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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  1. J.C. Dainty (Ed.), Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984)
  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]
  5. J. Ohtsubo, “Non-Gaussian speckle: a computer simulation,” Appl. Opt. 21, 4167 (1982)
    [Crossref] [PubMed]
  6. 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]
  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)
    [Crossref]
  9. H.M. Escamilla and E.R. Méndez “Speckle statistics from gamma-distributed random-phase screens,” J. Opt. Soc. Am. A 8, 1929 (1991)
    [Crossref]
  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)
    [Crossref]
  11. N. García 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. García-Martín, J.J. Sáenz, 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. García-Martín, R. Gómez-Medina, J.J. Sáenz, 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. Sánchez-Gil, M. Nieto-Vesperinas, F. Moreno, and F. González, “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 Random Media 8, 1 (1998)
    [Crossref]
  20. F. Moreno and F. González Eds., Light Scattering from Microestructures (Springer-Verlag, Berlin, 2000)
    [Crossref]
  21. M. Harris, G.N. Pearson, C.A. Hill, and J.M. Vaughan, “The fractal character of Gaussian-Lorentzian light,” Appl. Opt. 33, 7226 (1994).
    [Crossref] [PubMed]
  22. F. Moreno, F. González, 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. González, 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]

2000 (3)

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

A. García-Martín, J.J. Sáenz, 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]

A. García-Martín, R. Gómez-Medina, J.J. Sáenz, 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]

1998 (1)

A.P. Bates, K.I. Hopcraft, and E. Jakeman, “Non-Gaussian fluctuations of Stokes parameters in scattering by small particles”, Waves in Random Media 8, 1 (1998)
[Crossref]

1997 (1)

F. González, 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]

1996 (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]

1994 (2)

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]

M. Harris, G.N. Pearson, C.A. Hill, and J.M. Vaughan, “The fractal character of Gaussian-Lorentzian light,” Appl. Opt. 33, 7226 (1994).
[Crossref] [PubMed]

1993 (2)

F. Moreno, F. González, 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]

J.A. Sánchez-Gil, M. Nieto-Vesperinas, F. Moreno, and F. González, “Speckle statistics of electromagnetic waves scattered from perfectly conducting random rough surfaces,” J. Opt. Soc. Am A 10, 2628 (1993)
[Crossref]

1991 (2)

H.M. Escamilla and E.R. Méndez “Speckle statistics from gamma-distributed random-phase screens,” J. Opt. Soc. Am. A 8, 1929 (1991)
[Crossref]

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]

1989 (1)

N. García and A.Z. Genack, “Crossover to strong intensity correlations for microwave radiation in random media,” Phys. Rev. Lett. 63, 1678 (1989)
[Crossref] [PubMed]

1988 (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]

1986 (1)

1984 (2)

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]

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

1982 (1)

1972 (1)

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

Bates, A.P.

A.P. Bates, K.I. Hopcraft, and E. Jakeman, “Non-Gaussian fluctuations of Stokes parameters in scattering by small particles”, Waves in Random Media 8, 1 (1998)
[Crossref]

de Boer, J.F.

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]

Escamilla, H.M.

Faulkner, T.R.

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]

Feng, S.

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

García, N.

N. García and A.Z. Genack, “Crossover to strong intensity correlations for microwave radiation in random media,” Phys. Rev. Lett. 63, 1678 (1989)
[Crossref] [PubMed]

García-Martín, A.

A. García-Martín, J.J. Sáenz, 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]

A. García-Martín, R. Gómez-Medina, J.J. Sáenz, 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]

Genack, A.Z.

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

N. García and A.Z. Genack, “Crossover to strong intensity correlations for microwave radiation in random media,” Phys. Rev. Lett. 63, 1678 (1989)
[Crossref] [PubMed]

Gómez-Medina, R.

A. García-Martín, R. Gómez-Medina, J.J. Sáenz, 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]

González, F.

F. González, 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]

F. Moreno, F. González, 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]

J.A. Sánchez-Gil, M. Nieto-Vesperinas, F. Moreno, and F. González, “Speckle statistics of electromagnetic waves scattered from perfectly conducting random rough surfaces,” J. Opt. Soc. Am A 10, 2628 (1993)
[Crossref]

Goodman, J.W.

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

Harris, M.

Hill, C.A.

Hopcraft, K.I.

A.P. Bates, K.I. Hopcraft, and E. Jakeman, “Non-Gaussian fluctuations of Stokes parameters in scattering by small particles”, Waves in Random Media 8, 1 (1998)
[Crossref]

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]

Itoh, M.

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]

Jakeman, E.

A.P. Bates, K.I. Hopcraft, and E. Jakeman, “Non-Gaussian fluctuations of Stokes parameters in scattering by small particles”, Waves in Random Media 8, 1 (1998)
[Crossref]

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]

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

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]

Jordan, D.L.

Klewe, R.C.

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]

Lagendijk, A.

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]

Levine, B.M.

Méndez, E.R.

Moreno, F.

F. González, 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]

F. Moreno, F. González, 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]

J.A. Sánchez-Gil, M. Nieto-Vesperinas, F. Moreno, and F. González, “Speckle statistics of electromagnetic waves scattered from perfectly conducting random rough surfaces,” J. Opt. Soc. Am A 10, 2628 (1993)
[Crossref]

Nieto-Vesperinas, M.

A. García-Martín, R. Gómez-Medina, J.J. Sáenz, 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]

A. García-Martín, J.J. Sáenz, 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]

J.A. Sánchez-Gil, M. Nieto-Vesperinas, F. Moreno, and F. González, “Speckle statistics of electromagnetic waves scattered from perfectly conducting random rough surfaces,” J. Opt. Soc. Am A 10, 2628 (1993)
[Crossref]

Nieuwenhuizen, T.M.

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]

Ohtsubo, J.

Pearson, G.N.

Pnini, R.

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

Pusey, P.N.

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

Richards, P.H.

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]

Sáenz, J.J.

A. García-Martín, R. Gómez-Medina, J.J. Sáenz, 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]

A. García-Martín, J.J. Sáenz, 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]

Saiz, J.M.

F. González, 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]

F. Moreno, F. González, 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]

Sánchez-Gil, J.A.

J.A. Sánchez-Gil, M. Nieto-Vesperinas, F. Moreno, and F. González, “Speckle statistics of electromagnetic waves scattered from perfectly conducting random rough surfaces,” J. Opt. Soc. Am A 10, 2628 (1993)
[Crossref]

Schaefer, D.W.

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

Sebbah, P.

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

Takahashi, K.

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]

Tough, R.J.A.

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]

Valle, P.J.

F. González, 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]

F. Moreno, F. González, 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]

van Albada, M.P.

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]

van Rossum, M.C.W.

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]

Vaughan, J.M.

Walker, J.G.

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]

Watts, T.R.

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]

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. Sánchez-Gil, M. Nieto-Vesperinas, F. Moreno, and F. González, “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. Comm. (1)

F. González, 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. García-Martín, R. Gómez-Medina, J.J. Sáenz, 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. García-Martín, J.J. Sáenz, 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. García 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 Random Media (1)

A.P. Bates, K.I. Hopcraft, and E. Jakeman, “Non-Gaussian fluctuations of Stokes parameters in scattering by small particles”, Waves in Random Media 8, 1 (1998)
[Crossref]

Other (4)

F. Moreno and F. González 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)

Equations on this page are rendered with MathJax. Learn more.

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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