Abstract

Generally speaking, the difference between two cross-spectral densities (CSDs) does not represent a correlation function. We will furnish a sufficient condition so that such difference be a valid CSD. Using such a condition, we will show through some examples how new classes of CSDs can be generated.

© 2014 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. D. Ge, Y. Cai, and Q. Lin, Appl. Opt. 43, 4732 (2004).
    [CrossRef]
  3. Z.-H. Gu, E. R. Méndez, M. Ciftan, T. A. Leskova, and A. A. Maradudin, Opt. Lett. 30, 1605 (2005).
    [CrossRef]
  4. E. E. Garcia-Guerrero, E. R. Méndez, Z.-H. Gu, T. A. Leskova, and A. A. Maradudin, Opt. Express 18, 4816 (2010).
    [CrossRef]
  5. S. Sahin and O. Korotkova, Opt. Lett. 37, 2970 (2012).
    [CrossRef]
  6. J. Cang, X. Fang, and X. Liu, Opt. Laser Technol. 50, 65 (2013).
    [CrossRef]
  7. G. Wu, H. Guo, and D. Deng, Appl. Opt. 45, 366 (2006).
    [CrossRef]
  8. D. Xu, Y. Cai, D. Ge, and Q. Lin, Appl. Opt. 45, 369 (2006).
    [CrossRef]
  9. A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2004).
  10. F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
    [CrossRef]
  11. R. Martínez-Herrero, P. M. Mejías, and F. Gori, Opt. Lett. 34, 1399 (2009).
    [CrossRef]
  12. J. Turunen and P. Vahimaa, Opt. Express 16, 6433 (2008).
    [CrossRef]
  13. F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
    [CrossRef]
  14. V. Torres-Company, A. Valencia, and J. P. Torres, Opt. Lett. 34, 1177 (2009).
    [CrossRef]
  15. J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, J. Opt. Soc. Am. A 27, 2004 (2010).
    [CrossRef]
  16. J. Turunen and A. T. Friberg, in Progress in Optics, E. Wolf, ed. (Elsevier, 2009), Vol. 54, pp. 1–88.
  17. R. Zhang, X. Wang, X. Cheng, and Z. Qiu, J. Opt. Soc. Am. A 27, 2496 (2010).
    [CrossRef]
  18. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [CrossRef]
  19. Z. Tong and O. Korotkova, Opt. Lett. 37, 3240 (2012).
    [CrossRef]
  20. O. Korotkova, S. Sahin, and E. Shchepakina, J. Opt. Soc. Am. A 29, 2159 (2012).
    [CrossRef]
  21. Z. Mei and O. Korotkova, Opt. Lett. 38, 91 (2013).
    [CrossRef]
  22. H. Lajunen and T. Saastamoinen, Opt. Express 21, 190 (2013).
    [CrossRef]
  23. P. De Santis, F. Gori, G. Guattari, and C. Palma, J. Opt. Soc. Am. A 3, 1258 (1986).
    [CrossRef]
  24. F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).
    [CrossRef]
  25. P. Vahimaa and J. Turunen, Opt. Express 14, 1376 (2006).
    [CrossRef]

2013 (3)

2012 (3)

2011 (1)

2010 (3)

2009 (3)

2008 (1)

2007 (1)

2006 (3)

2005 (1)

2004 (1)

1986 (1)

1978 (1)

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).
[CrossRef]

Berlinet, A.

A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2004).

Cai, Y.

Cang, J.

J. Cang, X. Fang, and X. Liu, Opt. Laser Technol. 50, 65 (2013).
[CrossRef]

Cheng, X.

Ciftan, M.

De Santis, P.

Deng, D.

Fang, X.

J. Cang, X. Fang, and X. Liu, Opt. Laser Technol. 50, 65 (2013).
[CrossRef]

Friberg, A. T.

J. Turunen and A. T. Friberg, in Progress in Optics, E. Wolf, ed. (Elsevier, 2009), Vol. 54, pp. 1–88.

Garcia-Guerrero, E. E.

Ge, D.

Gori, F.

Gu, Z.-H.

Guattari, G.

Guo, H.

Korotkova, O.

Lajunen, H.

Leskova, T. A.

Lin, Q.

Liu, X.

J. Cang, X. Fang, and X. Liu, Opt. Laser Technol. 50, 65 (2013).
[CrossRef]

Mandel, L.

