Abstract

A method of calculating the light scattering of irregularly shaped particles by a ray-tracing program is presented together with a new procedure for the three-dimensional reconstruction of the particle shapes. The simulation is based on geometrical optics. The paths of rays are calculated until they encounter specific end conditions (e.g., detection by a transducer). The result of the calculation is the scattering function of the particle in any arbitrary orientation. The results of the program have been successfully compared with those of the Mie theory with microwave-scattering experiments and light-scattering measurements involving individual, electrodynamically suspended particles.

© 1991 Optical Society of America

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References

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  1. R. Brossmann, “Die Lichstreuung an kleinen Teilchen als Grundlage einer Teilchengrössenbestimmung,” Dissertation an der Fakultät für Chemieingenieurwesen (Universität Karlsruhe, Karlsruhe, Germany, 1966).
  2. J. Gebhardt, A. Anselm, “Effect of particle shape on the response of single particle optical counters,”in Proceedings, International Symposium on Optical Particle Sizing: Theory and Practice, G. Gouesbet, G. Gréhan, eds. (Plenum, New York, 1988), pp. 393–409.
  3. R. R. Pinnik, H. J. Auvermann, “Response characteristics of Knollenberg light-scattering aerosol counters,” J. Aerosol. Sci. 10, 55–74 (1979).
    [CrossRef]
  4. M. Bottlinger, H. Umhauer, “Scattered light particle size counting analysis: influence of shape and structure,” in Proceedings, International Symposium on Optical Particle Sizing: Theory and Practice, G. Gouesbet, G. Gréhan, eds. (Plenum, New York, 1988).
  5. M. Bottlinger, “Quantifizierung und Eliminierung des Einflusses von Partikelform und struktur auf Ergebnis der Streulicht-Partikelgrößen-Zählanalyse,” Dissertation an der Fakultät für Chemieingenieurwesen (Universität Karlsruhe, Karlsruhe, Germany, 1989).
  6. P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  7. R. H. Zerull, R. H. Giese, “Scattering of particles of nonspherical shape,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuermann, ed. (Plenum, New York, 1979), pp. 273–282.
  8. M. Bottlinger, H. Umhauer, “Single particle light scattering size analysis: quantification and elimination of the effect of particle shape and structure,” Part. Part. Syst. Charact. 6, 100–109 (1989).
    [CrossRef]

1989 (1)

M. Bottlinger, H. Umhauer, “Single particle light scattering size analysis: quantification and elimination of the effect of particle shape and structure,” Part. Part. Syst. Charact. 6, 100–109 (1989).
[CrossRef]

1979 (1)

R. R. Pinnik, H. J. Auvermann, “Response characteristics of Knollenberg light-scattering aerosol counters,” J. Aerosol. Sci. 10, 55–74 (1979).
[CrossRef]

1975 (1)

Anselm, A.

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

Auvermann, H. J.

R. R. Pinnik, H. J. Auvermann, “Response characteristics of Knollenberg light-scattering aerosol counters,” J. Aerosol. Sci. 10, 55–74 (1979).
[CrossRef]

Barber, P.

Bottlinger, M.

M. Bottlinger, H. Umhauer, “Single particle light scattering size analysis: quantification and elimination of the effect of particle shape and structure,” Part. Part. Syst. Charact. 6, 100–109 (1989).
[CrossRef]

M. Bottlinger, “Quantifizierung und Eliminierung des Einflusses von Partikelform und struktur auf Ergebnis der Streulicht-Partikelgrößen-Zählanalyse,” Dissertation an der Fakultät für Chemieingenieurwesen (Universität Karlsruhe, Karlsruhe, Germany, 1989).

M. Bottlinger, H. Umhauer, “Scattered light particle size counting analysis: influence of shape and structure,” in Proceedings, International Symposium on Optical Particle Sizing: Theory and Practice, G. Gouesbet, G. Gréhan, eds. (Plenum, New York, 1988).

Brossmann, R.

R. Brossmann, “Die Lichstreuung an kleinen Teilchen als Grundlage einer Teilchengrössenbestimmung,” Dissertation an der Fakultät für Chemieingenieurwesen (Universität Karlsruhe, Karlsruhe, Germany, 1966).

Gebhardt, J.

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

Giese, R. H.

R. H. Zerull, R. H. Giese, “Scattering of particles of nonspherical shape,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuermann, ed. (Plenum, New York, 1979), pp. 273–282.

Pinnik, R. R.

R. R. Pinnik, H. J. Auvermann, “Response characteristics of Knollenberg light-scattering aerosol counters,” J. Aerosol. Sci. 10, 55–74 (1979).
[CrossRef]

Umhauer, H.

