Abstract

In this paper, we study the behavior of the scattering efficiency Qsca, the absorption efficiency Qabs, the single-scattering albedo ω, the asymmetry factor g, and the backscattered fraction for isotropically incident radiation β̅ for randomly oriented rotationally symmetric nonspherical particles of radii r = r0[1 + ∊Tn(cosθs)], where Tn is a Chebyshev polynomial of order n. By taking n = 2,3,4,6,8, and 20, and = −0. 2 to 0.2 in steps of 0.05, twenty-three different shapes have been considered for these Chebyshev particles. The scattering calculations have been carried out using the Extended Boundary Conditions Method for individual particles with refractive index m=1.50.02i in the equal-volume-sphere size parameter range 1 ≤ x ≤ 25. Unshape-averaged and shape-averaged nonspherical single-scattering quantities have then been compared to corresponding size-averaged (over Δx = 0.1x) spherical results. It is shown that nonsphericity always increases Qabs for size parameters larger than ∼10, while it decreases g—and correspondingly increases β̅—in the size range 8 ≤ x ≤ 15. Qsca seems to be on the average somewhat larger for nonspherical particles, while ω tends to be smaller. Concavity almost always enhances the spherical–nonspherical differences.

© 1986 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. W. J. Wiscombe, “Mie Scattering Calculations: Advances in Technique and Fast, Vector-Speed Computer Codes,” NCAR Tech. Note NCAR/TN-140+STR (National Center for Atmospheric Research, Boulder, CO, 1979).
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    [CrossRef] [PubMed]
  5. J. R. Hodkinson, “Light Scattering and Extinction by Irregular Particles Larger than the Wavelength,” in Electromagnetic Scattering, M. Kerker, Ed. (Pergamon, New York, 1963), p. 87.
  6. A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113 (1970).
    [CrossRef] [PubMed]
  7. R. G. Pinnick, D. E. Carroll, D. J. Hofmann, “Polarized Light Scattered from Monodisperse Randomly Oriented Nonspherical Aerosol Particles: Measurements,” Appl. Opt. 15, 384 (1976).
    [CrossRef] [PubMed]
  8. A. Coletti, “Light Scattering by Nonspherical Particles: A Laboratory Study,” Aerosol Sci. 3, 39 (1984).
    [CrossRef]
  9. J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, “Microwave Analogue to the Scattering of Light by Nonspherical Particles,” J. Appl. Phys. 32, 233 (1961).
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  12. W. J. Wiscombe, A. Mugnai, “Single Scattering from Nonspherical Chebyshev Particles: A Compendium of Calculations,” NASA Ref. Publ. 1157 (NASA/GSFC, Greenbelt, MD, Jan.1986).
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    [CrossRef]
  14. P. C. Waterman, “Symmetry, Unitarity, and Geometry in Electromagnetic Scattering,” Phys. Rev. D 3, 825 (1971).
    [CrossRef]
  15. P. Barber, C. Yeh, “Scattering of Electromagnetic Waves by Arbitrarily Shaped Dielectric Bodies,” Appl. Opt. 14, 2864 (1975).
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  16. A. Mugnai, W. J. Wiscombe, “Scattering of Radiation by Moderately Nonspherical Particles,” J. Atmos. Sci. 37, 1291 (1980).
    [CrossRef]
  17. W. J. Wiscombe, A. Mugnai, “Scattering from Nonspherical Chebyshev Particles. 2: Phase Function and Degree of Polarization,” (in preparation).
  18. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  19. R. F. Millar, “Rayleigh Hypothesis in Scattering Problems,” Electron. Lett. 5, 416 (1969).
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  23. P. Barber, “Differential Scattering of Electromagnetic Waves by Homogeneous Isotropic Dielectric Bodies,” Ph.D. Thesis, UCLA, Los Angeles (1973) (available from University Microfilms, Ann Arbor, MI).
  24. E. M. Patterson, D. A. Gillette, B. H. Stockton, “Complex Index of Refraction Between 300 and 700 nm for Saharan Aerosols,” J. Geophys. Res. 82, 3153 (1977).
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  28. P. Barber, “Resonance Electromagnetic Absorption by Nonspherical Dielectric Objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
    [CrossRef]
  29. H. M. Nussenzveig, W. J. Wiscombe, “Forward Optical Glory,” Opt. Lett. 5, 455 (1980).
    [CrossRef] [PubMed]
  30. W. J. Wiscombe, G. W. Grams, “The Backscattered Fraction in Two-Stream Approximations,” J. Atmos. Sci. 33, 2440 (1976).
    [CrossRef]
  31. E. P. Shettle, J. A. Weinman, “The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation,” J. Atmos. Sci. 27, 1048 (1970).
    [CrossRef]
  32. J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta-Eddington Approximation for Radiative Flux Transfer,” J. Atmos. Sci. 33, 2452 (1976).
    [CrossRef]
  33. J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chýlek, “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]
  34. V. Erma, “Perturbation Solution for the Scattering of Electromagnetic Waves from Conductors of Arbitrary Shape. II. General Case,” Phys. Rev. 176, 1544 (1968).
    [CrossRef]
  35. P. Chýlek, “Extinction Cross Sections of Arbitrarily Shaped Randomly Oriented Nonspherical Particles,” J. Opt. Soc. Am. 67, 1348 (1977).
    [CrossRef]
  36. 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]
  37. M. B. Baker, A. Coletti, “Uncertainties in the Evaluation of the Shortwave Radiative Properties of an Aerosol Layer due to Experimental and Numerical Errors,” Appl. Opt. 21, 2244 (1982).
    [CrossRef] [PubMed]

