Abstract

The angular distribution of scattered light in the main lobe of the Fraunhofer diffraction pattern of a particle changes rapidly with its size, but is largely independent of its refractive index. Even when the particle is so small (diameter less than a few wavelengths) that its forward lobe must be calculated from the Mie theory, the relative angular distribution within the central part is found to be given approximately by the Fraunhofer formula with obliquity factor, even for particles smaller than one wavelength, except near a minimum in the particle extinction efficiency factor calculated from the Mie theory. A measurement of the ratio between the scattered intensities at a pair of convenient angles within the lobe can thus give a useful estimate of the size of spherical and nonspherical particles without knowing their refractive index. The sizing error caused by the narrowing of the lobe near an extinction minimum is acceptable for many practical purposes, and can in any case be detected by comparing the size estimates derived from measurements at two different wavelengths. Families of curves for sizing by this simple procedure have been prepared. Sideways scattering instruments have been preferred hitherto because of their easier construction. A realization of their possibilities for sizing unknown particles should, however, stimulate the development of suitable forward scattering instruments.

© 1966 Optical Society of America

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References

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  1. H. C. Van de Hulst, Light-Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  2. R. B. Penndorf, J. Opt. Soc. Am. 52, 797 (1962).
    [CrossRef]
  3. S. H. Maron, J. Colloid Sci. 18, 107 and 391 (1963); see also M. Kerker, W. A. Farone, L. B. Smith, E. Matijević, J. Colloid Sci. 19, 193 (1964).
    [CrossRef]
  4. R. Speiser, B. A. Brice, J. Opt. Soc. Am. 36, 364 (1946).
  5. W. H. Aughey, F. J. Baum, J. Opt. Soc. Am. 44, 833 (1954).
    [CrossRef]
  6. R S. Stein, P. M. Doty, J. Am. Chem. Soc. 68, 159 (1946).
    [CrossRef]
  7. C. Wippler, G. Scheibling, J. Chim. Phys. 51, 201 (1954).
  8. R. Teucher, Dechema Monograph. 44, 83 (1963).
  9. C. A. Zanoni, H. A. Hill, J. Opt. Soc. Am. 55, 1608 (1965).
    [CrossRef]
  10. M. L. Polanyi, Rev. Sci. Instr. 30, 626 (1959).
    [CrossRef]
  11. N. Kleine, Das Ärztliche Laboratorium 5, 133 (1961).
  12. B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
    [CrossRef]
  13. R. O. Gumprecht, C. M. Sliepeevich, J. Phys. Chem. 57, 90 (1953).
    [CrossRef]
  14. J. H. Chin, Ph.D. Thesis, U. of Michigan (1955).
  15. M. Minnaert, Light and Colour in the Open Air (Dover Publications, Inc., New York, 1961).
  16. J. Mc. K. Ellison, Proc. Phys. Soc. (London) Sec. B. 70102 (1957).
    [CrossRef]
  17. V. Vouk, Ph.D. Thesis, U. of London (1948).

1965

1964

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

1963

R. Teucher, Dechema Monograph. 44, 83 (1963).

S. H. Maron, J. Colloid Sci. 18, 107 and 391 (1963); see also M. Kerker, W. A. Farone, L. B. Smith, E. Matijević, J. Colloid Sci. 19, 193 (1964).
[CrossRef]

1962

1961

N. Kleine, Das Ärztliche Laboratorium 5, 133 (1961).

1959

M. L. Polanyi, Rev. Sci. Instr. 30, 626 (1959).
[CrossRef]

1957

J. Mc. K. Ellison, Proc. Phys. Soc. (London) Sec. B. 70102 (1957).
[CrossRef]

1954

C. Wippler, G. Scheibling, J. Chim. Phys. 51, 201 (1954).

W. H. Aughey, F. J. Baum, J. Opt. Soc. Am. 44, 833 (1954).
[CrossRef]

1953

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

1946

R S. Stein, P. M. Doty, J. Am. Chem. Soc. 68, 159 (1946).
[CrossRef]

R. Speiser, B. A. Brice, J. Opt. Soc. Am. 36, 364 (1946).

Aughey, W. H.

Baum, F. J.

