Abstract

The entire light scattering matrix is experimentally determined for two fused silica cylinders illuminated at normal incidence (λ441.6 nm). Radii of 0.960 ± 0.002 and 3.091 ± 0.003 μm are determined by comparison with Mie theory indicating that micron-sized fiber radii can be determined to within a few nanometers by polarized light scattering techniques. The single fiber provides a good calibration source for polarization nephalometers, being free from problems inherent with spheres in solution. The fiber is a well-known geometry which is amenable to perturbation toward irregular shapes, and as such it provides the starting point for studying scattering from irregular particles.

© 1981 Optical Society of America

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References

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  1. W. A. Farone, M. Kerker, J. Opt. Soc. Am. 56, 81 (1966).
  2. A. van der Meulen, L. Strackee, Appl. Opt. 18, 3751 (1979).
    [PubMed]
  3. L. S. Watkins, J. Opt. Soc. Am. 64, 767 (1974).
    [CrossRef]
  4. J. L. Lundberg, J. Colloid Interface Sci. 29, 565 (1969).
    [CrossRef]
  5. W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci., USA 73, 486 (1976).
    [CrossRef] [PubMed]
  6. R. B. L. Biehl, M.S. Thesis, Department of Microbiology, U. Ariz. (1979).
  7. A. J. Hunt, D. R. Huffman, Rev. Sci. Instrum. 44, 1753 (1973).
    [CrossRef]
  8. R. J. Perry, A. J. Hunt, D. R. Huffman, Appl. Opt. 17, 2700 (1978).
    [CrossRef] [PubMed]
  9. R. C. Thompson, J. R. Bottiger, E. S. Fry, Appl. Opt. 19, 1323 (1980).
    [CrossRef] [PubMed]
  10. J. C. Kemp, J. Opt. Soc. Am. 59, 950 (1969).
  11. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957); M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969); D. R. Huffman, C. F. Bohren, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1981).
  12. C. F. Bohren, Department of Meteorology, Penn. State U., private communication (1979).
  13. F. Perrin, J. Chem. Phys. 10, 415 (1942).
    [CrossRef]
  14. W. S. Bickel, W. Gilliar, B. Bell, Appl. Opt. 19, 3671 (1980).
    [CrossRef] [PubMed]
  15. W. S. Bickel, B. W. Bell, W. Gilliar, M. K. Stein, Y. Hashim, W. Bailey, Proceedings, 1981 Chemical Systems Laboratory Conference on Obscuration and Aerosol Research, to be published 1982.

1980

1979

1978

1976

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci., USA 73, 486 (1976).
[CrossRef] [PubMed]

1974

1973

A. J. Hunt, D. R. Huffman, Rev. Sci. Instrum. 44, 1753 (1973).
[CrossRef]

1969

J. L. Lundberg, J. Colloid Interface Sci. 29, 565 (1969).
[CrossRef]

J. C. Kemp, J. Opt. Soc. Am. 59, 950 (1969).

1966

W. A. Farone, M. Kerker, J. Opt. Soc. Am. 56, 81 (1966).

1942

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Bailey, W.

W. S. Bickel, B. W. Bell, W. Gilliar, M. K. Stein, Y. Hashim, W. Bailey, Proceedings, 1981 Chemical Systems Laboratory Conference on Obscuration and Aerosol Research, to be published 1982.

Bell, B.

Bell, B. W.

W. S. Bickel, B. W. Bell, W. Gilliar, M. K. Stein, Y. Hashim, W. Bailey, Proceedings, 1981 Chemical Systems Laboratory Conference on Obscuration and Aerosol Research, to be published 1982.

Bickel, W. S.

W. S. Bickel, W. Gilliar, B. Bell, Appl. Opt. 19, 3671 (1980).
[CrossRef] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci., USA 73, 486 (1976).
[CrossRef] [PubMed]

W. S. Bickel, B. W. Bell, W. Gilliar, M. K. Stein, Y. Hashim, W. Bailey, Proceedings, 1981 Chemical Systems Laboratory Conference on Obscuration and Aerosol Research, to be published 1982.

Biehl, R. B. L.

R. B. L. Biehl, M.S. Thesis, Department of Microbiology, U. Ariz. (1979).

Bohren, C. F.

C. F. Bohren, Department of Meteorology, Penn. State U., private communication (1979).

Bottiger, J. R.

