Abstract

We propose what we believe to be a novel unidirectional phase-Doppler method for sizing moving spherical particles on the basis of the phase difference of two polarized Doppler beat signals in a single scattering direction. Light scattered by a moving particle is divided into two rays, which are detected with different polarization angles to transmit dominantly reflected or refracted rays. The phase difference between two signals is linearly proportional to the particle diameter with a given particle refractive index and geometrical parameters of the optical system. To explore the optimum polarization condition, we numerically investigated the phase–diameter properties in relation to polarization angles by using the geometrical optics approximation and generalized Lorenz–Mie theory. We also performed experiments with polystyrene and glass particles to verify the usefulness of the proposed method.

© 2001 Optical Society of America

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    [CrossRef]
  2. F. Durst, M. Zaré, “Laser Doppler measurements in two-phase flows,” in Proceedings of the LDA-75 Symposium Copenhagen: The Accuracy of Flow Measurements by the Laser Doppler Method (Technical University of Denmark, Skovlunde, Denmark, 1975), pp. 403–429.
  3. W. D. Bachalo, “Method for measuring the size and velocity of spheres by dual-beam light-scatter interferometry,” Appl. Opt. 19, 363–370 (1980).
    [CrossRef] [PubMed]
  4. A. Naqwi, F. Durst, “Analysis of the laser light scattering interferometric devices for the in-line diagnostic of moving particles,” Appl. Opt. 32, 4003–4018 (1993).
    [PubMed]
  5. K. Bauckhage, H.-H. Flögel, “Simultaneous measurement of droplet size and velocity in nozzle sprays,” in Proceedings of the 2nd International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1984), paper 18-1, pp. 1–6.
  6. A. J. Jolly, C. J. Bates, “Spray droplet characterization of internal mix air-assist atomizers using PDA techniques,” in Proceedings of the 11th European Conference of ILASS-Europe on Atomization and Sprays (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 97–106.
  7. H.-H. von Benzon, P. Buchhave, “The phase-Doppler method applied to very small particles,” Part. Part. Syst. Charact. 11, 55–62 (1994).
    [CrossRef]
  8. M. Saffman, “The use of polarized light for optical particle sizing,” in Laser Anemometry in Fluid Mechanics III, R. Adrian, I. Asanuma, D. Duráo, F. Durst, H. Mishina, J. Whitelaw, eds. (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1988), pp. 387–398.
  9. G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 291–294.
  10. G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–1.
  11. G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
    [CrossRef]
  12. Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA-system without Gaussian beam defects,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 461–470.
  13. N. Yokoi, Y. Aizu, H. Mishina, “Estimation of particle trajectory effects and their reduction using polarization in phase Doppler particle measurements,” Opt. Eng. 38, 1869–1882 (1999).
    [CrossRef]
  14. N. Yokoi, Y. Aizu, H. Mishina, “Novel phase Doppler method for particle size measurements using a single directional polarized detection,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference, V. Piuri, M. Savino, eds. (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 1352–1357.
  15. S. V. Sanker, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–2.
  16. A. Naqwi, “Innovative phase Doppler systems and their applications,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 245–260.
  17. Y. Aizu, H. Washiyama, H. Mishina, “Particle sizing by planar-phase Doppler system,” Opt. Rev. 1, 121–124 (1994).
    [CrossRef]
  18. Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
    [CrossRef]
  19. A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 283–286.
  20. A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. 2. Computational results and their discussion,” Part. Part. Syst. Charact. 9, 66–80 (1992).
    [CrossRef]
  21. F. Onofri, G. Gréhan, G. Gouesbet, T.-H. Xu, G. Brenn, C. Tropea, “Phase-Doppler anemometry with dual burst technique for particle refractive index measurements,” in Proceedings of the 7th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), paper 21.4.
  22. F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
    [CrossRef]
  23. C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual mode phase Doppler anemometer,” in Proceedings of the 7th International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), pp. 287–296.
  24. C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
    [CrossRef]
  25. U. Manasse, T. Wriedt, K. Bauckhage, “Phase-Doppler sizing of optically absorbing liquid droplets: comparison between Mie theory and experiment,” Part. Part. Syst. Charact. 9, 176–185 (1992).
    [CrossRef]
  26. A. Naqwi, “Sizing of irregular particles using a phase Doppler system,” Part. Part. Syst. Charact. 13, 343–349 (1996).
    [CrossRef]
  27. P. Haugen, H.-H. von Benzon, “Phase Doppler measurement of the diameter of large particles: considerations for optimization,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 301–306.
  28. Y. Aizu, N. Yokoi, H. Mishina, “Uni-directional phase Doppler method,” in Proceedings of the 5th International Congress on Optical Particle Sizing (University of Minnesota, Minneapolis, Minnesota, 1998), pp. 287–290.
  29. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  30. W. J. Glantschnig, S.-H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20, 2499–2510 (1981).
    [CrossRef] [PubMed]
  31. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
  32. G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
  33. G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 393–405.
  34. G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

