Abstract

We report experimental measurements of the extinction in a suspension of dielectric spheres. We find that the model originally introduced by Keller is in good agreement with the data provided that nonlocal effects are properly taken into account. We also find that the simple criterion establishing the regime of independent scattering previously introduced is not consistent with our data.

© 2001 Optical Society of America

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References

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  1. U. Frisch, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A. Bharucha-Reid, ed. (Academic, New York, 1968), pp. 75–198.
  2. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1982).
  3. L. Tsang, J. A. Kong, “Effective propagation constant for coherent electromagnetic wave propagation in media embedded with dielectric scatterers,” J. Appl. Phys. 53, 7162–7173 (1982).
    [Crossref]
  4. R. West, D. Gibbs, L. Tsang, A. K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1834–1838 (1994).
    [Crossref]
  5. A. Nashashibi, K. Sarabandi, “Experimental characterization of the effective propagation constant of dense random media,” IEEE Trans. Antennas Propag. 47, 1454–1462 (1999).
    [Crossref]
  6. L. M. Zurk, L. Tsang, K. H. Ding, D. P. Winnebrenner, “Monte-Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries,” J. Opt. Soc. Am. A 12, 1772–1781 (1995).
    [Crossref]
  7. L. Tsang, C. E. Mandt, K. H. Ding, “Monte-Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell equations,” Opt. Lett. 47, 314–317 (1992).
    [Crossref]
  8. P. R. Siqueira, K. Sarabandi, “Method of moment evaluation of the two-dimensional quasi-crystalline approximation,” IEEE Trans. Antennas Propag. 44, 1067–1096 (1996).
    [Crossref]
  9. K. Sarabandi, P. R. Siqueira, “Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity,” IEEE Trans. Antennas Propag. 45, 858–867 (1997).
    [Crossref]
  10. P. R. Siqueira, K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
    [Crossref]
  11. J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
    [Crossref]
  12. L. Hespel, “Etude expérimentale et théorique du transfert radiatif dans les milieux diffusants. Détermination expérimentale des propriétés radiatives aux forts taux de charge,” Ph.D. dissertation (Ecole Centrale, Paris, 1999).
  13. J. D. Cartigny, “Radiative transfer with dependent scattering of particles,” Ph.D. dissertation (University of California, Berkeley, California, 1984).
  14. J. D. Cartigny, Y. Yamada, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1—theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
    [Crossref]
  15. Y. Yamada, J. D. Cartigny, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 2—experimental investigation,” J. Heat Transfer 108, 614–618 (1986).
    [Crossref]
  16. P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
    [Crossref]
  17. V. P. Dick, A. P. Ivanov, “Extinction of light in dispersive media with high particle concentrations: applicability limits of the interference approximation,” J. Opt. Soc. Am. A 16, 1034–1039 (1999).
    [Crossref]
  18. J. B. Keller, “Stochastic equations and wave propagation in random media,” Proc. Symp. Appl. Math. 16, 145–170 (1964).
    [Crossref]
  19. A. Ishimaru, Y. Kuga, “Attenuation constant of coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
    [Crossref]
  20. B. Gélebart, D. Ferrand, H. J. Schnorenberg, S. Avrillier, “Attenuation of a coherent field in a dense scattering medium,” in Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Mueller, eds., Proc. SPIE2626, 66–74 (1995).
    [Crossref]
  21. H. C. Hottel, A. F. Sarofim, W. H. Dalzeel, L. A. Vasolos, “Optical properties of coatings. Effect of pigment concentration,” AIAA J. 9, 1895–1898 (1971).
    [Crossref]
  22. G. Mie, “Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
    [Crossref]
  23. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  24. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).
  25. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).
  26. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  27. D. E. Müller, “A method for solving algebraic equations using an automatic computer,” Math. Tables Aids Computa. 10, 208–215 (1956).
    [Crossref]
  28. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1981).
  29. C. C. Lu, Y. M. Wang, W. C. Chew, L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random particles,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (IEEE, New York, 1993), pp. 1292–1295.

