Abstract

A laser light-scattering instrument has been designed to permit an investigation of the spatial intensity distribution of light scattered by individual airborne particles constrained within a laminar flow, with a view to providing a means of classifying the particles in terms of their shape and size. Ultimately, a means of detecting small concentrations of potentially hazardous particles, such as asbestos fiber, is sought. The instrument captures data relating to the spatial distribution of light scattered from individual particles in flow. As part of an investigation to optimize orientation control over particles within the sample airstream, the instrument has been challenged with nonspherical particles of defined shape and size, and a simple theoretical treatment based on the Rayleigh–Gans formalism has been used to model the spatial intensity distribution of light scattered from these particle types and hence derive particle orientation data. Both experimental and theoretical scattering data are presented, showing good agreement for all particle types examined.

© 1994 Optical Society of America

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References

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  1. J. G. Firth, “Future trends,” in Proceedings of the International Symposium—Clean Air at Work, R. H. Brown, M. Curtis, K. J. Saunders, S. Vandendriessche, eds. (Royal Society of Chemistry, London, 1992), pp. 469–473.
  2. J. Gebhart, A. Anselm, “Effect of particle shape on the response of single particle optical counters,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 393–409.
  3. M. Bottlinger, H. Umhauer, “Scattered light particle-size counting analysis—influence of shape and structure,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 363–369.
  4. R. T. Killinger, R. H. Zerull, “Effects of shape and orientation to be considered for optical particle sizing,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 419–429.
  5. P. H. Kaye, E. Hirst, J. M. Clark, F. Micheli, “Airborne particle shape and size classification from spatial light scattering profiles,” J. Aerosol Sci. 23, 597–611 (1992).
    [Crossref]
  6. M. Bartholdi, G. C. Salzman, R. D. Heibert, M. Kerker, “Differential light scattering photometer for rapid analysis of single particles in flow,” Appl. Opt. 19, 1573–1581 (1980).
    [Crossref] [PubMed]
  7. P. H. Kaye, F. Micheli, M. C. Tracey, E. Hirst, A. M. Gundlach, “The production of precision silicon micromachined nonspherical particles for aerosol studies,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 201–204 (1992)].
  8. P. H. Kaye, E. Hirst, F. Micheli, “The characterisation of airborne particles by analysis of spatial light scattering profiles,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 321–324 (1992)].
  9. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  10. M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
    [Crossref]
  11. S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–417 (1982).
    [Crossref]
  12. P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrary shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [Crossref] [PubMed]
  13. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1988), Chap. 8, p. 201.

1992 (1)

P. H. Kaye, E. Hirst, J. M. Clark, F. Micheli, “Airborne particle shape and size classification from spatial light scattering profiles,” J. Aerosol Sci. 23, 597–611 (1992).
[Crossref]

1990 (1)

M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
[Crossref]

1982 (1)

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–417 (1982).
[Crossref]

1980 (1)

1975 (1)

Anselm, A.

J. Gebhart, A. Anselm, “Effect of particle shape on the response of single particle optical counters,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 393–409.

Barber, P.

Bartholdi, M.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1988), Chap. 8, p. 201.

Bottlinger, M.

M. Bottlinger, H. Umhauer, “Scattered light particle-size counting analysis—influence of shape and structure,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 363–369.

Casalnuovo, S. A.

M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
[Crossref]

Clark, J. M.

P. H. Kaye, E. Hirst, J. M. Clark, F. Micheli, “Airborne particle shape and size classification from spatial light scattering profiles,” J. Aerosol Sci. 23, 597–611 (1992).
[Crossref]

Firth, J. G.

J. G. Firth, “Future trends,” in Proceedings of the International Symposium—Clean Air at Work, R. H. Brown, M. Curtis, K. J. Saunders, S. Vandendriessche, eds. (Royal Society of Chemistry, London, 1992), pp. 469–473.

Gebhart, J.

J. Gebhart, A. Anselm, “Effect of particle shape on the response of single particle optical counters,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 393–409.

Glisson, A. W.

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–417 (1982).
[Crossref]

Gundlach, A. M.

P. H. Kaye, F. Micheli, M. C. Tracey, E. Hirst, A. M. Gundlach, “The production of precision silicon micromachined nonspherical particles for aerosol studies,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 201–204 (1992)].

Hanson, R. W.

M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
[Crossref]

Heibert, R. D.

Hirst, E.

