Abstract

The intensity of scattering I(θ) by transparent and absorbing spheres has been calculated from exact Mie theory for values of radius from 0.1 μm to 100 μm, wavelength 5461 Å, and the following values of refractive index mim′: (1) m = 1.01, 1.05, 1.1 (0.1) 2.0, m′ = 0; (2) m = 2, m′ = 0.002, 0.02, 0.2, and 2. The calculations have been made for a range of scattering angle θ large enough to indicate the first maximum in I(θ)θ2. According to the Sloan method for determining particle radius, the location of this maximum is inversely proportional to radius, independent of refractive index. The exact calculations show that this is accurate for radii above 10 μm, but for smaller particles the value of the refractive index affects the location to some extent.

© 1973 Optical Society of America

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References

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  1. C. K. Sloan, C. H. Arrington, papers presented at the 125th National Meeting, American Chemical Society, Kansas City, Mo., April 1954;C. K. Sloan, J. Phys. Chem. 59, 834 (1955).
    [CrossRef]
  2. W. H. Aughey, F. J. Baum, J. Opt. Soc. Am. 44, 833 (1954); a modified version is available from the Phoenix Precision Instrument Co.
    [CrossRef]
  3. P. F. Mullaney, M. A. van Dilla, J. R. Coulter, P. N. Dean, Rev. Sci. Instrum. 40, 1029 (1969).
    [CrossRef] [PubMed]
  4. A. M. Wims, M. E. Myers, J. Coll. Interface Sci. 39, 447 (1972).
    [CrossRef]
  5. M. E. Myers, A. M. Wims, Appl. Opt. 11, 947 (1972).
    [CrossRef] [PubMed]
  6. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  7. M. Kerker, The Scattering of Light (Academic Press, New York, 1969), p. 343f.
  8. P. J. Livesey, F. W. Billmeyer, J. Coll. Interface Sci. 30, 447 (1969).
    [CrossRef]
  9. M. Gouy, Ann. Phys. Chim. (6), 8, 145 (1886).
  10. G. Wolfson, Handbuch der Physik (Springer, Berlin, 1928), Vol. 28, Chap. 7, p. 288f.
  11. R. D. Gumprecht, C. M. Sliepcevich, J. Phys. Chem. 57, 90 (1953).
    [CrossRef]
  12. See Ref. 7, Chap. 8.
  13. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), p. 395f.
  14. Ref. 6, p. 85f.

1972

A. M. Wims, M. E. Myers, J. Coll. Interface Sci. 39, 447 (1972).
[CrossRef]

M. E. Myers, A. M. Wims, Appl. Opt. 11, 947 (1972).
[CrossRef] [PubMed]

1969

P. J. Livesey, F. W. Billmeyer, J. Coll. Interface Sci. 30, 447 (1969).
[CrossRef]

P. F. Mullaney, M. A. van Dilla, J. R. Coulter, P. N. Dean, Rev. Sci. Instrum. 40, 1029 (1969).
[CrossRef] [PubMed]

1954

1953

R. D. Gumprecht, C. M. Sliepcevich, J. Phys. Chem. 57, 90 (1953).
[CrossRef]

1886

M. Gouy, Ann. Phys. Chim. (6), 8, 145 (1886).

Arrington, C. H.

C. K. Sloan, C. H. Arrington, papers presented at the 125th National Meeting, American Chemical Society, Kansas City, Mo., April 1954;C. K. Sloan, J. Phys. Chem. 59, 834 (1955).
[CrossRef]

Aughey, W. H.

Baum, F. J.

Billmeyer, F. W.

P. J. Livesey, F. W. Billmeyer, J. Coll. Interface Sci. 30, 447 (1969).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), p. 395f.

Coulter, J. R.

P. F. Mullaney, M. A. van Dilla, J. R. Coulter, P. N. Dean, Rev. Sci. Instrum. 40, 1029 (1969).
[CrossRef] [PubMed]

Dean, P. N.

P. F. Mullaney, M. A. van Dilla, J. R. Coulter, P. N. Dean, Rev. Sci. Instrum. 40, 1029 (1969).
[CrossRef] [PubMed]

Gouy, M.

M. Gouy, Ann. Phys. Chim. (6), 8, 145 (1886).

Gumprecht, R. D.

R. D. Gumprecht, C. M. Sliepcevich, J. Phys. Chem. 57, 90 (1953).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light (Academic Press, New York, 1969), p. 343f.

