Abstract

The calculated angular scattering properties of over 250 randomly oriented nonspherical Chebyshev particles are examined for the effect of three factors: size; concavity vs convexity; and amount of deformation from a sphere. Both shape and size averaging are performed to reveal general features of the angular scattering not discernible for particular shapes and sizes. Comparisons with a comparably extensive experimental study published by Zerull in 1976 reveal remarkable qualitative similarities, even though Zerull used greatly different shapes from ours. This augurs well for the eventual development of a general theory of nonspherical scattering, although such a theory must account for concavity in addition to the amount of deviation from a sphere; and it cannot be entirely deterministic, as the third paper in this series will argue.

© 1988 Optical Society of America

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References

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  1. A. Mugnai, W. J. Wiscombe, “Scattering from Nonspherical Chebyshev Particles. 1: Cross Sections, Single-Scattering Albedo, Asymmetry Factor, and Backscattered Fraction,” Appl. Opt. 25, 1235 (1986).
    [Crossref] [PubMed]
  2. A. Mugnai, W. J. Wiscombe, “Scattering from Nonspherical Chebyshev Particles. 3: Variability of Angular Scattering Patterns,” Appl. Opt. (in preparation).
  3. A. Mugnai, W. J. Wiscombe, “Scattering of Radiation by Moderately Nonspherical Particles,” J. Atmos. Sci. 37, 1291 (1980).
    [Crossref]
  4. W. J. Wiscombe, A. Mugnai, “Single Scattering from Nonspherical Chebyshev Particles: a Compendium of Calculations,” NASA Ref. Publ. 1157 (NASA/Goddard Space Flight Center, Greenbelt, MD, 1986).
  5. R. H. Zerull, “Scattering Measurements of Dielectric and Absorbing Nonspherical Particles,” Beitr. Phys. Atmos. 49, 166 (1976).
  6. D. W. Schuerman, R. Wang, B. Gustafson, R. Schaefer, “Systematic Studies of Light Scattering. 1: Particle Shape,” Appl. Opt. 20, 4039 (1981).
    [Crossref] [PubMed]
  7. A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113 (1970).
    [Crossref] [PubMed]
  8. R. Perry, A. Hunt, D. Huffman, “Experimental Determination of Mueller Scattering Matrices for Nonspherical Particles,” Appl. Opt. 17, 2700 (1978).
    [Crossref] [PubMed]
  9. J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurements for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 283.
    [Crossref]
  10. A. Coletti, “Light Scattering by Nonspherical Particles: A Laboratory Study,” Aerosol Sci. 3, 39 (1984).
    [Crossref]
  11. S. Shipley, J. Weinman, “A Numerical Study of Scattering by Large Dielectric Spheres,” J. Opt. Soc. Am. 68, 130 (1978).
    [Crossref]
  12. D. J. Kennison, “AUTOGRAPH: The Unabridged Write-up,” NCAR Tech. Note NCAR/TN-245+IA (National Center for Atmospheric Research, Boulder, CO, 1985).
  13. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981; reprinted from 1957 edition).
  14. S. Asano, M. Sato, “Light Scattering by Randomly Oriented Spheroidal Particles,” Appl. Opt. 19, 962 (1980).
    [Crossref] [PubMed]
  15. V. Erma, “Perturbation Solution for the Scattering of Electromagnetic Waves from Conductors of Arbitrary Shape. II. General Case,” Phys. Rev. 176, 1544 (1968).
    [Crossref]
  16. J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation Approach to Light Scattering by Nonspherical Particles,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 135.
    [Crossref]
  17. J. B. Pollack, J. N. Cuzzi, “Scattering by Nonspherical Particles of Size Comparable to a Wavelength: a New Semi-Empirical Theory and Its Application to Tropospheric Aerosols,” J. Atmos. Sci. 37, 868 (1980).
    [Crossref]

1986 (1)

1984 (1)

A. Coletti, “Light Scattering by Nonspherical Particles: A Laboratory Study,” Aerosol Sci. 3, 39 (1984).
[Crossref]

1981 (1)

1980 (3)

A. Mugnai, W. J. Wiscombe, “Scattering of Radiation by Moderately Nonspherical Particles,” J. Atmos. Sci. 37, 1291 (1980).
[Crossref]

S. Asano, M. Sato, “Light Scattering by Randomly Oriented Spheroidal Particles,” Appl. Opt. 19, 962 (1980).
[Crossref] [PubMed]

J. B. Pollack, J. N. Cuzzi, “Scattering by Nonspherical Particles of Size Comparable to a Wavelength: a New Semi-Empirical Theory and Its Application to Tropospheric Aerosols,” J. Atmos. Sci. 37, 868 (1980).
[Crossref]

1978 (2)

1976 (1)

R. H. Zerull, “Scattering Measurements of Dielectric and Absorbing Nonspherical Particles,” Beitr. Phys. Atmos. 49, 166 (1976).