1999

N. Yokoi, Y. Aizu, H. Mishina, “Estimation of particle trajectory effects and their reduction using polarization in phase Doppler particle measurements,” Opt. Eng. 38, 1869–1882 (1999).
[CrossRef]

1996

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

A. Naqwi, “Sizing of irregular particles using a phase Doppler system,” Part. Part. Syst. Charact. 13, 343–349 (1996).
[CrossRef]

1994

H.-H. von Benzon, P. Buchhave, “The phase-Doppler method applied to very small particles,” Part. Part. Syst. Charact. 11, 55–62 (1994).
[CrossRef]

Y. Aizu, H. Washiyama, H. Mishina, “Particle sizing by planar-phase Doppler system,” Opt. Rev. 1, 121–124 (1994).
[CrossRef]

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

1993

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

A. Naqwi, F. Durst, “Analysis of the laser light scattering interferometric devices for the in-line diagnostic of moving particles,” Appl. Opt. 32, 4003–4018 (1993).
[PubMed]

1992

U. Manasse, T. Wriedt, K. Bauckhage, “Phase-Doppler sizing of optically absorbing liquid droplets: comparison between Mie theory and experiment,” Part. Part. Syst. Charact. 9, 176–185 (1992).
[CrossRef]

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. 2. Computational results and their discussion,” Part. Part. Syst. Charact. 9, 66–80 (1992).
[CrossRef]

1990

1988

1981

1980

1964

Y. Yeh, H. Z. Cummins, “Localized fluid flow measurements with an He–Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[CrossRef]

Aizu, Y.

N. Yokoi, Y. Aizu, H. Mishina, “Estimation of particle trajectory effects and their reduction using polarization in phase Doppler particle measurements,” Opt. Eng. 38, 1869–1882 (1999).
[CrossRef]

Y. Aizu, H. Washiyama, H. Mishina, “Particle sizing by planar-phase Doppler system,” Opt. Rev. 1, 121–124 (1994).
[CrossRef]

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA-system without Gaussian beam defects,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 461–470.

Y. Aizu, N. Yokoi, H. Mishina, “Uni-directional phase Doppler method,” in Proceedings of the 5th International Congress on Optical Particle Sizing (University of Minnesota, Minneapolis, Minnesota, 1998), pp. 287–290.

N. Yokoi, Y. Aizu, H. Mishina, “Novel phase Doppler method for particle size measurements using a single directional polarized detection,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference, V. Piuri, M. Savino, eds. (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 1352–1357.

Bachalo, W. D.

W. D. Bachalo, “Method for measuring the size and velocity of spheres by dual-beam light-scatter interferometry,” Appl. Opt. 19, 363–370 (1980).
[CrossRef] [PubMed]

S. V. Sanker, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–2.

Bates, C. J.

