Abstract

Formulation of the scattering problem as an integral permits calculation of the scattered field without any restrictions upon particle shape or internal structure (distribution of dielectric constant). However, the internal field must be known. Here, we approximate the internal field for a structured sphere by that of a homogeneous sphere whose dielectric constant is obtained from the volume weighted average of the polarizability. This approximation should be accurate for sufficiently small variations of the dielectric constant. The resulting algorithm has been tested by comparison with the boundary value solution for concentric spheres. For dielectric constants corresponding to aqueous suspensions of biological particles, the results are quite accurate for dimensionless sizes (circumference over wavelength) no greater than 7. The backscatter is particularly sensitive to small changes in morphology, including less symmetrical dispositions of the internal structure than those modeled by concentric spheres. Although the algorithm is also accurate for more highly refractive particles (corresponding to atmospheric aerosols), in this case the scattering is much less sensitive to changes in internal structure, even in the backward directions.

© 1978 Optical Society of America

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  1. D. S. Saxon, Lectures on the Scattering of Light, Department of Meteorology, University of California, Los Angeles, California, 1955. See also, R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).
  2. A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).
  3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  4. M. Kerker and D. D. Cooke, Appl. Opt. 15, 2105 (1976).
  5. P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
  6. P. Dusel, M. Kerker, and D. D. Cooke, J. Opt. Soc. Am. (to be published).
  7. S. Asano and G. Yamamoto, Appl. Opt. 14, 29 (1975).
  8. P. W. Barber and C. Yeh, Appl. Opt. 14, 2864 (1975).
  9. We follow the notation of H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396(1976), Appendix B, with the following modifications: the quantities ω0, k1, ε1, k2 there are denoted here by ω, k′, ε1, and k, respectively, whereas µ1, µ2, and ε2 there are set equal to unity in the present discussion.
  10. See, for example, Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (Natl. Bur. of Stand., U.S. GPO, Washington, D.C. 1965).

Abramowitz, M.

See, for example, Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (Natl. Bur. of Stand., U.S. GPO, Washington, D.C. 1965).

Aden, A. L.

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).

Asano, S.

S. Asano and G. Yamamoto, Appl. Opt. 14, 29 (1975).

Barber, P. W.

P. W. Barber and C. Yeh, Appl. Opt. 14, 2864 (1975).

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

Chew, H.

We follow the notation of H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396(1976), Appendix B, with the following modifications: the quantities ω0, k1, ε1, k2 there are denoted here by ω, k′, ε1, and k, respectively, whereas µ1, µ2, and ε2 there are set equal to unity in the present discussion.

Cooke, D. D.

P. Dusel, M. Kerker, and D. D. Cooke, J. Opt. Soc. Am. (to be published).

M. Kerker and D. D. Cooke, Appl. Opt. 15, 2105 (1976).

Dusel, P.

P. Dusel, M. Kerker, and D. D. Cooke, J. Opt. Soc. Am. (to be published).

Kerker, M.

P. Dusel, M. Kerker, and D. D. Cooke, J. Opt. Soc. Am. (to be published).

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).

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

M. Kerker and D. D. Cooke, Appl. Opt. 15, 2105 (1976).

We follow the notation of H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396(1976), Appendix B, with the following modifications: the quantities ω0, k1, ε1, k2 there are denoted here by ω, k′, ε1, and k, respectively, whereas µ1, µ2, and ε2 there are set equal to unity in the present discussion.

McNulty, P. J.

We follow the notation of H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396(1976), Appendix B, with the following modifications: the quantities ω0, k1, ε1, k2 there are denoted here by ω, k′, ε1, and k, respectively, whereas µ1, µ2, and ε2 there are set equal to unity in the present discussion.

Saxon, D. S.

D. S. Saxon, Lectures on the Scattering of Light, Department of Meteorology, University of California, Los Angeles, California, 1955. See also, R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).

Stegun, I.

See, for example, Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (Natl. Bur. of Stand., U.S. GPO, Washington, D.C. 1965).

Yamamoto, G.

S. Asano and G. Yamamoto, Appl. Opt. 14, 29 (1975).

Yeh, C.

P. W. Barber and C. Yeh, Appl. Opt. 14, 2864 (1975).

Other (10)

D. S. Saxon, Lectures on the Scattering of Light, Department of Meteorology, University of California, Los Angeles, California, 1955. See also, R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).

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

M. Kerker and D. D. Cooke, Appl. Opt. 15, 2105 (1976).

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

P. Dusel, M. Kerker, and D. D. Cooke, J. Opt. Soc. Am. (to be published).

S. Asano and G. Yamamoto, Appl. Opt. 14, 29 (1975).

P. W. Barber and C. Yeh, Appl. Opt. 14, 2864 (1975).

We follow the notation of H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396(1976), Appendix B, with the following modifications: the quantities ω0, k1, ε1, k2 there are denoted here by ω, k′, ε1, and k, respectively, whereas µ1, µ2, and ε2 there are set equal to unity in the present discussion.

See, for example, Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (Natl. Bur. of Stand., U.S. GPO, Washington, D.C. 1965).

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