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

Maradudin, A. A.

Martínez-Herrero, R.

Mei, Z.

Mejías, P. M.

Méndez, E. R.

Palma, C.

Qiu, Z.

Ramírez-Sánchez, V.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
[CrossRef]

Shchepakina, E.

Shirai, T.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

Tervo, J.

Thomas-Agnan, C.

A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2004).

Tong, Z.

Torres, J. P.

Torres-Company, V.

Turunen, J.

Vahimaa, P.

Valencia, A.

Wang, X.

Wolf, E.

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

Wu, G.

Wyrowski, F.

Xu, D.

Zhang, R.

Appl. Opt. (3)

J. Opt. A (1)

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).
[CrossRef]

Opt. Express (4)

Opt. Laser Technol. (1)

J. Cang, X. Fang, and X. Liu, Opt. Laser Technol. 50, 65 (2013).
[CrossRef]

Opt. Lett. (8)

Other (3)

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

A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2004).

J. Turunen and A. T. Friberg, in Progress in Optics, E. Wolf, ed. (Elsevier, 2009), Vol. 54, pp. 1–88.

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Figures (3)

Fig. 1.
Fig. 1.

Spectral degree of coherence, as a function of x1, corresponding to the CSD in Eq. (17), with A1=A2=1, c1=3, c2=1, and x2=0 (dashed), x2=1.5 (solid line).

Fig. 2.
Fig. 2.

Spectral degree of coherence, as a function of x1, corresponding to the CSD in Eq. (21), with A1=1.5, A2=1, L1=0.1, L2=0.2, and x2=1 (dotted), 3 (dashed), 5 (solid line).

Fig. 3.
Fig. 3.

Spectral degree of coherence as a function of x1, for the difference of two CSDs of the GSM type, with α=10, γ1=1, γ2=4, A1=A2=1, and x2=0 (dotted), 0.2 (dashed), 0.4 (solid line).

Equations (27)

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F(ρ1,ρ2)=W1(ρ1,ρ2)W2(ρ1,ρ2).
Wi(ρ1,ρ2)=Ui*(ρ1)Ui(ρ2);(i=1,2),
F(ρ1,ρ2)g(ρ1)g*(ρ2)d2ρ1d2ρ2=|U2(ρ)g*(ρ)d2ρ|2.
W(ρ1,ρ2)=p(v)H*(ρ1,v)H(ρ2,v)d2v,
WK(r1,r2)=W(ρ1,ρ2)K*(ρ1,r1)K(ρ2,r2)d2ρ1d2ρ2.
WK(r1,r2)=p(v)HK*(r1,v)HK(r2,v)d2v,
HK(r,v)=H(ρ,v)K(ρ,r)d2ρ.
p(v)=n=0pnδ(vvn);pn0,n.
W(ρ1,ρ2)=n=0pnH*(ρ1,vn)H(ρ2,vn).
p(v)=p1(v)p2(v).
W(ρ1,ρ2)=W1(ρ1,ρ2)W2(ρ1,ρ2),
Wj(ρ1,ρ2)=pj(v)H*(ρ1,v)H(ρ2,v)d2v;(j=1,2).
W(x1,x2)=q(x1)q(x2)μ(x1x2),
H(x,v)=q(x)exp(2πixv);p(v)=μ˜(v),
H(x,v)=q(x)exp(2πix2v)
W(x1,x2)=Acq(x1)q(x2)sinc[c(x12x22)],
W(x1,x2)=q(x1)q(x2){A1c1sinc[c1(x12x22)]A2c2sinc[c2(x12x22)]},
H(x,v)=step(x)exp(vx),
p(v)=Astep(v)exp(vL),
W(x1,x2)=Astep(x1)step(x2)L+x1+x2.
W(x1,x2)=step(x1)step(x2)×(A1L1+x1+x2A2L2+x1+x2).
p(v)=step(v)[A1exp(vL1)A2exp(vL2)],
H(x,v)=exp[α(xv)2],
p(v)=Aexp(γv2)
W(x1,x2)=Bexp[x12+x224σ2(x1x2)22δ2],
B=Aπγ+2α;14σ2=αγγ+2α;12δ2=α2γ+2α.
p(v)=A1exp(γ1v2)A2exp(γ2v2).

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