Abstract

Measurements of polarized light scattered from monodisperse nonspherical randomly oriented aerosol particles are presented along with Mie theoretical results for spheres of approximately the same cross sectional area. For slightly nonspherical particles of sodium chloride and potassium sulfate with size parameter (defined as the ratio of the particle circumference to the wavelength) greater than about five, the intensity of light scattered is generally more than as predicted by Mie theory in the forward scattering lobe, but less at nonforward angles. For particles with size parameter less than five, the Mie results more closely match the measurements. Measured angular scattering patterns for randomly oriented particles are smoother than the Mie theoretical results and are nearly the same for salt and potassium sulfate particles of the same size. Measurements of particle depolarization are nearly independent of scattering angle.

© 1976 Optical Society of America

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  1. R. S. Powell, R. R. Circle, D. C. Vogel, P. D. Woodson, B. Donn, Planet. Space Sci. 15, 1641 (1967).
    [CrossRef]
  2. A. C. Holland, G. Gagne, Appl. Opt. 9, 1113 (1970).
    [CrossRef] [PubMed]
  3. D. H. Napper, R. H. Ottewill, in Proceedings of the Interdisciplinary Conference, M. Kerker, Ed., Clarkson College of Technology, Potsdam, New York (August1962).
  4. D. A. Cross, P. Latimer, Appl. Opt. 11, 1225 (1972).
    [CrossRef] [PubMed]
  5. J. J. Petres, G. Deželić, J. Colloid Interface Sci. 50, 2, 296 (1975).
    [CrossRef]
  6. R. G. Quiney, A. I. Carswell, Appl. Opt. 11, 1611 (1972).
    [CrossRef] [PubMed]
  7. D. T. Phillips, P. J. Wyatt, Appl. Opt. 11, 2082 (1972).
    [CrossRef] [PubMed]
  8. R. J. Hodkinson, in Proceedings of the Interdisciplinary Conference, M. Kerker, Ed., Clarkson College of Technology, Potsdam, New York (August1962).
  9. R. G. Pinnick, J. M. Rosen, D. J. Hofmann, Appl. Opt. 12, 1 (1973).
  10. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  11. F. Perrin, J. Chem. Phys. 10, 415 (1942).
    [CrossRef]
  12. D. D. Cooke, M. Kerker, J. Colloid Interface Sci. 42, 1, 150 (1973).
    [CrossRef]
  13. J. A. Davidson, E. A. Collins, J. Colloid Interface Sci. 40, 3, 437 (1972).
    [CrossRef]
  14. D. T. Phillips, P. J. Wyatt, R. M. Berkman, J. Colloid Interface Sci. 34, 1, 159 (1970).
    [CrossRef]
  15. N. K. Mehta, A. Grimison, A. McB. Block, Appl Opt. 10, 2031 (1971).
    [CrossRef] [PubMed]
  16. D. W. Cooper, J. W. Davis, R. L. Byers, Aerosol Sci. 5, 117 (1974).
    [CrossRef]

1975 (1)

J. J. Petres, G. Deželić, J. Colloid Interface Sci. 50, 2, 296 (1975).
[CrossRef]

1974 (1)

D. W. Cooper, J. W. Davis, R. L. Byers, Aerosol Sci. 5, 117 (1974).
[CrossRef]

1973 (2)

D. D. Cooke, M. Kerker, J. Colloid Interface Sci. 42, 1, 150 (1973).
[CrossRef]

R. G. Pinnick, J. M. Rosen, D. J. Hofmann, Appl. Opt. 12, 1 (1973).

1972 (4)

1971 (1)

N. K. Mehta, A. Grimison, A. McB. Block, Appl Opt. 10, 2031 (1971).
[CrossRef] [PubMed]

1970 (2)

A. C. Holland, G. Gagne, Appl. Opt. 9, 1113 (1970).
[CrossRef] [PubMed]

D. T. Phillips, P. J. Wyatt, R. M. Berkman, J. Colloid Interface Sci. 34, 1, 159 (1970).
[CrossRef]

1967 (1)

R. S. Powell, R. R. Circle, D. C. Vogel, P. D. Woodson, B. Donn, Planet. Space Sci. 15, 1641 (1967).
[CrossRef]

1942 (1)

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Berkman, R. M.