2000 (1)

P. R. Siqueira, K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
[Crossref]

1999 (2)

A. Nashashibi, K. Sarabandi, “Experimental characterization of the effective propagation constant of dense random media,” IEEE Trans. Antennas Propag. 47, 1454–1462 (1999).
[Crossref]

V. P. Dick, A. P. Ivanov, “Extinction of light in dispersive media with high particle concentrations: applicability limits of the interference approximation,” J. Opt. Soc. Am. A 16, 1034–1039 (1999).
[Crossref]

1997 (1)

K. Sarabandi, P. R. Siqueira, “Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity,” IEEE Trans. Antennas Propag. 45, 858–867 (1997).
[Crossref]

1996 (1)

P. R. Siqueira, K. Sarabandi, “Method of moment evaluation of the two-dimensional quasi-crystalline approximation,” IEEE Trans. Antennas Propag. 44, 1067–1096 (1996).
[Crossref]

1995 (1)

1994 (1)

R. West, D. Gibbs, L. Tsang, A. K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1834–1838 (1994).
[Crossref]

1992 (1)

L. Tsang, C. E. Mandt, K. H. Ding, “Monte-Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell equations,” Opt. Lett. 47, 314–317 (1992).
[Crossref]

1988 (1)

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

1986 (2)

J. D. Cartigny, Y. Yamada, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1—theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

Y. Yamada, J. D. Cartigny, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 2—experimental investigation,” J. Heat Transfer 108, 614–618 (1986).
[Crossref]

1982 (2)

A. Ishimaru, Y. Kuga, “Attenuation constant of coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
[Crossref]

L. Tsang, J. A. Kong, “Effective propagation constant for coherent electromagnetic wave propagation in media embedded with dielectric scatterers,” J. Appl. Phys. 53, 7162–7173 (1982).
[Crossref]

1971 (1)

H. C. Hottel, A. F. Sarofim, W. H. Dalzeel, L. A. Vasolos, “Optical properties of coatings. Effect of pigment concentration,” AIAA J. 9, 1895–1898 (1971).
[Crossref]

1964 (1)

J. B. Keller, “Stochastic equations and wave propagation in random media,” Proc. Symp. Appl. Math. 16, 145–170 (1964).
[Crossref]

1958 (1)

J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

1956 (1)

D. E. Müller, “A method for solving algebraic equations using an automatic computer,” Math. Tables Aids Computa. 10, 208–215 (1956).
[Crossref]

1908 (1)

G. Mie, “Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[Crossref]

Akkermans, E.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

Avrillier, S.

B. Gélebart, D. Ferrand, H. J. Schnorenberg, S. Avrillier, “Attenuation of a coherent field in a dense scattering medium,” in Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Mueller, eds., Proc. SPIE2626, 66–74 (1995).
[Crossref]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Cartigny, J. D.

Y. Yamada, J. D. Cartigny, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 2—experimental investigation,” J. Heat Transfer 108, 614–618 (1986).
[Crossref]

J. D. Cartigny, Y. Yamada, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1—theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

J. D. Cartigny, “Radiative transfer with dependent scattering of particles,” Ph.D. dissertation (University of California, Berkeley, California, 1984).

Chew, W. C.

C. C. Lu, Y. M. Wang, W. C. Chew, L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random particles,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (IEEE, New York, 1993), pp. 1292–1295.

Dalzeel, W. H.

H. C. Hottel, A. F. Sarofim, W. H. Dalzeel, L. A. Vasolos, “Optical properties of coatings. Effect of pigment concentration,” AIAA J. 9, 1895–1898 (1971).
[Crossref]

Dick, V. P.

Ding, K. H.

L. M. Zurk, L. Tsang, K. H. Ding, D. P. Winnebrenner, “Monte-Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries,” J. Opt. Soc. Am. A 12, 1772–1781 (1995).
[Crossref]

L. Tsang, C. E. Mandt, K. H. Ding, “Monte-Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell equations,” Opt. Lett. 47, 314–317 (1992).
[Crossref]

Ferrand, D.

B. Gélebart, D. Ferrand, H. J. Schnorenberg, S. Avrillier, “Attenuation of a coherent field in a dense scattering medium,” in Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Mueller, eds., Proc. SPIE2626, 66–74 (1995).
[Crossref]

Frisch, U.

