Abstract

Several possibilities for the use of elastic light scattering in the backscatter range (scattering angle ϑs> 140 deg) for determination of size, velocity, and refractive index of spherical particles are investigated. First the phase Doppler technique is considered. Numerical simulations of light scattering with the Lorenz-Mie theory are used to show that the phase Doppler technique is unsuitable for such backscatter configurations, except for special measurement conditions. The time-shift (or pulse-displacement) technique is then considered by use of the Fourier-Lorenz-Mie theory. Simulations show that up to four fractional signals can be obtained by use of the technique in backscatter, corresponding to the scattering order or modes: surface wave (long path), reflection, second-order refraction (inner path), and a mixture of second-order refraction (outer path) and surface wave (short path). Signal characteristics as a function of particle size, refractive index, and particle ellipticity are studied. Suggestions for a practical measurement instrument are put forward.

© 2002 Optical Society of America

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References

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  1. S. L. Soo, Instrumentation for Fluid-Particle Flow (Andrew Publishing, Norwich, N.Y., 1999).
  2. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, England, 1999).
  3. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  4. H. Bultynck, “Développements de sondes laser Doppler miniatures pour la mesure de particules dans des écoulemnets réels complexes,” Ph.D. dissertation (Université de Rouen, Mont Saint Aignan, France, 1998).
  5. E. A. Hovenac, J. A. Lock, “Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” J. Opt. Soc. Am. A 9, 781–795 (1992).
    [CrossRef]
  6. F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (1996).
    [CrossRef]
  7. H. Bultynck, F. Onofri, G. Gréhan, G. Gouesbet, “Sonde Phase Doppler miniature: applications aux diagnostics en milieux hostiles,” in Proceedings of the Fifth Congress on Francophone de Vélocimétrie Laser (Complex de Recherche Interprofessionnel en Aerothermochimie, Université et Institut National des Sciences Appliqués de Rouen, Rouen, France, 1996).
  8. 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]
  9. H.-E. Albrecht, M. Borys, K. Hübner, “Generalized theory for simultaneous measurement of particle size and velocity using laser-Doppler- and laser-two-focus methods,” Part. Part. Syst. Charact. 10, 138–145 (1993).
    [CrossRef]
  10. M. Borys, “Analyse des Amplituden- und Phasenverhaltens von Laser-Doppler-Signalen zur Grössenbestimmung sphärischer Teilchen,” Ph.D. dissertation (Universität Rostock, Shaker-Verlag, Aachen, Germany, 1996).
  11. B. Pavlovski, N. Semidetnov, “Simultaneous measurement of velocity, size and concentrations for particles moving in two-phase flow,” Meas. Tech. (USSR) (Izmer. Tekh.) 9, 40–42 (1991),in Russian.
  12. C. F. Hess, C. P. Wood, “Pulse displacement technique to measure particle size and velocity in high density application,” in Laser Techniques and Applications to Fluid Mechanics, R. J. Adrian, D. F. G. Durãu, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1993), pp. 131–144.
    [CrossRef]
  13. S. M. Lin, D. R. Waterman, A. H. Lettington, “Measurement of droplet velocity, size, and refractive index using the pulse displacement technique,” Meas. Sci. Technol. 11, L1–L4 (2000).
    [CrossRef]
  14. H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
    [CrossRef]
  15. H.-E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Die Berechnung der Streuintensität eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik (Stuttgart) 100, 118–124 (1995).
  16. V. Strunck, H. Müller, D. Dopheide, “Traversionsfreier LDA-Grenzschichtmessungen mit Mikrometerauflösung im Messvolumen,” in Proceedings of Lasermethoden in der Strömungsmesstechnik, W. Merzkirch, F. Peters, B. Ruck, D. Dopheide, A. Leder, eds. (Shaker-Verlag, Aachen, Germany, 1998), paper 28.
  17. J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow interferometry with wire diffraction for simultaneous measurement of droplet temperature, size and velocity,” Part. Part. Syst. Charact. 14, 186–192 (1997).
  18. H. Lohner, P. Lehmann, K. Bauckhage, “Detection based on rainbow refractometry of droplet sphericity in liquid-liquid systems,” Appl. Opt. 38, 1127–1132 (1999).
    [CrossRef]
  19. H.-E. Albrecht, M. Borys, M. Wenzel, Th. Wriedt, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 1. Reflective mode operation,” Part. Part. Syst. Charact. 11, 339–344 (1994).
    [CrossRef]
  20. H.-E. Albrecht, M. Borys, M. Wenzel, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 2. Analysis by extension of geometrical optics to the laser beam; refractive mode operation,” Part. Part. Syst. Charact. 13, 18–26 (1996).
    [CrossRef]
  21. H. Nobach, “Analysis of dual-burst laser Doppler signals,” Meas. Sci. Technol. 13, 33–44 (2002).
    [CrossRef]
  22. J. Domnick, H. Ertl, C. Tropea, “Processing of phase Doppler signals using the cross spectral density function,” in Application of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durao, F. Durst, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1989), pp. 473–483.
    [CrossRef]
  23. K. Hishida, K. Kobashi, M. Maeda, “Improvement of LDA/PDA using a digital signal processor (DSP),” in Proceedings of the Third International Conference on Laser Anemometry (BHRA Information Services, Cranfield, Bedford MK41 OAJ, UK, 1989), paper S2.