D. T. Phillips, P. J. Wyatt, R. M. Berkman, J. Colloid Interface Sci. 34, 1, 159 (1970).
[CrossRef]

Block, A. McB.

N. K. Mehta, A. Grimison, A. McB. Block, Appl Opt. 10, 2031 (1971).
[CrossRef] [PubMed]

Byers, R. L.

D. W. Cooper, J. W. Davis, R. L. Byers, Aerosol Sci. 5, 117 (1974).
[CrossRef]

Carswell, A. I.

Circle, R. R.

R. S. Powell, R. R. Circle, D. C. Vogel, P. D. Woodson, B. Donn, Planet. Space Sci. 15, 1641 (1967).
[CrossRef]

Collins, E. A.

J. A. Davidson, E. A. Collins, J. Colloid Interface Sci. 40, 3, 437 (1972).
[CrossRef]

Cooke, D. D.

D. D. Cooke, M. Kerker, J. Colloid Interface Sci. 42, 1, 150 (1973).
[CrossRef]

Cooper, D. W.

D. W. Cooper, J. W. Davis, R. L. Byers, Aerosol Sci. 5, 117 (1974).
[CrossRef]

Cross, D. A.

Davidson, J. A.

J. A. Davidson, E. A. Collins, J. Colloid Interface Sci. 40, 3, 437 (1972).
[CrossRef]

Davis, J. W.

D. W. Cooper, J. W. Davis, R. L. Byers, Aerosol Sci. 5, 117 (1974).
[CrossRef]

Deželic, G.

J. J. Petres, G. Deželić, J. Colloid Interface Sci. 50, 2, 296 (1975).
[CrossRef]

Donn, B.

R. S. Powell, R. R. Circle, D. C. Vogel, P. D. Woodson, B. Donn, Planet. Space Sci. 15, 1641 (1967).
[CrossRef]

Gagne, G.

Grimison, A.

N. K. Mehta, A. Grimison, A. McB. Block, Appl Opt. 10, 2031 (1971).
[CrossRef] [PubMed]

Hodkinson, R. J.

R. J. Hodkinson, in Proceedings of the Interdisciplinary Conference, M. Kerker, Ed., Clarkson College of Technology, Potsdam, New York (August1962).

Hofmann, D. J.

Holland, A. C.

Kerker, M.

D. D. Cooke, M. Kerker, J. Colloid Interface Sci. 42, 1, 150 (1973).
[CrossRef]

Latimer, P.

Mehta, N. K.

N. K. Mehta, A. Grimison, A. McB. Block, Appl Opt. 10, 2031 (1971).
[CrossRef] [PubMed]

Napper, D. H.

D. H. Napper, R. H. Ottewill, in Proceedings of the Interdisciplinary Conference, M. Kerker, Ed., Clarkson College of Technology, Potsdam, New York (August1962).

Ottewill, R. H.

D. H. Napper, R. H. Ottewill, in Proceedings of the Interdisciplinary Conference, M. Kerker, Ed., Clarkson College of Technology, Potsdam, New York (August1962).

Perrin, F.

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Petres, J. J.

J. J. Petres, G. Deželić, J. Colloid Interface Sci. 50, 2, 296 (1975).
[CrossRef]

Phillips, D. T.

D. T. Phillips, P. J. Wyatt, Appl. Opt. 11, 2082 (1972).
[CrossRef] [PubMed]

D. T. Phillips, P. J. Wyatt, R. M. Berkman, J. Colloid Interface Sci. 34, 1, 159 (1970).
[CrossRef]

Pinnick, R. G.

Powell, R. S.