U. Frisch, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A. Bharucha-Reid, ed. (Academic, New York, 1968), pp. 75–198.

Fung, A. K.

R. West, D. Gibbs, L. Tsang, A. K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1834–1838 (1994).
[Crossref]

Gélebart, B.

B. Gélebart, D. Ferrand, H. J. Schnorenberg, S. Avrillier, “Attenuation of a coherent field in a dense scattering medium,” in Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Mueller, eds., Proc. SPIE2626, 66–74 (1995).
[Crossref]

Gibbs, D.

R. West, D. Gibbs, L. Tsang, A. K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1834–1838 (1994).
[Crossref]

Hespel, L.

L. Hespel, “Etude expérimentale et théorique du transfert radiatif dans les milieux diffusants. Détermination expérimentale des propriétés radiatives aux forts taux de charge,” Ph.D. dissertation (Ecole Centrale, Paris, 1999).

Hottel, H. C.

H. C. Hottel, A. F. Sarofim, W. H. Dalzeel, L. A. Vasolos, “Optical properties of coatings. Effect of pigment concentration,” AIAA J. 9, 1895–1898 (1971).
[Crossref]

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1981).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishimaru, A.

Ivanov, A. P.

Keller, J. B.

J. B. Keller, “Stochastic equations and wave propagation in random media,” Proc. Symp. Appl. Math. 16, 145–170 (1964).
[Crossref]

Kong, J. A.

L. Tsang, J. A. Kong, “Effective propagation constant for coherent electromagnetic wave propagation in media embedded with dielectric scatterers,” J. Appl. Phys. 53, 7162–7173 (1982).
[Crossref]

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1982).

Kuga, Y.

Lu, C. C.

C. C. Lu, Y. M. Wang, W. C. Chew, L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random particles,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (IEEE, New York, 1993), pp. 1292–1295.

Mandt, C. E.

L. Tsang, C. E. Mandt, K. H. Ding, “Monte-Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell equations,” Opt. Lett. 47, 314–317 (1992).
[Crossref]

Maret, G.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

Maynard, R.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).

Mie, G.

G. Mie, “Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[Crossref]

Müller, D. E.

D. E. Müller, “A method for solving algebraic equations using an automatic computer,” Math. Tables Aids Computa. 10, 208–215 (1956).
[Crossref]

Nashashibi, A.

A. Nashashibi, K. Sarabandi, “Experimental characterization of the effective propagation constant of dense random media,” IEEE Trans. Antennas Propag. 47, 1454–1462 (1999).
[Crossref]

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

Percus, J. K.

J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

Sarabandi, K.

P. R. Siqueira, K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
[Crossref]

A. Nashashibi, K. Sarabandi, “Experimental characterization of the effective propagation constant of dense random media,” IEEE Trans. Antennas Propag. 47, 1454–1462 (1999).
[Crossref]

K. Sarabandi, P. R. Siqueira, “Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity,” IEEE Trans. Antennas Propag. 45, 858–867 (1997).
[Crossref]

P. R. Siqueira, K. Sarabandi, “Method of moment evaluation of the two-dimensional quasi-crystalline approximation,” IEEE Trans. Antennas Propag. 44, 1067–1096 (1996).
[Crossref]

Sarofim, A. F.

H. C. Hottel, A. F. Sarofim, W. H. Dalzeel, L. A. Vasolos, “Optical properties of coatings. Effect of pigment concentration,” AIAA J. 9, 1895–1898 (1971).
[Crossref]

Schnorenberg, H. J.

B. Gélebart, D. Ferrand, H. J. Schnorenberg, S. Avrillier, “Attenuation of a coherent field in a dense scattering medium,” in Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Mueller, eds., Proc. SPIE2626, 66–74 (1995).
[Crossref]

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1982).

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1981).

Siqueira, P. R.

P. R. Siqueira, K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
[Crossref]

K. Sarabandi, P. R. Siqueira, “Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity,” IEEE Trans. Antennas Propag. 45, 858–867 (1997).
[Crossref]

P. R. Siqueira, K. Sarabandi, “Method of moment evaluation of the two-dimensional quasi-crystalline approximation,” IEEE Trans. Antennas Propag. 44, 1067–1096 (1996).
[Crossref]

Tien, C. L.