1984 (1)

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

1982 (1)

1981 (2)

D. W. Schuerman, R. Wang, B. Gustafson, R. Schaefer, “Systematic Studies of Light Scattering. 1: Particle Shape,” Appl. Opt. 20, 4039 (1981).
[CrossRef] [PubMed]

H. E. Gerber, E. E. Hindman, “First International Workshop on Light Absorption by Aerosol Particles: Background, Activities, and Preliminary Results, 28 July-8 August 1980, Ft. Collins, Colo.,” Bull. Am. Meteorol. Soc. 62, 1321 (1981).

1980 (5)

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]

W. J. Wiscombe, “Improved Mie Scattering Algorithms,” Appl. Opt. 19, 1505 (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]

H. M. Nussenzveig, W. J. Wiscombe, “Forward Optical Glory,” Opt. Lett. 5, 455 (1980).
[CrossRef] [PubMed]

1978 (1)

1977 (3)

P. Chýlek, “Extinction Cross Sections of Arbitrarily Shaped Randomly Oriented Nonspherical Particles,” J. Opt. Soc. Am. 67, 1348 (1977).
[CrossRef]

E. M. Patterson, D. A. Gillette, B. H. Stockton, “Complex Index of Refraction Between 300 and 700 nm for Saharan Aerosols,” J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

P. Barber, “Resonance Electromagnetic Absorption by Nonspherical Dielectric Objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

1976 (4)

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta-Eddington Approximation for Radiative Flux Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

W. J. Wiscombe, G. W. Grams, “The Backscattered Fraction in Two-Stream Approximations,” J. Atmos. Sci. 33, 2440 (1976).
[CrossRef]

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

R. G. Pinnick, D. E. Carroll, D. J. Hofmann, “Polarized Light Scattered from Monodisperse Randomly Oriented Nonspherical Aerosol Particles: Measurements,” Appl. Opt. 15, 384 (1976).
[CrossRef] [PubMed]

1975 (2)

1973 (1)

R. F. Millar, “The Rayleigh Hypothesis and a Related Least-Squares Solution to Scattering Problems for Periodic Surfaces and Other Scatterers,” Radio Sci. 8, 785 (1973).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, Unitarity, and Geometry in Electromagnetic Scattering,” Phys. Rev. D 3, 825 (1971).
[CrossRef]

1970 (2)

E. P. Shettle, J. A. Weinman, “The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation,” J. Atmos. Sci. 27, 1048 (1970).
[CrossRef]

A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113 (1970).
[CrossRef] [PubMed]

1969 (1)

R. F. Millar, “Rayleigh Hypothesis in Scattering Problems,” Electron. Lett. 5, 416 (1969).
[CrossRef]

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]

1965 (1)

P. C. Waterman, “Matrix Formulation of Electromagnetic Scattering,” Proc. IEEE 53, 805 (1965).
[CrossRef]

1961 (1)

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, “Microwave Analogue to the Scattering of Light by Nonspherical Particles,” J. Appl. Phys. 32, 233 (1961).
[CrossRef]

1955 (1)

J. R. Wait, “Scattering of a Plane Wave from a Circular Dielectric Cylinder at Oblique Incidence,” Can. J. Phys. 33, 189 (1955).
[CrossRef]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys 25, 377 (1908).
[CrossRef]

Asano, S.

