Abstract

A simple method is demonstrated to determine the diameters of dielectric spheres from 0.2 to 1.0 mm by observing the scattering of visible light. Theoretical calculations show that there is an approximately linear relationship between the size of the scattering sphere and the number of maxima and minima in the scattered field as a function of angle when the radius in the 200–1000-wavelength region.

© 1998 Optical Society of America

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References

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  1. E. D. Hirleman, ed., Proceedings of the Second International Congress on Optical Particle Sizing (Arizona State University, Tempe, Ariz., 1990).
  2. M. Maeda, S. Nakae, M. Ikegami, eds., Proceedings of the Third International Congress on Optical Particle Sizing (VCH Verlagsgesellschaft, Weinheim, Germany, 1994).
  3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  4. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  5. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  6. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  7. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Bohren, C. F.

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

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Huffman, D. R.

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

Kerker, M.

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

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 (Dover, New York, 1981).

Other

E. D. Hirleman, ed., Proceedings of the Second International Congress on Optical Particle Sizing (Arizona State University, Tempe, Ariz., 1990).

M. Maeda, S. Nakae, M. Ikegami, eds., Proceedings of the Third International Congress on Optical Particle Sizing (VCH Verlagsgesellschaft, Weinheim, Germany, 1994).

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

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

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

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Figures (9)

Fig. 1
Fig. 1

Plane wave scattering from a dielectric sphere.

Fig. 2
Fig. 2

Calculated scattered intensity for spheres with a = 456.1 μm and a = 643.8 μm as a function of scattering angles between 25° and 30°.

Fig. 3
Fig. 3

Number of intensity maxima between 25° and 30° scattering angles as a function of size parameter x = ka for n 1/n 2 = 1.33/1.515 refractive indices.

Fig. 4
Fig. 4

Block diagram of the experimental apparatus for the measurement in the scattering experiment.

Fig. 5
Fig. 5

(a) Scattering intensity pattern and (b) selected center strip part of the scattering pattern for a sphere with a dye concentration of 2.0 g/L and a = 456.1 μm.

Fig. 6
Fig. 6

Scattering intensity as a function of scattering angle for a sphere with a dye concentration of 1.5 g/L and a = 643.8 μm.

Fig. 7
Fig. 7

Comparison of experimental and theoretical scattering intensity patterns for a sphere with a dye concentration of 2.0 g/L and a = 456.1 μm.

Fig. 8
Fig. 8

Comparison of experimental and theoretical scattering intensity patterns for a sphere with a dye concentration of 1.5 g/L and a = 643.8 μm.

Fig. 9
Fig. 9

Comparison of experimental and theoretical scattering intensity patterns for a glass sphere with a = 0.490 ± 0.005 mm and n = 1.90.

Equations (9)

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i θ ,   ϕ = λ 2 4 π 2 cos 2   ϕ i 1 + sin 2   ϕ i 2 ,
i 1 = n = 1 2 n + 1 n n + 1 a n τ n cos   θ + b n π n cos   θ 2 ,
i 2 = n = 1 2 n + 1 n n + 1 a n π n cos   θ + b n τ n cos   θ 2 .
τ n cos   θ = d d θ   P n 1 cos   θ ,
π n cos   θ = P n 1 cos   θ / sin   θ ,
a n = j n k 1 a k 2 rj n k 2 r r = a - j n k 2 a k 1 rj n k 1 r r = a j n k 1 a k 2 rh n 1 k 2 r r = a - h n 1 k 2 a k 1 rj n k 1 r r = a ,
b n = k 2 2 j n k 2 a k 1 rj n k 1 r r = a - k 1 2 j n k 1 a k 2 rj n k 2 r r = a k 2 2 h n 1 k 2 a k 1 rj n k 1 r r = a - k 1 2 j n k 1 a k 2 rh n 1 k 2 r r = a ,
i θ = λ 2 8 π 2 i 1 + i 2 .
Q s = 2 π k 2 2 n = 1 2 n + 1 | a n r | 2 + | b n r | 2     m 2 .

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