Brice, B. A.

R. Speiser, B. A. Brice, J. Opt. Soc. Am. 36, 364 (1946).

Chin, J. H.

J. H. Chin, Ph.D. Thesis, U. of Michigan (1955).

Doty, P. M.

R S. Stein, P. M. Doty, J. Am. Chem. Soc. 68, 159 (1946).
[CrossRef]

Ellison, J. Mc. K.

J. Mc. K. Ellison, Proc. Phys. Soc. (London) Sec. B. 70102 (1957).
[CrossRef]

Gumprecht, R. O.

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

Hill, H. A.

Kleine, N.

N. Kleine, Das Ärztliche Laboratorium 5, 133 (1961).

Maron, S. H.

S. H. Maron, J. Colloid Sci. 18, 107 and 391 (1963); see also M. Kerker, W. A. Farone, L. B. Smith, E. Matijević, J. Colloid Sci. 19, 193 (1964).
[CrossRef]

Minnaert, M.

M. Minnaert, Light and Colour in the Open Air (Dover Publications, Inc., New York, 1961).

Penndorf, R. B.

Polanyi, M. L.

M. L. Polanyi, Rev. Sci. Instr. 30, 626 (1959).
[CrossRef]

Scheibling, G.

C. Wippler, G. Scheibling, J. Chim. Phys. 51, 201 (1954).

Silverman, B. A.

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

Sliepeevich, C. M.

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

Speiser, R.

R. Speiser, B. A. Brice, J. Opt. Soc. Am. 36, 364 (1946).

Stein, R S.

R S. Stein, P. M. Doty, J. Am. Chem. Soc. 68, 159 (1946).
[CrossRef]

Teucher, R.

R. Teucher, Dechema Monograph. 44, 83 (1963).

Thompson, B. J.

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

Van de Hulst, H. C.

H. C. Van de Hulst, Light-Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

Vouk, V.

V. Vouk, Ph.D. Thesis, U. of London (1948).

Ward, J. H.

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

Wippler, C.

C. Wippler, G. Scheibling, J. Chim. Phys. 51, 201 (1954).

Zanoni, C. A.

Das Ärztliche Laboratorium

N. Kleine, Das Ärztliche Laboratorium 5, 133 (1961).

Dechema Monograph.

R. Teucher, Dechema Monograph. 44, 83 (1963).

J. Am. Chem. Soc.

R S. Stein, P. M. Doty, J. Am. Chem. Soc. 68, 159 (1946).
[CrossRef]

J. Appl. Meteorol.

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

J. Chim. Phys.

C. Wippler, G. Scheibling, J. Chim. Phys. 51, 201 (1954).

J. Colloid Sci.

S. H. Maron, J. Colloid Sci. 18, 107 and 391 (1963); see also M. Kerker, W. A. Farone, L. B. Smith, E. Matijević, J. Colloid Sci. 19, 193 (1964).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Chem.

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

Proc. Phys. Soc. (London) Sec. B.

J. Mc. K. Ellison, Proc. Phys. Soc. (London) Sec. B. 70102 (1957).
[CrossRef]

Rev. Sci. Instr.

M. L. Polanyi, Rev. Sci. Instr. 30, 626 (1959).
[CrossRef]

Other

H. C. Van de Hulst, Light-Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

V. Vouk, Ph.D. Thesis, U. of London (1948).

J. H. Chin, Ph.D. Thesis, U. of Michigan (1955).

M. Minnaert, Light and Colour in the Open Air (Dover Publications, Inc., New York, 1961).

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Figures (2)

Fig. 1
Fig. 1

Scattering within the forward lobe: Mie-theory calculations for various refractive indices compared with the Fraunhofer diffraction formula with obliquity correction.

Fig. 2
Fig. 2

Schemes of particle sizing, based on scattering measurements within a forward lobe given by the Fraunhofer diffraction formula with obliquity correction. (a) Scattered intensity coefficients. (b) Goniometer instrument readings. (c) Annular instrument readings.

Tables (1)

Tables Icon

Table I Principal Published Mie Theory Computations of the Angular Distribution of Scattered Intensity for Medium and Large Transparent and Moderately Absorbing Spheres

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