Abstract

It is shown how the phenomenon of correlation-induced spectral changes generated on scattering of a polychromatic plane wave on a spatially homogeneous random medium may be used to determine the correlation function of the scattering potential of the medium.

© 2007 Optical Society of America

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References

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  1. E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
    [CrossRef] [PubMed]
  2. E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
    [CrossRef]
  3. For a review of these investigations up to 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
    [CrossRef]
  4. D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128 (1994).
    [CrossRef]
  5. T. Visser, D. Fischer, and E. Wolf, J. Opt. Soc. Am. A 23, 1631 (2006).
    [CrossRef]
  6. A. Dogariu and E. Wolf, in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E.M.Sevick-Muraca, J.A.Izatt, and M.N.Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998), pp. 26-29.
  7. A. Dogariu and E. Wolf, Opt. Lett. 23, 1340 (1998).
    [CrossRef]
  8. G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
    [CrossRef]
  9. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).
  10. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  11. M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th (expanded) ed. (Cambridge University Press, 1999).
  12. P. Roman, Advanced Quantum Theory (Addison-Wesley, 1965).
  13. R. W. James, The Optical Principles of the Diffraction of X-rays (Bell and Sons, 1948), pp. 14-16.

2006

1999

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

1998

1996

For a review of these investigations up to 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

1994

1989

1986

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th (expanded) ed. (Cambridge University Press, 1999).

Dogariu, A.

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

A. Dogariu and E. Wolf, in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E.M.Sevick-Muraca, J.A.Izatt, and M.N.Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998), pp. 26-29.

Fischer, D.

Fischer, D. G.

Foley, J. T.

Gbur, G.

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

Gori, F.

James, D. F. V.

For a review of these investigations up to 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

James, R. W.

R. W. James, The Optical Principles of the Diffraction of X-rays (Bell and Sons, 1948), pp. 14-16.

Mandel, L.

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

Roman, P.

P. Roman, Advanced Quantum Theory (Addison-Wesley, 1965).

Visser, T.

Wolf, E.

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

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

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

For a review of these investigations up to 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[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. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

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

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th (expanded) ed. (Cambridge University Press, 1999).

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

A. Dogariu and E. Wolf, in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E.M.Sevick-Muraca, J.A.Izatt, and M.N.Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998), pp. 26-29.

J. Opt. Soc. Am. A

Opt. Commun.

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

Rep. Prog. Phys.

For a review of these investigations up to 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

Other

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

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

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th (expanded) ed. (Cambridge University Press, 1999).

P. Roman, Advanced Quantum Theory (Addison-Wesley, 1965).

R. W. James, The Optical Principles of the Diffraction of X-rays (Bell and Sons, 1948), pp. 14-16.

A. Dogariu and E. Wolf, in Biomedical Optical Spectroscopy and Diagnostics/Therapeutic Laser Applications, E.M.Sevick-Muraca, J.A.Izatt, and M.N.Ediger, eds., Vol. 22 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998), pp. 26-29.

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Figures (2)

Fig. 1
Fig. 1

Illustrating the notation.

Fig. 2
Fig. 2

Scattering of a polychromatic plane wave with spectral density given by Eq. (10) on a medium whose correlation function is given by Eq. (9). (a) The direct problem: the scattering amplitude f ( θ , ω ) [Eq. (12)]. (b) The inverse problem: the value of the effective normalized size parameter k σ , determined from the scattering amplitude f ( θ , ω ) by the use of the inversion formula (13).

Equations (13)

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W ( i ) ( r 1 , r 2 , ω ) = U ( i ) * ( r 1 , ω ) U ( i ) ( r 2 , ω ) ,
U ( i ) ( r , ω ) = a ( ω ) e i k s 0 r ,
C F ( r 1 , r 2 , ω ) = F * ( r 1 , ω ) F ( r 2 , ω ) m ,
C F ( r 1 , r 2 , ω ) C F ( r 2 r 1 , ω ) .
S ( ) ( r s , ω ) = V r 2 C ̃ F [ k ( s s 0 ) , ω ] S ( i ) ( ω ) ,
C ̃ F ( K , ω ) = C F ( r , ω ) e i K r d 3 r
K = k ( s s 0 ) .
K 2 k ,
C F ( r , ω ) = A ( 2 π σ 2 ) 3 2 exp ( r 2 2 σ 2 ) .
S ( i ) ( ω ) = B exp [ ( ω ω 0 ) 2 2 Γ 0 2 ] .
S ( ) ( r s , ω ) = A V r 2 k 4 f ( θ , ω ) S ( i ) ( ω ) ,
f ( θ , ω ) = exp [ 2 k 2 σ 2 sin 2 ( θ 2 ) ] ,
k σ = 1 2 sin ( θ 2 ) ln f ( θ , ω ) .

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