Abstract

A novel method is developed to improve the accuracy of particle sizing in laser phase-Doppler anemometry (PDA). In this method the vector sum of refractive and reflective rays is taken into consideration in describing a dual-mechanism-scattering model caused by a nonuniformly illuminated PDA measurement volume. The constraint of the single-mechanism-scattering model in the conventional PDA is removed. As a result the error caused by the measurement-volume effect, which consists of a Gaussian-beam defect and a slit effect, can be eliminated. This new method can be easily implemented with minimal modification of the conventional PDA system. The results of simulation based on the generalized Lorenz–Mie theory show that the new method can provide a PDA system free from the measurement-volume effect.

© 1999 Optical Society of America

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References

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  1. M. Saffman, “The use of polarized light for optical particle sizing,” presented at the Third International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 14–17 July 1986.
  2. W. D. Bachalo, S. V. Sankar, “Analysis of the light scattering interferometry for spheres larger than the light wavelength,” presented at the Fourth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1988.
  3. S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometer: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.
  4. G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” presented at the International Conference on Multiphase Flows ’91, Tsukuba, Japan, 24–27 September 1991.
  5. H.-H. Qiu, M. Sommerfeld, “The impact of signal processing on the accuracy of phase-Doppler measurements,” presented at the Sixth Workshop on Two Phase Flow Predictions, Erlangen, Germany, 30 March–2 April 1992.
  6. H.-H. Qiu, C. T. Hsu, “Optimization of optical parameters for particle sizing in multiphase flows by using EPDA,” Opt. Laser Eng. 30, 3–15 (1998).
    [Crossref]
  7. H.-H. Qiu, C. T. Hsu, “Minimum deviation of spatial frequency in large particle sizing,” Appl. Opt. 37, 6787–6794 (1998).
    [Crossref]
  8. F. Durst, C. Tropea, T.-H. Xu, “The slit effect in phase Doppler anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Applications, X. Shen, X. Sun, eds. (International Academic Publishers, Beijing, 1994), pp. 38–43.
  9. H.-H. Qiu, C. T. Hsu, “A Fourier optics method for the simulation of measurement-volume effect by the slit constraint,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.
  10. Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA systems without Gaussian beam defects,” presented at the Third International Conference on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.
  11. C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1994.
  12. K. Bauckhage, “The phase-Doppler-difference-method, a new-laser-Doppler technique for simultaneous size and velocity measurements. 1. Description of the method,” Part. Part. Syst. Charact. 5, 16–22 (1988).
    [Crossref]

1998 (2)

H.-H. Qiu, C. T. Hsu, “Optimization of optical parameters for particle sizing in multiphase flows by using EPDA,” Opt. Laser Eng. 30, 3–15 (1998).
[Crossref]

H.-H. Qiu, C. T. Hsu, “Minimum deviation of spatial frequency in large particle sizing,” Appl. Opt. 37, 6787–6794 (1998).
[Crossref]

1988 (1)

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

Aizu, Y.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA systems without Gaussian beam defects,” presented at the Third International Conference on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

Bachalo, W. D.

W. D. Bachalo, S. V. Sankar, “Analysis of the light scattering interferometry for spheres larger than the light wavelength,” presented at the Fourth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1988.

S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometer: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.

Bauckhage, K.

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

Durst, F.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA systems without Gaussian beam defects,” presented at the Third International Conference on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” presented at the International Conference on Multiphase Flows ’91, Tsukuba, Japan, 24–27 September 1991.

F. Durst, C. Tropea, T.-H. Xu, “The slit effect in phase Doppler anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Applications, X. Shen, X. Sun, eds. (International Academic Publishers, Beijing, 1994), pp. 38–43.

Gouesbet, G.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” presented at the International Conference on Multiphase Flows ’91, Tsukuba, Japan, 24–27 September 1991.

Grehan, G.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” presented at the International Conference on Multiphase Flows ’91, Tsukuba, Japan, 24–27 September 1991.

Gréhan, G.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA systems without Gaussian beam defects,” presented at the Third International Conference on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1994.