A. J. Jolly, C. J. Bates, “Spray droplet characterization of internal mix air-assist atomizers using PDA techniques,” in Proceedings of the 11th European Conference of ILASS-Europe on Atomization and Sprays (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 97–106.

Bauckhage, K.

U. Manasse, T. Wriedt, K. Bauckhage, “Phase-Doppler sizing of optically absorbing liquid droplets: comparison between Mie theory and experiment,” Part. Part. Syst. Charact. 9, 176–185 (1992).
[CrossRef]

K. Bauckhage, H.-H. Flögel, “Simultaneous measurement of droplet size and velocity in nozzle sprays,” in Proceedings of the 2nd International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1984), paper 18-1, pp. 1–6.

Brenn, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

F. Onofri, G. Gréhan, G. Gouesbet, T.-H. Xu, G. Brenn, C. Tropea, “Phase-Doppler anemometry with dual burst technique for particle refractive index measurements,” in Proceedings of the 7th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), paper 21.4.

Buchhave, P.

H.-H. von Benzon, P. Buchhave, “The phase-Doppler method applied to very small particles,” Part. Part. Syst. Charact. 11, 55–62 (1994).
[CrossRef]

Chen, S.-H.

Cummins, H. Z.

Y. Yeh, H. Z. Cummins, “Localized fluid flow measurements with an He–Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[CrossRef]

Domnick, J.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

Durst, F.

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

A. Naqwi, F. Durst, “Analysis of the laser light scattering interferometric devices for the in-line diagnostic of moving particles,” Appl. Opt. 32, 4003–4018 (1993).
[PubMed]

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. 2. Computational results and their discussion,” Part. Part. Syst. Charact. 9, 66–80 (1992).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 291–294.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 283–286.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA-system without Gaussian beam defects,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 461–470.

F. Durst, M. Zaré, “Laser Doppler measurements in two-phase flows,” in Proceedings of the LDA-75 Symposium Copenhagen: The Accuracy of Flow Measurements by the Laser Doppler Method (Technical University of Denmark, Skovlunde, Denmark, 1975), pp. 403–429.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–1.

Flögel, H.-H.

K. Bauckhage, H.-H. Flögel, “Simultaneous measurement of droplet size and velocity in nozzle sprays,” in Proceedings of the 2nd International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1984), paper 18-1, pp. 1–6.

Girasole, T.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Glantschnig, W. J.

Gouesbet, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–1.

G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

F. Onofri, G. Gréhan, G. Gouesbet, T.-H. Xu, G. Brenn, C. Tropea, “Phase-Doppler anemometry with dual burst technique for particle refractive index measurements,” in Proceedings of the 7th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), paper 21.4.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 291–294.

G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 393–405.

Gréhan, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–1.

F. Onofri, G. Gréhan, G. Gouesbet, T.-H. Xu, G. Brenn, C. Tropea, “Phase-Doppler anemometry with dual burst technique for particle refractive index measurements,” in Proceedings of the 7th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), paper 21.4.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual mode phase Doppler anemometer,” in Proceedings of the 7th International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), pp. 287–296.

G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 291–294.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA-system without Gaussian beam defects,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 461–470.

Haugen, P.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

P. Haugen, H.-H. von Benzon, “Phase Doppler measurement of the diameter of large particles: considerations for optimization,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 301–306.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual mode phase Doppler anemometer,” in Proceedings of the 7th International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), pp. 287–296.

Inenaga, A.

S. V. Sanker, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–2.

Jolly, A. J.

A. J. Jolly, C. J. Bates, “Spray droplet characterization of internal mix air-assist atomizers using PDA techniques,” in Proceedings of the 11th European Conference of ILASS-Europe on Atomization and Sprays (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 97–106.

Liu, X.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 283–286.

Maheu, B.

Manasse, U.

