Abstract

Mueller matrices for micrometer-sized objects (2 ≤ ka ≤ 15) have been calculated for spherical and randomly oriented nonspherical and inhomogeneous bodies with relative refractive indices <1.3. These matrices were found to be highly different from the Rayleigh-Debye matrix as well as from the matrices observed for particles with higher contrast. Some general conclusions have been drawn for homogeneous spherical and nonspherical particles. Layered spheres and spheres with a small imaginary part of the refractive index show some unusual polarization behavior. It was not possible to deduce general features for layered spheres because of their complexity. We found almost invariant Mueller matrices for particles with small absorption in the investigated Mie region.

© 1989 Optical Society of America

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References

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  1. A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113–1121 (1970).
    [CrossRef] [PubMed]
  2. R. G. Pinnick, D. E. Carrol, D. J. Hofmann, “Polarized Light Scattered from Monodisperse Randomly Oriented Nonspherical Aerosol Particles: Measurements,” Appl. Opt. 15, 384–393 (1976).
    [CrossRef] [PubMed]
  3. R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental Determinations of Mueller Scattering Matrices for Nonspherical Particles,” Appl. Opt. 17, 2700–2710 (1978).
    [CrossRef] [PubMed]
  4. R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions Via the Mueller Matrix,” Appl. Opt. 19, 1323–1332 (1980).
    [CrossRef] [PubMed]
  5. J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurement for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980).
    [CrossRef]
  6. S. Asano, M. Sato, “Light Scattering by Randomly Oriented Spheroidal Particles,” Appl. Opt. 19, 962–974 (1980).
    [CrossRef] [PubMed]
  7. S. Asano, “Light Scattering by Horizontally Oriented Spheroidal Particles,” Appl. Opt. 22, 1390–1396 (1983).
    [CrossRef] [PubMed]
  8. K. N. Liou, Q. Cai, P. W. Barber, S. C. Hill, “Scattering Phase Matrix Comparison for Randomly Hexagonal Cylinders and Spheroids,” Appl. Opt. 22, 1684–1687 (1983).
    [CrossRef] [PubMed]
  9. P. E. Geller, T. G. Tsuei, P. W. Barber, “Information Content of the Scattering Matrix for Spheroidal Particles,” Appl. Opt. 24, 2391–2396 (1985).
    [CrossRef] [PubMed]
  10. V. J. Iafelice, W. S. Bickel, “Polarized Light Scattering Matrix Elements for Micron-Sized Rectangular Aluminium Lines on Reflecting Optical Surfaces,” Appl. Opt. 26, 1799–1805 (1987).
    [CrossRef]
  11. G. F. Beardsley, “Mueller Scattering Matrix of Sea Water,” J. Opt. Soc. Am. 58, 52 (1968).
    [CrossRef]
  12. W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarisation Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. U.S.A. 73, 486 (1976).
    [CrossRef] [PubMed]
  13. W. S. Bickel, M. E. Stafford, “Biological Particles as Irregularly Shaped Scatterers,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980).
    [CrossRef]
  14. K. J. Voss, E. S. Fry, “Measurement of Mueller Matrix for Ocean Water,” Appl. Opt. 23, 4427–4439 (1984).
    [CrossRef] [PubMed]
  15. W. S. Bickel, Arleen J. Watkins, Gordon Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,” Am. J. Phys. 55, 559–561 (1987).
    [CrossRef]
  16. P. C. Waterman, “Symmetry, Unitarity and Geometry in Electro Magnetic Scattering,” Phys. Rev. D 3, 825 (1971).
    [CrossRef]
  17. P. Barber, C. Yeh, “Scattering of Electromagnetic Waves by Arbitrarily Shaped Dielectric Bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  18. G. G. Stokes, “On the Composition and Resolution of Streams of Polarized Light from Different Sources,” Trans. Cambridge Philos. Soc. 9, 399 (1853).
  19. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  20. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  21. H. Mueller, “The Fundation of Optics,” J. Opt. Soc. Am. 38, 661 (1948).
  22. W. J. Perrin, “Polarization of Light Scattered by Isotropic Opalescent Media,” J. Chem. Phys. 10, 415 (1942).
    [CrossRef]
  23. K. D. Abhyankar, A. L. Fymat, “Relations between the Elements of the Phase Matrix for Scattering,” J. Math. Phys. 10, 1935 (1969).
    [CrossRef]
  24. E. S. Fry, G. W. Kattawar, “Relationships Between Elements of the Stokes Matrix,” Appl. Opt. 20, 2811–2814 (1981).
    [CrossRef] [PubMed]
  25. P. C. Waterman, “Matrix Methods in Potential Theory and Electromagnetic Scattering,” J. Appl. Phys. 50, 4550 (1979).
    [CrossRef]
  26. P. W. Barber, “Resonance Electromagnetic Absorption by Nonspherical Dielectric Objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
    [CrossRef]
  27. D. S. Wang, P. W. Barber, “Scattering by Inhomogeneous Nonspherical Objects,” Appl. Opt. 18, 1190–1197 (1979).
    [CrossRef] [PubMed]
  28. M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317– (1983).
    [CrossRef]
  29. P. W. Barber, D. S. Y. Wang, M. B. Long, “Scattering Calculations Using a Microcomputer,” Appl. Opt. 20, 1121–1123 (1981).
    [CrossRef] [PubMed]
  30. O. Glatter, M. Hofer, C. Jorde, W.-D. Eigner, “Interpretation of Elastic Light Scattering Data in Real Space,” J Colloid Interface Sci. 105, 577– (1985).
    [CrossRef]
  31. O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space II: Nonspherical and Inhomogeneous Monodisperse Systems,” J. Colloid Interface Sci. 122, 484 (1988).
    [CrossRef]
  32. O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space III: Determination of Size Distributions of Polydisperse Systems,” J. Colloid Interface Sci. 122, 496 (1988).
    [CrossRef]
  33. M. Hofer, J. Schurz, O. Glatter, “Oil-Water Emulsions: Particle Size Distribution from Elastic Light Scattering Data,” J. Colloid Interface Sci. (198x), in press.
  34. R. W. Schaefer, “Calculations of the Light Scattered by Randomly Oriented Ensembles of Spheroids of Size Comparable to the Wavelength,” Ph.D. Thesis, State University of New York at Albany (1980).
  35. R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M University (1978).
  36. J. R. Bottinger, “Measured Light Scattering Matrices of Single Cubic Particles,” Ph.D Thesis, Texas A&M University (1978).