Haugen, P.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1994.

Hsu, C. T.

H.-H. Qiu, C. T. Hsu, “Minimum deviation of spatial frequency in large particle sizing,” Appl. Opt. 37, 6787–6794 (1998).
[Crossref]

H.-H. Qiu, C. T. Hsu, “Optimization of optical parameters for particle sizing in multiphase flows by using EPDA,” Opt. Laser Eng. 30, 3–15 (1998).
[Crossref]

H.-H. Qiu, C. T. Hsu, “A Fourier optics method for the simulation of measurement-volume effect by the slit constraint,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.

Inenaga, A. S.

S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometer: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.

Naqwi, A.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” presented at the International Conference on Multiphase Flows ’91, Tsukuba, Japan, 24–27 September 1991.

Onofri, F.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA systems without Gaussian beam defects,” presented at the Third International Conference on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1994.

Qiu, H.-H.

H.-H. Qiu, C. T. Hsu, “Minimum deviation of spatial frequency in large particle sizing,” Appl. Opt. 37, 6787–6794 (1998).
[Crossref]

H.-H. Qiu, C. T. Hsu, “Optimization of optical parameters for particle sizing in multiphase flows by using EPDA,” Opt. Laser Eng. 30, 3–15 (1998).
[Crossref]

H.-H. Qiu, M. Sommerfeld, “The impact of signal processing on the accuracy of phase-Doppler measurements,” presented at the Sixth Workshop on Two Phase Flow Predictions, Erlangen, Germany, 30 March–2 April 1992.

H.-H. Qiu, C. T. Hsu, “A Fourier optics method for the simulation of measurement-volume effect by the slit constraint,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.

Saffman, M.

M. Saffman, “The use of polarized light for optical particle sizing,” presented at the Third International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 14–17 July 1986.

Sankar, S. V.

W. D. Bachalo, S. V. Sankar, “Analysis of the light scattering interferometry for spheres larger than the light wavelength,” presented at the Fourth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1988.

S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometer: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.

Sommerfeld, M.

H.-H. Qiu, M. Sommerfeld, “The impact of signal processing on the accuracy of phase-Doppler measurements,” presented at the Sixth Workshop on Two Phase Flow Predictions, Erlangen, Germany, 30 March–2 April 1992.

Tropea, C.

F. Durst, C. Tropea, T.-H. Xu, “The slit effect in phase Doppler anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Applications, X. Shen, X. Sun, eds. (International Academic Publishers, Beijing, 1994), pp. 38–43.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1994.

Xu, T.-H.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1994.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA systems without Gaussian beam defects,” presented at the Third International Conference on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

F. Durst, C. Tropea, T.-H. Xu, “The slit effect in phase Doppler anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Applications, X. Shen, X. Sun, eds. (International Academic Publishers, Beijing, 1994), pp. 38–43.

Appl. Opt. (1)

Opt. Laser Eng. (1)

H.-H. Qiu, C. T. Hsu, “Optimization of optical parameters for particle sizing in multiphase flows by using EPDA,” Opt. Laser Eng. 30, 3–15 (1998).
[Crossref]

Part. Part. Syst. Charact. (1)

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

Other (9)

F. Durst, C. Tropea, T.-H. Xu, “The slit effect in phase Doppler anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Applications, X. Shen, X. Sun, eds. (International Academic Publishers, Beijing, 1994), pp. 38–43.

H.-H. Qiu, C. T. Hsu, “A Fourier optics method for the simulation of measurement-volume effect by the slit constraint,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA systems without Gaussian beam defects,” presented at the Third International Conference on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1994.

M. Saffman, “The use of polarized light for optical particle sizing,” presented at the Third International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 14–17 July 1986.

W. D. Bachalo, S. V. Sankar, “Analysis of the light scattering interferometry for spheres larger than the light wavelength,” presented at the Fourth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1988.

S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometer: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” presented at the International Conference on Multiphase Flows ’91, Tsukuba, Japan, 24–27 September 1991.

