Abstract

The passage of light through dispersion layers consisting of large weakly absorbing scatterers has been investigated. Measurements of the transmittance and the angular structure of scattered radiation have been made. The dependence of these characteristics on the thickness and the concentration of scatterers has been analyzed.

© 1999 Optical Society of America

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References

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  1. O. D. Chvolson, “Einer matematischen theorie. Der enner defusion des lightes,” Bull. Acad. Imp. Sci. St. Petersbourg, 13, Book 3, 83–101 (1889).
  2. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  3. V. V. Sobolev, Radiant Energy Transfer in the Atmosphere of Stars and Planets (Gosteorizgat, Moscow, 1956), in Russian.
  4. I. Ya. Minin, Radiation Transfer Theory in the Atmosphere of Planets (Nauka, Moscow, 1988), in Russian.
  5. E. P. Zege, I. L. Katsev, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
    [CrossRef]
  6. A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Densely Packed Disperse Media (NaukaTechnika, Minsk, 1988), in Russian.
  7. Yu. N. Barabanenkov “On relative increase in the radiation extinction length as a result of correlation of weak scatterers,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 18, 720–726 (1982), in Russian.
  8. A. Ishimaru, Y. Kuga, “Attenuation constant of a coherent field in dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
    [CrossRef]
  9. Yu. N. Barabanenkov, Yu. A. Kravtsov, S. M. Rytov, V. I. Tatarsky, “The state of the theory of waves distribution in a random medium,” Usp. Fiz. Nauk 1, 3–42 (1970), in Russian.
  10. S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
    [CrossRef]
  11. V. L. Kuzmin, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 166, 247–278 (1996), in Russian.
    [CrossRef]
  12. L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).
  13. S. Fraden, G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
    [CrossRef] [PubMed]
  14. V. Twersky, “Propagation in pair-correlated distributions of small-spaced lossy scatterers,” J. Opt. Soc. Am. 69, 1567–1572 (1979).
    [CrossRef]
  15. C. J. Walled, “Multiple scattering of classical waves in systems with liquidlike correlations: formulation as a liquid-state theory,” Phys. Rev. E 52, 3115–3126 (1995).
    [CrossRef]
  16. C. M. Scukoulis, S. Datta, E. N. Economou, “Propogation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
    [CrossRef]
  17. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, Orlando, Fla., 1978), Vol. 2, Chap. 14.
  18. 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, 1854–1858 (1994).
    [CrossRef]
  19. V. P. Dick, V. A. Loiko, A. P. Ivanov, “Light transmission by a monolayer of particles: comparison of experimental data with calculation as a single scattering approximation,” Appl. Opt. 36, 6119–6122 (1997).
    [CrossRef] [PubMed]
  20. V. P. Dick, V. A. Loiko, A. P. Ivanov, “Angular structure of radiation scattered by monolayer of particles: experimental study,” Appl. Opt. 36, 4235–4240 (1997).
    [CrossRef] [PubMed]
  21. J. M. ZimanModels of Disorders (Cambridge U. Press, Cambridge, UK, 1979), Chap. 4.

1997 (2)

1996 (1)

V. L. Kuzmin, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 166, 247–278 (1996), in Russian.
[CrossRef]

1995 (1)

C. J. Walled, “Multiple scattering of classical waves in systems with liquidlike correlations: formulation as a liquid-state theory,” Phys. Rev. E 52, 3115–3126 (1995).
[CrossRef]

1994 (2)

1991 (1)

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

1990 (1)

S. Fraden, G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[CrossRef] [PubMed]

1982 (2)

Yu. N. Barabanenkov “On relative increase in the radiation extinction length as a result of correlation of weak scatterers,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 18, 720–726 (1982), in Russian.

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

1979 (1)

1970 (1)

Yu. N. Barabanenkov, Yu. A. Kravtsov, S. M. Rytov, V. I. Tatarsky, “The state of the theory of waves distribution in a random medium,” Usp. Fiz. Nauk 1, 3–42 (1970), in Russian.

1889 (1)

O. D. Chvolson, “Einer matematischen theorie. Der enner defusion des lightes,” Bull. Acad. Imp. Sci. St. Petersbourg, 13, Book 3, 83–101 (1889).

