Abstract

The ranges of refractive index and particle size over which the anomalous diffraction approximation is valid to within 15%, 50%, and 100% are mapped. The approximation is found to have a broader range of applicability for the extinction efficiency than the Rayleigh-Gans approximation. The large range of validity explains the success of schemes for determining particle size distributions of spheres from extinction measurements based on analytic inversions of formulas containing the approximation.

© 1968 Optical Society of America

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References

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  1. M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, S. Kitani, J. Colloid Sci. 19, 213 (1964).
    [CrossRef]
  2. M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, E. Matijevic, J. Phys. Chem. 67, 2105 (1963).
    [CrossRef]
  3. W. F. Espenscheid, M. Kerker, E. Matijevic, J. Phys. Chem. 68, 3093 (1964).
    [CrossRef]
  4. R. T. Jacobsen, M. Kerker, E. Matijevic, J. Phys. Chem. 71, 514 (1967).
    [CrossRef]
  5. K. S. Shifrin, A. Y. Perelman, V. G. Bakhtiyarov, Opt. Spectrosc. 20, 386 (1966).
  6. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  7. M. Kerker, W. A. Farone, E. Matijevic, J. Opt. Soc. Amer. 53, 758 (1963).
    [CrossRef]
  8. L. Lorenz, Skrifter Norske Videnskaps–Akad. Oslo, I. Mat. Natur. Kl. 6, 405 (1890) and Oerevres Sci. 1, 405 (1898); A. E. H. Love, Proc. London Math. Soc. 30, 308 (1899); G. Mie, Ann. Physik 25, 377 (1908); P. Debye, Ann. Physik 30, 59 (1909); T. S. Bromwich, Phil. Mag. 38, 144 (1919).
    [CrossRef]
  9. J. R. Hodkinson, Appl. Opt. 5, 839 (1966).
    [CrossRef] [PubMed]

1967 (1)

R. T. Jacobsen, M. Kerker, E. Matijevic, J. Phys. Chem. 71, 514 (1967).
[CrossRef]

1966 (2)

K. S. Shifrin, A. Y. Perelman, V. G. Bakhtiyarov, Opt. Spectrosc. 20, 386 (1966).

J. R. Hodkinson, Appl. Opt. 5, 839 (1966).
[CrossRef] [PubMed]

1964 (2)

W. F. Espenscheid, M. Kerker, E. Matijevic, J. Phys. Chem. 68, 3093 (1964).
[CrossRef]

M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, S. Kitani, J. Colloid Sci. 19, 213 (1964).
[CrossRef]

1963 (2)

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, E. Matijevic, J. Phys. Chem. 67, 2105 (1963).
[CrossRef]

M. Kerker, W. A. Farone, E. Matijevic, J. Opt. Soc. Amer. 53, 758 (1963).
[CrossRef]

1890 (1)

L. Lorenz, Skrifter Norske Videnskaps–Akad. Oslo, I. Mat. Natur. Kl. 6, 405 (1890) and Oerevres Sci. 1, 405 (1898); A. E. H. Love, Proc. London Math. Soc. 30, 308 (1899); G. Mie, Ann. Physik 25, 377 (1908); P. Debye, Ann. Physik 30, 59 (1909); T. S. Bromwich, Phil. Mag. 38, 144 (1919).
[CrossRef]

Bakhtiyarov, V. G.

K. S. Shifrin, A. Y. Perelman, V. G. Bakhtiyarov, Opt. Spectrosc. 20, 386 (1966).

Cohen, G. L.

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, E. Matijevic, J. Phys. Chem. 67, 2105 (1963).
[CrossRef]

Daby, E.

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, E. Matijevic, J. Phys. Chem. 67, 2105 (1963).
[CrossRef]

Espenscheid, W. F.

W. F. Espenscheid, M. Kerker, E. Matijevic, J. Phys. Chem. 68, 3093 (1964).
[CrossRef]

M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, S. Kitani, J. Colloid Sci. 19, 213 (1964).
[CrossRef]

Farone, W. A.

M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, S. Kitani, J. Colloid Sci. 19, 213 (1964).
[CrossRef]

M. Kerker, W. A. Farone, E. Matijevic, J. Opt. Soc. Amer. 53, 758 (1963).
[CrossRef]

Hodkinson, J. R.

Jacobsen, R. T.

R. T. Jacobsen, M. Kerker, E. Matijevic, J. Phys. Chem. 71, 514 (1967).
[CrossRef]

Kerker, M.

R. T. Jacobsen, M. Kerker, E. Matijevic, J. Phys. Chem. 71, 514 (1967).
[CrossRef]

W. F. Espenscheid, M. Kerker, E. Matijevic, J. Phys. Chem. 68, 3093 (1964).
[CrossRef]

M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, S. Kitani, J. Colloid Sci. 19, 213 (1964).
[CrossRef]

M. Kerker, W. A. Farone, E. Matijevic, J. Opt. Soc. Amer. 53, 758 (1963).
[CrossRef]

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, E. Matijevic, J. Phys. Chem. 67, 2105 (1963).
[CrossRef]

Kitani, S.

M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, S. Kitani, J. Colloid Sci. 19, 213 (1964).
[CrossRef]

Kratohvil, J. P.