2002 (1)

H. Nobach, “Analysis of dual-burst laser Doppler signals,” Meas. Sci. Technol. 13, 33–44 (2002).
[CrossRef]

2000 (1)

S. M. Lin, D. R. Waterman, A. H. Lettington, “Measurement of droplet velocity, size, and refractive index using the pulse displacement technique,” Meas. Sci. Technol. 11, L1–L4 (2000).
[CrossRef]

1999 (2)

H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

H. Lohner, P. Lehmann, K. Bauckhage, “Detection based on rainbow refractometry of droplet sphericity in liquid-liquid systems,” Appl. Opt. 38, 1127–1132 (1999).
[CrossRef]

1997 (1)

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow interferometry with wire diffraction for simultaneous measurement of droplet temperature, size and velocity,” Part. Part. Syst. Charact. 14, 186–192 (1997).

1996 (2)

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (1996).
[CrossRef]

H.-E. Albrecht, M. Borys, M. Wenzel, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 2. Analysis by extension of geometrical optics to the laser beam; refractive mode operation,” Part. Part. Syst. Charact. 13, 18–26 (1996).
[CrossRef]

1995 (1)

H.-E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Die Berechnung der Streuintensität eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik (Stuttgart) 100, 118–124 (1995).

1994 (1)

H.-E. Albrecht, M. Borys, M. Wenzel, Th. Wriedt, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 1. Reflective mode operation,” Part. Part. Syst. Charact. 11, 339–344 (1994).
[CrossRef]

1993 (2)

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]

H.-E. Albrecht, M. Borys, K. Hübner, “Generalized theory for simultaneous measurement of particle size and velocity using laser-Doppler- and laser-two-focus methods,” Part. Part. Syst. Charact. 10, 138–145 (1993).
[CrossRef]

1992 (1)

1991 (1)

B. Pavlovski, N. Semidetnov, “Simultaneous measurement of velocity, size and concentrations for particles moving in two-phase flow,” Meas. Tech. (USSR) (Izmer. Tekh.) 9, 40–42 (1991),in Russian.

Albrecht, H.-E.

H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

H.-E. Albrecht, M. Borys, M. Wenzel, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 2. Analysis by extension of geometrical optics to the laser beam; refractive mode operation,” Part. Part. Syst. Charact. 13, 18–26 (1996).
[CrossRef]

H.-E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Die Berechnung der Streuintensität eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik (Stuttgart) 100, 118–124 (1995).

