Abstract

The light scattering properties of twenty-eight particles, spanning four sizes (near the resonance region) and seven related shapes (a 4:1 cylinder, 4:1 and 2:1 prolate spheroids, a sphere, 2:1 and 4:1 oblate spheroids, and a 4:1 disk), are presented for a common index of refraction, m = 1.61–i0.004, representing silicates. Microwave analog and theoretical methods were used to derive the scattered intensity and degree of polarization as a function of the scattering angle along with the extinction. All results refer to an ensemble or a cloud of identical particles because averages have been taken over random particle orientations. The degree of polarization, backscatter, and the radiation-pressure cross section are most sensitive to particle shape, implying that the use of Mie theory may be inappropriate for many applications.

© 1981 Optical Society of America

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Corrections

D. W. Schuerman, R. T. Wang, B. Å. S. Gustafson, and R. W. Schaefer, "Systematic studies of light scattering. 1: Particle shape; errata," Appl. Opt. 21, 369-369 (1982)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-21-3-369

References

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  1. S. Asano, G. Yamamoto, Appl. Opt. 14, 29 (1975).
    [PubMed]
  2. A. C. Lind, R. T. Wang, J. M. Greenberg, Appl. Opt. 4, 1555 (1965).
    [CrossRef]
  3. A. C. Lind, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1966).
  4. R. T. Wang, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1968).
  5. R. T. Wang, R. W. Detenbeck, F. Giovane, J. M. Greenberg, Final Report, NSF ATM75-15663 (1977).
  6. R. T. Wang, J. M. Greenberg, Final Report, NASA NSG-7353 (1978).
  7. D. W. Schuerman, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 227.
    [CrossRef]
  8. B. Å. S. Gustafson, Reports from the Observatory of Lund, Sweden, No. 17 (1980).
  9. K. F. Ratcliff, N. Y. Misconi, S. J. Paddock, in I.A.U. Symposium No. 90, Solid Particles in the Solar System, I. Halliday, B. A. McIntosh, Eds. (Reidel, Dordrecht, 1980), p. 391.
    [CrossRef]
  10. R. H. Zerull, Beitr. Phys. Atmos. 49, 168 (1976).
  11. R. H. Zerull, R. H. Giese, in Planets, Stars and Nebulae Studied with Photopolarimetry, T. Gehrels, Ed. (U. Ariz. Press, Tucson, 1974), p. 901.
  12. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  13. R. W. Schaefer, Ph.D. Thesis, State U. New York at Albany (1980).
  14. J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, J. Appl. Phys. 32, 233 (1961).
    [CrossRef]
  15. S. Asano, M. Sato, Appl. Opt. 19, 962 (1980).
    [CrossRef] [PubMed]
  16. However, Schaefer13 did find that 4:1 oblate and prolate spheroids with m = 1.33–i0.01 produce linear polarizations near 100%.
  17. H. C. van de Hulst, Thesis Utrecht, Recherches Astron. Obs. d’Utrecht II, Part I (1946).
  18. J. M. Greenberg, R. T. Wang, L. Bangs, Nature (London) Phys. Sci. 230, 110 (1971).
    [CrossRef]
  19. R. T. Wang, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 255.
    [CrossRef]
  20. R. T. Wang, D. W. Schuerman, in Proceedings, 1981 CSL Scientific Conference on Obscuration and Aerosol Research, R. Kohl, Ed. (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Ground, Md., 1982), in press.
  21. J. M. Greenberg in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 7.
    [CrossRef]
  22. A. Cohen, P. Alpert, Appl. Opt. 19, 558 (1980).
    [CrossRef] [PubMed]
  23. M. Kerker, Planet. Space Sci. 29, 127 (1981).
    [CrossRef]
  24. D. W. Schuerman, Astrophys. J. 238, 337 (1980).
    [CrossRef]

1981 (1)

M. Kerker, Planet. Space Sci. 29, 127 (1981).
[CrossRef]

1980 (3)

1976 (1)

R. H. Zerull, Beitr. Phys. Atmos. 49, 168 (1976).

1975 (1)

1971 (1)

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

1965 (1)

1961 (1)

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, J. Appl. Phys. 32, 233 (1961).
[CrossRef]

Alpert, P.

