Abstract

The T-matrix method is shown to be an efficient and accurate procedure for calculating the scattering matrix for randomly oriented nonspherical particles. Calculated scattering matrix elements for spheroidal particles are identical to those obtained by the spheroidal harmonic approach. T-matrix calculations for a randomly oriented finite length cylinder agree well with microwave scattering measurements. Analysis of the information content of the angular variation of the matrix elements for a set of moderately sized absorbing spheroidal particles is presented. It is found that the Fourier spectrum of the phase function and a parameter related to the depolarization ratio contain particle size and shape information, respectively.

© 1985 Optical Society of America

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References

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  1. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  2. W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarization Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. USA 73, 486 (1976).
    [CrossRef] [PubMed]
  3. R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental Determinations of Mueller Matrices for Nonspherical Particles,” Appl. Opt. 17, 2700 (1978).
    [CrossRef] [PubMed]
  4. A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113 (1970).
    [CrossRef] [PubMed]
  5. R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions via the Mueller Matrix,” Appl. Opt. 19, 1323 (1980).
    [CrossRef] [PubMed]
  6. 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. Schuerman, Ed. (Plenum, New York, 1980), pp. 283–290.
    [CrossRef]
  7. S. Asano, M. Sato, “Light Scattering by Randomly Oriented Spheroidal Particles,” Appl. Opt. 19, 962 (1980).
    [CrossRef] [PubMed]
  8. R. W. Schaefer, “Calculations of the Light Scattered by Randomly Oriented Ensembles of Spheroids of Size Comparable to the Wavelength,” Ph.D. Dissertation, State University of New York at Albany (1980).
  9. D. W. Schuerman, R. T. Wang, B. A. S. Gustafson, R. W. Schaefer, “Systematic Studies of Light Scattering. 1: Particle Shape,” Appl. Opt. 20, 4039 (1981).
    [CrossRef] [PubMed]
  10. P. C. Waterman, “Symmetry, Unitarity, and Geometry in Electromagnetic Scattering,” Phys. Rev. D 3, 825 (1971).
    [CrossRef]
  11. P. Barber, C. Yeh, “Scattering of Electromagnetic Waves by Arbitrarily Shaped Dielectric Bodies,” Appl. Opt. 14, 2864 (1975).
    [CrossRef] [PubMed]
  12. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  13. P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
    [CrossRef]
  14. N. Ahmed, T. Natarajan, Discrete-Time Signals and Systems (Reston Publishing Co., Reston, Va., 1983).
  15. E. D. Brigham, The Fast Fourier Transform (Prentice-Hall, New York, 1974).

1982 (1)

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[CrossRef]

1981 (1)

1980 (2)

1978 (1)

1976 (1)

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarization Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

1975 (1)

1971 (1)

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

1970 (1)

Ahmed, N.

N. Ahmed, T. Natarajan, Discrete-Time Signals and Systems (Reston Publishing Co., Reston, Va., 1983).

Asano, S.

Barber, P.

Barber, P. W.

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[CrossRef]

Bickel, W. S.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarization Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Bohren, C. F.

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

Bottiger, J. R.

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions via the Mueller Matrix,” Appl. Opt. 19, 1323 (1980).
[CrossRef] [PubMed]

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. Schuerman, Ed. (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Brigham, E. D.

E. D. Brigham, The Fast Fourier Transform (Prentice-Hall, New York, 1974).

Davidson, J. F.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarization Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Feshbach, H.

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

Fry, E. S.

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions via the Mueller Matrix,” Appl. Opt. 19, 1323 (1980).
[CrossRef] [PubMed]

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. Schuerman, Ed. (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Gagne, G.

Gustafson, B. A. S.

Holland, A. C.

Huffman, D. R.

R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental Determinations of Mueller Matrices for Nonspherical Particles,” Appl. Opt. 17, 2700 (1978).
[CrossRef] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarization Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

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

Hunt, A. J.

Kilkson, R.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarization Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Massoudi, H.