H.-E. Albrecht, M. Borys, M. Wenzel, Th. Wriedt, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 1. Reflective mode operation,” Part. Part. Syst. Charact. 11, 339–344 (1994).
[CrossRef]

H.-E. Albrecht, M. Borys, K. Hübner, “Generalized theory for simultaneous measurement of particle size and velocity using laser-Doppler- and laser-two-focus methods,” Part. Part. Syst. Charact. 10, 138–145 (1993).
[CrossRef]

Bauckhage, K.

Bech, H.

H.-E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Die Berechnung der Streuintensität eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik (Stuttgart) 100, 118–124 (1995).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, England, 1999).

Borys, M.

H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

H.-E. Albrecht, M. Borys, M. Wenzel, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 2. Analysis by extension of geometrical optics to the laser beam; refractive mode operation,” Part. Part. Syst. Charact. 13, 18–26 (1996).
[CrossRef]

H.-E. Albrecht, M. Borys, M. Wenzel, Th. Wriedt, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 1. Reflective mode operation,” Part. Part. Syst. Charact. 11, 339–344 (1994).
[CrossRef]

H.-E. Albrecht, M. Borys, K. Hübner, “Generalized theory for simultaneous measurement of particle size and velocity using laser-Doppler- and laser-two-focus methods,” Part. Part. Syst. Charact. 10, 138–145 (1993).
[CrossRef]

M. Borys, “Analyse des Amplituden- und Phasenverhaltens von Laser-Doppler-Signalen zur Grössenbestimmung sphärischer Teilchen,” Ph.D. dissertation (Universität Rostock, Shaker-Verlag, Aachen, Germany, 1996).

Brenn, G.

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (1996).
[CrossRef]

Bultynck, H.

H. Bultynck, F. Onofri, G. Gréhan, G. Gouesbet, “Sonde Phase Doppler miniature: applications aux diagnostics en milieux hostiles,” in Proceedings of the Fifth Congress on Francophone de Vélocimétrie Laser (Complex de Recherche Interprofessionnel en Aerothermochimie, Université et Institut National des Sciences Appliqués de Rouen, Rouen, France, 1996).

H. Bultynck, “Développements de sondes laser Doppler miniatures pour la mesure de particules dans des écoulemnets réels complexes,” Ph.D. dissertation (Université de Rouen, Mont Saint Aignan, France, 1998).

Damaschke, N.

H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

H.-E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Die Berechnung der Streuintensität eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik (Stuttgart) 100, 118–124 (1995).

Domnick, J.

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (1996).
[CrossRef]

J. Domnick, H. Ertl, C. Tropea, “Processing of phase Doppler signals using the cross spectral density function,” in Application of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durao, F. Durst, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1989), pp. 473–483.
[CrossRef]

Dopheide, D.

V. Strunck, H. Müller, D. Dopheide, “Traversionsfreier LDA-Grenzschichtmessungen mit Mikrometerauflösung im Messvolumen,” in Proceedings of Lasermethoden in der Strömungsmesstechnik, W. Merzkirch, F. Peters, B. Ruck, D. Dopheide, A. Leder, eds. (Shaker-Verlag, Aachen, Germany, 1998), paper 28.

Durst, F.

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]

Ertl, H.

J. Domnick, H. Ertl, C. Tropea, “Processing of phase Doppler signals using the cross spectral density function,” in Application of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durao, F. Durst, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1989), pp. 473–483.
[CrossRef]

Feleke, M.

H.-E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Die Berechnung der Streuintensität eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik (Stuttgart) 100, 118–124 (1995).

Girasole, Th.

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (1996).
[CrossRef]

Gouesbet, G.