J. D. Cartigny, Y. Yamada, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1—theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

Y. Yamada, J. D. Cartigny, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 2—experimental investigation,” J. Heat Transfer 108, 614–618 (1986).
[Crossref]

Tsang, L.

L. M. Zurk, L. Tsang, K. H. Ding, D. P. Winnebrenner, “Monte-Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries,” J. Opt. Soc. Am. A 12, 1772–1781 (1995).
[Crossref]

R. West, D. Gibbs, L. Tsang, A. K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1834–1838 (1994).
[Crossref]

L. Tsang, C. E. Mandt, K. H. Ding, “Monte-Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell equations,” Opt. Lett. 47, 314–317 (1992).
[Crossref]

L. Tsang, J. A. Kong, “Effective propagation constant for coherent electromagnetic wave propagation in media embedded with dielectric scatterers,” J. Appl. Phys. 53, 7162–7173 (1982).
[Crossref]

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1982).

C. C. Lu, Y. M. Wang, W. C. Chew, L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random particles,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (IEEE, New York, 1993), pp. 1292–1295.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vasolos, L. A.

H. C. Hottel, A. F. Sarofim, W. H. Dalzeel, L. A. Vasolos, “Optical properties of coatings. Effect of pigment concentration,” AIAA J. 9, 1895–1898 (1971).
[Crossref]

Wang, Y. M.

C. C. Lu, Y. M. Wang, W. C. Chew, L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random particles,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (IEEE, New York, 1993), pp. 1292–1295.

West, R.

R. West, D. Gibbs, L. Tsang, A. K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1834–1838 (1994).
[Crossref]

Winnebrenner, D. P.

Wolf, P. E.

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

Yamada, Y.

Y. Yamada, J. D. Cartigny, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 2—experimental investigation,” J. Heat Transfer 108, 614–618 (1986).
[Crossref]

J. D. Cartigny, Y. Yamada, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1—theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

Yevick, G. J.

J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

Zurk, L. M.

AIAA J. (1)

H. C. Hottel, A. F. Sarofim, W. H. Dalzeel, L. A. Vasolos, “Optical properties of coatings. Effect of pigment concentration,” AIAA J. 9, 1895–1898 (1971).
[Crossref]

Ann. Phys. (Leipzig) (1)

G. Mie, “Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[Crossref]

IEEE Trans. Antennas Propag. (4)

P. R. Siqueira, K. Sarabandi, “Method of moment evaluation of the two-dimensional quasi-crystalline approximation,” IEEE Trans. Antennas Propag. 44, 1067–1096 (1996).
[Crossref]

K. Sarabandi, P. R. Siqueira, “Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity,” IEEE Trans. Antennas Propag. 45, 858–867 (1997).
[Crossref]

P. R. Siqueira, K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
[Crossref]

A. Nashashibi, K. Sarabandi, “Experimental characterization of the effective propagation constant of dense random media,” IEEE Trans. Antennas Propag. 47, 1454–1462 (1999).
[Crossref]

J. Appl. Phys. (1)

L. Tsang, J. A. Kong, “Effective propagation constant for coherent electromagnetic wave propagation in media embedded with dielectric scatterers,” J. Appl. Phys. 53, 7162–7173 (1982).
[Crossref]

J. Heat Transfer (2)

J. D. Cartigny, Y. Yamada, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 1—theoretical investigation,” J. Heat Transfer 108, 608–613 (1986).
[Crossref]

Y. Yamada, J. D. Cartigny, C. L. Tien, “Radiative transfer with dependent scattering by particles: part 2—experimental investigation,” J. Heat Transfer 108, 614–618 (1986).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys. (Paris) (1)

P. E. Wolf, G. Maret, E. Akkermans, R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[Crossref]

Math. Tables Aids Computa. (1)

D. E. Müller, “A method for solving algebraic equations using an automatic computer,” Math. Tables Aids Computa. 10, 208–215 (1956).
[Crossref]