P. H. Kaye, E. Hirst, J. M. Clark, F. Micheli, “Airborne particle shape and size classification from spatial light scattering profiles,” J. Aerosol Sci. 23, 597–611 (1992).
[Crossref]

P. H. Kaye, E. Hirst, F. Micheli, “The characterisation of airborne particles by analysis of spatial light scattering profiles,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 321–324 (1992)].

P. H. Kaye, F. Micheli, M. C. Tracey, E. Hirst, A. M. Gundlach, “The production of precision silicon micromachined nonspherical particles for aerosol studies,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 201–204 (1992)].

Hoover, M. D.

M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
[Crossref]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1988), Chap. 8, p. 201.

Hurd, A. J.

M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
[Crossref]

Kaye, P. H.

P. H. Kaye, E. Hirst, J. M. Clark, F. Micheli, “Airborne particle shape and size classification from spatial light scattering profiles,” J. Aerosol Sci. 23, 597–611 (1992).
[Crossref]

P. H. Kaye, F. Micheli, M. C. Tracey, E. Hirst, A. M. Gundlach, “The production of precision silicon micromachined nonspherical particles for aerosol studies,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 201–204 (1992)].

P. H. Kaye, E. Hirst, F. Micheli, “The characterisation of airborne particles by analysis of spatial light scattering profiles,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 321–324 (1992)].

Kerker, M.

Killinger, R. T.

R. T. Killinger, R. H. Zerull, “Effects of shape and orientation to be considered for optical particle sizing,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 419–429.

Lipowicz, P. J.

M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
[Crossref]

Micheli, F.

P. H. Kaye, E. Hirst, J. M. Clark, F. Micheli, “Airborne particle shape and size classification from spatial light scattering profiles,” J. Aerosol Sci. 23, 597–611 (1992).
[Crossref]

P. H. Kaye, F. Micheli, M. C. Tracey, E. Hirst, A. M. Gundlach, “The production of precision silicon micromachined nonspherical particles for aerosol studies,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 201–204 (1992)].

P. H. Kaye, E. Hirst, F. Micheli, “The characterisation of airborne particles by analysis of spatial light scattering profiles,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 321–324 (1992)].

Rao, S. M.

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–417 (1982).
[Crossref]

Salzman, G. C.

Tracey, M. C.

P. H. Kaye, F. Micheli, M. C. Tracey, E. Hirst, A. M. Gundlach, “The production of precision silicon micromachined nonspherical particles for aerosol studies,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 201–204 (1992)].

Umhauer, H.

M. Bottlinger, H. Umhauer, “Scattered light particle-size counting analysis—influence of shape and structure,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 363–369.

Wilton, D. R.

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–417 (1982).
[Crossref]

Yeh, C.

Yeh, H. C.

M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
[Crossref]

Zerull, R. H.

R. T. Killinger, R. H. Zerull, “Effects of shape and orientation to be considered for optical particle sizing,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 419–429.

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–417 (1982).
[Crossref]

J. Aerosol Sci. (2)

P. H. Kaye, E. Hirst, J. M. Clark, F. Micheli, “Airborne particle shape and size classification from spatial light scattering profiles,” J. Aerosol Sci. 23, 597–611 (1992).
[Crossref]

M. D. Hoover, S. A. Casalnuovo, P. J. Lipowicz, H. C. Yeh, R. W. Hanson, A. J. Hurd, “Method for producing non-spherical monodisperse particles using integrated circuit fabrication techniques,” J. Aerosol Sci. 21, 569–575 (1990).
[Crossref]

Other (8)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1988), Chap. 8, p. 201.

P. H. Kaye, F. Micheli, M. C. Tracey, E. Hirst, A. M. Gundlach, “The production of precision silicon micromachined nonspherical particles for aerosol studies,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 201–204 (1992)].

P. H. Kaye, E. Hirst, F. Micheli, “The characterisation of airborne particles by analysis of spatial light scattering profiles,” in Proceedings of the 1992 European Aerosol Conference, Oxford [J. Aerosol Sci. 23S1, 321–324 (1992)].

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

J. G. Firth, “Future trends,” in Proceedings of the International Symposium—Clean Air at Work, R. H. Brown, M. Curtis, K. J. Saunders, S. Vandendriessche, eds. (Royal Society of Chemistry, London, 1992), pp. 469–473.

J. Gebhart, A. Anselm, “Effect of particle shape on the response of single particle optical counters,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 393–409.

M. Bottlinger, H. Umhauer, “Scattered light particle-size counting analysis—influence of shape and structure,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 363–369.

