Abstract

Based on an analysis of the response of a phase–Doppler system to a Rayleigh scatterer, the basic requirements for the application of this technique in the Rayleigh and near-Rayleigh range are established. Using Mie-scattering theory, we computed the response curves of the corresponding phase–Doppler systems for various materials. The possibilities for particle sizing as well as particle material recognition in the submicrometer range are highlighted. Measurements with submicrometer latex spheres in water demonstrate the feasibility of the application of the phase–Doppler technique in the near-Rayleigh range.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Durst, M. Zaré, “Laser Doppler measurements in two-phase flows,” presented at the Laser Doppler Anemometry Symposium, Copenhagen, 1975.
  2. W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
    [CrossRef]
  3. M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration, and velocity of spherical particles by a laser Doppler method,” presented at the Second International Symposium on Application of Laser Anemometry to Fluid in Mechanics, Lisbon, 1984.
  4. K. Bauckhage, “The phase-Doppler-difference method, a new laser-Doppler technique for simultaneous size and velocity measurements. Part 1: Description of the method,” Part. Part. Syst. Charact. 5, 16–22 (1988).
    [CrossRef]
  5. M. J. Houser, W. D. Bachalo, “Extension of the phase/ Doppler particle analyzer to submicron particle measurements,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 57–66 (1985).
  6. N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe anemometry,” J. Phys. D 9, 1839–1848 (1976).
    [CrossRef]
  7. J. D. Pendleton, “Mie and refraction theory comparison for particle sizing with the laser velocimetry,” Appl. Opt. 21, 684–688 (1982).
    [CrossRef] [PubMed]
  8. A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. Part 1: Theory and numerical treatments; Part 2: Computational results and their discussion,” Part. Part. Syst. Charact. (to be published).
  9. C. F. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  10. H. Raszillier, “Das Elektromagnetische Streuproblem der Laser-Droppler-Anemometrie,” Report LSTM 252/T, University of Erlangen (1989).
  11. G. Kraft, “Submikron-Teilchengrössenbestimmung mittels Phasen-Doppler-Anemometrie,” diploma thesis (University of Erlangen, Erlangen, 1990).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1986), p. 621.
  13. J. B. A. Card, A. R. Jones, “Measurement of the refractive index of atomized liquid drops by light scattering,” in Proceedings of the Second International Congress on Optical Particle Sizing (Arizona State U. Press, Tempe, Ariz., 1990), pp. 316–324.
  14. A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in Proceedings of the International Conference on Multiphase Flows (University of Tsukuba, Tsukuba 305, Japan, 1991.)
  15. J. Domnick, H. Ertel, C. Tropea, “Processing of phase–Doppler signals using the cross spectral density function,” in Applications of Laser Anemometry to Fluid Mechanics, (Springer-Verlag, Berlin, 1989), pp. 473–483.
    [CrossRef]

1988

K. Bauckhage, “The phase-Doppler-difference method, a new laser-Doppler technique for simultaneous size and velocity measurements. Part 1: Description of the method,” Part. Part. Syst. Charact. 5, 16–22 (1988).
[CrossRef]

1984

W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

1982

1976

N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe anemometry,” J. Phys. D 9, 1839–1848 (1976).
[CrossRef]

Bachalo, W. D.

W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

M. J. Houser, W. D. Bachalo, “Extension of the phase/ Doppler particle analyzer to submicron particle measurements,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 57–66 (1985).

Bauckhage, K.

K. Bauckhage, “The phase-Doppler-difference method, a new laser-Doppler technique for simultaneous size and velocity measurements. Part 1: Description of the method,” Part. Part. Syst. Charact. 5, 16–22 (1988).
[CrossRef]

Bohren, C. F.

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1986), p. 621.

Buchhave, P.

M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration, and velocity of spherical particles by a laser Doppler method,” presented at the Second International Symposium on Application of Laser Anemometry to Fluid in Mechanics, Lisbon, 1984.

Card, J. B. A.

J. B. A. Card, A. R. Jones, “Measurement of the refractive index of atomized liquid drops by light scattering,” in Proceedings of the Second International Congress on Optical Particle Sizing (Arizona State U. Press, Tempe, Ariz., 1990), pp. 316–324.

Domnick, J.

J. Domnick, H. Ertel, C. Tropea, “Processing of phase–Doppler signals using the cross spectral density function,” in Applications of Laser Anemometry to Fluid Mechanics, (Springer-Verlag, Berlin, 1989), pp. 473–483.
[CrossRef]

Durst, F.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in Proceedings of the International Conference on Multiphase Flows (University of Tsukuba, Tsukuba 305, Japan, 1991.)