Asano, S.

Bangs, L.

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

Cohen, A.

Detenbeck, R. W.

R. T. Wang, R. W. Detenbeck, F. Giovane, J. M. Greenberg, Final Report, NSF ATM75-15663 (1977).

Giese, R. H.

R. H. Zerull, R. H. Giese, in Planets, Stars and Nebulae Studied with Photopolarimetry, T. Gehrels, Ed. (U. Ariz. Press, Tucson, 1974), p. 901.

Giovane, F.

R. T. Wang, R. W. Detenbeck, F. Giovane, J. M. Greenberg, Final Report, NSF ATM75-15663 (1977).

Greenberg, J. M.

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

A. C. Lind, R. T. Wang, J. M. Greenberg, Appl. Opt. 4, 1555 (1965).
[CrossRef]

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, J. Appl. Phys. 32, 233 (1961).
[CrossRef]

J. M. Greenberg in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 7.
[CrossRef]

R. T. Wang, J. M. Greenberg, Final Report, NASA NSG-7353 (1978).

R. T. Wang, R. W. Detenbeck, F. Giovane, J. M. Greenberg, Final Report, NSF ATM75-15663 (1977).

Gustafson, B. Å. S.

B. Å. S. Gustafson, Reports from the Observatory of Lund, Sweden, No. 17 (1980).

Kerker, M.

M. Kerker, Planet. Space Sci. 29, 127 (1981).
[CrossRef]

Lind, A. C.

A. C. Lind, R. T. Wang, J. M. Greenberg, Appl. Opt. 4, 1555 (1965).
[CrossRef]

A. C. Lind, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1966).

Misconi, N. Y.

K. F. Ratcliff, N. Y. Misconi, S. J. Paddock, in I.A.U. Symposium No. 90, Solid Particles in the Solar System, I. Halliday, B. A. McIntosh, Eds. (Reidel, Dordrecht, 1980), p. 391.
[CrossRef]

Paddock, S. J.

K. F. Ratcliff, N. Y. Misconi, S. J. Paddock, in I.A.U. Symposium No. 90, Solid Particles in the Solar System, I. Halliday, B. A. McIntosh, Eds. (Reidel, Dordrecht, 1980), p. 391.
[CrossRef]

Pedersen, J. C.

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, J. Appl. Phys. 32, 233 (1961).
[CrossRef]

Pedersen, N. E.

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, J. Appl. Phys. 32, 233 (1961).
[CrossRef]

Ratcliff, K. F.

K. F. Ratcliff, N. Y. Misconi, S. J. Paddock, in I.A.U. Symposium No. 90, Solid Particles in the Solar System, I. Halliday, B. A. McIntosh, Eds. (Reidel, Dordrecht, 1980), p. 391.
[CrossRef]

Sato, M.

Schaefer, R. W.

R. W. Schaefer, Ph.D. Thesis, State U. New York at Albany (1980).

Schuerman, D. W.

D. W. Schuerman, Astrophys. J. 238, 337 (1980).
[CrossRef]

R. T. Wang, D. W. Schuerman, in Proceedings, 1981 CSL Scientific Conference on Obscuration and Aerosol Research, R. Kohl, Ed. (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Ground, Md., 1982), in press.

D. W. Schuerman, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 227.
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Thesis Utrecht, Recherches Astron. Obs. d’Utrecht II, Part I (1946).

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

Wang, R. T.

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

A. C. Lind, R. T. Wang, J. M. Greenberg, Appl. Opt. 4, 1555 (1965).
[CrossRef]

R. T. Wang, D. W. Schuerman, in Proceedings, 1981 CSL Scientific Conference on Obscuration and Aerosol Research, R. Kohl, Ed. (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Ground, Md., 1982), in press.

