Abstract

A size/shape distribution of spheroids was chosen to approximate a group of micrometer sized soil particles whose angular light scattering patterns had been measured previously. The scattering properties of the randomly oriented spheroids were calculated using the T-matrix method. The largest soil particles, those accounting for ~30% of the total scattering, were not included in the spheroid distribution because of computer limitations. These calculations were made to (1) investigate how well the measured scattering by soil particles is approximated by a similar distribution of spheroids and (2) use the data for spheroids to estimate some scattering properties that were too difficult to measure when the soil particles were studied previously. The shapes of the measured angular scattering patterns are better approximated by the distribution of spheroids than by a distribution of spheres of equal surface area or of equal volume.

© 1984 Optical Society of America

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References

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1981 (3)

E. M. Patterson, J. Geophys. Res. 86, 3236 (1981).
[CrossRef]

D. L. Jaggard et al., Atmos. Environ. 15, 2511 (1981).
[CrossRef]

D. W. Schuerman, R. T. Wang, B. A. S. Gustafson, R. W. Schaefer, Appl. Opt. 20, 4039 (1981).
[CrossRef] [PubMed]

1980 (1)

1979 (1)

K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 838 (1979).
[CrossRef]

1978 (1)

1977 (1)

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

1975 (1)

1971 (2)

P. C. Waterman, Phys. Rev. D 3, 825 (1971).
[CrossRef]

J. M. Greenberg, R. T. Wang, L. Bangs, Nature London 230, 110 (1971).
[CrossRef]

1970 (1)

1969 (1)

1963 (1)

1962 (1)

Asano, S.

Bangs, L.

J. M. Greenberg, R. T. Wang, L. Bangs, Nature London 230, 110 (1971).
[CrossRef]

Barber, P. W.

Cuzzi, J. N.

J. B. Pollack, J. N. Cuzzi, in Light Scattering Properties of Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 113.
[CrossRef]

Dave, J. V.

Fochtman, E. G.

J. D. Stockham, E. G. Fochtman, Particle Size Analysis (Ann Arbor Science, Ann Arbor, 1978), p. 10.

Gagne, G.

Gillette, D. A.

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

Glantz, M.

A. C. Hill, D. L. Jaggard, R. W. Shorthill, D. Stuart, M. Glantz, B. Taggart, S. Hammond, “Light Scattering Properties of Atmospheric Particles,” unpublished (Mar.1981).

Greenberg, J. M.

J. M. Greenberg, R. T. Wang, L. Bangs, Nature London 230, 110 (1971).
[CrossRef]

Greenleaves, I.

Gustafson, B. A. S.

Hammond, S.

A. C. Hill, D. L. Jaggard, R. W. Shorthill, D. Stuart, M. Glantz, B. Taggart, S. Hammond, “Light Scattering Properties of Atmospheric Particles,” unpublished (Mar.1981).

Hill, A. C.

A. C. Hill, D. L. Jaggard, R. W. Shorthill, D. Stuart, M. Glantz, B. Taggart, S. Hammond, “Light Scattering Properties of Atmospheric Particles,” unpublished (Mar.1981).

Hodkinson, J. R.

Holland, A. C.

Huffman, D. R.

Hunt, A. J.

Jaggard, D. L.

D. L. Jaggard et al., Atmos. Environ. 15, 2511 (1981).
[CrossRef]

A. C. Hill, D. L. Jaggard, R. W. Shorthill, D. Stuart, M. Glantz, B. Taggart, S. Hammond, “Light Scattering Properties of Atmospheric Particles,” unpublished (Mar.1981).

Kerker, M.

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), p. 91.

Liou, K. N.

K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 838 (1979).
[CrossRef]

Patterson, E. M.

E. M. Patterson, J. Geophys. Res. 86, 3236 (1981).
[CrossRef]

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

Penndorf, R.

Perry, R. J.

Pollack, J. B.

J. B. Pollack, J. N. Cuzzi, in Light Scattering Properties of Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 113.
[CrossRef]

Sassen, K.

K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 838 (1979).
[CrossRef]

Sato, M.

Schaefer, R. W.

Schuerman, D. W.

Shorthill, R. W.

A. C. Hill, D. L. Jaggard, R. W. Shorthill, D. Stuart, M. Glantz, B. Taggart, S. Hammond, “Light Scattering Properties of Atmospheric Particles,” unpublished (Mar.1981).

Stockham, J. D.

J. D. Stockham, E. G. Fochtman, Particle Size Analysis (Ann Arbor Science, Ann Arbor, 1978), p. 10.

Stockton, B. H.

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

Stuart, D.