Baker, M. B.

Barber, P.

P. Barber, “Resonance Electromagnetic Absorption by Nonspherical Dielectric Objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

P. Barber, C. Yeh, “Scattering of Electromagnetic Waves by Arbitrarily Shaped Dielectric Bodies,” Appl. Opt. 14, 2864 (1975).
[CrossRef] [PubMed]

P. Barber, “Differential Scattering of Electromagnetic Waves by Homogeneous Isotropic Dielectric Bodies,” Ph.D. Thesis, UCLA, Los Angeles (1973) (available from University Microfilms, Ann Arbor, MI).

Bohren, C. F.

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

Carroll, D. E.

Chýlek, P.

P. Chýlek, “Extinction Cross Sections of Arbitrarily Shaped Randomly Oriented Nonspherical Particles,” J. Opt. Soc. Am. 67, 1348 (1977).
[CrossRef]

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chýlek, “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.

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]

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Gagne, G.

Gerber, H. E.

H. E. Gerber, E. E. Hindman, “First International Workshop on Light Absorption by Aerosol Particles: Background, Activities, and Preliminary Results, 28 July-8 August 1980, Ft. Collins, Colo.,” Bull. Am. Meteorol. Soc. 62, 1321 (1981).

Gillespie, J. B.

Gillette, D. A.

E. M. Patterson, D. A. Gillette, B. H. Stockton, “Complex Index of Refraction Between 300 and 700 nm for Saharan Aerosols,” J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

Grams, G. W.

W. J. Wiscombe, G. W. Grams, “The Backscattered Fraction in Two-Stream Approximations,” J. Atmos. Sci. 33, 2440 (1976).
[CrossRef]

Greenberg, J. M.

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, “Microwave Analogue to the Scattering of Light by Nonspherical Particles,” J. Appl. Phys. 32, 233 (1961).
[CrossRef]

Gustafson, B.

Hindman, E. E.

H. E. Gerber, E. E. Hindman, “First International Workshop on Light Absorption by Aerosol Particles: Background, Activities, and Preliminary Results, 28 July-8 August 1980, Ft. Collins, Colo.,” Bull. Am. Meteorol. Soc. 62, 1321 (1981).

Hodkinson, J. R.

J. R. Hodkinson, “Light Scattering and Extinction by Irregular Particles Larger than the Wavelength,” in Electromagnetic Scattering, M. Kerker, Ed. (Pergamon, New York, 1963), p. 87.

Hofmann, D. J.

Holland, A. C.

Huffman, D. R.

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

Jennings, S. G.

Joseph, J. H.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta-Eddington Approximation for Radiative Flux Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Kiehl, J. T.

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chýlek, “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. Chýlek, “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]

Lindberg, J. D.

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys 25, 377 (1908).
[CrossRef]

Millar, R. F.

R. F. Millar, “The Rayleigh Hypothesis and a Related Least-Squares Solution to Scattering Problems for Periodic Surfaces and Other Scatterers,” Radio Sci. 8, 785 (1973).
[CrossRef]

R. F. Millar, “Rayleigh Hypothesis in Scattering Problems,” Electron. Lett. 5, 416 (1969).
[CrossRef]

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Mugnai, A.

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/GSFC, Greenbelt, MD, Jan.1986).

W. J. Wiscombe, A. Mugnai, “Scattering from Nonspherical Chebyshev Particles. 2: Phase Function and Degree of Polarization,” (in preparation).

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chýlek, “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]

Nussenzveig, H. M.

Patterson, E. M.

E. M. Patterson, D. A. Gillette, B. H. Stockton, “Complex Index of Refraction Between 300 and 700 nm for Saharan Aerosols,” J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

Pedersen, J. C.