R. T. Wang, J. M. Greenberg, Final Report, NASA NSG-7353 (1978).

R. T. Wang, R. W. Detenbeck, F. Giovane, J. M. Greenberg, Final Report, NSF ATM75-15663 (1977).

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

R. T. Wang, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1968).

Yamamoto, G.

Zerull, R. H.

R. H. Zerull, Beitr. Phys. Atmos. 49, 168 (1976).

R. H. Zerull, R. H. Giese, in Planets, Stars and Nebulae Studied with Photopolarimetry, T. Gehrels, Ed. (U. Ariz. Press, Tucson, 1974), p. 901.

Appl. Opt. (4)

Astrophys. J. (1)

D. W. Schuerman, Astrophys. J. 238, 337 (1980).
[CrossRef]

Beitr. Phys. Atmos. (1)

R. H. Zerull, Beitr. Phys. Atmos. 49, 168 (1976).

J. Appl. Phys. (1)

J. M. Greenberg, N. E. Pedersen, J. C. Pedersen, J. Appl. Phys. 32, 233 (1961).
[CrossRef]

Nature (London) Phys. Sci. (1)

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

Planet. Space Sci. (1)

M. Kerker, Planet. Space Sci. 29, 127 (1981).
[CrossRef]

Other (15)

However, Schaefer13 did find that 4:1 oblate and prolate spheroids with m = 1.33–i0.01 produce linear polarizations near 100%.

H. C. van de Hulst, Thesis Utrecht, Recherches Astron. Obs. d’Utrecht II, Part I (1946).

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

R. T. Wang, D. W. Schuerman, in Proceedings, 1981 CSL Scientific Conference on Obscuration and Aerosol Research, R. Kohl, Ed. (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Ground, Md., 1982), in press.

J. M. Greenberg in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 7.
[CrossRef]

R. H. Zerull, R. H. Giese, in Planets, Stars and Nebulae Studied with Photopolarimetry, T. Gehrels, Ed. (U. Ariz. Press, Tucson, 1974), p. 901.

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

R. W. Schaefer, Ph.D. Thesis, State U. New York at Albany (1980).

A. C. Lind, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1966).

R. T. Wang, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1968).

R. T. Wang, R. W. Detenbeck, F. Giovane, J. M. Greenberg, Final Report, NSF ATM75-15663 (1977).

R. T. Wang, J. M. Greenberg, Final Report, NASA NSG-7353 (1978).

D. W. Schuerman, in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980), p. 227.
[CrossRef]

B. Å. S. Gustafson, Reports from the Observatory of Lund, Sweden, No. 17 (1980).

K. F. Ratcliff, N. Y. Misconi, S. J. Paddock, in I.A.U. Symposium No. 90, Solid Particles in the Solar System, I. Halliday, B. A. McIntosh, Eds. (Reidel, Dordrecht, 1980), p. 391.
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Twenty-eight particle shapes (seven across any row) and sizes (four down any column) used in this study. The target number is given beneath each particle, and the number in parentheses above each particle indicates the figure in which the scattering results for that particle are presented. All particles have rotational symmetry about the axis that is parallel to the heavy arrow in the upper right; the wavelength is also shown.

Fig. 2
Fig. 2

Schematic view of the suspension and orientation mechanism in which the target (here a cylinder) is supported by nylon threads.

Fig. 3
Fig. 3

Comparison of theory (—) and analog (○) results for the 2:1 prolate spheroid, target 24, xs = 6.026.

Fig. 4
Fig. 4

Scattering results for target 1, a 4:1 cylinder (▲, analog data); for target 2, a 2:1 prolate spheroid (—, computed data); and for target 3, a 2:1 prolate spheroid (○, analog data). The three particles have equivalent surface areas; xs ≃ 3.3.