F. Durst, M. Zaré, “Laser Doppler measurements in two-phase flows,” presented at the Laser Doppler Anemometry Symposium, Copenhagen, 1975.

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. Part 1: Theory and numerical treatments; Part 2: Computational results and their discussion,” Part. Part. Syst. Charact. (to be published).

Ertel, H.

J. Domnick, H. Ertel, C. Tropea, “Processing of phase–Doppler signals using the cross spectral density function,” in Applications of Laser Anemometry to Fluid Mechanics, (Springer-Verlag, Berlin, 1989), pp. 473–483.
[CrossRef]

Hong, N. S.

N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe anemometry,” J. Phys. D 9, 1839–1848 (1976).
[CrossRef]

Houser, M. J.

W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

M. J. Houser, W. D. Bachalo, “Extension of the phase/ Doppler particle analyzer to submicron particle measurements,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 57–66 (1985).

Huffman, D.

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

Jones, A. R.

N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe anemometry,” J. Phys. D 9, 1839–1848 (1976).
[CrossRef]

J. B. A. Card, A. R. Jones, “Measurement of the refractive index of atomized liquid drops by light scattering,” in Proceedings of the Second International Congress on Optical Particle Sizing (Arizona State U. Press, Tempe, Ariz., 1990), pp. 316–324.

Kraft, G.

G. Kraft, “Submikron-Teilchengrössenbestimmung mittels Phasen-Doppler-Anemometrie,” diploma thesis (University of Erlangen, Erlangen, 1990).

Liu, X.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in Proceedings of the International Conference on Multiphase Flows (University of Tsukuba, Tsukuba 305, Japan, 1991.)

Naqwi, A.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in Proceedings of the International Conference on Multiphase Flows (University of Tsukuba, Tsukuba 305, Japan, 1991.)

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. Part 1: Theory and numerical treatments; Part 2: Computational results and their discussion,” Part. Part. Syst. Charact. (to be published).

Pendleton, J. D.

Raszillier, H.

H. Raszillier, “Das Elektromagnetische Streuproblem der Laser-Droppler-Anemometrie,” Report LSTM 252/T, University of Erlangen (1989).

Saffman, M.

M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration, and velocity of spherical particles by a laser Doppler method,” presented at the Second International Symposium on Application of Laser Anemometry to Fluid in Mechanics, Lisbon, 1984.

Tanger, H.

M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration, and velocity of spherical particles by a laser Doppler method,” presented at the Second International Symposium on Application of Laser Anemometry to Fluid in Mechanics, Lisbon, 1984.

Tropea, C.

J. Domnick, H. Ertel, C. Tropea, “Processing of phase–Doppler signals using the cross spectral density function,” in Applications of Laser Anemometry to Fluid Mechanics, (Springer-Verlag, Berlin, 1989), pp. 473–483.
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1986), p. 621.

Zaré, M.

F. Durst, M. Zaré, “Laser Doppler measurements in two-phase flows,” presented at the Laser Doppler Anemometry Symposium, Copenhagen, 1975.

Ziema, M.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in Proceedings of the International Conference on Multiphase Flows (University of Tsukuba, Tsukuba 305, Japan, 1991.)

Appl. Opt.

J. Phys. D

N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe anemometry,” J. Phys. D 9, 1839–1848 (1976).
[CrossRef]

Opt. Eng.

W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

Part. Part. Syst. Charact.

K. Bauckhage, “The phase-Doppler-difference method, a new laser-Doppler technique for simultaneous size and velocity measurements. Part 1: Description of the method,” Part. Part. Syst. Charact. 5, 16–22 (1988).
[CrossRef]

Other

M. J. Houser, W. D. Bachalo, “Extension of the phase/ Doppler particle analyzer to submicron particle measurements,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 57–66 (1985).

M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration, and velocity of spherical particles by a laser Doppler method,” presented at the Second International Symposium on Application of Laser Anemometry to Fluid in Mechanics, Lisbon, 1984.

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. Part 1: Theory and numerical treatments; Part 2: Computational results and their discussion,” Part. Part. Syst. Charact. (to be published).

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

H. Raszillier, “Das Elektromagnetische Streuproblem der Laser-Droppler-Anemometrie,” Report LSTM 252/T, University of Erlangen (1989).

G. Kraft, “Submikron-Teilchengrössenbestimmung mittels Phasen-Doppler-Anemometrie,” diploma thesis (University of Erlangen, Erlangen, 1990).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1986), p. 621.

J. B. A. Card, A. R. Jones, “Measurement of the refractive index of atomized liquid drops by light scattering,” in Proceedings of the Second International Congress on Optical Particle Sizing (Arizona State U. Press, Tempe, Ariz., 1990), pp. 316–324.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in Proceedings of the International Conference on Multiphase Flows (University of Tsukuba, Tsukuba 305, Japan, 1991.)