A. C. Hill, D. L. Jaggard, R. W. Shorthill, D. Stuart, M. Glantz, B. Taggart, S. Hammond, “Light Scattering Properties of Atmospheric Particles,” unpublished (Mar.1981).

Taggart, B.

A. C. Hill, D. L. Jaggard, R. W. Shorthill, D. Stuart, M. Glantz, B. Taggart, S. Hammond, “Light Scattering Properties of Atmospheric Particles,” unpublished (Mar.1981).

van Hulst, H. C.

H. C. van Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 362ff.

Wang, R. T.

D. W. Schuerman, R. T. Wang, B. A. S. Gustafson, R. W. Schaefer, Appl. Opt. 20, 4039 (1981).
[CrossRef] [PubMed]

J. M. Greenberg, R. T. Wang, L. Bangs, Nature London 230, 110 (1971).
[CrossRef]

R. T. Wang, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 255.
[CrossRef]

Waterman, P. C.

P. C. Waterman, Phys. Rev. D 3, 825 (1971).
[CrossRef]

Yeh, C.

Appl. Opt. (6)

Atmos. Environ. (1)

D. L. Jaggard et al., Atmos. Environ. 15, 2511 (1981).
[CrossRef]

J. Atmos. Sci. (1)

K. Sassen, K. N. Liou, J. Atmos. Sci. 36, 838 (1979).
[CrossRef]

J. Geophys. Res. (2)

E. M. Patterson, J. Geophys. Res. 86, 3236 (1981).
[CrossRef]

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

J. Opt. Soc. Am. (2)

Nature London (1)

J. M. Greenberg, R. T. Wang, L. Bangs, Nature London 230, 110 (1971).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, Phys. Rev. D 3, 825 (1971).
[CrossRef]

Other (7)

R. T. Wang, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 255.
[CrossRef]

J. B. Pollack, J. N. Cuzzi, in Light Scattering Properties of Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 113.
[CrossRef]

H. C. van Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 362ff.

Ref. 16, p. 107ff.

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), p. 91.

J. D. Stockham, E. G. Fochtman, Particle Size Analysis (Ann Arbor Science, Ann Arbor, 1978), p. 10.

A. C. Hill, D. L. Jaggard, R. W. Shorthill, D. Stuart, M. Glantz, B. Taggart, S. Hammond, “Light Scattering Properties of Atmospheric Particles,” unpublished (Mar.1981).

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Figures (8)

Fig. 1
Fig. 1

Scanning electron micrographs of the soil particles investigated in this paper: (a) angle from the vertical is 60°; (b) angle from the vertical is 0°.

Fig. 2
Fig. 2

Distribution of the soil particles: (a) shape distribution in terms of the axial ratio (a/b) of the spheroids chosen to approximate the soil particles; (b) size distribution of the soil particle in terms of the size parameters of equal surface spheres (xg = 2πrg/wavelength).

Fig. 3
Fig. 3

Example normalized scattering cross sections (Csct/πr2) plotted against the size parameters for equal volume spheres. The rapidly oscillating curve represents the normalized cross section for spheres (Qe = Csct/πr2).

Fig. 4
Fig. 4

Average normalized scattering cross sections plotted against the size parameters for equal volume spheres. The upper smooth curve is C sct / π r v 2. The lower smooth curve is C sct / π r g 2. The curve for spheres is also shown.

Fig. 5
Fig. 5

Normalized forward scattering, σ ( 0 ) / ( π r g 2 ) for spheroids (the solid smooth line), [i(0)]/(πx2) for spheres (the solid oscillating line).

Fig. 6
Fig. 6

(a)–(f) Calculated angular scattering by individual spheroids. The spheroids have rg − 0.3(0.2)1.5,1.67. The scattering by each larger spheroid is offset upward by 1.0 log.

Fig. 7
Fig. 7

Calculated angular scattering by a distribution of spheroids and by a distribution of equal surface area spheres. The size/shape distribution is as in Fig. 2 except that particles having xg > 20 are not included.

Fig. 8
Fig. 8

Measured angular scattering by a distribution of soil particles and calculated angular scattering by a distribution of equal surface area spheres. For the measured scattering curve the first 5 and last 6° have been estimated. Also the relative position of the measured curve was adjusted as described in the text.

Tables (1)

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Table I Shape Parameters and Surface Equivalent Radii of the 37 Spheroids Used to Compute the Average Angular Scattering

Equations (4)

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C ext / π r 2 = 2.0 + 2.05 x - 2 / 3 .
C ext G ¯ = C ext A / 4 = 2 ,
C abs / π r 2 = 0.224 x 1 / 3 - 0.24.
C ext = ( λ 2 / π ) Re { S ( 0 ) } ,

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