Abstract

We analyze the statistics of the co-polarized and cross-polarized scattered intensity from a flat substrate contaminated with spherical particles including multiple scattering between them. Both Gaussian and non-Gaussian regimes are considered. In particular, we focus on both the cross-polarized component and the probability of detecting zeros in the cross-polarized intensity, P(Icross=0). As it is shown, the latter gives information about particle interaction and can be measured with higher accuracy than other statistical parameters. A theoretical model for P(Icross=0) is presented for spherical Rayleigh scatterers. An scattering experiment was carried out to verify this model.

© 2002 Optical Society of America

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References

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  2. J. W. Goodman, Statistical Optics (Wiley, New York, 1985)
  3. D. W. Schaefer and P. N. Pusey, ?Statistics of Non-Gaussian scattered light,? Phys. Rev. Lett. 29, 843 (1972)
    [CrossRef]
  4. An excellent review can be found in E. Jakeman and R.J.A. Tough, ?Non-Gaussian models for the statistics of scattered waves,? Advances in Physics 37, 471-529 (1988)
    [CrossRef]
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    [CrossRef]
  7. E. Jakeman, ?Speckle statistics with a small number of scatterers,? Opt. Eng. 23, 453 (1984)
  8. B. M. Levine, ?Non-Gaussian speckle caused by thin phase screens of large root-mean-square phase variations and long single-scale autocorrelations,? J. Opt. Soc. Am. A 3, 1283 (1986)
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  9. H. M. Escamilla and E. R. M?ndez ?Speckle statistics from gamma-distributed random-phase screens,? J. Opt. Soc. Am. A 8, 1929 (1991)
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  10. M. Itoh and K. Takahashi, ?Measurement of aerosol particles by dynamic light-scttering. I: Effects of Non-Gaussian concentration fluctuation in real time photon correlation spectroscopy,? J. Aerosol Sci. 22, 815 (1991)
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  11. N. Garc?a and A. Z. Genack, ?Crossover to strong intensity correlations for microwave radiation in random media,? Phys. Rev. Lett. 63, 1678 (1989)
    [CrossRef] [PubMed]
  12. J. F. de Boer, M. C. W. van Rossum, M. P. van Albada, T. M. Nieuwenhuizen and A. Lagendijk, ?Diffusion of waves in a layer with a rough interface,? Phys. Rev. Lett. 73, 2567 (1994)
    [CrossRef] [PubMed]
  13. S. Feng in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 179-206
    [CrossRef]
  14. P. Sebbah, R. Pnini and A. Z. Genack, ?Field and intensity correlations in random media,? Phys. Rev. E 62, 7348 (2000)
    [CrossRef]
  15. A. Garc?a-Mart?n, J. J. S?enz and M. Nieto-Vesperinas, ?Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides,? Phys. Rev. Lett. 84, 3578 (2000)
    [CrossRef] [PubMed]
  16. A. Garc?a-Mart?n, R. G?mez-Medina, J. J. S?enz and M. Nieto-Vesperinas, ?Finite-size effects in the spatial distribution of the intensity reflected from disordered media,? Phys. Rev. B 62, 9386 (2000)
    [CrossRef]
  17. J. A. S?nchez-Gil, M. Nieto-Vesperinas, F. Moreno and F. Gonz?lez, ?Speckle statistics of electromagnetic waves scattered from perfectly conducting random rough surfaces,? J. Opt. Soc. Am A 10, 2628 (1993)
    [CrossRef]
  18. T. R. Watts, K. I. Hopcraft and T. R. Faulkner, ?Single measurement of probability density functions and their use in non-Gaussian light scattering,? J. Phys. A: Math. Gen. 29, 7501 (1996)
    [CrossRef]
  19. A. P. Bates, K. I. Hopcraft and E. Jakeman, ?Non-Gaussian fluctuations of Stokes parameters in scattering by small particles,? Waves in RandomMedia 8, 1 (1998)
    [CrossRef]
  20. F. Moreno and F. Gonz?lez Eds., Light Scattering from Microestructures (Springer-Verlag, Berlin, 2000)
    [CrossRef]
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  22. F. Moreno, F. Gonz?lez, J. M. Saiz, P. J. Valle and D. L. Jordan, ?Experimental study of copolarized light scattering by spherical light scattering on conducting flat substrates,? J. Opt. Soc. Am. A 10, 141 (1993)
    [CrossRef]
  23. F. Gonz?lez, J. M. Saiz, P. J. Valle and F. Moreno, ?Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects,? Opt. Comm. 137, 359 (1997).
    [CrossRef]

Advances in Physics (1)

