Abstract

The Equivalence theorem for the spectral density of light waves on weak scattering is discussed. It is shown that when a spatially coherent plane light wave is scattered from two entirely different media, the far-zone spectral density may have identical distribution provided the low-frequency antidiagonal spatial Fourier components of the correlation function of the media are the same. An example of light waves on scattering from a Gaussian Schell model medium is discussed, and the condition on which two different media may produce identical spectral densities is presented.

© 2014 Optical Society of America

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References

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  1. E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
    [CrossRef]
  2. D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128 (1994).
    [CrossRef]
  3. C. Ding, Y. Cai, Y. Zhang, and L. Pan, Phys. Lett. A 376, 2697 (2012).
    [CrossRef]
  4. Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
    [CrossRef]
  5. J. Li, Opt. Commun. 308, 164 (2013).
    [CrossRef]
  6. A. Dogariu and E. Wolf, Opt. Lett. 23, 1340 (1998).
    [CrossRef]
  7. Z. Mei and O. Korotkova, Opt. Express 20, 29296 (2012).
    [CrossRef]
  8. T. D. Visser, D. G. Fischer, and E. Wolf, J. Opt. Soc. Am. A 23, 1631 (2006).
    [CrossRef]
  9. S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
    [CrossRef]
  10. X. Du and D. Zhao, Opt. Lett. 35, 384 (2010).
    [CrossRef]
  11. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  12. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  13. M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
    [CrossRef]
  14. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  15. E. Collett and E. Wolf, Opt. Lett. 2, 27 (1978).
    [CrossRef]

2013 (1)

J. Li, Opt. Commun. 308, 164 (2013).
[CrossRef]

2012 (2)

C. Ding, Y. Cai, Y. Zhang, and L. Pan, Phys. Lett. A 376, 2697 (2012).
[CrossRef]

Z. Mei and O. Korotkova, Opt. Express 20, 29296 (2012).
[CrossRef]

2010 (1)

2009 (2)

S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
[CrossRef]

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef]

2007 (1)

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

2006 (1)

1998 (1)

1994 (1)

1989 (1)

1978 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Cai, Y.

C. Ding, Y. Cai, Y. Zhang, and L. Pan, Phys. Lett. A 376, 2697 (2012).
[CrossRef]

Chen, Y.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

Collett, E.

Ding, C.

C. Ding, Y. Cai, Y. Zhang, and L. Pan, Phys. Lett. A 376, 2697 (2012).
[CrossRef]

Dogariu, A.

Du, X.

Fischer, D. G.

Foley, J. T.

Gori, F.

Korotkova, O.

Lahiri, M.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef]

Li, J.

J. Li, Opt. Commun. 308, 164 (2013).
[CrossRef]

Mandel, L.

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

Mei, Z.

Pan, L.

C. Ding, Y. Cai, Y. Zhang, and L. Pan, Phys. Lett. A 376, 2697 (2012).
[CrossRef]

Sahin, S.

Shirai, T.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef]

Visser, T. D.

Wolf, E.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef]

T. D. Visser, D. G. Fischer, and E. Wolf, J. Opt. Soc. Am. A 23, 1631 (2006).
[CrossRef]

A. Dogariu and E. Wolf, Opt. Lett. 23, 1340 (1998).
[CrossRef]

D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128 (1994).
[CrossRef]

E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
[CrossRef]

E. Collett and E. Wolf, Opt. Lett. 2, 27 (1978).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Xin, Y.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

Zhang, Y.

C. Ding, Y. Cai, Y. Zhang, and L. Pan, Phys. Lett. A 376, 2697 (2012).
[CrossRef]

Zhao, D.

Zhao, Q.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

Zhou, M.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

J. Li, Opt. Commun. 308, 164 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Lett. A (1)

C. Ding, Y. Cai, Y. Zhang, and L. Pan, Phys. Lett. A 376, 2697 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

Illustration of notations.

Fig. 2.
Fig. 2.

Distribution of correlation functions with two different parameters: (a) B=1, σ=λ, μ=λ; (b) B=1, σ=2λ, μ=419λ/19.

Fig. 3.
Fig. 3.

Normalized spectral density of light waves scattered from different media with two different parameters: (a) B=1, σ=λ, μ=λ; (b) B=1, σ=2λ, μ=419λ/19.

Equations (25)

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W(i)(r1,r2,s0,ω)=U(i)*(r1,s0,ω)U(i)(r2,s0,ω),
U(i)(r,s0,ω)=a(ω)exp(iks0·r),
W(i)(r1,r2,s0,ω)=S(i)(ω)exp[iks0·(r2r1)],
S(i)(ω)=a*(ω)a(ω)
CF(r1,r2,ω)=F*(r1,ω)F(r2,ω)m,
F(r,ω)=k24π[n2(r,ω)1]
W(s)(rs1,rs2,s0,ω)=S(i)(ω)r2C˜F[k(s1s0),k(s2s0),ω],
C˜F[K1,K2,ω]=DDCF(r1,r2,ω)×exp[i(K1·r1+K2·r2)]d3r1d3r2
S(s)(rs,s0,ω)=S(i)(ω)r2C˜F[k(ss0),k(ss0),ω].
CF(r1,r2,ω)=[IF(r1,ω)]1/2[IF(r2,ω)]1/2μF(r1,r2,ω),
IF(r,ω)=CF(r,r,ω)
μF(r1,r2,ω)=CF(r1,r2,ω)[CF(r1,r1,ω)]1/2[CF(r2,r2,ω)]1/2
C˜F[k(ss0),k(ss0),ω]=DD[IF(r1,ω)]1/2[IF(r2,ω)]1/2μF(r1,r2,ω)×exp[ik(ss0)·(r2r1)]d3r1d3r2.
CF(r1,r2,ω)=Bexp[r12+r224σ2]exp[(r2r1)22μ2],
C˜F[K1,K2,ω]=DDBexp[r12+r224σ2]exp[(r2r1)22μ2]×exp[i(K1·r1+K2·r2)]d3r1d3r2.
RS=r2+r1,RD=r2r1.
C˜F(K1,K2,ω)=28Bπ3σ6μ3(4σ2+μ2)3/2exp[2σ2KS2]exp[2σ2μ24σ2+μ2KD2]
KS=K2+K12,KD=K2K12.
S(s)(rs,s0,ω)=1r2S(i)(ω)B25π3δ3exp[k2δ2(ss0)22],
1δ2=14σ2+1μ2.
S(s)(rs,s0,ω)=S(s)(rs0,s0,ω)exp[k2δ2(ss0)22],
S(s)(rs0,s0,ω)=1r2S(i)(ω)B(2π)322δ3
14σ12+1μ12=14σ22+1μ22.
s0=(0,0,1),s=[sx,sy,(1sx2sy2)1/2],
S(s)(rs,s0,ω)=S(s)(rs0,s0,ω)×exp{k2δ2[22(1sx2sy2)1/2]2}.

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