Abstract

The method of determination of the pair-structure factor of a collection of particles has been discussed. It is shown that the pair-structure factor of scattering potential of the collection of particles can be determined from the cross-spectral density function of the scattered field.

© 2010 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. T. Visser, D. Fischer, and E. Wolf, J. Opt. Soc. Am. A 23, 1631 (2006).
    [CrossRef]
  3. T. Shirai and T. Asakura, J. Opt. Soc. Am. A 12, 1354 (1995).
    [CrossRef]
  4. T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
    [CrossRef]
  5. A. Dogariu and E. Wolf, Opt. Lett. 23, 1340 (1998).
    [CrossRef]
  6. S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
    [CrossRef]
  7. S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
    [CrossRef] [PubMed]
  8. D. Zhao, O. Korotkova, and E. Wolf, Opt. Lett. 32, 3483 (2007).
    [CrossRef] [PubMed]
  9. G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
    [CrossRef]
  10. M. Lahiri, E. Wolf, D. G. Fisher, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
    [CrossRef] [PubMed]
  11. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  12. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  13. B. Kanseri and H. C. Kandpal, Opt. Lett. 33, 2410 (2008).
    [CrossRef] [PubMed]

2009 (2)

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

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

2008 (2)

B. Kanseri and H. C. Kandpal, Opt. Lett. 33, 2410 (2008).
[CrossRef] [PubMed]

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

2007 (1)

2006 (1)

1999 (1)

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

1998 (1)

1996 (1)

T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
[CrossRef]

1995 (1)

1989 (1)

Asakura, T.

T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
[CrossRef]

T. Shirai and T. Asakura, J. Opt. Soc. Am. A 12, 1354 (1995).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Dogariu, A.

Fischer, D.

Fisher, D. G.

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

Foley, J. T.

Gbur, G.

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

Gori, F.

Kandpal, H. C.

Kanseri, B.

Korotkova, O.

Lahiri, M.

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

Sahin, S.

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

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

Shirai, T.

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

T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
[CrossRef]

T. Shirai and T. Asakura, J. Opt. Soc. Am. A 12, 1354 (1995).
[CrossRef]

Visser, T.

Wolf, E.

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

D. Zhao, O. Korotkova, and E. Wolf, Opt. Lett. 32, 3483 (2007).
[CrossRef] [PubMed]

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]

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

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

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Zhao, D.

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

Opt. Commun. (2)

T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
[CrossRef]

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

Opt. Lett. (4)

Phys. Rev. A (1)

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

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

Other (2)

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

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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Figures (2)

Fig. 1
Fig. 1

Illustration of the notation.

Fig. 2
Fig. 2

(a) Normalized distributions of the assumed far-zone cross-spectral density function and (b) normalized distributions of the calculated pair-structure factor of the collection of particles with the particle radius of a = 0.15 λ . The parameters for simulation are λ = 0.6328 μ m , k = 2 π / λ , σ = 0.15 λ , w = 1 , δ = 0.5 , K 1 = | K 1 | , K 2 = | K 2 | .

Equations (19)

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W ( i ) ( r 1 , r 2 , s 0 , ω ) = U ( i ) ( r 1 , s 0 , ω ) U ( i ) ( r 2 , s 0 , ω ) ,
U ( i ) ( r , s 0 , ω ) = a ( ω ) exp ( i k s 0 r ) ,
W ( i ) ( r 1 , r 2 , s 0 , ω ) = S ( i ) ( ω ) exp [ i k s 0 ( r 2 r 1 ) ] ,
C F ( r 1 , r 2 , ω ) = F ( r 1 , ω ) F ( r 2 , ω ) m ,
W ( s ) ( r s 1 , r s 2 , s 0 , ω ) = S ( i ) ( ω ) r 2 C ̃ F [ K 1 , K 2 , ω ] ,
C ̃ F [ K 1 , K 2 , ω ] = D D C F ( r 1 , r 2 , ω ) exp [ i ( K 2 r 2 K 1 r 1 ) ] d 3 r 1 d 3 r 2
K 1 = k ( s 1 s 0 ) ,     K 2 = k ( s 2 s 0 ) ,
F ( r , ω ) = m = 1 L U m ( r r m , ω ) ,
U ( r , ω ) = B   exp [ r 2 2 σ 2 ] .
U ̃ ( K , ω ) = B ( 2 π ) ( 3 / 2 ) σ 3   exp [ K 2 σ 2 / 2 ] .
C F ( r 1 , r 2 , ω ) = m = 1 L n = 1 L U m ( r 1 r m , ω ) U n ( r 2 r n , ω ) .
C ̃ F ( K 1 , K 2 , ω ) = U ̃ ( K 1 , ω ) U ̃ ( K 2 , ω ) S ( K 1 , K 2 , ω ) ,
W ( s ) ( r s 1 , r s 2 , s 0 , ω ) = S ( i ) ( ω ) r 2 U ̃ ( K 1 , ω ) U ̃ ( K 2 , ω ) S ( K 1 , K 2 , ω ) .
S ( K 1 , K 2 , ω ) = r 2 U ̃ ( K 1 , ω ) U ̃ ( K 2 , ω ) W ( s ) ( r s 1 , r s 2 , s 0 , ω ) S ( i ) ( ω ) .
W ( s ) ( r s 1 , r s 2 , s 0 , ω ) = C   exp [ K 1 2 + K 2 2 ( k w ) 2 ] exp [ ( K 2 K 1 ) 2 ( k δ ) 2 ] ,
S ( K 1 , K 2 , ω ) = A   exp [ ( 1 ( k w ) 2 σ 2 2 ) ( K 2 2 + K 1 2 ) ] exp [ ( K 2 K 1 ) 2 ( k δ ) 2 ] ,
S ( K , ω ) = A   exp [ ( 2 ( k w ) 2 σ 2 ) K 2 ] .
μ ( K 1 , K 2 , ω ) = S ( K 1 , K 2 , ω ) S ( K 1 , ω ) S ( K 2 , ω ) .
μ ( K 1 , K 2 , ω ) = exp [ ( K 2 K 1 ) 2 ( k δ ) 2 ] .

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