R. S. Powell, R. R. Circle, D. C. Vogel, P. D. Woodson, B. Donn, Planet. Space Sci. 15, 1641 (1967).
[CrossRef]

Quiney, R. G.

Rosen, J. M.

Van de Hulst, H. C.

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

Vogel, D. C.

R. S. Powell, R. R. Circle, D. C. Vogel, P. D. Woodson, B. Donn, Planet. Space Sci. 15, 1641 (1967).
[CrossRef]

Woodson, P. D.

R. S. Powell, R. R. Circle, D. C. Vogel, P. D. Woodson, B. Donn, Planet. Space Sci. 15, 1641 (1967).
[CrossRef]

Wyatt, P. J.

D. T. Phillips, P. J. Wyatt, Appl. Opt. 11, 2082 (1972).
[CrossRef] [PubMed]

D. T. Phillips, P. J. Wyatt, R. M. Berkman, J. Colloid Interface Sci. 34, 1, 159 (1970).
[CrossRef]

Aerosol Sci. (1)

D. W. Cooper, J. W. Davis, R. L. Byers, Aerosol Sci. 5, 117 (1974).
[CrossRef]

Appl Opt. (1)

N. K. Mehta, A. Grimison, A. McB. Block, Appl Opt. 10, 2031 (1971).
[CrossRef] [PubMed]

Appl. Opt. (5)

J. Chem. Phys. (1)

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

J. Colloid Interface Sci. (4)

D. D. Cooke, M. Kerker, J. Colloid Interface Sci. 42, 1, 150 (1973).
[CrossRef]

J. A. Davidson, E. A. Collins, J. Colloid Interface Sci. 40, 3, 437 (1972).
[CrossRef]

D. T. Phillips, P. J. Wyatt, R. M. Berkman, J. Colloid Interface Sci. 34, 1, 159 (1970).
[CrossRef]

J. J. Petres, G. Deželić, J. Colloid Interface Sci. 50, 2, 296 (1975).
[CrossRef]

Planet. Space Sci. (1)

R. S. Powell, R. R. Circle, D. C. Vogel, P. D. Woodson, B. Donn, Planet. Space Sci. 15, 1641 (1967).
[CrossRef]

Other (3)

D. H. Napper, R. H. Ottewill, in Proceedings of the Interdisciplinary Conference, M. Kerker, Ed., Clarkson College of Technology, Potsdam, New York (August1962).

R. J. Hodkinson, in Proceedings of the Interdisciplinary Conference, M. Kerker, Ed., Clarkson College of Technology, Potsdam, New York (August1962).

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

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Figures (9)

Fig. 1
Fig. 1

A schematic of the apparatus used for measurement of the angular light scattering properties of aerosols.

Fig. 2
Fig. 2

A pulse height analyzer spectrum for monodisperse aerosol of sodium chloride for the incident light polarized in the plane of scattering and the same component of the scattered light measured. The scattering angle is 25°.

Fig. 3
Fig. 3

Angular scattering measurements (circles) and Mie theoretical results (smooth curves) for various spherical monodisperse aerosols. (a) Measurements and theory for the matrix element M2 vs scattering angle from the direction of forward scattering for uniform particles of polystyrene latex with refractive index 1.592–0i. The mean particle diameter as determined by electron microscope is 0.796 μ. The Mie results are for mean particle diameter of 0.82 μm. (b) Same as (a) except for matrix element M1. (c) Measurements and theory for the matrix element M1 vs scattering angle from the direction of forward scattering for uniform particles of polyvinyltoluene latex with refractive index 1.581–0i. The mean particle diameter as determined by an electron microscope is 2.02 μm. The Mie results are for mean particle diameter of 2.10 μm. (d) Measurements and theory for matrix element M2 vs scattering angle from the direction of forward scattering for uniform particles of oil made by the vibrating orifice technique. The value of the mean particle diameter of 1.18 μm used in the Mie calculations was picked for a best fit to the measurements.