1988

O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space II: Nonspherical and Inhomogeneous Monodisperse Systems,” J. Colloid Interface Sci. 122, 484 (1988).
[CrossRef]

O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space III: Determination of Size Distributions of Polydisperse Systems,” J. Colloid Interface Sci. 122, 496 (1988).
[CrossRef]

1987

V. J. Iafelice, W. S. Bickel, “Polarized Light Scattering Matrix Elements for Micron-Sized Rectangular Aluminium Lines on Reflecting Optical Surfaces,” Appl. Opt. 26, 1799–1805 (1987).
[CrossRef]

W. S. Bickel, Arleen J. Watkins, Gordon Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,” Am. J. Phys. 55, 559–561 (1987).
[CrossRef]

1985

P. E. Geller, T. G. Tsuei, P. W. Barber, “Information Content of the Scattering Matrix for Spheroidal Particles,” Appl. Opt. 24, 2391–2396 (1985).
[CrossRef] [PubMed]

O. Glatter, M. Hofer, C. Jorde, W.-D. Eigner, “Interpretation of Elastic Light Scattering Data in Real Space,” J Colloid Interface Sci. 105, 577– (1985).
[CrossRef]

1984

1983

1981

1980

1979

P. C. Waterman, “Matrix Methods in Potential Theory and Electromagnetic Scattering,” J. Appl. Phys. 50, 4550 (1979).
[CrossRef]

D. S. Wang, P. W. Barber, “Scattering by Inhomogeneous Nonspherical Objects,” Appl. Opt. 18, 1190–1197 (1979).
[CrossRef] [PubMed]

1978

1977

P. W. Barber, “Resonance Electromagnetic Absorption by Nonspherical Dielectric Objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

1976

R. G. Pinnick, D. E. Carrol, D. J. Hofmann, “Polarized Light Scattered from Monodisperse Randomly Oriented Nonspherical Aerosol Particles: Measurements,” Appl. Opt. 15, 384–393 (1976).
[CrossRef] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarisation Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. U.S.A. 73, 486 (1976).
[CrossRef] [PubMed]

1975

1971

P. C. Waterman, “Symmetry, Unitarity and Geometry in Electro Magnetic Scattering,” Phys. Rev. D 3, 825 (1971).
[CrossRef]

1970

1969

K. D. Abhyankar, A. L. Fymat, “Relations between the Elements of the Phase Matrix for Scattering,” J. Math. Phys. 10, 1935 (1969).
[CrossRef]

1968

1948

H. Mueller, “The Fundation of Optics,” J. Opt. Soc. Am. 38, 661 (1948).

1942

W. J. Perrin, “Polarization of Light Scattered by Isotropic Opalescent Media,” J. Chem. Phys. 10, 415 (1942).
[CrossRef]

1853

G. G. Stokes, “On the Composition and Resolution of Streams of Polarized Light from Different Sources,” Trans. Cambridge Philos. Soc. 9, 399 (1853).