An excellent review can be found in E. Jakeman and R.J.A. Tough, ?Non-Gaussian models for the statistics of scattered waves,? Advances in Physics 37, 471-529 (1988)
[CrossRef]

Appl. Opt. (2)

J. Aerosol Sci. (1)

M. Itoh and K. Takahashi, ?Measurement of aerosol particles by dynamic light-scttering. I: Effects of Non-Gaussian concentration fluctuation in real time photon correlation spectroscopy,? J. Aerosol Sci. 22, 815 (1991)
[CrossRef]

J. Opt. Soc. Am A (1)

J. A. S?nchez-Gil, M. Nieto-Vesperinas, F. Moreno and F. Gonz?lez, ?Speckle statistics of electromagnetic waves scattered from perfectly conducting random rough surfaces,? J. Opt. Soc. Am A 10, 2628 (1993)
[CrossRef]

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

J. Phys. A: Math. Gen. (1)

T. R. Watts, K. I. Hopcraft and T. R. Faulkner, ?Single measurement of probability density functions and their use in non-Gaussian light scattering,? J. Phys. A: Math. Gen. 29, 7501 (1996)
[CrossRef]

J. Phys. D: Appl. Phys. (1)

E. Jakeman, R. C. Klewe, P. H. Richards and J. G. Walker, ?Application of Non-Gaussian scattering of laser light to measurements in a propane flame,? J. Phys. D: Appl. Phys. 17, 1941 (1984)
[CrossRef]

Opt. Commun. (1)

F. Gonz?lez, J. M. Saiz, P. J. Valle and F. Moreno, ?Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects,? Opt. Comm. 137, 359 (1997).
[CrossRef]

Opt. Eng. (1)

E. Jakeman, ?Speckle statistics with a small number of scatterers,? Opt. Eng. 23, 453 (1984)

Phys. Rev. B (1)

A. Garc?a-Mart?n, R. G?mez-Medina, J. J. S?enz and M. Nieto-Vesperinas, ?Finite-size effects in the spatial distribution of the intensity reflected from disordered media,? Phys. Rev. B 62, 9386 (2000)
[CrossRef]

Phys. Rev. E (1)

P. Sebbah, R. Pnini and A. Z. Genack, ?Field and intensity correlations in random media,? Phys. Rev. E 62, 7348 (2000)
[CrossRef]

Phys. Rev. Lett. (4)

A. Garc?a-Mart?n, J. J. S?enz and M. Nieto-Vesperinas, ?Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides,? Phys. Rev. Lett. 84, 3578 (2000)
[CrossRef] [PubMed]

D. W. Schaefer and P. N. Pusey, ?Statistics of Non-Gaussian scattered light,? Phys. Rev. Lett. 29, 843 (1972)
[CrossRef]

N. Garc?a and A. Z. Genack, ?Crossover to strong intensity correlations for microwave radiation in random media,? Phys. Rev. Lett. 63, 1678 (1989)
[CrossRef] [PubMed]

J. F. de Boer, M. C. W. van Rossum, M. P. van Albada, T. M. Nieuwenhuizen and A. Lagendijk, ?Diffusion of waves in a layer with a rough interface,? Phys. Rev. Lett. 73, 2567 (1994)
[CrossRef] [PubMed]

Waves in RandomMedia (1)

A. P. Bates, K. I. Hopcraft and E. Jakeman, ?Non-Gaussian fluctuations of Stokes parameters in scattering by small particles,? Waves in RandomMedia 8, 1 (1998)
[CrossRef]

Other (4)

F. Moreno and F. Gonz?lez Eds., Light Scattering from Microestructures (Springer-Verlag, Berlin, 2000)
[CrossRef]

S. Feng in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 179-206
[CrossRef]

J. C. Dainty (Ed.), Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984)

J. W. Goodman, Statistical Optics (Wiley, New York, 1985)

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Figures (3)

Fig. 1.
Fig. 1.

Experimental set-up. The output polarization of the laser is perpendicular to the plane of the drawing (S polarization).

Fig. 2.
Fig. 2.

a) Experimental PDF of the copolarized backscattered intensity. The straight line would correspond to the pure Gaussian regime. b) Experimental PDF of the crosspolarized backscattered intensity.

Fig. 3.
Fig. 3.

Experimental values of P(Icross=0) (marked with dots) and their corresponding experimental errors, as a function of the size of the illuminated area w (see text for details). The continuous line corresponds to the fitted function given by Eq. 2.

Equations (3)

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P part ( I cross = 0 ) = P part ( l > L ) = e L d
P ( I cross = 0 ) = [ P part ( I cross = 0 ) ] N ¯ = exp [ ( L π d 3 ) ab ] = exp ( γab )
< I 2 > < I > 2 = 2 + 1 N ¯

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