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (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]

H. Bultynck, F. Onofri, G. Gréhan, G. Gouesbet, “Sonde Phase Doppler miniature: applications aux diagnostics en milieux hostiles,” in Proceedings of the Fifth Congress on Francophone de Vélocimétrie Laser (Complex de Recherche Interprofessionnel en Aerothermochimie, Université et Institut National des Sciences Appliqués de Rouen, Rouen, France, 1996).

Gréhan, G.

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (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]

H. Bultynck, F. Onofri, G. Gréhan, G. Gouesbet, “Sonde Phase Doppler miniature: applications aux diagnostics en milieux hostiles,” in Proceedings of the Fifth Congress on Francophone de Vélocimétrie Laser (Complex de Recherche Interprofessionnel en Aerothermochimie, Université et Institut National des Sciences Appliqués de Rouen, Rouen, France, 1996).

Hess, C. F.

C. F. Hess, C. P. Wood, “Pulse displacement technique to measure particle size and velocity in high density application,” in Laser Techniques and Applications to Fluid Mechanics, R. J. Adrian, D. F. G. Durãu, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1993), pp. 131–144.
[CrossRef]

Hishida, K.

K. Hishida, K. Kobashi, M. Maeda, “Improvement of LDA/PDA using a digital signal processor (DSP),” in Proceedings of the Third International Conference on Laser Anemometry (BHRA Information Services, Cranfield, Bedford MK41 OAJ, UK, 1989), paper S2.

Hovenac, E. A.

Hübner, K.

H.-E. Albrecht, M. Borys, K. Hübner, “Generalized theory for simultaneous measurement of particle size and velocity using laser-Doppler- and laser-two-focus methods,” Part. Part. Syst. Charact. 10, 138–145 (1993).
[CrossRef]

Kobashi, K.

K. Hishida, K. Kobashi, M. Maeda, “Improvement of LDA/PDA using a digital signal processor (DSP),” in Proceedings of the Third International Conference on Laser Anemometry (BHRA Information Services, Cranfield, Bedford MK41 OAJ, UK, 1989), paper S2.

Lehmann, P.

Lettington, A. H.

S. M. Lin, D. R. Waterman, A. H. Lettington, “Measurement of droplet velocity, size, and refractive index using the pulse displacement technique,” Meas. Sci. Technol. 11, L1–L4 (2000).
[CrossRef]

Lin, S. M.

S. M. Lin, D. R. Waterman, A. H. Lettington, “Measurement of droplet velocity, size, and refractive index using the pulse displacement technique,” Meas. Sci. Technol. 11, L1–L4 (2000).
[CrossRef]

Lock, J. A.

Lohner, H.

Maeda, M.

K. Hishida, K. Kobashi, M. Maeda, “Improvement of LDA/PDA using a digital signal processor (DSP),” in Proceedings of the Third International Conference on Laser Anemometry (BHRA Information Services, Cranfield, Bedford MK41 OAJ, UK, 1989), paper S2.

Müller, H.

V. Strunck, H. Müller, D. Dopheide, “Traversionsfreier LDA-Grenzschichtmessungen mit Mikrometerauflösung im Messvolumen,” in Proceedings of Lasermethoden in der Strömungsmesstechnik, W. Merzkirch, F. Peters, B. Ruck, D. Dopheide, A. Leder, eds. (Shaker-Verlag, Aachen, Germany, 1998), paper 28.

Naqwi, A.

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]

Nobach, H.

H. Nobach, “Analysis of dual-burst laser Doppler signals,” Meas. Sci. Technol. 13, 33–44 (2002).
[CrossRef]

Onofri, F.

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (1996).
[CrossRef]

H. Bultynck, F. Onofri, G. Gréhan, G. Gouesbet, “Sonde Phase Doppler miniature: applications aux diagnostics en milieux hostiles,” in Proceedings of the Fifth Congress on Francophone de Vélocimétrie Laser (Complex de Recherche Interprofessionnel en Aerothermochimie, Université et Institut National des Sciences Appliqués de Rouen, Rouen, France, 1996).

Pavlovski, B.