U. Manasse, T. Wriedt, K. Bauckhage, “Phase-Doppler sizing of optically absorbing liquid droplets: comparison between Mie theory and experiment,” Part. Part. Syst. Charact. 9, 176–185 (1992).
[CrossRef]

Mishina, H.

N. Yokoi, Y. Aizu, H. Mishina, “Estimation of particle trajectory effects and their reduction using polarization in phase Doppler particle measurements,” Opt. Eng. 38, 1869–1882 (1999).
[CrossRef]

Y. Aizu, H. Washiyama, H. Mishina, “Particle sizing by planar-phase Doppler system,” Opt. Rev. 1, 121–124 (1994).
[CrossRef]

Y. Aizu, N. Yokoi, H. Mishina, “Uni-directional phase Doppler method,” in Proceedings of the 5th International Congress on Optical Particle Sizing (University of Minnesota, Minneapolis, Minnesota, 1998), pp. 287–290.

N. Yokoi, Y. Aizu, H. Mishina, “Novel phase Doppler method for particle size measurements using a single directional polarized detection,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference, V. Piuri, M. Savino, eds. (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 1352–1357.

Naqwi, A.

A. Naqwi, “Sizing of irregular particles using a phase Doppler system,” Part. Part. Syst. Charact. 13, 343–349 (1996).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

A. Naqwi, F. Durst, “Analysis of the laser light scattering interferometric devices for the in-line diagnostic of moving particles,” Appl. Opt. 32, 4003–4018 (1993).
[PubMed]

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. 2. Computational results and their discussion,” Part. Part. Syst. Charact. 9, 66–80 (1992).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 291–294.

A. Naqwi, “Innovative phase Doppler systems and their applications,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 245–260.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 283–286.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–1.

Onofri, F.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA-system without Gaussian beam defects,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 461–470.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual mode phase Doppler anemometer,” in Proceedings of the 7th International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), pp. 287–296.

F. Onofri, G. Gréhan, G. Gouesbet, T.-H. Xu, G. Brenn, C. Tropea, “Phase-Doppler anemometry with dual burst technique for particle refractive index measurements,” in Proceedings of the 7th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), paper 21.4.

G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

Qiu, H.-H.

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

Saffman, M.

M. Saffman, “The use of polarized light for optical particle sizing,” in Laser Anemometry in Fluid Mechanics III, R. Adrian, I. Asanuma, D. Duráo, F. Durst, H. Mishina, J. Whitelaw, eds. (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1988), pp. 387–398.

Sanker, S. V.

S. V. Sanker, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–2.

Sommerfeld, M.

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

Stieglmeier, M.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual mode phase Doppler anemometer,” in Proceedings of the 7th International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), pp. 287–296.

Tropea, C.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual mode phase Doppler anemometer,” in Proceedings of the 7th International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), pp. 287–296.

F. Onofri, G. Gréhan, G. Gouesbet, T.-H. Xu, G. Brenn, C. Tropea, “Phase-Doppler anemometry with dual burst technique for particle refractive index measurements,” in Proceedings of the 7th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), paper 21.4.

G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

van de Hulst, H. C.

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

von Benzon, H.-H.

H.-H. von Benzon, P. Buchhave, “The phase-Doppler method applied to very small particles,” Part. Part. Syst. Charact. 11, 55–62 (1994).
[CrossRef]

P. Haugen, H.-H. von Benzon, “Phase Doppler measurement of the diameter of large particles: considerations for optimization,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 301–306.

Washiyama, H.

Y. Aizu, H. Washiyama, H. Mishina, “Particle sizing by planar-phase Doppler system,” Opt. Rev. 1, 121–124 (1994).
[CrossRef]

Wriedt, T.

U. Manasse, T. Wriedt, K. Bauckhage, “Phase-Doppler sizing of optically absorbing liquid droplets: comparison between Mie theory and experiment,” Part. Part. Syst. Charact. 9, 176–185 (1992).
[CrossRef]

Xu, T.-H.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA-system without Gaussian beam defects,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 461–470.

