Abstract

A method for evaluating the size of optically soft spheroidal particles by use of the angular structure of scattered light is proposed. It is based on the use of multilevel neural networks with a linear activation function. The retrieval errors of radius R of the equivolume sphere and aspect ratio e are investigated. The ranges of the size of R, e, and the refractive index are 0.31.51 µm, 0.2–1, and 1.01–1.02, respectively. The retrieval errors of the equivolume radius and aspect ratio are 0.004 µm and 0.02, respectively, for a three-level neural network (at a precisely measured angular distribution of scattered light). The retrieval errors of R and e for a one-level neural network are 2–5 times greater. The errors for a multilevel neural network increase faster than those for a single-level network.

© 2004 Optical Society of America

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References

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  1. V. P. Maltsev, Rev. Sci. Instrum. 71, 243 (2000).
    [CrossRef]
  2. C. W. Morris, A. Autret, and L. Boddy, Ecol. Modell. 146, 57 (2001).
    [CrossRef]
  3. A. G. Hoekstra and P. M. A. Sloot, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 585.
    [CrossRef]
  4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 198.
  5. M. I. Mishchenko, W. J. Wiscombe, J. W. Hovenier, and L. D. Travis, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 29.
    [CrossRef]
  6. Z. Ulanowski, Z. Wang, P. H. Kaye, and I. K. Ludlow, Appl. Opt. 37, 4027 (1998).
    [CrossRef]
  7. Z. Wang, Z. Ulanowski, and P. H. Kaye, Neural Comput. 8, 177 (1999).
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    [CrossRef] [PubMed]
  9. B. Widrow and M. A. Lehr, Proc. IEEE 78, 1415 (1990).
    [CrossRef]
  10. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974), p. 59.

2001 (1)

C. W. Morris, A. Autret, and L. Boddy, Ecol. Modell. 146, 57 (2001).
[CrossRef]

2000 (1)

V. P. Maltsev, Rev. Sci. Instrum. 71, 243 (2000).
[CrossRef]

1999 (1)

Z. Wang, Z. Ulanowski, and P. H. Kaye, Neural Comput. 8, 177 (1999).

1998 (1)

1990 (1)

B. Widrow and M. A. Lehr, Proc. IEEE 78, 1415 (1990).
[CrossRef]

1978 (1)

Autret, A.

C. W. Morris, A. Autret, and L. Boddy, Ecol. Modell. 146, 57 (2001).
[CrossRef]

Barber, P.

Boddy, L.

C. W. Morris, A. Autret, and L. Boddy, Ecol. Modell. 146, 57 (2001).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 198.

Hanson, R. J.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974), p. 59.

Hoekstra, A. G.

A. G. Hoekstra and P. M. A. Sloot, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 585.
[CrossRef]

Hovenier, J. W.

M. I. Mishchenko, W. J. Wiscombe, J. W. Hovenier, and L. D. Travis, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 29.
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 198.

Kaye, P. H.

Z. Wang, Z. Ulanowski, and P. H. Kaye, Neural Comput. 8, 177 (1999).

Z. Ulanowski, Z. Wang, P. H. Kaye, and I. K. Ludlow, Appl. Opt. 37, 4027 (1998).
[CrossRef]

Lawson, C. L.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974), p. 59.

Lehr, M. A.

B. Widrow and M. A. Lehr, Proc. IEEE 78, 1415 (1990).
[CrossRef]

Ludlow, I. K.

Maltsev, V. P.

V. P. Maltsev, Rev. Sci. Instrum. 71, 243 (2000).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, W. J. Wiscombe, J. W. Hovenier, and L. D. Travis, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 29.
[CrossRef]

Morris, C. W.

C. W. Morris, A. Autret, and L. Boddy, Ecol. Modell. 146, 57 (2001).
[CrossRef]

Sloot, P. M. A.

A. G. Hoekstra and P. M. A. Sloot, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 585.
[CrossRef]

Travis, L. D.

M. I. Mishchenko, W. J. Wiscombe, J. W. Hovenier, and L. D. Travis, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 29.
[CrossRef]

Ulanowski, Z.

Z. Wang, Z. Ulanowski, and P. H. Kaye, Neural Comput. 8, 177 (1999).

Z. Ulanowski, Z. Wang, P. H. Kaye, and I. K. Ludlow, Appl. Opt. 37, 4027 (1998).
[CrossRef]

Wang, D.-S.

Wang, Z.

Z. Wang, Z. Ulanowski, and P. H. Kaye, Neural Comput. 8, 177 (1999).

Z. Ulanowski, Z. Wang, P. H. Kaye, and I. K. Ludlow, Appl. Opt. 37, 4027 (1998).
[CrossRef]

Widrow, B.

B. Widrow and M. A. Lehr, Proc. IEEE 78, 1415 (1990).
[CrossRef]

Wiscombe, W. J.

M. I. Mishchenko, W. J. Wiscombe, J. W. Hovenier, and L. D. Travis, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 29.
[CrossRef]

Appl. Opt. (2)

Ecol. Modell. (1)

C. W. Morris, A. Autret, and L. Boddy, Ecol. Modell. 146, 57 (2001).
[CrossRef]

Neural Comput. (1)

Z. Wang, Z. Ulanowski, and P. H. Kaye, Neural Comput. 8, 177 (1999).

Proc. IEEE (1)

B. Widrow and M. A. Lehr, Proc. IEEE 78, 1415 (1990).
[CrossRef]

Rev. Sci. Instrum. (1)

V. P. Maltsev, Rev. Sci. Instrum. 71, 243 (2000).
[CrossRef]

Other (4)

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974), p. 59.

A. G. Hoekstra and P. M. A. Sloot, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 585.
[CrossRef]

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 198.

M. I. Mishchenko, W. J. Wiscombe, J. W. Hovenier, and L. D. Travis, in Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), p. 29.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Schematic representation of the three-level neural network.

Fig. 2
Fig. 2

Errors for retrieval of (a) R, (b) e, and (c) θ0 by the single-level (curve 1), two-level (curve 2), and three-level (curve 3) neural networks.

Equations (2)

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pα=k=0Nnwαkyk,  α=1,2,,Np.
k=0Nnynkwαk=pαn,  n=1,2,,NB,

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