Abstract

Rayleigh-Gans-Debye scattering theory is applicable to particles satisfying |m − 1| ≪ 1 and 2ka|m − 1| ≪ 1. It is often applied to large nonspherical particles such as bacteria where its validity is uncertain. The purpose of this study is to define the range of validity of the RGD approximation as applied to homogeneous nonspherical particles. Scattering calculations are made for a set of prolate spheroidal particles using the RGD approximation, and the results are compared to those obtained by the recently developed extended boundary condition method, a technique known to give accurate scattering results for nonspherical particles. Calculations for oriented particles with m = 1.05 verify that RGD error is dependent on particle orientation relative to the incident wave. Also, the error is found to increase with ka and to decrease with axial ratio for small particles, but increase with axial ratio for larger particles. Calculations for a particular randomly oriented particle show that the RGD approximation is more accurate for this case than if the incident wave is along the major dimension of the oriented particle.

© 1978 Optical Society of America

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Corrections

Peter W. Barber and Dau-Sing Wang, "Rayleigh-Gans-Debye applicability to scattering by nonspherical particles: corrigenda," Appl. Opt. 18, 962-963 (1979)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-18-7-962

References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. W. A. Farone, M. Kerker, E. Matijevic, in Interdisciplinary Conference on Electromagnetic Scattering, M. Kerker, Ed. (Pergamon, New York, 1963).
  3. M. Kerker, W. A. Farone, E. Matijevic, J. Opt. Soc. Am. 53, 758 (1963).
    [CrossRef]
  4. R. E. Buchanan, N. E. Gibbons, Eds., Bergey's Manual of Determinative Bacteriology (Williams and Wilkins, Baltimore, 1974).
  5. P. C. Waterman, Phys. Rev. D 3, 825 (1971).
    [CrossRef]
  6. P. Barber, C. Yeh, Appl. Opt. 14, 2864 (1975).
    [CrossRef] [PubMed]
  7. P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
    [CrossRef]
  8. S. Asano, G. Yamamoto, Appl. Opt. 14, 29 (1975).
    [PubMed]
  9. A. L. Koch, Biochim. Biophys. Acta 51, 429 (1961).
    [CrossRef]
  10. A. L. Koch, J. Theoret. Biol. 18, 133 (1968).
    [CrossRef]
  11. D. A. Cross, P. Latimer, Appl. Opt. 11, 1225 (1972).
    [CrossRef] [PubMed]
  12. J. J. Petres, G. Deželić, J. Coll. Interface Sci. 50, 296 (1975).
    [CrossRef]
  13. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  14. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  15. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  16. C. C. Johnson, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-23, 739 (1975).
    [CrossRef]

1977 (1)

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

1975 (4)

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

C. C. Johnson, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-23, 739 (1975).
[CrossRef]

S. Asano, G. Yamamoto, Appl. Opt. 14, 29 (1975).
[PubMed]

P. Barber, C. Yeh, Appl. Opt. 14, 2864 (1975).
[CrossRef] [PubMed]

1972 (1)

1971 (1)

P. C. Waterman, Phys. Rev. D 3, 825 (1971).
[CrossRef]

1968 (1)

A. L. Koch, J. Theoret. Biol. 18, 133 (1968).
[CrossRef]

1963 (1)

1961 (1)

A. L. Koch, Biochim. Biophys. Acta 51, 429 (1961).
[CrossRef]

Asano, S.

Barber, P.

Barber, P. W.

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

Cross, D. A.

Deželic, G.

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

Durney, C. H.

C. C. Johnson, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-23, 739 (1975).
[CrossRef]

Farone, W. A.

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

W. A. Farone, M. Kerker, E. Matijevic, in Interdisciplinary Conference on Electromagnetic Scattering, M. Kerker, Ed. (Pergamon, New York, 1963).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Johnson, C. C.

C. C. Johnson, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-23, 739 (1975).
[CrossRef]

Kerker, M.

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

W. A. Farone, M. Kerker, E. Matijevic, in Interdisciplinary Conference on Electromagnetic Scattering, M. Kerker, Ed. (Pergamon, New York, 1963).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Koch, A. L.