1970 (1)

1968 (1)

V. Erma, “Perturbation Solution for the Scattering of Electromagnetic Waves from Conductors of Arbitrary Shape. II. General Case,” Phys. Rev. 176, 1544 (1968).
[Crossref]

Asano, S.

Bottiger, J. R.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurements for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 283.
[Crossref]

Chylek, P.

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation Approach to Light Scattering by Nonspherical Particles,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 135.
[Crossref]

Coletti, A.

A. Coletti, “Light Scattering by Nonspherical Particles: A Laboratory Study,” Aerosol Sci. 3, 39 (1984).
[Crossref]

Cuzzi, J. N.

J. B. Pollack, J. N. Cuzzi, “Scattering by Nonspherical Particles of Size Comparable to a Wavelength: a New Semi-Empirical Theory and Its Application to Tropospheric Aerosols,” J. Atmos. Sci. 37, 868 (1980).
[Crossref]

Erma, V.

V. Erma, “Perturbation Solution for the Scattering of Electromagnetic Waves from Conductors of Arbitrary Shape. II. General Case,” Phys. Rev. 176, 1544 (1968).
[Crossref]

Fry, E. S.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurements for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 283.
[Crossref]

Gagne, G.

Gustafson, B.

Holland, A. C.

Huffman, D.

Hunt, A.

Kennison, D. J.

D. J. Kennison, “AUTOGRAPH: The Unabridged Write-up,” NCAR Tech. Note NCAR/TN-245+IA (National Center for Atmospheric Research, Boulder, CO, 1985).

Kiehl, J. T.

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation Approach to Light Scattering by Nonspherical Particles,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 135.
[Crossref]

Ko, M. W.

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation Approach to Light Scattering by Nonspherical Particles,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 135.
[Crossref]

Mugnai, A.

A. Mugnai, W. J. Wiscombe, “Scattering from Nonspherical Chebyshev Particles. 1: Cross Sections, Single-Scattering Albedo, Asymmetry Factor, and Backscattered Fraction,” Appl. Opt. 25, 1235 (1986).
[Crossref] [PubMed]

A. Mugnai, W. J. Wiscombe, “Scattering of Radiation by Moderately Nonspherical Particles,” J. Atmos. Sci. 37, 1291 (1980).
[Crossref]

A. Mugnai, W. J. Wiscombe, “Scattering from Nonspherical Chebyshev Particles. 3: Variability of Angular Scattering Patterns,” Appl. Opt. (in preparation).

W. J. Wiscombe, A. Mugnai, “Single Scattering from Nonspherical Chebyshev Particles: a Compendium of Calculations,” NASA Ref. Publ. 1157 (NASA/Goddard Space Flight Center, Greenbelt, MD, 1986).

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation Approach to Light Scattering by Nonspherical Particles,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 135.
[Crossref]

Perry, R.

Pollack, J. B.

J. B. Pollack, J. N. Cuzzi, “Scattering by Nonspherical Particles of Size Comparable to a Wavelength: a New Semi-Empirical Theory and Its Application to Tropospheric Aerosols,” J. Atmos. Sci. 37, 868 (1980).
[Crossref]

Sato, M.

Schaefer, R.

Schuerman, D. W.

Shipley, S.

Thompson, R. C.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurements for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 283.
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981; reprinted from 1957 edition).

Wang, R.

Weinman, J.

Wiscombe, W. J.

A. Mugnai, W. J. Wiscombe, “Scattering from Nonspherical Chebyshev Particles. 1: Cross Sections, Single-Scattering Albedo, Asymmetry Factor, and Backscattered Fraction,” Appl. Opt. 25, 1235 (1986).
[Crossref] [PubMed]

A. Mugnai, W. J. Wiscombe, “Scattering of Radiation by Moderately Nonspherical Particles,” J. Atmos. Sci. 37, 1291 (1980).
[Crossref]

W. J. Wiscombe, A. Mugnai, “Single Scattering from Nonspherical Chebyshev Particles: a Compendium of Calculations,” NASA Ref. Publ. 1157 (NASA/Goddard Space Flight Center, Greenbelt, MD, 1986).

A. Mugnai, W. J. Wiscombe, “Scattering from Nonspherical Chebyshev Particles. 3: Variability of Angular Scattering Patterns,” Appl. Opt. (in preparation).