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, “Microwave Analogue to the Scattering of Light by Nonspherical Particles,” J. Appl. Phys. 32, 233 (1961).
[CrossRef]

Pedersen, N. E.

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, “Microwave Analogue to the Scattering of Light by Nonspherical Particles,” J. Appl. Phys. 32, 233 (1961).
[CrossRef]

Pinnick, R. G.

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.

Shettle, E. P.

E. P. Shettle, J. A. Weinman, “The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation,” J. Atmos. Sci. 27, 1048 (1970).
[CrossRef]

Stockton, B. H.

E. M. Patterson, D. A. Gillette, B. H. Stockton, “Complex Index of Refraction Between 300 and 700 nm for Saharan Aerosols,” J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

Wait, J. R.

J. R. Wait, “Scattering of a Plane Wave from a Circular Dielectric Cylinder at Oblique Incidence,” Can. J. Phys. 33, 189 (1955).
[CrossRef]

Wang, R.

Waterman, P. C.

P. C. Waterman, “Symmetry, Unitarity, and Geometry in Electromagnetic Scattering,” Phys. Rev. D 3, 825 (1971).
[CrossRef]

P. C. Waterman, “Matrix Formulation of Electromagnetic Scattering,” Proc. IEEE 53, 805 (1965).
[CrossRef]

Weinman, J. A.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta-Eddington Approximation for Radiative Flux Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

E. P. Shettle, J. A. Weinman, “The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation,” J. Atmos. Sci. 27, 1048 (1970).
[CrossRef]

Wiscombe, W. J.

H. M. Nussenzveig, W. J. Wiscombe, “Forward Optical Glory,” Opt. Lett. 5, 455 (1980).
[CrossRef] [PubMed]

W. J. Wiscombe, “Improved Mie Scattering Algorithms,” Appl. Opt. 19, 1505 (1980).
[CrossRef] [PubMed]

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

W. J. Wiscombe, G. W. Grams, “The Backscattered Fraction in Two-Stream Approximations,” J. Atmos. Sci. 33, 2440 (1976).
[CrossRef]

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta-Eddington Approximation for Radiative Flux Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

W. J. Wiscombe, A. Mugnai, “Scattering from Nonspherical Chebyshev Particles. 2: Phase Function and Degree of Polarization,” (in preparation).

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

W. J. Wiscombe, “Mie Scattering Calculations: Advances in Technique and Fast, Vector-Speed Computer Codes,” NCAR Tech. Note NCAR/TN-140+STR (National Center for Atmospheric Research, Boulder, CO, 1979).

Yamamoto, G.

Yeh, C.

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]

Ann. Phys (1)

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys 25, 377 (1908).
[CrossRef]

Appl. Opt. (9)

Beitr. Phys. Atmos. (1)

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

Bull. Am. Meteorol. Soc. (1)

H. E. Gerber, E. E. Hindman, “First International Workshop on Light Absorption by Aerosol Particles: Background, Activities, and Preliminary Results, 28 July-8 August 1980, Ft. Collins, Colo.,” Bull. Am. Meteorol. Soc. 62, 1321 (1981).

Can. J. Phys. (1)

J. R. Wait, “Scattering of a Plane Wave from a Circular Dielectric Cylinder at Oblique Incidence,” Can. J. Phys. 33, 189 (1955).
[CrossRef]

Electron. Lett. (1)

R. F. Millar, “Rayleigh Hypothesis in Scattering Problems,” Electron. Lett. 5, 416 (1969).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. Barber, “Resonance Electromagnetic Absorption by Nonspherical Dielectric Objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

J. Appl. Phys. (1)

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, “Microwave Analogue to the Scattering of Light by Nonspherical Particles,” J. Appl. Phys. 32, 233 (1961).
[CrossRef]

J. Atmos. Sci. (5)

W. J. Wiscombe, G. W. Grams, “The Backscattered Fraction in Two-Stream Approximations,” J. Atmos. Sci. 33, 2440 (1976).
[CrossRef]

E. P. Shettle, J. A. Weinman, “The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation,” J. Atmos. Sci. 27, 1048 (1970).
[CrossRef]

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta-Eddington Approximation for Radiative Flux Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

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

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]