G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

F. Onofri, G. Gréhan, G. Gouesbet, T.-H. Xu, G. Brenn, C. Tropea, “Phase-Doppler anemometry with dual burst technique for particle refractive index measurements,” in Proceedings of the 7th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), paper 21.4.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual mode phase Doppler anemometer,” in Proceedings of the 7th International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), pp. 287–296.

Yeh, Y.

Y. Yeh, H. Z. Cummins, “Localized fluid flow measurements with an He–Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[CrossRef]

Yokoi, N.

N. Yokoi, Y. Aizu, H. Mishina, “Estimation of particle trajectory effects and their reduction using polarization in phase Doppler particle measurements,” Opt. Eng. 38, 1869–1882 (1999).
[CrossRef]

N. Yokoi, Y. Aizu, H. Mishina, “Novel phase Doppler method for particle size measurements using a single directional polarized detection,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference, V. Piuri, M. Savino, eds. (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 1352–1357.

Y. Aizu, N. Yokoi, H. Mishina, “Uni-directional phase Doppler method,” in Proceedings of the 5th International Congress on Optical Particle Sizing (University of Minnesota, Minneapolis, Minnesota, 1998), pp. 287–290.

Zaré, M.

F. Durst, M. Zaré, “Laser Doppler measurements in two-phase flows,” in Proceedings of the LDA-75 Symposium Copenhagen: The Accuracy of Flow Measurements by the Laser Doppler Method (Technical University of Denmark, Skovlunde, Denmark, 1975), pp. 403–429.

Ziema, M.

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 283–286.

Appl. Opt.

Appl. Phys. Lett.

Y. Yeh, H. Z. Cummins, “Localized fluid flow measurements with an He–Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

N. Yokoi, Y. Aizu, H. Mishina, “Estimation of particle trajectory effects and their reduction using polarization in phase Doppler particle measurements,” Opt. Eng. 38, 1869–1882 (1999).
[CrossRef]

Opt. Rev.

Y. Aizu, H. Washiyama, H. Mishina, “Particle sizing by planar-phase Doppler system,” Opt. Rev. 1, 121–124 (1994).
[CrossRef]

Part. Part. Syst. Charact.

Y. Aizu, J. Domnick, F. Durst, G. Gréhan, F. Onofri, H.-H. Qiu, M. Sommerfeld, T.-H. Xu, M. Ziema, “New generation of phase-Doppler instruments for particle velocity, size and concentration measurements,” Part. Part. Syst. Charact. 11, 43–54 (1994).
[CrossRef]

A. Naqwi, F. Durst, “Light scattering applied to LDA and PDA measurements. 2. Computational results and their discussion,” Part. Part. Syst. Charact. 9, 66–80 (1992).
[CrossRef]

H.-H. von Benzon, P. Buchhave, “The phase-Doppler method applied to very small particles,” Part. Part. Syst. Charact. 11, 55–62 (1994).
[CrossRef]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T.-H. Xu, C. Tropea, “Phase-Doppler anemometry with the dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–124 (1996).
[CrossRef]

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual-mode phase-Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

U. Manasse, T. Wriedt, K. Bauckhage, “Phase-Doppler sizing of optically absorbing liquid droplets: comparison between Mie theory and experiment,” Part. Part. Syst. Charact. 9, 176–185 (1992).
[CrossRef]

A. Naqwi, “Sizing of irregular particles using a phase Doppler system,” Part. Part. Syst. Charact. 13, 343–349 (1996).
[CrossRef]

Other

P. Haugen, H.-H. von Benzon, “Phase Doppler measurement of the diameter of large particles: considerations for optimization,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 301–306.

Y. Aizu, N. Yokoi, H. Mishina, “Uni-directional phase Doppler method,” in Proceedings of the 5th International Congress on Optical Particle Sizing (University of Minnesota, Minneapolis, Minnesota, 1998), pp. 287–290.