B. Pavlovski, N. Semidetnov, “Simultaneous measurement of velocity, size and concentrations for particles moving in two-phase flow,” Meas. Tech. (USSR) (Izmer. Tekh.) 9, 40–42 (1991),in Russian.

Riethmuller, M. L.

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow interferometry with wire diffraction for simultaneous measurement of droplet temperature, size and velocity,” Part. Part. Syst. Charact. 14, 186–192 (1997).

Semidetnov, N.

B. Pavlovski, N. Semidetnov, “Simultaneous measurement of velocity, size and concentrations for particles moving in two-phase flow,” Meas. Tech. (USSR) (Izmer. Tekh.) 9, 40–42 (1991),in Russian.

Soo, S. L.

S. L. Soo, Instrumentation for Fluid-Particle Flow (Andrew Publishing, Norwich, N.Y., 1999).

Strunck, V.

V. Strunck, H. Müller, D. Dopheide, “Traversionsfreier LDA-Grenzschichtmessungen mit Mikrometerauflösung im Messvolumen,” in Proceedings of Lasermethoden in der Strömungsmesstechnik, W. Merzkirch, F. Peters, B. Ruck, D. Dopheide, A. Leder, eds. (Shaker-Verlag, Aachen, Germany, 1998), paper 28.

Tropea, C.

H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (1996).
[CrossRef]

J. Domnick, H. Ertl, C. Tropea, “Processing of phase Doppler signals using the cross spectral density function,” in Application of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durao, F. Durst, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1989), pp. 473–483.
[CrossRef]

van Beeck, J. P. A. J.

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow interferometry with wire diffraction for simultaneous measurement of droplet temperature, size and velocity,” Part. Part. Syst. Charact. 14, 186–192 (1997).

van de Hulst, H. C.

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

Waterman, D. R.

S. M. Lin, D. R. Waterman, A. H. Lettington, “Measurement of droplet velocity, size, and refractive index using the pulse displacement technique,” Meas. Sci. Technol. 11, L1–L4 (2000).
[CrossRef]

Wenzel, M.

H.-E. Albrecht, M. Borys, M. Wenzel, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 2. Analysis by extension of geometrical optics to the laser beam; refractive mode operation,” Part. Part. Syst. Charact. 13, 18–26 (1996).
[CrossRef]

H.-E. Albrecht, M. Borys, M. Wenzel, Th. Wriedt, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 1. Reflective mode operation,” Part. Part. Syst. Charact. 11, 339–344 (1994).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, England, 1999).

Wood, C. P.

C. F. Hess, C. P. Wood, “Pulse displacement technique to measure particle size and velocity in high density application,” in Laser Techniques and Applications to Fluid Mechanics, R. J. Adrian, D. F. G. Durãu, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1993), pp. 131–144.
[CrossRef]

Wriedt, Th.

H.-E. Albrecht, M. Borys, M. Wenzel, Th. Wriedt, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 1. Reflective mode operation,” Part. Part. Syst. Charact. 11, 339–344 (1994).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (3)

S. M. Lin, D. R. Waterman, A. H. Lettington, “Measurement of droplet velocity, size, and refractive index using the pulse displacement technique,” Meas. Sci. Technol. 11, L1–L4 (2000).
[CrossRef]

H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

H. Nobach, “Analysis of dual-burst laser Doppler signals,” Meas. Sci. Technol. 13, 33–44 (2002).
[CrossRef]

Meas. Tech. (USSR) (Izmer. Tekh.) (1)

B. Pavlovski, N. Semidetnov, “Simultaneous measurement of velocity, size and concentrations for particles moving in two-phase flow,” Meas. Tech. (USSR) (Izmer. Tekh.) 9, 40–42 (1991),in Russian.

Optik (Stuttgart) (1)

H.-E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Die Berechnung der Streuintensität eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik (Stuttgart) 100, 118–124 (1995).