J. Geophys. Res. (1)

E. M. Patterson, D. A. Gillette, B. H. Stockton, “Complex Index of Refraction Between 300 and 700 nm for Saharan Aerosols,” J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (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]

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, Unitarity, and Geometry in Electromagnetic Scattering,” Phys. Rev. D 3, 825 (1971).
[CrossRef]

Proc. IEEE (1)

P. C. Waterman, “Matrix Formulation of Electromagnetic Scattering,” Proc. IEEE 53, 805 (1965).
[CrossRef]

Radio Sci. (1)

R. F. Millar, “The Rayleigh Hypothesis and a Related Least-Squares Solution to Scattering Problems for Periodic Surfaces and Other Scatterers,” Radio Sci. 8, 785 (1973).
[CrossRef]

Other (8)

P. Barber, “Differential Scattering of Electromagnetic Waves by Homogeneous Isotropic Dielectric Bodies,” Ph.D. Thesis, UCLA, Los Angeles (1973) (available from University Microfilms, Ann Arbor, MI).

W. J. Wiscombe, A. Mugnai, “Scattering from Nonspherical Chebyshev Particles. 2: Phase Function and Degree of Polarization,” (in preparation).

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chýlek, “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]

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

W. J. Wiscombe, “Mie Scattering Calculations: Advances in Technique and Fast, Vector-Speed Computer Codes,” NCAR Tech. Note NCAR/TN-140+STR (National Center for Atmospheric Research, Boulder, CO, 1979).

J. R. Hodkinson, “Light Scattering and Extinction by Irregular Particles Larger than the Wavelength,” in Electromagnetic Scattering, M. Kerker, Ed. (Pergamon, New York, 1963), p. 87.

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

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Figures (5)

Fig. 1
Fig. 1

Three-dimensional representation of the Chebyshev particles with || = 0.1. Tn(+e) and Tn(−e) indicate Chebyshev particles with waviness parameter n and deformation parameter = +e and −e, respectively.

Fig. 2
Fig. 2

Scattering efficiency Qsca, absorption efficiency Qabs, single-scattering albedo ω, asymmetry factor g, and backscattered fraction β ̅, vs Mie size parameter x, for a rectangular size distribution of spheres (over Δx = 0.1x) with refractive index ( m = 1.5 0.02 i ).

Fig. 3
Fig. 3

Percent differences δsca, δabs, δω, δg, and δ β ̅ between nonspherical and size-averaged (Δx = 0.1x) spherical Qsca, Qabs, ω, g, and β ̅, respectively, vs equal-volume-sphere size parameter x. All randomly oriented Chebyshev particles considered in this study (see Table I) are represented as well as the three indicated mixtures of them. Refractive index is 1.5−0.02i for all particles.

Fig. 4
Fig. 4

(a),(b) Asymmetry factor integrand fg [Eq. (4)] and backscattered fraction integrand f β ̅ [Eq. (7)] vs scattering angle θ for the mixture of all randomly oriented Chebyshev particles (solid line) and its size-averaged spherical counterpart (dashed line) for equal-volume-sphere size parameter x = 10; (c),(d) differences between the solid and dashed curves in (a) and (b).

Fig. 5
Fig. 5

ΔP sinθ vs scattering angle θ for equal-volume-sphere size parameter x = 10, where ΔP is the difference between the phase functions for the mixture of all randomly oriented Chebyshev particles and for its size-averaged spherical counterpart.

Tables (1)

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Table I Maximum Value xmax of the Equal-Volume-Sphere Size Parameter x for which Scattering Calculations have been Carried out a

Equations (10)

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r = r 0 [ 1 + T n ( cos θ s ) ]
| | > 1 / ( n 2 + 1 ) ,
ω = Q sca / Q ext ,
g = 0 π f g ( θ ) d θ ,
f g ( θ ) = 1 / 2 P ( cos θ ) sin θ cos θ .
P ( cos θ ) = 2 ( i 1 + i r ) / ( x 2 Q sca ) ,
½ 0 π P ( cos θ ) sin θ d θ = 1 .
β ̅ = 0 π f β ̅ ( θ ) d θ ,
f β ̅ ( θ ) = θ / ( 2 π ) P ( cos θ ) sin θ .
δ ω = ( Q abs / Q ext ) sphere ( δ sca δ abs ) .

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