A. L. Koch, J. Theoret. Biol. 18, 133 (1968).
[CrossRef]

A. L. Koch, Biochim. Biophys. Acta 51, 429 (1961).
[CrossRef]

Latimer, P.

Massoudi, H.

C. C. Johnson, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-23, 739 (1975).
[CrossRef]

Matijevic, E.

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

W. A. Farone, M. Kerker, E. Matijevic, in Interdisciplinary Conference on Electromagnetic Scattering, M. Kerker, Ed. (Pergamon, New York, 1963).

Petres, J. J.

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

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

van de Hulst, H. C.

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

Waterman, P. C.

P. C. Waterman, Phys. Rev. D 3, 825 (1971).
[CrossRef]

Yamamoto, G.

Yeh, C.

Appl. Opt. (3)

Biochim. Biophys. Acta (1)

A. L. Koch, Biochim. Biophys. Acta 51, 429 (1961).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

C. C. Johnson, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-23, 739 (1975).
[CrossRef]

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

J. Coll. Interface Sci. (1)

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

J. Opt. Soc. Am. (1)

J. Theoret. Biol. (1)

A. L. Koch, J. Theoret. Biol. 18, 133 (1968).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, Phys. Rev. D 3, 825 (1971).
[CrossRef]

Other (6)

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

W. A. Farone, M. Kerker, E. Matijevic, in Interdisciplinary Conference on Electromagnetic Scattering, M. Kerker, Ed. (Pergamon, New York, 1963).

R. E. Buchanan, N. E. Gibbons, Eds., Bergey's Manual of Determinative Bacteriology (Williams and Wilkins, Baltimore, 1974).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

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Figures (9)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Scattering cross section (normalized to πa2) as a function of angle of incidence. Incident wave is unpolarized.

Fig. 3
Fig. 3

Scattering cross section (normalized to πa2) as a function of ka and axial ratio a:b.

Fig. 4
Fig. 4

Rayleigh-Gans-Debye error for a sphere.

Fig. 5
Fig. 5

Differential scattering cross section (normalized to πa2) for a sphere. Vertical polarization. The plotting increment is one degree in this and subsequent differential scattering cross-section curves.

Fig. 6
Fig. 6

Differential scattering cross section (normalized to πa2) for a 4:1 prolate spheroid, end-on incidence. Vertical polarization.

Fig. 7
Fig. 7

Differential scattering cross section (normalized to πa2) for a 4:1 prolate spheroid, broadside incidence. Vertical polarization.

Fig. 8
Fig. 8

Scattering cross section (normalized to πa2) as a function of ka for a randomly oriented 4:1 prolate spheroid.

Fig. 9
Fig. 9

Differential scattering cross section (normalized to πa2) for a randomly oriented 4:1 prolate spheroid. Vertical polarization.

Equations (14)

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σ s = 0 2 π 0 π σ d sin θ d θ d ϕ ,
σ d ( o , i ) = k 4 4 π 2 V 2 sin 2 χ ( m 1 ) 2 P ( θ ) .
P ( θ ) = { [ 3 / ( u 3 ) ] ( sin u u cos u ) } 2 ,
u = 2 k a sin θ 2 ( cos 2 β + b 2 a 2 sin 2 β ) 1 / 2 .
cos β = cos α sin ( θ / 2 ) + sin α cos ( θ / 2 ) cos ϕ .
E i ( r ) = ν = 1 D ν [ a ν M ν 1 ( k r ) + b ν N ν 1 ( k r ) ] ,
E s ( r ) = ν = 1 4 D ν [ f ν M ν 3 ( k r ) + g ν N ν 3 ( k r ) ] ,
[ f ν g ν ] = [ K + m J L + m I I + m L J + m K ] × [ K + m J L + m I I + m L J + m K ] 1 [ a ν 4 b ν 4 ] .
I = k 2 π s n M ν 3 ( k r ) × M μ 1 ( k r ) d S ,
σ d ( o , i ) = | E s ( o , i ) | 2 .
σ s u = ( σ s + σ s 2 ) ,
σ s = 0 2 π 0 π σ d sin θ d θ d ϕ
σ s = 0 2 π 0 π σ s sin θ d θ d ϕ .
P ( θ ) random = 0 π / 2 P ( θ ) sin β d β .

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