Fig. 5
Fig. 5

Scattering results for target 8, a 4:1 cylinder (▲, analog data); for target 9, a 2:1 prolate spheroid (—, computed data); and for target 10, a 2:1 prolate spheroid (⋯, computed data). The three particles have equivalent surface areas; xs ≃ 4.0.

Fig. 6
Fig. 6

Scattering results for target 15, a 4:1 cylinder (▲, analog data); for target 16, a 4:1 prolate spheroid (—, computed data); and for target 17, a 2:1 prolate spheroid (○, analog data). The three particles have equivalent surface areas; xs ≃ 5.0.

Fig. 7
Fig. 7

Scattering results for target 22, a 4:1 cylinder (▲, analog data); for target 23, a 4:1 prolate spheriod (—, computed data); and for target 24, a 2:1 prolate spheroid (⋯, computed data). The three particles have equivalent surface areas; xs ≃ 6.1.

Fig. 8
Fig. 8

Mie curves for target 4, xs ≃ 3.3 (⋯, computed data) and for target 18, xs ≃ 5.0 (—, computed data).

Fig. 9
Fig. 9

Mie curves for target 11, xs ≃ 4.0 (⋯, computed data) and for target 25, xs ≃ 6.1 (—, computed data).

Fig. 10
Fig. 10

Scattering results for target 5, a 2:1 oblate spheroid (○, analog data); for target 6, a 4:1 oblate spheroid (—, computed data); and for target 7, a 4:1 disk (▲, analog data). The three particles have equivalent surface areas; xs ≃ 3.3.

Fig. 11
Fig. 11

Scattering results for target 12,a 2:1 oblate spheroid (○, analog data); for target 13, a 4:1 oblate spheroid (—, computed data); and for target 14, a 4:1 disk (▲, analog data). The three particles have equivalent surface areas; xs ≃ 4.0.

Fig. 12
Fig. 12

Scattering results for target 19, a 2:1 oblate spheroid (○, analog data); for target 20, a 4:1 oblate spheroid (—, computed data); and for target 21, a 4:1 disk (▲, analog data). The three particles have equivalent surface areas; xs ≃ 5.0.

Fig. 13
Fig. 13

Scattering results for target 26, a 2:1 oblate spheroid (○, analog data); for target 27, a 4:1 oblate spheroid (—, computed data); and for target 28, a 4:1 disk (▲, analog data). The three particles have equivalent surface areas; xs ≃ 6.1.

Fig. 14
Fig. 14

Extinction efficiency vs the volume-equivalent phase-shift parameter, ρv = 2xv(m − 1), for 4:1 cylinders (△), 4:1 prolate spheroids (□), 2:1 prolate spheroids (○), 2:1 oblate spheroids (●), 4:1 oblate spheroids (■), and 4:1 disks (▲). The solid line represents spheres.

Tables (2)

Tables Icon

Table I Target Parameters a

Tables Icon

Table II Relative Values of β for the Twenty-Eight Particles a

Equations (7)

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C ext = 4 π k 2 S ( 0 ) sin ϕ ( 0 ) = 4 π k 2 Re [ S ( 0 ) ] ;
P ( θ ) = i 11 ( θ ) - i 22 ( θ ) i 11 ( θ ) + 2 i 12 ( θ ) + i 22 ( θ ) ;
C sca = π k 2 0 π [ i 11 ( θ ) + 2 i 12 ( θ ) + i 22 ( θ ) ] sin θ d θ ,             k = 2 π / λ , Q sca = C sca / π a s 2 ,             a s = radius of equal - surface - area sphere ;
Q ext = C ext π a s 2             and             Q ext , V = C ext / π a v 2 , a v = radius of equal - volume sphere ;
C abs = C ext - C sca ,             Q abs = Q ext - Q sca .
cos θ ¯ = π k 2 0 π [ i 11 ( θ ) + 2 i 12 ( θ ) + i 22 ( θ ) ] cos θ sin θ d θ C sca ;
C pr = C ext - cos θ ¯ C sca ,             Q pr = C pr / π a s 2 .

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