H.-H. Qiu, M. Sommerfeld, “The impact of signal processing on the accuracy of phase-Doppler measurements,” presented at the Sixth Workshop on Two Phase Flow Predictions, Erlangen, Germany, 30 March–2 April 1992.

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Figures (13)

Fig. 1
Fig. 1

Description of different scattering mechanisms caused by Gaussian-beam illumination.

Fig. 2
Fig. 2

Description of different scattering mechanisms caused by the slit effect.

Fig. 3
Fig. 3

Optical layout of four-detector phase Doppler anemometry: APD, avalanche photodiode.

Fig. 4
Fig. 4

Vector analysis of the superposition of refractive and reflective rays.

Fig. 5
Fig. 5

Determination of the C 1 = C 0 point based on Eqs. (2) and (3).

Fig. 6
Fig. 6

MVE free line depending on the off-axis angle and the relative refractive index of the media.

Fig. 7
Fig. 7

Comparison of the phase-measurement results between the conventional method and the new approach (X = Z = 0 µm, r 0 = 50 µm).

Fig. 8
Fig. 8

Comparison of the phase-measurement results between the conventional method and the new approach (X = Z = 0 µm, r 0 = 50 µm).

Fig. 9
Fig. 9

Comparison of the phase-measurement results between the conventional method and the new approach (X = Z = 0 µm, r 0 = 50 µm).

Fig. 10
Fig. 10

Comparison of the phase-measurement results between the conventional method and the new approach (Y = -60 µm, Z = 0 µm, r 0 = 50 µm).

Fig. 11
Fig. 11

Comparison of the phase-measurement results between the conventional method and the new approach (Y = -60 µm, Z = 0 µm, r 0 = 50 µm).

Fig. 12
Fig. 12

Comparison of the phase-measurement results between the conventional method and the new approach (Y = -60 µm, Z = 0 µm, r 0 = 50 µm).

Fig. 13
Fig. 13

Comparison of the phase-measurement results between the conventional method and the new approach (Y = -60 µm, Z = 0 µm, r 0 = 50 µm).

Tables (1)

Tables Icon

Table 1 Optical Parameters

Equations (11)

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ϕ141=ϕ11-ϕ41=2ϕ11=C11D,
C11=4πλ1+m2-2 m1-sinθ2sin ψ1+cosθ2cos ψ1 cos φ1/21/2-1+m2-2 m1+sinθ2sin ψ1+cosθ2cos ψ1 cos φ1/21/2,
C10=2π2λ1+sinθ2sin ψ1-cosθ2cos ψ1 cos φ1/2-1-sinθ2sin ψ1-cosθ2cos ψ1 cos φ1/2.
ϕ140=2π-ϕ10-ϕ40=2π-2ϕ10=2π-C10D.
ϕ14=2ϕ1=2 arctanI11 sin ϕ11-I10 sin ϕ10I11 cos ϕ11+I10 cos ϕ10=2 arctanI11 sinC11D2-I10 sinC10D2I11 cosC11D2+I10 cosC10D2,
ϕ23=2ϕ2=2 arctanI21 sin ϕ21-I20 sin ϕ20I21 cos ϕ21+I20 cos ϕ20=2 arctanI21 sinC21D2-I20 sinC20D2I21 cosC21D2+I20 cosC20D2,
C21=4πλ1+m2-2 m1-sinθ2sin ψ2+cosθ2cos ψ2 cos φ1/21/2-1+m2-2 m×1+sinθ2sin ψ2+cosθ2cos ψ2 cos φ1/21/2,
C20=2π2λ1+sinθ2sin ψ2-cosθ2cos ψ2 cos φ1/2-1-sinθ2sin ψ2-cosθ2cos ψ2 cos φ1/2.
ϕ14=2 arctanI1-I0I1+I0tanC1D2, ϕ23=2 arctanI1-I0I1+I0tanC2D2.
tanϕ142tanϕ232=tanC1D2tanC2D2.
D=4C1arctan1-2 tanϕ232tanϕ1421/2,

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