Part. Part. Syst. Charact. (6)

H.-E. Albrecht, M. Borys, M. Wenzel, Th. Wriedt, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 1. Reflective mode operation,” Part. Part. Syst. Charact. 11, 339–344 (1994).
[CrossRef]

H.-E. Albrecht, M. Borys, M. Wenzel, “Influence of the measurement volume on the phase error in phase Doppler anemometry. Part 2. Analysis by extension of geometrical optics to the laser beam; refractive mode operation,” Part. Part. Syst. Charact. 13, 18–26 (1996).
[CrossRef]

F. Onofri, Th. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, C. Tropea, “Phase-Doppler anemometry with dual burst technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Charact. 13, 112–123 (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]

H.-E. Albrecht, M. Borys, K. Hübner, “Generalized theory for simultaneous measurement of particle size and velocity using laser-Doppler- and laser-two-focus methods,” Part. Part. Syst. Charact. 10, 138–145 (1993).
[CrossRef]

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow interferometry with wire diffraction for simultaneous measurement of droplet temperature, size and velocity,” Part. Part. Syst. Charact. 14, 186–192 (1997).

Other (10)

J. Domnick, H. Ertl, C. Tropea, “Processing of phase Doppler signals using the cross spectral density function,” in Application of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durao, F. Durst, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1989), pp. 473–483.
[CrossRef]

K. Hishida, K. Kobashi, M. Maeda, “Improvement of LDA/PDA using a digital signal processor (DSP),” in Proceedings of the Third International Conference on Laser Anemometry (BHRA Information Services, Cranfield, Bedford MK41 OAJ, UK, 1989), paper S2.

M. Borys, “Analyse des Amplituden- und Phasenverhaltens von Laser-Doppler-Signalen zur Grössenbestimmung sphärischer Teilchen,” Ph.D. dissertation (Universität Rostock, Shaker-Verlag, Aachen, Germany, 1996).

H. Bultynck, F. Onofri, G. Gréhan, G. Gouesbet, “Sonde Phase Doppler miniature: applications aux diagnostics en milieux hostiles,” in Proceedings of the Fifth Congress on Francophone de Vélocimétrie Laser (Complex de Recherche Interprofessionnel en Aerothermochimie, Université et Institut National des Sciences Appliqués de Rouen, Rouen, France, 1996).

S. L. Soo, Instrumentation for Fluid-Particle Flow (Andrew Publishing, Norwich, N.Y., 1999).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, England, 1999).

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

H. Bultynck, “Développements de sondes laser Doppler miniatures pour la mesure de particules dans des écoulemnets réels complexes,” Ph.D. dissertation (Université de Rouen, Mont Saint Aignan, France, 1998).

C. F. Hess, C. P. Wood, “Pulse displacement technique to measure particle size and velocity in high density application,” in Laser Techniques and Applications to Fluid Mechanics, R. J. Adrian, D. F. G. Durãu, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, Germany, 1993), pp. 131–144.
[CrossRef]

V. Strunck, H. Müller, D. Dopheide, “Traversionsfreier LDA-Grenzschichtmessungen mit Mikrometerauflösung im Messvolumen,” in Proceedings of Lasermethoden in der Strömungsmesstechnik, W. Merzkirch, F. Peters, B. Ruck, D. Dopheide, A. Leder, eds. (Shaker-Verlag, Aachen, Germany, 1998), paper 28.

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Figures (21)

Fig. 1
Fig. 1

Scattering angle regions of dominant scattering order. The maps are processed from scattering functions of particles in the range of x m = 64–1290 (10–200 µm) for the two polarization components. The contour lines give the 92%, 94%, 96%, and 98% regions of dominance. The numbers in parentheses give the scattering order (reflection p = 1, first-order refraction p = 2, second-order refraction p = 3). ——, Total reflection; ......., rainbow angle; ---, critical angle. (a) Perpendicular polarization and (b) parallel polarization.