J. Domnick, H. Ertel, C. Tropea, “Processing of phase–Doppler signals using the cross spectral density function,” in Applications of Laser Anemometry to Fluid Mechanics, (Springer-Verlag, Berlin, 1989), pp. 473–483.
[CrossRef]

F. Durst, M. Zaré, “Laser Doppler measurements in two-phase flows,” presented at the Laser Doppler Anemometry Symposium, Copenhagen, 1975.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Optical arrangement of a phase–Doppler system pertinent to the signal simulation scheme.

Fig. 2
Fig. 2

Distribution of the functions G and H for Rayleigh scattering: the E vectors are normal to the plane of the beams.

Fig. 3
Fig. 3

Rayleigh scattering from the dual-beam system. The E vectors are in the plane of the beams, the beam angle is 90°: (a) function H ; (b) function G .

Fig. 4
Fig. 4

Rayleigh scattering from the dual-beam system. The E vectors are at 45° from the plane of the beams, the beam angle is 90°: (a) function H ; (b) function G .

Fig. 5
Fig. 5

Limiting behavior of the particle phase in a phase–Doppler system.

Fig. 6
Fig. 6

Response curves for small water droplets: (a) perpendicular polarization, receiving-cone angle, 10°; (b) perpendicular polarization, receiving-cone angle, 20°; (c) parallel polarization, receiving-cone angle, 20°.

Fig. 7
Fig. 7

Signal visibility for small water droplets: (a) perpendicular polarization, receiving-cone angle, 10°; (b) perpendicular polarization, receiving-cone angle, 20°; (c) parallel polarization, receiving-cone angle, 20°.

Fig. 8
Fig. 8

Response curves for absorbing and nonabsorbing particles. (a) iron particles; (b) glass beads.

Fig. 9
Fig. 9

Forward-scattering patterns for a 2-μm iron particle. (The particle center is located on a dark fringe in the upper diagram and on a bright fringe in the lower diagram.)

Fig. 10
Fig. 10

Optical layout for verification experiments with submicrometer particles.

Fig. 11
Fig. 11

Probability distributions of the measured signal phase for latex particles: (a) particle diameter 0.75 μm, (b) particle diameter 0.5 μm.

Fig. 12
Fig. 12

Comparison between theory and experiment for elevation angles of −3° and +33°.

Fig. 13
Fig. 13

Comparison between theory and experiment for elevation angles of 0° and +45°.

Equations (17)

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

I s = E 0 2 k 2 r 2 { G + 2 [ H exp ( i ω D t ) ] } ,
G = cos 2 φ a | S 2 a | 2 + sin 2 φ a | S 1 a | 2 + cos 2 φ t | S 2 t | 2 + sin 2 φ t | S 1 t | 2 ;
H = cos φ a cos φ t S 2 a S 2 t * ê θ a ê θ e t cos φ a sin φ t S 2 a S 1 t * ê θ a ê φ t sin φ a cos φ t S 1 a S 2 t * ê φ a ê θ t + sin φ a sin φ t S 1 a S 1 t * ê φ a ê φ t .
I s = I 0 k 2 r 2 [ G + 2 ( H r cos ω D t + H i sin ω D t ) ] ,
I s = I 0 k 2 r 2 ( G ± 2 H r ) ,
P s = Ω I s r 2 d Ω ,
= I 0 k 2 [ + 2 ( H r ¯ cos ω D t + H i ¯ sin ω D t ) ] ,
P s = P ̅ s [ 1 + ν cos ( ω D t + Δ ) ] ,
P ̅ s = I 0 k 2 ,
ν = 2 ( H ̅ r 2 + H ̅ i 2 ) 1 / 2 ,
Δ = tan 1 ( H i ¯ H r ¯ ) .
S 1 = i q 3 ( m 2 1 m 2 + 2 ) ,
S 2 = i q 3 ( m 2 1 m 2 + 2 ) cos θ ,
G = 2 q 6 | m 2 1 m 2 + 2 | 2 G ,
H = q 6 | m 2 1 m 2 + 2 | 2 H ,
G = ½ ( cos 2 φ a cos 2 θ a + sin 2 φ a + cos 2 φ t cos 2 θ t + sin 2 φ t ) ,
H = ( cos φ a cos φ t cos θ a cos θ t ê θ a ê θ t cos φ a sin φ t cos θ a ê θ a ê φ t sin φ a cos φ t cos θ t ê φ a ê θ t + sin φ a sin φ t ê φ a ê ϕ t ) .

Metrics