Fig. 4
Fig. 4

Measurements (circles) and Mie theory (smooth curves) for the matrix element S11 or S22 vs scattering angle from the direction of forward scattering for uniform particles of sodium chloride. Electron microscope micrographs of the particles are presented with the corresponding angular scattering measurements. The solid curves are Mie theoretical results for homogeneous spheres of the same cross-sectional areas determined by electron microscope and for the refractive index of salt: 1.54–0i. The dashed curves are Mie results for spheres of the same size and refractive index, but containing a void, the size of the void (shown in percent volume) adjusted to give the best fit to the measurements. All the Mie results are normalized to scattering measurements on polystyrene shown in Fig. 3(a).

Fig. 5
Fig. 5

Measurements (circles) and Mie theory (smooth curves) for the matrix element S11 and S22 vs scattering angle from the direction of forward scattering for uniform particles of sodium chloride. Also shown in (c) and (d) are measurements (squares) of particle depolarization corresponding to the matrix element S12. Electron microscope micrographs of the particles are presented with the corresponding angular scattering measurements. The solid curves are Mie theoretical results for homogeneous spheres of the same cross-sectional areas determined by electron microscope and for the refractive index of salt: 1.54–0i. The dashed curves are Mie results for spheres of the same size and refractive index, but, containing a void, the size of the void (shown in percent volume) adjusted to give the best fit to the measurements. All the Mie results are normalized to scattering measurements on polystyrene shown in Fig. 3(a).

Fig. 6
Fig. 6

An enlargment of the transmission electron microscope micrographs of the salt particles shown in Fig. 5(c).

Fig. 7
Fig. 7

Measurements (circles) and Mie theory (smooth curves) for the matrix element S11, and S22 vs scattering angle from the direction of forward scattering for uniform particles of potassium sulfate. Electron microscope micrographs of the particles are presented with the corresponding angular scattering measurements. The solid curves are Mie theoretical results for homogeneous spheres of equal cross-sectional areas as determined by electron microscope and for the refractive index of potassium sulfate: 1.49–0i. The dashed curves are Mie results for spheres of the same cross-sectional area and refractive index, but containing a fictitious void, the size of the void (shown in percent volume) adjusted to give the best fit to the measurements. All the Mie results are normalized to scattering measurements on polystyrene shown in Fig. 3(a).

Fig. 8
Fig. 8

Measurements (circles) and Mie theory (smooth curves) for the matrix element S11 and S22 vs scattering angle from the direction of forward scattering for uniform particles of potassium sulfate. Also shown in (b) are measurements of the particle depolarization corresponding to the matrix element S12. Electron microscope micrographs of the particles are presented with the corresponding angular scattering measurements. The solid curves are Mie theoretical results for homogeneous spheres of equal cross-sectional areas as determined by electron microscope and for the refractive index of potassium sulfate: 1.49–0i. The dashed curves are Mie results for spheres of the same cross-sectional area and refractive index, but containing a void, the size of the void (shown in percent volume) adjusted to give the best fit to the measurements. All the Mie results are normalized to scattering measurements on polystyrene shown in Fig. 3(a).

Fig. 9
Fig. 9

Scanning electron microscope micrographs of potassium sulfate particles made by the vibrating capillary method. There are two distinct particle sizes here. The substrate is Nuclepore filter material. The smaller particles are approximately 0.80 μm in diameter.

Equations (3)

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[ I l s I r s U s V s ] = 1 k 2 [ S i j ] [ I l 0 I r 0 U 0 V 0 ] .
[ S 11 S 12 0 0 S 12 S 22 0 0 0 0 S 33 S 34 0 0 S 34 S 44 ] .
S 11 = M 2 ( m , x , θ ) ; S 22 = M 1 ( m , x , θ ) ; S 12 = 0 ; S 33 = S 44 = S 21 ( m , x , θ ) ; S 34 = D 21 ( m , x , θ ) .

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