Fig. 2
Fig. 2

Scattering intensity as a function of scattering angle and two polarization components for a spherical particle of 100-µm diameter and m = 1.42. We performed the computations using the LMT, and we obtained the scattering orders using a Debye series decomposition.

Fig. 3
Fig. 3

Scattering orders or modes that contribute to the signal in the near backscatter region for m > 1.

Fig. 4
Fig. 4

Optical arrangement for a time-shift system in backscatter.

Fig. 5
Fig. 5

Signal received at the photodetector of a planar phase Doppler system for a trajectory in the x direction (Θ = 7.4 deg, ψ = 25 deg, λ = 514.5 nm, d p = 80 µm, d b = 20 µm, y p0 = 0 µm, z p0 = -50 µm). (a) Calculated with the FLMT and Debye series decomposition of the scattering orders and (b) experiment.

Fig. 6
Fig. 6

Influence of scattering angle on fractional signal separation for three different elevation angles (d p = 80 µm, Θ = 4 deg, λ = 514.5 nm, d b = 20 µm).

Fig. 7
Fig. 7

Planar optical configuration with separated measurement volumes.

Fig. 8
Fig. 8

Simulated signals from two receivers of a planar optical configuration: upper half, receiver 1, ψ b = -25 deg; lower half, receiver 2, ψ b = 25 deg. (Θ = 4 deg, λ = 514.5 nm, d p = 100 µm, d b = 20 µm).

Fig. 9
Fig. 9

Simulated (FLMT) ac and dc signal power as a function of particle position in the y = 0 plane in the region of the illuminated volume. Upper half, dc part; lower half, ac part (Θ = 4 deg, ψ = 20 deg, λ = 514.5 nm, d p = 120 µm).

Fig. 10
Fig. 10

Signals and dc and ac parts for two particle trajectories parallel to the x axis at z = 0 µm and z = 160 µm for the configuration from Fig. 9. (a) Receiver 2, dc part; (b) amplitude of the ac part; (c) total signal z p0 = 0 µm; (d) z p0 = 160 µm.

Fig. 11
Fig. 11

Influence of oblique particle trajectories on the position of the signal maxima.

Fig. 12
Fig. 12

Changes of the signal structure and time shifts due to refractive index changes (d p = 80 µm, ψ = 20 deg, Θ = 4 deg, λ = 514.5 nm, d b = 20 µm). (a) Total signal and (b) fractional signal positions. Symbols show the FLMT with Debye decomposition: ■, p = 1; ○, p = 3.1; ▲, p = 3.2.

Fig. 13
Fig. 13

Geometry of light scattering from an elliptical particle.

Fig. 14
Fig. 14

Normalized incident point position for various detector scattering angles and aspect ratios of ellipticity a/ b = ●, 0.8; ▲, 0.9; —, 1.0; △, 1.1; □, 1.2; ○, 1.3 (m = 1.33). Upper half, reflection (p = 1) normalized incident point is negative; lower half, second-order refraction (p = 3.1).

Fig. 15
Fig. 15

Relative incident point shift of reflective and refractive (p = 3.1) fractional signals as a function of aspect ratio of ellipticity (m = 1.33).

Fig. 16
Fig. 16

Definition of normalized incident points: (a) reflection and (b) second-order refraction.

Fig. 17
Fig. 17

Normalized displacement of the measurement volume on the x axis for reflection.

Fig. 18
Fig. 18

Normalized volume displacement for second-order refraction for refractive indices of m = 1.33 and m = 1.5.

Fig. 19
Fig. 19

Ray paths of second-order refraction for m = 1.5 and ψ = 10 deg.

Fig. 20
Fig. 20

(a) Linear fit to the ratio of the averaged envelope function and its derivative. (b) Gauss fit to the averaged envelope and the modified envelope function after the first iteration (highest peak removed).