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

F. Durst, M. Zaré, “Laser Doppler measurements in two-phase flows,” in Proceedings of the LDA-75 Symposium Copenhagen: The Accuracy of Flow Measurements by the Laser Doppler Method (Technical University of Denmark, Skovlunde, Denmark, 1975), pp. 403–429.

G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 393–405.

G. Brenn, J. Domnick, C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, G. Gouesbet, “The dual burst technique and its application to optically non-homogeneous particles,” in Proceedings of the 4th International Congress on Optical Particle Sizing (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 397–406.

C. Tropea, T.-H. Xu, F. Onofri, G. Gréhan, P. Haugen, M. Stieglmeier, “Dual mode phase Doppler anemometer,” in Proceedings of the 7th International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), pp. 287–296.

Y. Aizu, F. Durst, G. Gréhan, F. Onofri, T.-H. Xu, “PDA-system without Gaussian beam defects,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 461–470.

K. Bauckhage, H.-H. Flögel, “Simultaneous measurement of droplet size and velocity in nozzle sprays,” in Proceedings of the 2nd International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1984), paper 18-1, pp. 1–6.

A. J. Jolly, C. J. Bates, “Spray droplet characterization of internal mix air-assist atomizers using PDA techniques,” in Proceedings of the 11th European Conference of ILASS-Europe on Atomization and Sprays (Nürnberg Messe, Nürnberg, Germany, 1995), pp. 97–106.

M. Saffman, “The use of polarized light for optical particle sizing,” in Laser Anemometry in Fluid Mechanics III, R. Adrian, I. Asanuma, D. Duráo, F. Durst, H. Mishina, J. Whitelaw, eds. (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1988), pp. 387–398.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of phase Doppler system using generalized Lorenz–Mie theory,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 291–294.

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–1.

F. Onofri, G. Gréhan, G. Gouesbet, T.-H. Xu, G. Brenn, C. Tropea, “Phase-Doppler anemometry with dual burst technique for particle refractive index measurements,” in Proceedings of the 7th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1994), paper 21.4.

A. Naqwi, F. Durst, M. Ziema, X. Liu, “Particle material recognition using a phase Doppler system,” in International Conference on Multiphase Flows ’91 (American Society of Mechanical Engineers, New York, 1991), pp. 283–286.

N. Yokoi, Y. Aizu, H. Mishina, “Novel phase Doppler method for particle size measurements using a single directional polarized detection,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference, V. Piuri, M. Savino, eds. (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 1352–1357.

S. V. Sanker, A. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” in Proceedings of the 6th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Ladoan-Instituto Superior Técnico, Lisbon, Portugal, 1992), paper 12–2.

A. Naqwi, “Innovative phase Doppler systems and their applications,” in Proceedings of the 3rd International Congress on Optical Particle Sizing (Keio University, Yokohama, Japan, 23–26 August 1993), pp. 245–260.

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Figures (17)

Fig. 1
Fig. 1

Optical geometry of the UPDA system. BS, beam splitter.

Fig. 2
Fig. 2

Theoretical phase–diameter relations for the reflected (dotted line) and the refracted (solid line) rays obtained by the geometrical optics approximation for m = 1.192.

Fig. 3
Fig. 3

Optical geometry of the conventional PDA system.

Fig. 4
Fig. 4

Schematic description of the polarization change in rays reflected and refracted by a small particle.

Fig. 5
Fig. 5

Computed scattering intensity patterns |SNp|2 of the reflected (N = 0) and the refracted (N = 1) rays for perpendicular (p = 1) and parallel (p = 2) polarizations, respectively, with conditions of m = 1.192, d p = 50 µm, and y = 0.

Fig. 6
Fig. 6

Change of polarization angles in the reflected and the refracted rays as a function of the incident-beam polarization angle and the scattering angle.

Fig. 7
Fig. 7

Determination of the analyzer angle for transmitting exclusively reflected or refracted rays.

