica, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
    [Crossref]
  10. 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] [PubMed]
  11. D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
    [Crossref]
  12. S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B.-Q. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 023068 (2013).
    [Crossref]
  13. D.-Y. Duan, S.-J. Du, and Y.-J. Xia, “Multiwavelength ghost imaging,” Phys. Rev. A 88, 053842 (2013).
    [Crossref]
  14. N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Quantum Commun. Quantum Imaging 7815(2), 199–283 (2010).
  15. D.-Y. Duan and Y.-J. Xia, “Computational ghost imaging with nonlocal quantum correlations,” arXiv:1801.10045v2 (2018).
  16. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Two-color ghost imaging,” Phys. Rev. A 79, 033808 (2009).
    [Crossref]
  17. Fred W. Billmeyer and Max Saltzman, Principles of Color Technology, 2nd ed. (Wiley-Interscience, 1981).

2018 (1)

2017 (1)

2016 (1)

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

2014 (1)

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

2013 (4)

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B.-Q. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 023068 (2013).
[Crossref]

D.-Y. Duan, S.-J. Du, and Y.-J. Xia, “Multiwavelength ghost imaging,” Phys. Rev. A 88, 053842 (2013).
[Crossref]

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref] [PubMed]

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

2011 (1)

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

2010 (1)

N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Quantum Commun. Quantum Imaging 7815(2), 199–283 (2010).

2009 (3)

2005 (1)

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

1995 (1)

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

Billmeyer, Fred W.

Fred W. Billmeyer and Max Saltzman, Principles of Color Technology, 2nd ed. (Wiley-Interscience, 1981).

Bina, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref] [PubMed]

Bowman, R.

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B.-Q. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 023068 (2013).
[Crossref]

Boyd, R. W.

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

Chan, K. W. C.

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

Chen, L.-M.

Chen, X.-H.

Cheng, J.

D’Angelo, M.

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

Deacon, K. S.

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

Du, G.-H.

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Du, S.-J.

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

D.-Y. Duan, S.-J. Du, and Y.-J. Xia, “Multiwavelength ghost imaging,” Phys. Rev. A 88, 053842 (2013).
[Crossref]

Duan, D.-Y.

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

D.-Y. Duan, S.-J. Du, and Y.-J. Xia, “Multiwavelength ghost imaging,” Phys. Rev. A 88, 053842 (2013).
[Crossref]

D.-Y. Duan and Y.-J. Xia, “Computational ghost imaging with nonlocal quantum correlations,” arXiv:1801.10045v2 (2018).

Edgar, M. P.

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B.-Q. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 023068 (2013).
[Crossref]

Fan, C.-Y.

Ferri, F.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref] [PubMed]

Gatti, A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref] [PubMed]

Han, S.-S.

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Hardy, N. D.

N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Quantum Commun. Quantum Imaging 7815(2), 199–283 (2010).

He, Y.-H.

Jiang, S.-S.

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

Jonathan, P.

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B.-Q. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 023068 (2013).
[Crossref]

Liu, Q.

Liu, Y.-Y.

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

Lu, R.-H.

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Lugiato, L. A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref] [PubMed]

Luo, K.-H.

Magatti, D.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref] [PubMed]

Meyers, R. E.

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

Molteni, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref] [PubMed]

O’Sullivan, M. N.

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

Padgett, M. J.

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B.-Q. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 023068 (2013).
[Crossref]

Pittman, T. B.

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

Qiao, C.-H.

Saltzman, Max

Fred W. Billmeyer and Max Saltzman, Principles of Color Technology, 2nd ed. (Wiley-Interscience, 1981).

Scarcelli, G.

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

Schori, A.

Sergienko, A. V.

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

Shapiro, J. H.

N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Quantum Commun. Quantum Imaging 7815(2), 199–283 (2010).

Shen, H.

Shi, D.-F.

Shih, Y.

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

A. Valenica, 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. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).
[Crossref] [PubMed]

Shwartz, S.

Strekalov, D. V.

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

Sun, B.-Q.

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B.-Q. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 023068 (2013).
[Crossref]

Valenica, A.

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

Wang, B.-B.

Wang, Y.-J.

Welsh, S. S.

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B.-Q. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 023068 (2013).
[Crossref]

Wu, L.-A.

Xia, Y.-J.

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

D.-Y. Duan, S.-J. Du, and Y.-J. Xia, “Multiwavelength ghost imaging,” Phys. Rev. A 88, 053842 (2013).
[Crossref]

D.-Y. Duan and Y.-J. Xia, “Computational ghost imaging with nonlocal quantum correlations,” arXiv:1801.10045v2 (2018).

Xiao, T.-Q.

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Xie, H.-L.

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Yan, L.-

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

Yu, H.

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Zhang, A.-X.

Zhang, J.-H.

Zhang, L.

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

Zhang, P.-F.

Zhu, D.-M.

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

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

Eur. Phys. J. D (1)

D.-Y. Duan, S.-J. Du, L.- Yan, S.-S. Jiang, Y.-Y. Liu, L. Zhang, and Y.-J. Xia, “Color of ghost imaging,” Eur. Phys. J. D 68, 11 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Optica (1)

Phys. Rev. A (3)

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

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

D.-Y. Duan, S.-J. Du, and Y.-J. Xia, “Multiwavelength ghost imaging,” Phys. Rev. A 88, 053842 (2013).
[Crossref]

Phys. Rev. Lett. (3)

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

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering Differential Ghost Imaging in Turbid Media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref] [PubMed]

H. Yu, R.-H. Lu, S.-S. Han, H.-L. Xie, G.-H. Du, T.-Q. Xiao, and D.-M. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Quantum Commun. Quantum Imaging (1)

N. D. Hardy and J. H. Shapiro, “Ghost imaging in reflection: resolution, contrast, and signal-to-noise ratio,” Quantum Commun. Quantum Imaging 7815(2), 199–283 (2010).