R. T. Killinger, R. H. Zerull, “Effects of shape and orientation to be considered for optical particle sizing,” in Proceedings of the International Symposium on Optical Particle Sizing, Theory and Practice (Plenum, New York, 1988), pp. 419–429.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of optical-scattering chamber used to record spatial light-scattering data from individual particles carried within an airstream through a focused laser beam.

Fig. 2
Fig. 2

Scanning electron micrograph of the silicon dioxide micromachined particles used as standard reference fibers in the study. The experimental scattering profiles shown in Figs. 35, below, were recorded from individual particles of this type.

Fig. 3
Fig. 3

(a) Experimental scattering profile recorded from a single silicon dioxide fiber (1.5 μm × 1.5 μm × 12 μm). Each white dot corresponds to a single photon scattered to the image intensifier. The laser beam propagation axis is orthogonal to the plane of the page toward the center of the image. The inner dark circle circumference corresponds to scattering at 28° to the beam axis, and the outer circumference corresponds to scattering at 141°. The full 360° of azimuth is captured, and the image therefore corresponds to 83% of the total sphere of scattering about the particle. (b) Corresponding best-fit theoretical profile resulting from a fiber model illuminated as indicated in (c). (c) Schematic diagram showing the orientation of the theoretical fiber model with respect to the direction of incident illumination (indicated by the arrow). In this case the fiber has a face toward the illumination.

Fig. 4
Fig. 4

(a) Experimental scattering profile from a silicon dioxide fiber identical in form to that which produced the data in Fig. 3(a). The image-acquisition time was 2 μs. Here the spreading of the radiation in the vertical plane is related to edge-on illumination of the particle, as indicated in (c). (b) Corresponding best-fit theoretical profile resulting from a fiber model illuminated as indicated in (c). (c) schematic diagram showing the orientation of the theoretical fiber model with respect to the direction of incident illumination (indicated by the arrow). In this case the fiber is almost edge-on to the illumination.

Fig. 5
Fig. 5

(a) Experimental scattering profile from a silicon dioxide fiber identical in form to that which produced the data in Fig. 3(a). The scattering profile exhibits vertical spreading. The image-acquisition time was 2 μs. (b) Corresponding best-fit profile resulting from a theoretical fiber model. (c) Schematic diagram showing the orientation of the theoretical fiber model with respect to the direction of incident illumination (indicated by the arrow). In this case the fiber is rotated 10° about its long axis. The 5° tilt from the vertical accounts for the main bar of scattering adopting a conic-section form.

Fig. 6
Fig. 6

(a) Experimental scattering profile from a single crystal drawn from an aerosol of salt crystals. The image-acquisition time was 2 μs. (b) Best-fit theoretical profile corresponding to a cube with 5-μm sides. (c) Diagram showing the incident illumination direction in relation to the cubic array. A 15° rotation of the cube around the illumination direction was also applied to produce the profile in (b).

Fig. 7
Fig. 7

(a) Experimental scattering profile from a single copper flake drawn from an aerosol. The image-acquisition time was 2 μs. (b) Theoretical profile corresponding to a cuboid with 3-μm sides and a thickness of 0. 1 μm. (c) Diagram showing the incident illumination direction (indicated by the arrow) in relation to the array of point scatterers used as the model in (b).

Equations (10)

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m - 1 1 ,             k d m - 1 1 ,
[ d 0 0 ] T ,             [ 0 d 0 ] T ,             [ 0 0 d ] T ,
[ cos β 0 - sin β 0 1 0 sin β 0 cos β ] ,     [ 1 0 0 0 cos α - sin α 0 sin α cos α ] ,     [ cos γ - sin γ 0 sin γ cos γ 0 0 0 1 ] ,
2 π ( p · k ^ - p · s ^ ) / λ ,
[ sin θ cos ϕ sin θ sin ϕ cos θ ] T ,
δ i = 2 π d [ - x i sin θ cos ϕ - y i sin θ sin ϕ + z i ( 1 - cos θ ) ] / λ ,
A = [ 1 + exp ( i δ ) + exp ( i 2 δ ) + + exp ( i N δ ) ] = [ 1 - exp ( i N δ ) ] / [ 1 - exp ( i δ ) ] = sin ( N δ / 2 ) / sin ( δ / 2 ) ,
δ ^ = δ λ / 2 π d ,
A = S sin ( π S δ ^ / λ ) / ( π S δ ^ / λ ) ,
A T = V i = 1 3 sin ( π S i δ ^ i / λ ) π S i δ ^ i / λ ,

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