Abhyankar, K. D.

K. D. Abhyankar, A. L. Fymat, “Relations between the Elements of the Phase Matrix for Scattering,” J. Math. Phys. 10, 1935 (1969).
[CrossRef]

Asano, S.

Barber, P.

Barber, P. W.

Beardsley, G. F.

Bickel, W. S.

W. S. Bickel, Arleen J. Watkins, Gordon Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,” Am. J. Phys. 55, 559–561 (1987).
[CrossRef]

V. J. Iafelice, W. S. Bickel, “Polarized Light Scattering Matrix Elements for Micron-Sized Rectangular Aluminium Lines on Reflecting Optical Surfaces,” Appl. Opt. 26, 1799–1805 (1987).
[CrossRef]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarisation Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. U.S.A. 73, 486 (1976).
[CrossRef] [PubMed]

W. S. Bickel, M. E. Stafford, “Biological Particles as Irregularly Shaped Scatterers,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bottiger, J. R.

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions Via the Mueller Matrix,” Appl. Opt. 19, 1323–1332 (1980).
[CrossRef] [PubMed]

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurement for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980).
[CrossRef]

Bottinger, J. R.

J. R. Bottinger, “Measured Light Scattering Matrices of Single Cubic Particles,” Ph.D Thesis, Texas A&M University (1978).

Cai, Q.

Carrol, D. E.

Davidson, J. F.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarisation Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. U.S.A. 73, 486 (1976).
[CrossRef] [PubMed]

Durney, C. H.

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317– (1983).
[CrossRef]

Eigner, W.-D.

O. Glatter, M. Hofer, C. Jorde, W.-D. Eigner, “Interpretation of Elastic Light Scattering Data in Real Space,” J Colloid Interface Sci. 105, 577– (1985).
[CrossRef]

Fry, E. S.

Fymat, A. L.

K. D. Abhyankar, A. L. Fymat, “Relations between the Elements of the Phase Matrix for Scattering,” J. Math. Phys. 10, 1935 (1969).
[CrossRef]

Gagne, G.

Geller, P. E.

Glatter, O.

O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space II: Nonspherical and Inhomogeneous Monodisperse Systems,” J. Colloid Interface Sci. 122, 484 (1988).
[CrossRef]

O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space III: Determination of Size Distributions of Polydisperse Systems,” J. Colloid Interface Sci. 122, 496 (1988).
[CrossRef]

O. Glatter, M. Hofer, C. Jorde, W.-D. Eigner, “Interpretation of Elastic Light Scattering Data in Real Space,” J Colloid Interface Sci. 105, 577– (1985).
[CrossRef]

M. Hofer, J. Schurz, O. Glatter, “Oil-Water Emulsions: Particle Size Distribution from Elastic Light Scattering Data,” J. Colloid Interface Sci. (198x), in press.

Hill, S. C.

Hofer, M.

O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space II: Nonspherical and Inhomogeneous Monodisperse Systems,” J. Colloid Interface Sci. 122, 484 (1988).
[CrossRef]

O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space III: Determination of Size Distributions of Polydisperse Systems,” J. Colloid Interface Sci. 122, 496 (1988).
[CrossRef]

O. Glatter, M. Hofer, C. Jorde, W.-D. Eigner, “Interpretation of Elastic Light Scattering Data in Real Space,” J Colloid Interface Sci. 105, 577– (1985).
[CrossRef]

M. Hofer, J. Schurz, O. Glatter, “Oil-Water Emulsions: Particle Size Distribution from Elastic Light Scattering Data,” J. Colloid Interface Sci. (198x), in press.

Hofmann, D. J.

Holland, A. C.

Huffman, D. R.

R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental Determinations of Mueller Scattering Matrices for Nonspherical Particles,” Appl. Opt. 17, 2700–2710 (1978).
[CrossRef] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarisation Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. U.S.A. 73, 486 (1976).
[CrossRef] [PubMed]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hunt, A. J.

Iafelice, V. J.

Iskander, M. F.

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317– (1983).
[CrossRef]

Jorde, C.