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[CrossRef]

Morse, P. M.

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

Natarajan, T.

N. Ahmed, T. Natarajan, Discrete-Time Signals and Systems (Reston Publishing Co., Reston, Va., 1983).

Perry, R. J.

Sato, M.

Schaefer, R. W.

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

R. W. Schaefer, “Calculations of the Light Scattered by Randomly Oriented Ensembles of Spheroids of Size Comparable to the Wavelength,” Ph.D. Dissertation, State University of New York at Albany (1980).

Schuerman, D. W.

Thompson, R. C.

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions via the Mueller Matrix,” Appl. Opt. 19, 1323 (1980).
[CrossRef] [PubMed]

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. Schuerman, Ed. (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Wang, R. T.

Waterman, P. C.

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

Yeh, C.

Aerosol Sci. Technol. (1)

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[CrossRef]

Appl. Opt. (6)

Phys. Rev. D (1)

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

Proc. Natl. Acad. Sci. USA (1)

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarization Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Other (6)

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. Schuerman, Ed. (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

R. W. Schaefer, “Calculations of the Light Scattered by Randomly Oriented Ensembles of Spheroids of Size Comparable to the Wavelength,” Ph.D. Dissertation, State University of New York at Albany (1980).

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

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

N. Ahmed, T. Natarajan, Discrete-Time Signals and Systems (Reston Publishing Co., Reston, Va., 1983).

E. D. Brigham, The Fast Fourier Transform (Prentice-Hall, New York, 1974).

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Figures (5)

Fig. 1
Fig. 1

(a) P11 (log scale) and (b) −P12/P11 for a 4:1 cylinder with ka = 6.1993 and m = 1.61 + i0.004. Comparison of T-matrix calculations, (—) and microwave scattering measurements (○).

Fig. 2
Fig. 2

Six independent scattering matrix elements for a 1.5:1 prolate spheroid with ka = 3.276 and m = 1.68 + i0.0001: (a) P11 (log scale); (b) −P12/P11 and 1 − P22/P11; (c) P43/P11; (d) P33/P11 and P44/P11.

Fig. 3
Fig. 3

A 50% frequency of P11 as a function of normalized volume k3V for different spheroid axial ratios. The axial ratio is noted on each curve.

Fig. 4
Fig. 4

A 50% frequency of P11 as a function of axial ratio for different normalized volumes. k3V is noted on each curve.

Fig. 5
Fig. 5

Average power of 1 − P22/P11 as a function of axial ratio for different normalized volumes. k3V is noted on each curve.

Tables (1)

Tables Icon

Table I ka for Spheroidal Particles

Equations (10)

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[ I s Q s U s V s ] = 1 k 2 r 2 [ S 11 S 12 S 13 S 14 S 21 S 22 S 23 S 24 S 31 S 32 S 33 S 34 S 41 S 42 S 43 S 44 ] [ I i Q i U i V i ] ,
[ E s E s ] = exp [ i k ( r z ) ] i k r [ S 2 S 3 S 4 S 1 ] [ E i E i ] ,
[ S 11 S 12 0 0 S 12 S 22 0 0 0 0 S 33 S 43 0 0 S 43 S 44 ] .
1 4 π 4 π P 11 d Ω = 1
k 2 C sca ¯ 4 π P i j = S i j ( i , j = 1 , 2 , 3 , 4 ) ,
[ I s Q s U s V s ] = C sca 4 π r 2 ¯ [ P 11 P 12 0 0 P 12 P 22 0 0 0 0 P 33 P 43 0 0 P 43 P 44 ] I i Q i U i V i ] .
E ¯ s ( k r ¯ ) = ν = 1 D ν [ f ν M ¯ ν 3 ( k r ¯ ) + g ν N ¯ ν 3 ( k r ¯ ) ] ,
[ f g ] = [ T ] [ a b ] .
average power = n = 0 N / 2 P n ,
average power = 1 N n = 0 N 1 x 2 ( n ) .

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