Abstract

The optical properties of films containing spherical particles in a nonabsorbing matrix have been modeled by using a four-flux radiative transfer theory. The forward average path-length parameter takes into account the different path lengths for collimated and diffuse components of the radiation field. This parameter, whose value was known only in special cases, has been used previously as a fitting quantity. We establish a method for evaluating the forward average path-length parameter in a rigorous way. Single-scattering parameters are evaluated from the Lorenz–Mie theory, and multiple-scattering effects are taken into account by means of an extended Hartel’s theory.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-flux models to solve the scattering transfer equation in terms of Lorenz–Mie parameters,” Appl. Opt. 23, 3353–3362 (1984).
    [CrossRef]
  2. Y. P. Wang, S. W. Zheng, K. F. Ren, “Four-flux model with adjusted average crossing parameter to solve the scattering transfer equation,” Appl. Opt. 28, 24–26 (1989).
    [CrossRef] [PubMed]
  3. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 10.
  4. G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, Berlin, 1969).
    [CrossRef]
  5. C. Sagan, J. B. Pollack, “Anisotropic nonconservative scattering and the clouds of venus,” J. Geophys. Res. 72, 469–477 (1967).
    [CrossRef]
  6. P. Kubelka, “New contributions to the optics of intensely light scattering materials. Part I,” J. Opt. Soc. Am. 38, 448–457 (1948).
    [CrossRef] [PubMed]
  7. P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology II,” J. Colloid Interface Sci. 39, 551–567 (1972).
    [CrossRef]
  8. W. Hartel, “Zur Theorie der Lichtstreuung durch trübe Schichten besonders Trübgläser,” Licht 10, 141–143, 165, 190, 191, 214, 215, 232–234 (1940).
  9. S. E. Orchard, “Multiple scattering by spherical dielectric particles,” J. Opt. Soc. Am. 55, 737 (1965).
    [CrossRef]
  10. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.
  11. C. M. Chu, S. W. Churchill, “Representation of the angular distribution of radiation scattered by a spherical particle,” J. Opt. Soc. Am. 45, 958–962 (1955).
    [CrossRef]
  12. G. C. Clark, C. M. Chu, S. W. Churchil, “Angular distribution coefficients for radiation scattered by a spherical particle,” J. Opt. Soc. Am. 47, 81–84 (1957).
    [CrossRef]

1989

1984

1972

P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology II,” J. Colloid Interface Sci. 39, 551–567 (1972).
[CrossRef]

1967

C. Sagan, J. B. Pollack, “Anisotropic nonconservative scattering and the clouds of venus,” J. Geophys. Res. 72, 469–477 (1967).
[CrossRef]

1965

1957

1955

1948

1940

W. Hartel, “Zur Theorie der Lichtstreuung durch trübe Schichten besonders Trübgläser,” Licht 10, 141–143, 165, 190, 191, 214, 215, 232–234 (1940).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.

Chu, C. M.

Churchil, S. W.

Churchill, S. W.

Clark, G. C.

Gouesbet, G.

Hartel, W.

W. Hartel, “Zur Theorie der Lichtstreuung durch trübe Schichten besonders Trübgläser,” Licht 10, 141–143, 165, 190, 191, 214, 215, 232–234 (1940).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 10.

Kortüm, G.

G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, Berlin, 1969).
[CrossRef]

Kubelka, P.

Letoulouzan, J. N.

Maheu, B.

Mudgett, P. S.

P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology II,” J. Colloid Interface Sci. 39, 551–567 (1972).
[CrossRef]

Orchard, S. E.

Pollack, J. B.

C. Sagan, J. B. Pollack, “Anisotropic nonconservative scattering and the clouds of venus,” J. Geophys. Res. 72, 469–477 (1967).
[CrossRef]

Ren, K. F.

Richards, L. W.

P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology II,” J. Colloid Interface Sci. 39, 551–567 (1972).
[CrossRef]

Sagan, C.

C. Sagan, J. B. Pollack, “Anisotropic nonconservative scattering and the clouds of venus,” J. Geophys. Res. 72, 469–477 (1967).
[CrossRef]

Wang, Y. P.

Zheng, S. W.

Appl. Opt.

J. Colloid Interface Sci.

P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology II,” J. Colloid Interface Sci. 39, 551–567 (1972).
[CrossRef]

J. Geophys. Res.

C. Sagan, J. B. Pollack, “Anisotropic nonconservative scattering and the clouds of venus,” J. Geophys. Res. 72, 469–477 (1967).
[CrossRef]

J. Opt. Soc. Am.

Licht

W. Hartel, “Zur Theorie der Lichtstreuung durch trübe Schichten besonders Trübgläser,” Licht 10, 141–143, 165, 190, 191, 214, 215, 232–234 (1940).

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 10.

G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, Berlin, 1969).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Forward average path-length parameter as a function of the optical depth for different size parameters. The particle volume fraction and free-space wavelength of the impinging radiation are 0.05 and 0.55 µm, respectively. For each case the particle refractive index divided by the matrix refractive index is also shown.

Equations (11)

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

ξ=01Iz, μdμ01Iz, μμdμ.
Iz, μ=i=0 ciz Piμ.
ciz=2i+14πj=1 Qjzωi/ω02i+1j,
dQ1dz=-ξ1α+βQ1+α exp-τ, dQjdz=-ξjα+β Qj+ξj-1αQj-1,
ωi=2i+1x2Qextn=1m=1n2n+12m+1nn+1mm+1×WnmηnmiInmi+VnmνnmiJnmi1+δnm,
Wnm=Reanam*+bnbm*, Vnm=Reanbm*+bnam*,
Inmi=-11πnπm+τnτmPiμdμ, Jnmi=-11πnτm+πmτnPiμdμ,
πn=dPndμ, τn=μ dPndμ-1-μ2d2Pndμ2,
Inmi=nn+1+mm+1-ii+12×n+i-m!m+i-n!n+m-i!n+m+i+1!×n+m+i2!n+i-m2!m+i-n2!n+m-i22,
Jnmi=n+m-in+i-m+1m+i-n+1×n+i-m+1!m+i-n+1!n+m-i-1!n+m+i+1!×n+m+i+12!n+i-m+12!m+i-n+12!n+m-i-12!2
ξ=21+n=1cngnc01+2c13c0+2 n=2 cnhnc0, with gn=01 Pnμdμ, hn=01 Pnμμdμ.

Metrics