Zerull, R. H.

R. H. Zerull, “Scattering Measurements of Dielectric and Absorbing Nonspherical Particles,” Beitr. Phys. Atmos. 49, 166 (1976).

Aerosol Sci. (1)

A. Coletti, “Light Scattering by Nonspherical Particles: A Laboratory Study,” Aerosol Sci. 3, 39 (1984).
[Crossref]

Appl. Opt. (5)

Beitr. Phys. Atmos. (1)

R. H. Zerull, “Scattering Measurements of Dielectric and Absorbing Nonspherical Particles,” Beitr. Phys. Atmos. 49, 166 (1976).

J. Atmos. Sci. (2)

J. B. Pollack, J. N. Cuzzi, “Scattering by Nonspherical Particles of Size Comparable to a Wavelength: a New Semi-Empirical Theory and Its Application to Tropospheric Aerosols,” J. Atmos. Sci. 37, 868 (1980).
[Crossref]

A. Mugnai, W. J. Wiscombe, “Scattering of Radiation by Moderately Nonspherical Particles,” J. Atmos. Sci. 37, 1291 (1980).
[Crossref]

J. Opt. Soc. Am. (1)

Phys. Rev. (1)

V. Erma, “Perturbation Solution for the Scattering of Electromagnetic Waves from Conductors of Arbitrary Shape. II. General Case,” Phys. Rev. 176, 1544 (1968).
[Crossref]

Other (6)

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation Approach to Light Scattering by Nonspherical Particles,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 135.
[Crossref]

D. J. Kennison, “AUTOGRAPH: The Unabridged Write-up,” NCAR Tech. Note NCAR/TN-245+IA (National Center for Atmospheric Research, Boulder, CO, 1985).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981; reprinted from 1957 edition).

W. J. Wiscombe, A. Mugnai, “Single Scattering from Nonspherical Chebyshev Particles: a Compendium of Calculations,” NASA Ref. Publ. 1157 (NASA/Goddard Space Flight Center, Greenbelt, MD, 1986).

A. Mugnai, W. J. Wiscombe, “Scattering from Nonspherical Chebyshev Particles. 3: Variability of Angular Scattering Patterns,” Appl. Opt. (in preparation).

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurements for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 283.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Perpendicular scattered intensities for mixtures of all concave and all convex 〈Tn〉 particles, and for micro-size-averaged spheres, averaged over the six small size parameter ranges from Table I (left column); corresponding nonspherical–spherical percent differences (right column). Part I: x = 1–3, x = 3–5, x = 5–8. Part II: x = 8–12, x = 12–16, x = 16–20.

Fig. 2
Fig. 2

As in Fig. 1 but for parallel intensities. Part I: x = 1–3, x = 3–5, x = 5–8. Part II: x = 8–12, x = 12–16, x = 16–20.

Fig. 3
Fig. 3

Perpendicular scattered intensities for mixtures of all nonspherical 〈Tn〉 particles with relative deformation from a sphere || = 0.05, 0.10, and 0.15, and for micro-size-averaged spheres, averaged over three small size ranges x = 1–3, 3–5, and 5–8 (left column); corresponding nonspherical–spherical percent differences (right column).

Fig. 4
Fig. 4

As in Fig. 3 but for parallel intensities.

Fig. 5
Fig. 5

Perpendicular (left column) and parallel (right column) scattered intensities for mixtures of nonspherical 〈Tn〉 particles and for micro-size-averaged spheres, averaged over three small size ranges x = 8–12, 12–16, and 16–20. For all size ranges, 〈Tn〉 particles have relative deformation from a sphere || = 0.05 and 0.10; in addition, for x = 8–12, there are || = 0.15 results.

Fig. 6
Fig. 6

Perpendicular and parallel intensities for Zerull5Fig. 4 cubes (top row) and for a mixture of all nonspherical 〈Tn〉 particles with relative deformation from a sphere || = 0.15 (bottom row) along with corresponding micro-size-averaged sphere intensities. Zerull’s and our index of refraction m and size parameter x are shown on each plot.

Fig. 7
Fig. 7

Perpendicular and parallel intensities for Zerull5 Fig. 9 convex and concave particles (top row) and for mixtures of all convex and all concave nonspherical 〈Tn〉 particles (bottom row) along with corresponding micro-size-averaged sphere intensities. Zerull’s and our index of refraction m and size parameter x are shown on each plot.

Tables (1)

Tables Icon

Table I Number of Studied Chebyshev Particles in each Range of Size Parameter as a Function of the Relative Deformation from a Sphere ||a

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