Opt. Lett. (1)

L. Tsang, C. E. Mandt, K. H. Ding, “Monte-Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell equations,” Opt. Lett. 47, 314–317 (1992).
[Crossref]

Phys. Rev. (1)

J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[Crossref]

Proc. Symp. Appl. Math. (1)

J. B. Keller, “Stochastic equations and wave propagation in random media,” Proc. Symp. Appl. Math. 16, 145–170 (1964).
[Crossref]

Other (11)

B. Gélebart, D. Ferrand, H. J. Schnorenberg, S. Avrillier, “Attenuation of a coherent field in a dense scattering medium,” in Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Mueller, eds., Proc. SPIE2626, 66–74 (1995).
[Crossref]

L. Hespel, “Etude expérimentale et théorique du transfert radiatif dans les milieux diffusants. Détermination expérimentale des propriétés radiatives aux forts taux de charge,” Ph.D. dissertation (Ecole Centrale, Paris, 1999).

J. D. Cartigny, “Radiative transfer with dependent scattering of particles,” Ph.D. dissertation (University of California, Berkeley, California, 1984).

U. Frisch, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A. Bharucha-Reid, ed. (Academic, New York, 1968), pp. 75–198.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1982).

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1981).

C. C. Lu, Y. M. Wang, W. C. Chew, L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random particles,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (IEEE, New York, 1993), pp. 1292–1295.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for collimated intensity measurement.

Fig. 2
Fig. 2

Extinction evolution (Ked/Kei is the dependent–independent extinction coefficient ratio) as function of the volume fraction f for the latex solutions: (a) K010 d=0.13 µm; (b) K070 d=0.67 µm; and (c) K200 d=1.98 µm. The measurements (Exp) are compared with the Keller approximate (app) and exact (exa) models and the coherent model.

Fig. 3
Fig. 3

Extinction coefficient (Ked/Kei is the dependent–independent extinction coefficient ratio) as function of the volume fraction f for the scattering medium defined by x=0.99 and =n2=1.038 (absolute values). The data obtained from Ref. 4 and their uncertainties are compared with the Keller model stated in the exact form and the approximate form.

Fig. 4
Fig. 4

Extinction coefficient (Ked/Kei is the dependent–independent extinction coefficient ratio) as function of the volume fraction f for the scattering medium defined by x=0.2 and =n2=3.2 (absolute values). The data obtained from Ref. 29 and their uncertainties are compared with the Keller model stated in the exact and the approximate form.

Fig. 5
Fig. 5

Experimental limits between independent (ind) and dependent scattering (dep) for the different latex solutions. The experimental limits are defined by ΔKext/Kext=5%. These limits are compared with the classical relation (Eq. 10) with c/λ=0.5. The exact values of d are 0.13, 0.525, 0.67, 1.03, 1.98, and 2.91 µm.

Tables (1)

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Table 1 Comparison of Measured (exp) and Calculated (Mie) Optical Thickness

Equations (12)

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P(rm, rn)=P(rm)P(rn)g(|rm-rn|,f)=P(rm)P(rn)+P(rm)P(rn)×[g(|rm-rn|,f)-1].
F(θ, f)=1+24f0R2[g(R, f)-1]sin (βR)βRdR,
β=nmatrix4πdλ0sin(θ/2),R=r/d,
Kextcoh(f)=γ(f)KextMie,
γ(f)=120πF(θ, f)P(θ)sin θdθ.
CRD=2πdλ0|nparticle-nmatrix|=2x|n-1|1,
k2=k02+4πiS(0)ρk-[4πS(0)ρ]2k20[g(r, ρ)-1]×exp(ik0r)sin(kr)kdr,
k2=k02+4πiS(0)ρk0-[4πS(0)ρ]2k020[g(r, ρ)-1]×exp(ik0r)sin(k0r)kdr.
k2=k02+4πiS(0)ρk0+[4πS(0)ρ]2k020dexp(ik0r)sin(k0r)kdr.
Kextdep-KextindKextind>0.05.
x=cλπf1/30.9047-f1/3,
loglogKextMieKextdep=0.25-5.1cλ0.

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