Abstract

The anomalous-diffraction theory (ADT) of extinction of light by soft particles is shown to be determined by a statistical distribution of the geometrical paths of individual rays inside the particles. Light extinction depends on the mean and the mean-squared geometrical paths of the rays. Analytical formulas for optical efficiencies from a Gaussian distribution of the geometrical paths of rays are derived. This Gaussian ray approximation reduces to the exact ADT in the intermediate case of light scattering for an arbitrary soft particle and describes well the extinction of light from a system of randomly oriented and (or) polydisperse particles. The implications for probing of the sizes and shapes of particles by light extinction are discussed.

© 2003 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  2. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, San Diego, Calif., 1999).
  3. S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
    [CrossRef]
  4. W. A. Farone and M. J. I. Robinson, Appl. Opt. 7, 643 (1968).
    [CrossRef] [PubMed]
  5. F. D. Bryant and P. Latimer, J. Colloid Interface Sci. 30, 291 (1969).
    [CrossRef]
  6. Y. Liu, W. P. Arnott, and J. Hallett, Appl. Opt. 37, 5019 (1998).
    [CrossRef]
  7. J. F. Hansen and L. D. Travis, Space Sci. Rev. 16, 527 (1974).
    [CrossRef]
  8. M. G. Kendall, Kendall’s Advanced Theory of Statistics (Oxford U. Press, Oxford, 1999).
  9. P. Chýlek and J. Li, Opt. Commun. 117, 389 (1995).
    [CrossRef]
  10. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  11. A. A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Wiley, New York, 1999).
  12. L. E. Paramonov, Opt. Spektrosk. 77, 660 (1994).

1998

1995

P. Chýlek and J. Li, Opt. Commun. 117, 389 (1995).
[CrossRef]

1994

L. E. Paramonov, Opt. Spektrosk. 77, 660 (1994).

1987

S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
[CrossRef]

1974

J. F. Hansen and L. D. Travis, Space Sci. Rev. 16, 527 (1974).
[CrossRef]

1969

F. D. Bryant and P. Latimer, J. Colloid Interface Sci. 30, 291 (1969).
[CrossRef]

1968

Ackerman, S. A.

S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
[CrossRef]

Arnott, W. P.

Bohren, C. F.

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

Bryant, F. D.

F. D. Bryant and P. Latimer, J. Colloid Interface Sci. 30, 291 (1969).
[CrossRef]

Chýlek, P.

P. Chýlek and J. Li, Opt. Commun. 117, 389 (1995).
[CrossRef]

Farone, W. A.

Hallett, J.

Hansen, J. F.

J. F. Hansen and L. D. Travis, Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Huffman, D. R.

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

Kendall, M. G.

M. G. Kendall, Kendall’s Advanced Theory of Statistics (Oxford U. Press, Oxford, 1999).

Kokhanovsky, A. A.

A. A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Wiley, New York, 1999).

Latimer, P.

F. D. Bryant and P. Latimer, J. Colloid Interface Sci. 30, 291 (1969).
[CrossRef]

Li, J.

P. Chýlek and J. Li, Opt. Commun. 117, 389 (1995).
[CrossRef]

Liu, Y.

Paramonov, L. E.

L. E. Paramonov, Opt. Spektrosk. 77, 660 (1994).

Robinson, M. J. I.

Stephens, G. L.

S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
[CrossRef]

Travis, L. D.

J. F. Hansen and L. D. Travis, Space Sci. Rev. 16, 527 (1974).
[CrossRef]

van de Hulst, H. C.

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

Appl. Opt.

J. Atmos. Sci.

S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
[CrossRef]

J. Colloid Interface Sci.

F. D. Bryant and P. Latimer, J. Colloid Interface Sci. 30, 291 (1969).
[CrossRef]

Opt. Commun.

P. Chýlek and J. Li, Opt. Commun. 117, 389 (1995).
[CrossRef]

Opt. Spektrosk.

L. E. Paramonov, Opt. Spektrosk. 77, 660 (1994).

Space Sci. Rev.

J. F. Hansen and L. D. Travis, Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Other

M. G. Kendall, Kendall’s Advanced Theory of Statistics (Oxford U. Press, Oxford, 1999).

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

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, San Diego, Calif., 1999).

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

A. A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Wiley, New York, 1999).

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Figures (2)

Fig. 1
Fig. 1

Ray distributions for a spheroid at a fixed orientation χ=0 (FX), randomly oriented (RN), polydisperse at a fixed orientation (POL FX), and randomly oriented polydisperse (POL RN). The axial ratio of the spheroid is (a) =2 and (b) =0.5. Log-normal size distribution nx with am=1 and σ=0.2 is also plotted as insets.

Fig. 2
Fig. 2

Extinction and absorption efficiencies of (a) a sphere and (b) a polydisperse sphere with a log-normal radius distribution of am=1 and σ=0.2 calculated with Mie, ADT, and Gaussian ray approximations. Complex refractive index, m=1.05-i0.0005. The size distribution has already been shown as insets in Fig. 1.

Equations (11)

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Qext=2PRP1-exp-iklmr-1×exp-klmidP,  Qabs=1PP1-exp-2klmidP,  Qsca=Qext-Qabs,
Q¯=PQP.
Qext=2R1-exp-iklmr-1×exp-klmipldl,  Qabs=1-exp-2klmipldl.
ppoll=1/xp0l/xnxx2dxnxx2dx,
p0l=12-2 sin2χ+cos2 χlHl×H2-2 sin2 χ+cos2 χ1/2-l,
nx=12π1/2σr-1 exp-ln2r/am2σ2,
ppoll=-2 sin2 χ+cos2 χl4×erfc1/2σln-2 sin2 χ+cos2 χ1/2l/2amam2 exp2σ2
ppol,rnl=01ppollπ2-2 sin2 χ+cos2 χ1/2d cos χ01π2-2 sin2 χ+cos2 χ1/2d cos χ
px=12πσ exp-x-μ22σ2.
Qext=2-2 coskmr-1μ-kσ2mi×exp-kμmi-k2σ2mr-12-mi22,  Qabs=1-exp-2kmiμ-kmiσ2
Qext=2kmil+k2mr-12-mi2l2,  Qabs=2kmil-2k2mi2l2,  Qsca=k2m-12l2,

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