Livesey, P. J.

P. J. Livesey, F. W. Billmeyer, J. Coll. Interface Sci. 30, 447 (1969).
[CrossRef]

Mullaney, P. F.

P. F. Mullaney, M. A. van Dilla, J. R. Coulter, P. N. Dean, Rev. Sci. Instrum. 40, 1029 (1969).
[CrossRef] [PubMed]

Myers, M. E.

M. E. Myers, A. M. Wims, Appl. Opt. 11, 947 (1972).
[CrossRef] [PubMed]

A. M. Wims, M. E. Myers, J. Coll. Interface Sci. 39, 447 (1972).
[CrossRef]

Sliepcevich, C. M.

R. D. Gumprecht, C. M. Sliepcevich, J. Phys. Chem. 57, 90 (1953).
[CrossRef]

Sloan, C. K.

C. K. Sloan, C. H. Arrington, papers presented at the 125th National Meeting, American Chemical Society, Kansas City, Mo., April 1954;C. K. Sloan, J. Phys. Chem. 59, 834 (1955).
[CrossRef]

van de Hulst, H. C.

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

van Dilla, M. A.

P. F. Mullaney, M. A. van Dilla, J. R. Coulter, P. N. Dean, Rev. Sci. Instrum. 40, 1029 (1969).
[CrossRef] [PubMed]

Wims, A. M.

M. E. Myers, A. M. Wims, Appl. Opt. 11, 947 (1972).
[CrossRef] [PubMed]

A. M. Wims, M. E. Myers, J. Coll. Interface Sci. 39, 447 (1972).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), p. 395f.

Wolfson, G.

G. Wolfson, Handbuch der Physik (Springer, Berlin, 1928), Vol. 28, Chap. 7, p. 288f.

Ann. Phys. Chim. (6)

M. Gouy, Ann. Phys. Chim. (6), 8, 145 (1886).

Appl. Opt.

J. Coll. Interface Sci.

P. J. Livesey, F. W. Billmeyer, J. Coll. Interface Sci. 30, 447 (1969).
[CrossRef]

A. M. Wims, M. E. Myers, J. Coll. Interface Sci. 39, 447 (1972).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Chem.

R. D. Gumprecht, C. M. Sliepcevich, J. Phys. Chem. 57, 90 (1953).
[CrossRef]

Rev. Sci. Instrum.

P. F. Mullaney, M. A. van Dilla, J. R. Coulter, P. N. Dean, Rev. Sci. Instrum. 40, 1029 (1969).
[CrossRef] [PubMed]

Other

See Ref. 7, Chap. 8.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), p. 395f.

Ref. 6, p. 85f.

C. K. Sloan, C. H. Arrington, papers presented at the 125th National Meeting, American Chemical Society, Kansas City, Mo., April 1954;C. K. Sloan, J. Phys. Chem. 59, 834 (1955).
[CrossRef]

G. Wolfson, Handbuch der Physik (Springer, Berlin, 1928), Vol. 28, Chap. 7, p. 288f.

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

M. Kerker, The Scattering of Light (Academic Press, New York, 1969), p. 343f.

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Figures (5)

Fig. 1
Fig. 1

i(θ)θ2 vs θ for 1-μ radius transparent spheres of various m, compared with values calculated from Fraunhofer diffraction theory. Wavelength 5461 Å in all figures.

Fig. 2
Fig. 2

Dependence of θmax, absolute forward scattering, and scattering coefficients for 1-μ spheres on m. The dashed line represents diffraction value.

Fig. 3
Fig. 3

As Fig. 2, but for 10-μ spheres.

Fig. 4
Fig. 4

θmax vs m for transparent spheres. Dashed line is diffraction value. Rayleigh-Gans value is shown at m = 1.

Fig. 5
Fig. 5

Absolute forward scattering vs r for m = 101. The straight lines correspond to the R.G. and F.D. approximations.

Tables (1)

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Table I θmax, Mie Theory

Equations (4)

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I ( θ ) = I ( 0 ) [ 2 J 1 ( ρ ) / ρ ] 2
I ( 0 ) = ( π r 2 / λ ) 2
I ( θ ) = λ 2 8 π 2 [ i i ( θ ) + i 2 ( θ ) ] = λ 2 8 π 2 i ( θ )
I ( θ ) = k 4 V 2 m - 1 2 4 π 2 [ G ( 2 α sin θ 2 ) ] 2 [ 1 + cos 2 θ 2 ] ,

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