Barabanenkov, Yu. N.

Yu. N. Barabanenkov “On relative increase in the radiation extinction length as a result of correlation of weak scatterers,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 18, 720–726 (1982), in Russian.

Yu. N. Barabanenkov, Yu. A. Kravtsov, S. M. Rytov, V. I. Tatarsky, “The state of the theory of waves distribution in a random medium,” Usp. Fiz. Nauk 1, 3–42 (1970), in Russian.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Chvolson, O. D.

O. D. Chvolson, “Einer matematischen theorie. Der enner defusion des lightes,” Bull. Acad. Imp. Sci. St. Petersbourg, 13, Book 3, 83–101 (1889).

Datta, S.

C. M. Scukoulis, S. Datta, E. N. Economou, “Propogation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

Dick, V. P.

Economou, E. N.

C. M. Scukoulis, S. Datta, E. N. Economou, “Propogation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

Fraden, S.

S. Fraden, G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[CrossRef] [PubMed]

Fung, A. K.

Gibbs, D.

Ishimaru, A.

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

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, Orlando, Fla., 1978), Vol. 2, Chap. 14.

Ivanov, A. P.

John, S.

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

Katsev, I. L.

E. P. Zege, I. L. Katsev, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

Kong, J.

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).

Kravtsov, Yu. A.

Yu. N. Barabanenkov, Yu. A. Kravtsov, S. M. Rytov, V. I. Tatarsky, “The state of the theory of waves distribution in a random medium,” Usp. Fiz. Nauk 1, 3–42 (1970), in Russian.

Kuga, Y.

Kuzmin, V. L.

V. L. Kuzmin, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 166, 247–278 (1996), in Russian.
[CrossRef]

Loiko, V. A.

Maret, G.

S. Fraden, G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[CrossRef] [PubMed]

Minin, I. Ya.

I. Ya. Minin, Radiation Transfer Theory in the Atmosphere of Planets (Nauka, Moscow, 1988), in Russian.

Romanov, V. P.

V. L. Kuzmin, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 166, 247–278 (1996), in Russian.
[CrossRef]

Rytov, S. M.

Yu. N. Barabanenkov, Yu. A. Kravtsov, S. M. Rytov, V. I. Tatarsky, “The state of the theory of waves distribution in a random medium,” Usp. Fiz. Nauk 1, 3–42 (1970), in Russian.

Scukoulis, C. M.

C. M. Scukoulis, S. Datta, E. N. Economou, “Propogation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

Shin, R.

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).

Sobolev, V. V.

V. V. Sobolev, Radiant Energy Transfer in the Atmosphere of Stars and Planets (Gosteorizgat, Moscow, 1956), in Russian.

Tatarsky, V. I.

Yu. N. Barabanenkov, Yu. A. Kravtsov, S. M. Rytov, V. I. Tatarsky, “The state of the theory of waves distribution in a random medium,” Usp. Fiz. Nauk 1, 3–42 (1970), in Russian.

Tsang, L.

Twersky, V.

Walled, C. J.

C. J. Walled, “Multiple scattering of classical waves in systems with liquidlike correlations: formulation as a liquid-state theory,” Phys. Rev. E 52, 3115–3126 (1995).
[CrossRef]

West, R.

Zege, E. P.

E. P. Zege, I. L. Katsev, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

Ziman, J. M.

J. M. ZimanModels of Disorders (Cambridge U. Press, Cambridge, UK, 1979), Chap. 4.

Appl. Opt. (2)

Bull. Acad. Imp. Sci. St. Petersbourg (1)

O. D. Chvolson, “Einer matematischen theorie. Der enner defusion des lightes,” Bull. Acad. Imp. Sci. St. Petersbourg, 13, Book 3, 83–101 (1889).

Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana (1)

Yu. N. Barabanenkov “On relative increase in the radiation extinction length as a result of correlation of weak scatterers,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 18, 720–726 (1982), in Russian.