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, E. Matijevic, J. Phys. Chem. 67, 2105 (1963).
[CrossRef]

Lorenz, L.

L. Lorenz, Skrifter Norske Videnskaps–Akad. Oslo, I. Mat. Natur. Kl. 6, 405 (1890) and Oerevres Sci. 1, 405 (1898); A. E. H. Love, Proc. London Math. Soc. 30, 308 (1899); G. Mie, Ann. Physik 25, 377 (1908); P. Debye, Ann. Physik 30, 59 (1909); T. S. Bromwich, Phil. Mag. 38, 144 (1919).
[CrossRef]

Matijevic, E.

R. T. Jacobsen, M. Kerker, E. Matijevic, J. Phys. Chem. 71, 514 (1967).
[CrossRef]

M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, S. Kitani, J. Colloid Sci. 19, 213 (1964).
[CrossRef]

W. F. Espenscheid, M. Kerker, E. Matijevic, J. Phys. Chem. 68, 3093 (1964).
[CrossRef]

M. Kerker, W. A. Farone, E. Matijevic, J. Opt. Soc. Amer. 53, 758 (1963).
[CrossRef]

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, E. Matijevic, J. Phys. Chem. 67, 2105 (1963).
[CrossRef]

Perelman, A. Y.

K. S. Shifrin, A. Y. Perelman, V. G. Bakhtiyarov, Opt. Spectrosc. 20, 386 (1966).

Shifrin, K. S.

K. S. Shifrin, A. Y. Perelman, V. G. Bakhtiyarov, Opt. Spectrosc. 20, 386 (1966).

van de Hulst, H. C.

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

Appl. Opt. (1)

J. Colloid Sci. (1)

M. Kerker, E. Matijevic, W. F. Espenscheid, W. A. Farone, S. Kitani, J. Colloid Sci. 19, 213 (1964).
[CrossRef]

J. Opt. Soc. Amer. (1)

M. Kerker, W. A. Farone, E. Matijevic, J. Opt. Soc. Amer. 53, 758 (1963).
[CrossRef]

J. Phys. Chem. (3)

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, E. Matijevic, J. Phys. Chem. 67, 2105 (1963).
[CrossRef]

W. F. Espenscheid, M. Kerker, E. Matijevic, J. Phys. Chem. 68, 3093 (1964).
[CrossRef]

R. T. Jacobsen, M. Kerker, E. Matijevic, J. Phys. Chem. 71, 514 (1967).
[CrossRef]

Opt. Spectrosc. (1)

K. S. Shifrin, A. Y. Perelman, V. G. Bakhtiyarov, Opt. Spectrosc. 20, 386 (1966).

Skrifter Norske Videnskaps–Akad. Oslo, I. Mat. Natur. Kl. (1)

L. Lorenz, Skrifter Norske Videnskaps–Akad. Oslo, I. Mat. Natur. Kl. 6, 405 (1890) and Oerevres Sci. 1, 405 (1898); A. E. H. Love, Proc. London Math. Soc. 30, 308 (1899); G. Mie, Ann. Physik 25, 377 (1908); P. Debye, Ann. Physik 30, 59 (1909); T. S. Bromwich, Phil. Mag. 38, 144 (1919).
[CrossRef]

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

Error contour diagram for extinction efficiencies, Qext. Points in region I agree with Mie theory to within 15%, region II to 50%, and region III to 100%. The parameter k = 2π/λ.

Fig. 2
Fig. 2

Same as Fig. 1 except for I1 at ϑ = 10° and points in region IV do not agree with Mie theory within 100%.

Fig. 3
Fig. 3

Same as Fig. 2 except for I1 at ϑ = 20°.

Fig. 4
Fig. 4

Same as Fig. 2 except for I1 at ϑ = 30°.

Equations (16)

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m - 1 1 ,
x m - 1 1 ,
2 x m - 1 1 ,
ρ = 2 x m - 1
ρ * = ρ ( 1 - i tan β ) ,
tan β = n 2 / n 1 - 1 .
Q e x t = 2 - 4 exp ( - ρ tan β ) ( cos β ρ ) sin ( ρ - β ) - 4 exp ( - ρ tan β ) ( cos β ρ ) 2 cos ( ρ - 2 β ) + 4 ( cos β ρ ) 2 cos 2 β .
Q e x t = 2 - ( 4 / ρ ) sin ρ + ( 4 / ρ 2 ) [ 1 - cos ρ ] .
I 1 = x 4 A ( ρ * , z ) 2 ,
I 2 = I 1 cos 2 θ ,
A ( ρ * , z ) = 0 π / 2 ( 1 - exp [ - ( i ρ + ρ tan β ) sin τ ] ) × J 0 ( z cos τ ) cos τ sin τ d τ ,
A ( ρ * , z ) = ( π / 6 n ) [ y 0 + 4 y 1 + 2 y 2 + 4 y 3 + + 4 y n - 1 + y n ] ,
Re y n = ( 1 - e - N n cos ψ n ) J 0 ( z cos τ n ) sin τ n cos τ n ,
Im y n = ( e - N n sin ψ n ) J 0 ( z cos τ n ) sin τ n cos τ n .
ψ n = ρ sin τ n ,
N n = ρ tan β sin τ n .

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