Fig. 21
Fig. 21

Particle size estimates from simulated signals by use of various fractional signals and a 20-µm measurement volume diameter (ψ = ±20 deg, Θ = 4 deg, λ = 514.5 nm, m = 1.33): —, geometrical-optics prediction; ●, signal processing of complete signal; □, signal processing of Debye orders. (a) SWSP plus second-order refraction (p = 3.2), (b) second-order refraction (p = 3.1), (c) reflection (p = 1).

Equations (40)

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rmaxp=-xi,p-yi,p0+001z,
ri,p=xi,pyi,pzi,p
rmax,=p=-xi,p+zi,p tanΘ/2-yi,p0+tanΘ/201z.
rmax,p=12-x1i,p+x2i,p+z1i,p-z2i,ptanΘ/2-y1i,p+y2i,p-[z1i,p+z2i,p)+x1i,p-x2i,pcot Θ/2
rmaxp=-12x1i,p+x2i,p0z1i,p+z2i,p-ξp.
xmax=p=-xi,p±zi,p+zp0tanΘ/21mz tanΘ/2-myyi,p+yp0cos2Θ/21mz tanΘ/22+mycos (Θ/2,
xmaxp=-xˆp-mzx¯p+z¯ptanΘ/2+mzzp0-zˆptanΘ/2+yp0-ŷpmycos2Θ/21+mz2 tan2Θ/2+mycos2Θ/2,
rˆp=xˆpŷpzˆp=12x1i,p+x2i,py1i,p+y2i,pz1i,p+z2i,p, x¯p=x1i,p-x2i,p2, z¯p=z1i,p-z2i,p2.
xmaxp-xˆp+yp0my+zp0mz Θ/21+my.
Δt12p=Δxmaxpvx=xmax,1p-xmax,2pvx-1vxxˆ1p+xˆ2p1+my
Δt12p=1=xmax,11-xmax,21vx=-dp22vxcos ψ cos ϕ tan (Θ/2)-sin ψ1-cos ψ cos ϕ cosΘ/2-sin ψ sinΘ/21/2-cos ψ cos ϕ tanΘ/2+sin ψ1-cos ψ cos ϕ cosΘ/2+sin ψ sinΘ/21/2,
Δt121=dpvxsinψ2tanΘ/2Θ/2, ψ  Θ/2, ϕ=180 deg.
δp=Δprpxˆprp, Δt12pdpvx δp, δ1=sinψ2.
ϑs=π+2θi-2θt=π+2θi-4 arcsinsin θim,
Δt12p=dp2vxδ1p-δ2p,
ueti=|uacti+juacti| t=ti, i=1, 2,, Ns,
cti=exp-αηti2,
ηpre=8NbT2,
ue AV=ue AVti+1-ue AVti-12fs,
ufitti=a exp-ηti-τ2,
ufitti=-2aηti-τexp-ηti-τ2.
ufittiufitti=2ητ-ti
ue AVtiue AVti=ri
mini=1Ns wi2ητ-ti-ri2,
η=-12DSr1S1Sr0S0,
τ=-1DS2Sr1S1Sr0,
S0=i=1Ns wi, S1=i=1Ns witi, S2=i=1Ns witi2, Sr0=i=1Ns wiri, Sr1=i=1Ns wiriti,
D=S2S1S1S0.
wi=exp-αηti-I2,
mini=1Ns wiufitti-ue AVti2,
a=i=1Ns wiue AV exp-ηti-τ2i=1Ns wi exp-ηti-τ2.
ue AVti-ufitti.
max0, ue AVti-ufitti.
ue AVnewti=1-exp-ηti-τ2×max0, ue AVti-ufitti.
η¯=1NbNdk=1NbNd ηk
1ηnew=1η¯-1ηpre.
Ukfl=i=1Ns wiuktiexp-2πjfltil=0Ns-1, fl=lfs/Ns,
wi=ue LPtiudcti
Sfl=k=1NbNd Skfl,
φkfl=argUkfl.

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