O. Glatter, M. Hofer, C. Jorde, W.-D. Eigner, “Interpretation of Elastic Light Scattering Data in Real Space,” J Colloid Interface Sci. 105, 577– (1985).
[CrossRef]

Kattawar, G. W.

Kilkson, R.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarisation Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. U.S.A. 73, 486 (1976).
[CrossRef] [PubMed]

Lakhtakia, A.

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317– (1983).
[CrossRef]

Liou, K. N.

Long, M. B.

Mueller, H.

H. Mueller, “The Fundation of Optics,” J. Opt. Soc. Am. 38, 661 (1948).

Perrin, W. J.

W. J. Perrin, “Polarization of Light Scattered by Isotropic Opalescent Media,” J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Perry, R. J.

Pinnick, R. G.

Sato, M.

Schaefer, R. W.

R. W. Schaefer, “Calculations of the Light Scattered by Randomly Oriented Ensembles of Spheroids of Size Comparable to the Wavelength,” Ph.D. Thesis, State University of New York at Albany (1980).

Schurz, J.

M. Hofer, J. Schurz, O. Glatter, “Oil-Water Emulsions: Particle Size Distribution from Elastic Light Scattering Data,” J. Colloid Interface Sci. (198x), in press.

Stafford, M. E.

W. S. Bickel, M. E. Stafford, “Biological Particles as Irregularly Shaped Scatterers,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980).
[CrossRef]

Stokes, G. G.

G. G. Stokes, “On the Composition and Resolution of Streams of Polarized Light from Different Sources,” Trans. Cambridge Philos. Soc. 9, 399 (1853).

Thompson, R. C.

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions Via the Mueller Matrix,” Appl. Opt. 19, 1323–1332 (1980).
[CrossRef] [PubMed]

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurement for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980).
[CrossRef]

R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M University (1978).

Tsuei, T. G.

van de Hulst, H. C.

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

Videen, Gordon

W. S. Bickel, Arleen J. Watkins, Gordon Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,” Am. J. Phys. 55, 559–561 (1987).
[CrossRef]

Voss, K. J.

Wang, D. S.

Wang, D. S. Y.

Waterman, P. C.

P. C. Waterman, “Matrix Methods in Potential Theory and Electromagnetic Scattering,” J. Appl. Phys. 50, 4550 (1979).
[CrossRef]

P. C. Waterman, “Symmetry, Unitarity and Geometry in Electro Magnetic Scattering,” Phys. Rev. D 3, 825 (1971).
[CrossRef]

Watkins, Arleen J.

W. S. Bickel, Arleen J. Watkins, Gordon Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,” Am. J. Phys. 55, 559–561 (1987).
[CrossRef]

Yeh, C.

Am. J. Phys.

W. S. Bickel, Arleen J. Watkins, Gordon Videen, “The light-scattering Mueller matrix elements for Rayleigh, Rayleigh-Gans, and Mie spheres,” Am. J. Phys. 55, 559–561 (1987).
[CrossRef]

Appl. Opt.

K. J. Voss, E. S. Fry, “Measurement of Mueller Matrix for Ocean Water,” Appl. Opt. 23, 4427–4439 (1984).
[CrossRef] [PubMed]

E. S. Fry, G. W. Kattawar, “Relationships Between Elements of the Stokes Matrix,” Appl. Opt. 20, 2811–2814 (1981).
[CrossRef] [PubMed]

P. W. Barber, D. S. Y. Wang, M. B. Long, “Scattering Calculations Using a Microcomputer,” Appl. Opt. 20, 1121–1123 (1981).
[CrossRef] [PubMed]

S. Asano, M. Sato, “Light Scattering by Randomly Oriented Spheroidal Particles,” Appl. Opt. 19, 962–974 (1980).
[CrossRef] [PubMed]

S. Asano, “Light Scattering by Horizontally Oriented Spheroidal Particles,” Appl. Opt. 22, 1390–1396 (1983).
[CrossRef] [PubMed]

K. N. Liou, Q. Cai, P. W. Barber, S. C. Hill, “Scattering Phase Matrix Comparison for Randomly Hexagonal Cylinders and Spheroids,” Appl. Opt. 22, 1684–1687 (1983).
[CrossRef] [PubMed]

P. E. Geller, T. G. Tsuei, P. W. Barber, “Information Content of the Scattering Matrix for Spheroidal Particles,” Appl. Opt. 24, 2391–2396 (1985).
[CrossRef] [PubMed]