Davidson, J. F.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci., USA 73, 486 (1976).
[CrossRef] [PubMed]

Farone, W. A.

W. A. Farone, M. Kerker, J. Opt. Soc. Am. 56, 81 (1966).

Fry, E. S.

Gilliar, W.

W. S. Bickel, W. Gilliar, B. Bell, Appl. Opt. 19, 3671 (1980).
[CrossRef] [PubMed]

W. S. Bickel, B. W. Bell, W. Gilliar, M. K. Stein, Y. Hashim, W. Bailey, Proceedings, 1981 Chemical Systems Laboratory Conference on Obscuration and Aerosol Research, to be published 1982.

Hashim, Y.

W. S. Bickel, B. W. Bell, W. Gilliar, M. K. Stein, Y. Hashim, W. Bailey, Proceedings, 1981 Chemical Systems Laboratory Conference on Obscuration and Aerosol Research, to be published 1982.

Huffman, D. R.

R. J. Perry, A. J. Hunt, D. R. Huffman, Appl. Opt. 17, 2700 (1978).
[CrossRef] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci., USA 73, 486 (1976).
[CrossRef] [PubMed]

A. J. Hunt, D. R. Huffman, Rev. Sci. Instrum. 44, 1753 (1973).
[CrossRef]

Hunt, A. J.

Kemp, J. C.

Kerker, M.

W. A. Farone, M. Kerker, J. Opt. Soc. Am. 56, 81 (1966).

Kilkson, R.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci., USA 73, 486 (1976).
[CrossRef] [PubMed]

Lundberg, J. L.

J. L. Lundberg, J. Colloid Interface Sci. 29, 565 (1969).
[CrossRef]

Perrin, F.

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Perry, R. J.

Stein, M. K.

W. S. Bickel, B. W. Bell, W. Gilliar, M. K. Stein, Y. Hashim, W. Bailey, Proceedings, 1981 Chemical Systems Laboratory Conference on Obscuration and Aerosol Research, to be published 1982.

Strackee, L.

Thompson, R. C.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957); M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969); D. R. Huffman, C. F. Bohren, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1981).

van der Meulen, A.

Watkins, L. S.

Appl. Opt.

J. Chem. Phys.

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

J. Colloid Interface Sci.

J. L. Lundberg, J. Colloid Interface Sci. 29, 565 (1969).
[CrossRef]

J. Opt. Soc. Am.

Proc. Natl. Acad. Sci., USA

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci., USA 73, 486 (1976).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

A. J. Hunt, D. R. Huffman, Rev. Sci. Instrum. 44, 1753 (1973).
[CrossRef]

Other

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957); M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969); D. R. Huffman, C. F. Bohren, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1981).

C. F. Bohren, Department of Meteorology, Penn. State U., private communication (1979).

R. B. L. Biehl, M.S. Thesis, Department of Microbiology, U. Ariz. (1979).

W. S. Bickel, B. W. Bell, W. Gilliar, M. K. Stein, Y. Hashim, W. Bailey, Proceedings, 1981 Chemical Systems Laboratory Conference on Obscuration and Aerosol Research, to be published 1982.

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Figures (3)

Fig. 1
Fig. 1

Orientations of the optical elements required to measure the S i j * ( θ ) where ○ ≡ linear polarizer, □ ≡ modulator, and ○ F ≡ λ/4 plate. The angle indicated is the transmission axis for the polarizers, fast axis for the λ/4 wave plates, and fast axis for the modulator. The beam travels into the page, and angles are measured CCW from horizontal. The lock-in frequency required is shown in the upper right corner of each element. The elemental combination actually measured is shown at the bottom of each block.

Fig. 2
Fig. 2

Experimental (…) and theoretical (—) matrix elements for a fused silica cylinder. The radius determined was 0.960 ± 0.002 μm.

Fig. 3
Fig. 3

Experimental (…) and theoretical (—) matrix elements for a fused silica cylinder. The radius determined was 3.091 ± 0.003 μm.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

S 34 * = S 34 + S 14 S 41 + S 11 ,             S 12 * = S 12 S 11 ,             S 21 * = S 11 + S 21 .
[ S 11 S 12 S 11 0 0 S 12 + S 11 1 0 0 S 11 S 12 S 11 S 33 S 11 S 34 S 11 S 11 S 12 S 11 - S 34 S 11 S 33 S 11 ] .

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