Abstract

The simple equation for the spherical albedo of a semi-infinite turbid medium is obtained. The accuracy of the approximation was studied with the numerical solution of the radiative transfer equation. The error is smaller than 10% for water clouds in the visible and the near infrared.

© 1998 Optical Society of America

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References

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  1. E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
  2. L. T. Perelman, J. Wu, I. Itzkan, M. S. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1343 (1994).
    [CrossRef] [PubMed]
  3. G. V. Rozenberg, “Optical characteristics of thick weakly absorbing scattering layers,” Dokl. AN SSSR 145, 775–777 (1962).

1994 (1)

L. T. Perelman, J. Wu, I. Itzkan, M. S. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1343 (1994).
[CrossRef] [PubMed]

1962 (1)

G. V. Rozenberg, “Optical characteristics of thick weakly absorbing scattering layers,” Dokl. AN SSSR 145, 775–777 (1962).

Feld, M. S.

L. T. Perelman, J. Wu, I. Itzkan, M. S. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1343 (1994).
[CrossRef] [PubMed]

Itzkan, I.

L. T. Perelman, J. Wu, I. Itzkan, M. S. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1343 (1994).
[CrossRef] [PubMed]

Ivanov, A. P.

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

Katsev, I. L.

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

Perelman, L. T.

L. T. Perelman, J. Wu, I. Itzkan, M. S. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1343 (1994).
[CrossRef] [PubMed]

Rozenberg, G. V.

G. V. Rozenberg, “Optical characteristics of thick weakly absorbing scattering layers,” Dokl. AN SSSR 145, 775–777 (1962).

Wu, J.

L. T. Perelman, J. Wu, I. Itzkan, M. S. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1343 (1994).
[CrossRef] [PubMed]

Zege, E. P.

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

Dokl. AN SSSR (1)

G. V. Rozenberg, “Optical characteristics of thick weakly absorbing scattering layers,” Dokl. AN SSSR 145, 775–777 (1962).

Phys. Rev. Lett. (1)

L. T. Perelman, J. Wu, I. Itzkan, M. S. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1343 (1994).
[CrossRef] [PubMed]

Other (1)

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

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Figures (2)

Fig. 1
Fig. 1

Dependence of the spherical albedo of a semi-infinite medium on the single scattering albedo at g=0.85, calculationed with Eq. (8) (solid curve) and with Eq. (10) (dashed curve).

Fig. 2
Fig. 2

Dependence of the spherical albedo of a semi-infinite water cloud with particle size distribution (11) on the wavelength, calculated with Eq. (8) (solid curve) and with the numerical solution of the radiative transfer equation (symbols).

Equations (11)

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R=2π01µdμ01μ0dμ002πr(μ, μ0, ψ)dψ,
g=120πp(θ)cos θ sin θdθ
R=exp-αln 1ω1-g1/2,
R=1-41-ω3(1-g)1/2.
R=1-α1-ω1-g1/2,
limω1ln1ω=1-ω
α=43.
R=exp-4ln 1ω3(1-g)1/2.
limω0 R(ω)=0,limω1 R(ω)=1,
R=exp-41-ω3(1-g)1/2.
f(a)=Ba6 exp(-1.5a),

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