Fig. 8
Fig. 8

Simulated results of (a) phase–diameter relations and (b) intensity–diameter relations obtained for the analyzer angles of ω a0 = -50 deg and ω a1 = -10 deg with m = 1.192 and ω p = 45 deg.

Fig. 9
Fig. 9

Simulated phase–diameter relations with the optimum analyzer angles ω a0, ω a1, and ω p = 45 deg for (a) m = 1.132, (b) m = 1.334, and (c) m = 1.59, respectively.

Fig. 10
Fig. 10

Computed intensity patterns of the reflected and the refracted rays transmitted through the analyzers of (a) ω a0 = -50 deg and (b) ω a1 = -10 deg, as a function of the extinction ratio ζ and the off-axis angle ϕ with m = 1.192, d p = 50 µm, and y = 0.

Fig. 11
Fig. 11

Simulated phase–diameter relations as a function of the extinction ratio ζ for the analyzer angles of (a) ω a0 = -50 deg and (b) ω a1 = -10 deg with m = 1.192, y = 0, and ω p = 45 deg.

Fig. 12
Fig. 12

Simulated results of (a) phase–diameter relations and (b) intensity–diameter relations obtained as a function of the extinction coefficient (imaginary part of n) for the analyzer angle of ω a1 = -10 deg with ω p = 45 deg and y = 0.

Fig. 13
Fig. 13

Typical recorded Doppler beat signals of PD1 (for refraction) and PD0 (for reflection) for the nominal particle diameter d p of (a) 20.00 µm, (b) 40.25 µm, and (c) 68.00 µm. The phase difference is denoted by ΔΦ .

Fig. 14
Fig. 14

Light scattering by the particle located at (a) the lower edge and (b) the center of the probe cross-sectional area.

Fig. 15
Fig. 15

Histograms of the particle diameter measured with the UPDA system for polystyrene particles in water (m = 1.192) with the nominal diameter d p of (a) 20.00 µm, (b) 40.25 µm, and (c) 68.00 µm.

Fig. 16
Fig. 16

Histograms of the particle diameter measured using the CPDA system for polystyrene particles in water (m = 1.192) with the nominal diameter d p of 41.1 µm.

Fig. 17
Fig. 17

Measured diameter versus nominal diameter of polystyrene particles in water (m = 1.192) and glass particles in water (m = 1.132).

Tables (2)

Tables Icon

Table 1 Polarization Angles of Reflected and Refracted Rays and Their Differences Obtained by the Geometrical Optics Approximation for Various Relative Refractive Indices of Particles, m

Tables Icon

Table 2 Recommended Measuring Conditions of the UPDA System for Various Relative Refractive Indices of Particles, m

Equations (11)

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

Φ0i=kdp21 + sin α sin ψ - cos α cos ψ cos ϕ1/2 - 1 - sin α sin ψ - cos α cos ψ cos ϕ1/2=dpF0i,
Φ1i=-kdp1+m2-m21+sin α sin ψ+cos α cos ψ cos ϕ1/21/2- 1 + m2 - m2(1 - sin α sin ψ+cos α cos ψ cos ϕ)1/21/2=dpF1i,
F0i=k21+sin α sin ψ-cos α cos ψ cos ϕ1/2-1-sin α sin ψ-cos α cos ψ cos ϕ1/2,
F1i=-k1+m2-m21+sin α sin ψ+cos α cos ψ cos ϕ1/21/2-1+m2-m21-sin α sin ψ+cos α cos ψ cos ϕ1/21/2,
ΔΦ=Φ01-Φ11=dpF01-F11.
ΔΦ0=Φ01-Φ02,
ΔΦ1=Φ11-Φ12.
ηN=tan-1SN1 sin ωpSN2 cos ωp,  -π2ηNπ2,
SD=1nnΦGLMT-Φtheory21/2.
ζ=90/0,
n=m-iκ,

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