Other (2)

D.-Y. Duan and Y.-J. Xia, “Computational ghost imaging with nonlocal quantum correlations,” arXiv:1801.10045v2 (2018).

Fred W. Billmeyer and Max Saltzman, Principles of Color Technology, 2nd ed. (Wiley-Interscience, 1981).

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Figures (2)

Fig. 1
Fig. 1 (Color online) (a) Two-wavelength GI with RGGP. (b) CGI with two-wavelength source. (c) Two-wavelength GI with SLM. SLM: spatial light modulator; DM: dichroic mirror; BS: beam splitter; BD: bucket detector.
Fig. 2
Fig. 2 (a) color object. Top row: GI with RGGP, (b)image with λ1 = 532nm and λ2 = 633nm, (c) image with λ1 = 532nm, (d) image with λ2 = 633nm. Middle row: CGI, (e) image with λ1 = 532nm and λ2 = 633nm, (f) image with λ1 = 532nm, (g) image with λ2 = 633nm. Bottom row: GI with SLM, (h) image with λ1 = 532nm and λ2 = 633nm, (i) object beam λ1 = 532nm, idle beam λ2 = 633nm, (j) object beam λ2 = 633nm, idle beam λ1 = 532nm.

Equations (7)

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

C ( ρ i , ρ o , t ) = δ I im ( ρ i , t ) δ I om ( ρ o , t ) ,
C ( ρ i , ρ o , t ) = | E i 1 ( ρ i , t ) | 2 | E o 1 ( ρ o , t ) | 2 | E i 1 ( ρ i , t ) | 2 | E o 1 ( ρ o , t ) | 2 + | E i 2 ( ρ i , t ) | 2 | E o 2 ( ρ o , t ) | 2 | E i 2 ( ρ i , t ) | 2 | E o 2 ( ρ o , t ) | 2 = C 1 ( ρ i , ρ o , t ) + C 2 ( ρ i , ρ o , t ) .
C m ( ρ i , ρ o , t ) = d ω im d ω i m d q i m d q im d ω om d ω om d q om d q om × H im * ( ρ im , q im ; ω im ) H im ( ρ im , q im ; ω im ) × H om * ( ρ om , q om ; ω om ) H om ( ρ om , q rm ; ω om ) × e i ( ω im ω im ) t e i ( ω on ω on ) t T * ( ρ o ) T ( ρ o ) × G ( q im , q im , q om , q om , ω im , ω im , ω om , ω om ) ,
G ( q im , q im , q om , q om , ω im , ω im , ω om , ω om ) = V * ( q im ) V ( q om ) V * ( q om ) V ( q im ) × ε im * ( ω im ) ε im ( ω im ) ε om * ( ω om ) ε om ( ω om )
C m ( ρ i , ρ o , t ) = B | d ρ i d ρ o W ( ρ i , ρ o ) H i ( ρ i , ρ i ; Ω 1 ) H o * ( ρ o , ρ o ; Ω 2 ) O ( ρ ) | 2 ,
C ( ρ s , ρ d , t ) = | E s 1 ( ρ s , t ) | 2 | E d 1 ( ρ d , t ) | 2 | E s 1 ( ρ s , t ) | 2 | E d 1 ( ρ d , t ) | 2 + | E s 2 ( ρ s , t ) | 2 | E s 2 ( ρ d , t ) | 2 | E s 2 ( ρ s , t ) | 2 | E s 2 ( ρ d , t ) | 2 + | E s 1 ( ρ s , t ) | 2 | E d 2 ( ρ d , t ) | 2 | E s 1 ( ρ s , t ) | 2 | E d 2 ( ρ d , t ) | 2 + | E s 2 ( ρ s , t ) | 2 | E d 1 ( ρ d , t ) | 2 | E s 2 ( ρ s , t ) | 2 | E d 1 ( ρ d , t ) | 2 = C 1 ( ρ s , ρ d , t ) + C 2 ( ρ s , ρ d , t ) + C 3 ( ρ s , ρ d , t ) + C 4 ( ρ s , ρ d , t ) ,
C ( ρ i , ρ o , t ) = | E i 1 ( ρ i , t ) | 2 | E o 1 ( ρ o , t ) | 2 | E i 1 ( ρ i , t ) | 2 | E o 1 ( ρ o , t ) | 2 + | E i 2 ( ρ i , t ) | 2 | E o 2 ( ρ o , t ) | 2 | E i 2 ( ρ i , t ) | 2 | E o 2 ( ρ o , t ) | 2 + | E i 1 ( ρ i , t ) | 2 | E o 2 ( ρ o , t ) | 2 | E i 1 ( ρ i , t ) | 2 | E o 2 ( ρ o , t ) | 2 + | E i 2 ( ρ i , t ) | 2 | E o 1 ( ρ o , t ) | 2 | E i 2 ( ρ i , t ) | 2 | E o 1 ( ρ o , t ) | 2 = C 1 ( ρ i , ρ o , t ) + C 2 ( ρ i , ρ o , t ) + C 3 ( ρ i , ρ o , t ) + C 4 ( ρ i , ρ o , t ) .

Metrics