V. J. Iafelice, W. S. Bickel, “Polarized Light Scattering Matrix Elements for Micron-Sized Rectangular Aluminium Lines on Reflecting Optical Surfaces,” Appl. Opt. 26, 1799–1805 (1987).
[CrossRef]

A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113–1121 (1970).
[CrossRef] [PubMed]

R. G. Pinnick, D. E. Carrol, D. J. Hofmann, “Polarized Light Scattered from Monodisperse Randomly Oriented Nonspherical Aerosol Particles: Measurements,” Appl. Opt. 15, 384–393 (1976).
[CrossRef] [PubMed]

R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental Determinations of Mueller Scattering Matrices for Nonspherical Particles,” Appl. Opt. 17, 2700–2710 (1978).
[CrossRef] [PubMed]

R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of Polarized Light Interactions Via the Mueller Matrix,” Appl. Opt. 19, 1323–1332 (1980).
[CrossRef] [PubMed]

P. Barber, C. Yeh, “Scattering of Electromagnetic Waves by Arbitrarily Shaped Dielectric Bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

D. S. Wang, P. W. Barber, “Scattering by Inhomogeneous Nonspherical Objects,” Appl. Opt. 18, 1190–1197 (1979).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag.

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317– (1983).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

P. W. Barber, “Resonance Electromagnetic Absorption by Nonspherical Dielectric Objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

J Colloid Interface Sci.

O. Glatter, M. Hofer, C. Jorde, W.-D. Eigner, “Interpretation of Elastic Light Scattering Data in Real Space,” J Colloid Interface Sci. 105, 577– (1985).
[CrossRef]

J. Appl. Phys.

P. C. Waterman, “Matrix Methods in Potential Theory and Electromagnetic Scattering,” J. Appl. Phys. 50, 4550 (1979).
[CrossRef]

J. Chem. Phys.

W. J. Perrin, “Polarization of Light Scattered by Isotropic Opalescent Media,” J. Chem. Phys. 10, 415 (1942).
[CrossRef]

J. Colloid Interface Sci.

O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space II: Nonspherical and Inhomogeneous Monodisperse Systems,” J. Colloid Interface Sci. 122, 484 (1988).
[CrossRef]

O. Glatter, M. Hofer, “Interpretation of Elastic Light Scattering Data in Real Space III: Determination of Size Distributions of Polydisperse Systems,” J. Colloid Interface Sci. 122, 496 (1988).
[CrossRef]

J. Math. Phys.

K. D. Abhyankar, A. L. Fymat, “Relations between the Elements of the Phase Matrix for Scattering,” J. Math. Phys. 10, 1935 (1969).
[CrossRef]

J. Opt. Soc. Am.

H. Mueller, “The Fundation of Optics,” J. Opt. Soc. Am. 38, 661 (1948).

G. F. Beardsley, “Mueller Scattering Matrix of Sea Water,” J. Opt. Soc. Am. 58, 52 (1968).
[CrossRef]

Phys. Rev. D

P. C. Waterman, “Symmetry, Unitarity and Geometry in Electro Magnetic Scattering,” Phys. Rev. D 3, 825 (1971).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of Polarisation Effects in Light Scattering: A New Biophysical Tool,” Proc. Natl. Acad. Sci. U.S.A. 73, 486 (1976).
[CrossRef] [PubMed]

Trans. Cambridge Philos. Soc.

G. G. Stokes, “On the Composition and Resolution of Streams of Polarized Light from Different Sources,” Trans. Cambridge Philos. Soc. 9, 399 (1853).

Other

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

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase Matrix Measurement for Electromagnetic Scattering by Sphere Aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980).
[CrossRef]

W. S. Bickel, M. E. Stafford, “Biological Particles as Irregularly Shaped Scatterers,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed. (Plenum, New York, 1980).
[CrossRef]

M. Hofer, J. Schurz, O. Glatter, “Oil-Water Emulsions: Particle Size Distribution from Elastic Light Scattering Data,” J. Colloid Interface Sci. (198x), in press.

R. W. Schaefer, “Calculations of the Light Scattered by Randomly Oriented Ensembles of Spheroids of Size Comparable to the Wavelength,” Ph.D. Thesis, State University of New York at Albany (1980).

R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M University (1978).

J. R. Bottinger, “Measured Light Scattering Matrices of Single Cubic Particles,” Ph.D Thesis, Texas A&M University (1978).