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Phys. Rev. B (1)

C. M. Scukoulis, S. Datta, E. N. Economou, “Propogation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

Phys. Rev. E (1)

C. J. Walled, “Multiple scattering of classical waves in systems with liquidlike correlations: formulation as a liquid-state theory,” Phys. Rev. E 52, 3115–3126 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

S. Fraden, G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[CrossRef] [PubMed]

Phys. Today (1)

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

Usp. Fiz. Nauk (2)

V. L. Kuzmin, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 166, 247–278 (1996), in Russian.
[CrossRef]

Yu. N. Barabanenkov, Yu. A. Kravtsov, S. M. Rytov, V. I. Tatarsky, “The state of the theory of waves distribution in a random medium,” Usp. Fiz. Nauk 1, 3–42 (1970), in Russian.

Other (8)

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

V. V. Sobolev, Radiant Energy Transfer in the Atmosphere of Stars and Planets (Gosteorizgat, Moscow, 1956), in Russian.

I. Ya. Minin, Radiation Transfer Theory in the Atmosphere of Planets (Nauka, Moscow, 1988), in Russian.

E. P. Zege, I. L. Katsev, A. P. Ivanov, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Densely Packed Disperse Media (NaukaTechnika, Minsk, 1988), in Russian.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, Orlando, Fla., 1978), Vol. 2, Chap. 14.

J. M. ZimanModels of Disorders (Cambridge U. Press, Cambridge, UK, 1979), Chap. 4.

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Figures (8)

Fig. 1
Fig. 1

Transmittance versus overlap coefficient for the slab of latex particles with diameter d = 3.75 µm in water at λ = 420 nm and λ = 650 nm for several values of C v and FOV: C v < 0.006, FOV = 4.6° (open circles); C v = 0.4, FOV = 4.6° (filled circles); C v < 0.006, FOV = 35 arc min (open triangles); and C v < 0.4, FOV = 35 arc min (filled triangles). Solid and dashed curves join points that are experimental results.

Fig. 2
Fig. 2

Transmittance versus overlap coefficient for the slab of rice starch particles with modal size of particles d mod = 6.4 µm in water at λ = 650 nm for several values of C v and FOV: C v < 0.006, FOV = 4.6° (open circles); C v = 0.4, FOV = 4.6° (filled circles); C v < 0.006, FOV = 35 arc min (open triangles); and C v < 0.4, FOV = 35 arc min (filled triangle). Solid and dashed curves join points that are experimental results.

Fig. 3
Fig. 3

Transmittance versus overlap coefficient for the slab of rice starch particles (d mod = 6.4 µm) in a mixture of alcohols at λ = 650 nm for several values of C v and FOV: C v < 0.006, FOV = 4.6° (open circles); C v = 0.4, FOV = 4.6° (filled circles); C v < 0.006, FOV = 35 arc min (open triangles); and C v < 0.4, FOV = 35 arc min (filled triangles). Solid and dashed curves join points that are experimental results.

Fig. 4
Fig. 4

Transmittance versus overlap coefficient for the slab of rice starch particles (d mod = 6.4 µm) in a mixture of alcohols at λ = 650 nm for C v < 0.006 (open circles, squares, and triangles); C v = 0.23 (filled squares); C v = 0.4 (filled triangles); and C v = 0.5 (filled circles). Solid and dashed curves joint points that are experimental results.

Fig. 5
Fig. 5

Structural factor versus μ = 4x sin(θ/2) at various values of C v .

Fig. 6
Fig. 6

Scattering intensity angular distribution for the slab of latex particles (d = 3.75 µm) in water at various values of η at λ = 420 nm and λ = 650 nm. C v = 0.4 (solid curves); C v < 0.006 (dashed curves).

Fig. 7
Fig. 7

Scattering intensity angular distribution for the slab of rice starch d mod = 6.4 µm in water at various values of η at λ = 650 nm. C v = 0.5 (solid curves); C v < 0.005 (dashed curves).

Fig. 8
Fig. 8

Scattering intensity angular distribution for the slab of rice starch particles in a mixture of alcohols at various values of η at λ = 650 nm. C v = 0.4 (solid curves); C v = 0.005 (dashed curves).

Equations (2)

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Jθ=PΛQpθSθ.
Sθ=1+24Cv0Wz-1z2sin μzμzdz

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