M. Bottlinger, H. Umhauer, “Single particle light scattering size analysis: quantification and elimination of the effect of particle shape and structure,” Part. Part. Syst. Charact. 6, 100–109 (1989).
[CrossRef]

M. Bottlinger, H. Umhauer, “Scattered light particle size counting analysis: influence of shape and structure,” in Proceedings, International Symposium on Optical Particle Sizing: Theory and Practice, G. Gouesbet, G. Gréhan, eds. (Plenum, New York, 1988).

Yeh, C.

Zerull, R. H.

R. H. Zerull, R. H. Giese, “Scattering of particles of nonspherical shape,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuermann, ed. (Plenum, New York, 1979), pp. 273–282.

Appl. Opt. (1)

J. Aerosol. Sci. (1)

R. R. Pinnik, H. J. Auvermann, “Response characteristics of Knollenberg light-scattering aerosol counters,” J. Aerosol. Sci. 10, 55–74 (1979).
[CrossRef]

Part. Part. Syst. Charact. (1)

M. Bottlinger, H. Umhauer, “Single particle light scattering size analysis: quantification and elimination of the effect of particle shape and structure,” Part. Part. Syst. Charact. 6, 100–109 (1989).
[CrossRef]

Other (5)

R. H. Zerull, R. H. Giese, “Scattering of particles of nonspherical shape,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuermann, ed. (Plenum, New York, 1979), pp. 273–282.

M. Bottlinger, H. Umhauer, “Scattered light particle size counting analysis: influence of shape and structure,” in Proceedings, International Symposium on Optical Particle Sizing: Theory and Practice, G. Gouesbet, G. Gréhan, eds. (Plenum, New York, 1988).

M. Bottlinger, “Quantifizierung und Eliminierung des Einflusses von Partikelform und struktur auf Ergebnis der Streulicht-Partikelgrößen-Zählanalyse,” Dissertation an der Fakultät für Chemieingenieurwesen (Universität Karlsruhe, Karlsruhe, Germany, 1989).

R. Brossmann, “Die Lichstreuung an kleinen Teilchen als Grundlage einer Teilchengrössenbestimmung,” Dissertation an der Fakultät für Chemieingenieurwesen (Universität Karlsruhe, Karlsruhe, Germany, 1966).

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

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Figures (10)

Fig. 1
Fig. 1

Principle of ray tracing. The primary rays are aimed at the particle surface represented by a polyhedron built from triangular planes. The refracted and reflected rays are calculated.

Fig. 2
Fig. 2

Vectors of the light ray components. The circles denote vectors perpendicular to the scattering plane.

Fig. 3
Fig. 3

Schematic diagram of the setup used for recording the images of particles from three orthogonal directions. For macroscopic objects the video camera was used directly. A Macintosh Plus enhanced with a 68020 accelerator board was utilized for image processing and ray-tracing calculations.

Fig. 4
Fig. 4

Spatial relations of the three contours of the particle depicted for an ellipsoid.

Fig. 5
Fig. 5

Reconstruction of a particle from the contour lines of its projection images. One contour is approximated by a polygon and scaled to fit inside the confines created by the two other contours.

Fig. 6
Fig. 6

Reconstruction of a real quartz particle (Xp = 60 μm, calculated from the mean area of the three orthogonal projection images). The representation of the particle is achieved by drawing the scaled polygons from back to front. The ray-tracing program determines from the structure its own internal description based on triangular planes.

Fig. 7
Fig. 7

Scattering by spheres and comparison between Mie theory and the ray-tracing technique. For ray tracing the sphere was approximated by a polyhedron.

Fig. 8
Fig. 8

Elongated Teflon object and its computer reconstruction in different orientations. The longer axis has a length of 10 cm.

Fig. 9
Fig. 9

Comparison between microwave analogy measurement and the result of ray tracing. Both the structure of the scattering functions and the absolute intensities agree well.

Fig. 10
Fig. 10

Light scattering by individual quartz particles. The particles were electrodynamically suspended, and multiple-light- scattering measurements were carried out with a white-light- scattering instrument (scattering angle, 90°). The results are the density distributions of the measured intensities. They are compared with the results of the ray-tracing calculations. All distributions have been normalized by their mean.

Equations (9)

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D P = 2 sin ψ cos ϕ sin ( ψ + ϕ ) cos ( ψ ϕ ) A p ,
D s = 2 sin ψ cos ϕ sin ( ψ + ϕ ) A s ,
R p = tan ( ϕ ψ ) tan ( ϕ + ψ ) A p ,
R s = sin ( ϕ ψ ) sin ( ϕ + ψ ) A s .
sin ϕ sin ψ = n rel = n 2 n 1 .
D = 2 n rel + 1 A ,
R = n rel 1 n rel + 1 A .
I det I 0 = I F cal I 0 F k ,
[ I s 1 I s 2 U s V s ] = 1 k 2 r 2 [ A i j ] [ I 01 I 02 U 0 V 0 ] .

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