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Fig. 1
Fig. 1

Phase functions (P11) for randomly oriented bodies with different m but constant maximum dimension of the particle (ka = 11.2) normalized to 105 at zero scattering angle: (a) represents spheres; (b), (c), (d), and (e) represent oblate spheroids with axial ratios of 0.9, 0.8, 0.4, and 0.2, respectively; (f) shows prolate spheroids with an axial ratio of 5.

Fig. 2
Fig. 2

M12 (= −P12/P11) for randomly oriented bodies with different m but constant maximum dimension of the particle (ka = 11.2): (a) represents spheres; (b), (c), (d), and (e) represent oblate spheroids with axial ratios of 0.9, 0.8, 0.4, and 0.2, respectively; (f) shows prolate spheroids with an axial ratio of 5.

Fig. 3
Fig. 3

Ratio of depolarized light to the total scattered light (M22 = P22/P11) for randomly oriented bodies with different m but constant maximum dimension of the particle (ka = 11.2): (a), (b), (c), (d), and (e) represent oblate spheroids with axial ratios of 0.9, 0.8, 0.6, 0.4, and 0.2, respectively; (f) shows prolate spheroids with an axial ratio of 5.

Fig. 4
Fig. 4

M34 (= P34/P11) for randomly oriented bodies with different m but constant maximum dimension of the particle (ka = 11.2): (a) represents spheres; (b), (c), (d), and (e) represent oblate spheroids with axial ratios of 0.9, 0.8, 0.4, and 0.2, respectively; (f) shows prolate spheroids with an axial ratio of 5.

Fig. 5
Fig. 5

M33 (= P33/P11) for spheres with different relative refractive index but same maximum dimension (ka = 11.2).

Fig. 6
Fig. 6

M33 (=P33/P11) for randomly oriented bodies with different m but constant maximum dimension of the particle (ka = 11.2): (a), (b), (c), (d), and (e) represent oblate spheroids with axial ratios of 0.9, 0.8, 0.6, 0.4, and 0.2, respectively; (f) shows prolate spheroids with an axial ratio of 5.

Fig. 7
Fig. 7

M44 (=P44/P11) for randomly oriented bodies with different m but constant maximum dimension of the particle (ka = 11.2): (a), (b), (c), (d), and (e) represent oblate spheroids with axial ratios of 0.9, 0.8, 0.6, 0.4, and 0.2, respectively; (f) shows prolate spheroids with an axial ratio of 5.

Fig. 8
Fig. 8

Phase function P11 for two layered spheres and a layered oblate spheroid with the same maximum dimension of core [ka(i) = 6.1] and shell [ka(o) = 9.2] but different index of refraction in the layers [(i) stands for inner, (o) for outer region]: m(i) = 0.9 and m(o) = 1.1 (sphere: full lines, oblate: dashed lines); m(i) = 1.1 and m(o) = 0.9 (sphere: dash–dot lines).

Fig. 9
Fig. 9

M12, M22, M33, and M44 for two layered spheres and a layered oblate spheroid with the same maximum dimension of core [ka(i) = 6.1] and shell [ka(o) = 9.2] but different index of refraction in the layers [(i) stands for inner, (o) for outer region]: m(i) = 0.9 and m(o) = 1.1 (sphere: full lines, oblate: dashed lines); m(i) = 1.1 and m(o) = 0.9 (sphere: dash–dot lines).

Fig. 10
Fig. 10

Mueller matrix of two spheres with the same maximum dimension (ka = 11.2) and the same real part of the refractive index: the full lines represent the sphere with zero imaginary part; the dash–dot lines the sphere with an imaginary part of the refractive index equal to 0.0409.

Equations (7)

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I = E E * + E E * , Q = E E * E E * , U = E E * + E E * , V = i E E * E E * .
[ I s Q s U s V s ] = ( k 2 r 2 ) 1 [ S 11 S 12 S 13 S 14 S 21 S 22 S 23 S 24 S 31 S 32 S 33 S 34 S 41 S 42 S 43 S 44 ] [ I i , Q i , U i , V i , ]
S 11 S 12 0 0 S 12 S 22 0 0 0 0 S 33 S 34 0 0 S 34 S 44
( 4 π ) 1 4 π P 11 d Ω = 1 ,
[ I s Q s U s V s ] = C sca ( 4 π r 2 ) 1 [ P 11 P 12 0 0 P 12 P 22 0 0 0 0 P 33 P 34 0 0 P 34 P 44 ] [ I i , Q i , U i , V i , ]
P 11 M 12 0 0 M 12 M 22 0 0 0 0 M 33 M 34 0 0 M 34 M 44
[ f g ] = [ T ] [ a b ]

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