Abstract

The time-shift technique, also known as the pulsed-displacement technique, is revisited as a method to measure size, velocity, and relative refractive index of spherical, transparent particles. Building on the basic measurement principle, we introduce several new innovations, making the technique significantly more attractive for use outside of the laboratory. These innovations include two possibilities for velocity measurement, validation criteria for one- and two-detector arrangements, and approaches to achieve higher bandwidths, and, in particular, lower measurable sizes. We discuss numerous optical configuration examples to illustrate the flexibility of this technique to meet various application requirements.

© 2014 Optical Society of America

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  1. C. Tropea, “Optical particle characterization in flows,” Annu. Rev. Fluid Mech. 43, 399–426 (2011).
    [CrossRef]
  2. N. Semidetnov, “Investigation of laser Doppler anemometer as instrument for two-phase flow measurements,” (in Russian) Ph.D. thesis (Leningrad Institute for Precision Mechanics and Optics, 1985).
  3. C. F. Hess and 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. Durão, F. Durst, M. V. Heitor, M. Maeda, and J. H. Whitelaw, eds. (Springer-Verlag, 1993), pp. 131–144.
  4. S. M. Lin, D. R. Waterman, and A. H. Lettington, “Measurement of droplet velocity, size and refractive index using the pulse displacement technique,” Meas. Sci. Technol. 11, L1–L4 (2000).
    [CrossRef]
  5. N. Damaschke, H. Nobach, N. Semidetnov, and C. Tropea, “Optical particle sizing in backscatter,” Appl. Opt. 41, 5713–5727 (2002).
    [CrossRef]
  6. H.-E. Albrecht, N. Damaschke, M. Borys, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2002), p. 738.
  7. R. Semiat and A. E. Dukler, “Simultaneous measurement of size and velocity of bubbles or drops: a new optical technique,” AIChE J. 27, 148–159 (1981).
    [CrossRef]
  8. A. Cartellier, “Local velocity and size measurements of particles in dense suspensions: theory and design of endoscopic grating velocimeter-granulometers,” Appl. Opt. 31, 3493–3505 (1992).
    [CrossRef]
  9. A. Brankovic, I. G. Currie, and W. W. Martin, “Laser Doppler measurements of bubble dynamics,” Phys. Fluids 27, 348–355 (1984).
    [CrossRef]
  10. P. Y. W. Yu and R. L. Varty, “Laser-Doppler measurement of the velocity and diameter of bubbles using the triple-peak technique,” Int. J. Multiphase Flow 14, 765–776 (1988).
    [CrossRef]
  11. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Annalen der physik 335, 57–136 (1909).
  12. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der physik 330, 377–445 (1908).
  13. W. J. Glantschnig and S. H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20, 2499–2509 (1981).
    [CrossRef]
  14. H. C. van de Hulst, Light Scattering by Small Particles (Courier Dover, 1957).
  15. E. Hecht, Optik (Oldenbourg, 2005).
  16. W. Schäfer, “Time-shift technique for particle characterization in sprays,” PhD Thesis (Technical University of Darmstadt, Institute for Fluid Mechanics and Aerodynamics, 2013).
  17. M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46, 3811–3820 (2007).
    [CrossRef]
  18. http://www.dow.com/optim/optim-advantage/physical-properties/refractive.htm .
  19. J. Rheims, J. Kser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
    [CrossRef]

2011 (1)

C. Tropea, “Optical particle characterization in flows,” Annu. Rev. Fluid Mech. 43, 399–426 (2011).
[CrossRef]

2007 (1)

2002 (1)

2000 (1)

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

1997 (1)

J. Rheims, J. Kser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

1992 (1)

1988 (1)

P. Y. W. Yu and R. L. Varty, “Laser-Doppler measurement of the velocity and diameter of bubbles using the triple-peak technique,” Int. J. Multiphase Flow 14, 765–776 (1988).
[CrossRef]

1984 (1)

A. Brankovic, I. G. Currie, and W. W. Martin, “Laser Doppler measurements of bubble dynamics,” Phys. Fluids 27, 348–355 (1984).
[CrossRef]

1981 (2)

R. Semiat and A. E. Dukler, “Simultaneous measurement of size and velocity of bubbles or drops: a new optical technique,” AIChE J. 27, 148–159 (1981).
[CrossRef]

W. J. Glantschnig and S. H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20, 2499–2509 (1981).
[CrossRef]

1909 (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Annalen der physik 335, 57–136 (1909).

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der physik 330, 377–445 (1908).

Albrecht, H.-E.

H.-E. Albrecht, N. Damaschke, M. Borys, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2002), p. 738.

Borys, M.

H.-E. Albrecht, N. Damaschke, M. Borys, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2002), p. 738.

Brankovic, A.

A. Brankovic, I. G. Currie, and W. W. Martin, “Laser Doppler measurements of bubble dynamics,” Phys. Fluids 27, 348–355 (1984).
[CrossRef]

Cartellier, A.

Chen, S. H.

Currie, I. G.

A. Brankovic, I. G. Currie, and W. W. Martin, “Laser Doppler measurements of bubble dynamics,” Phys. Fluids 27, 348–355 (1984).
[CrossRef]

Daimon, M.

Damaschke, N.

N. Damaschke, H. Nobach, N. Semidetnov, and C. Tropea, “Optical particle sizing in backscatter,” Appl. Opt. 41, 5713–5727 (2002).
[CrossRef]

H.-E. Albrecht, N. Damaschke, M. Borys, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2002), p. 738.

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Annalen der physik 335, 57–136 (1909).

Dukler, A. E.

R. Semiat and A. E. Dukler, “Simultaneous measurement of size and velocity of bubbles or drops: a new optical technique,” AIChE J. 27, 148–159 (1981).
[CrossRef]

Glantschnig, W. J.

Hecht, E.

E. Hecht, Optik (Oldenbourg, 2005).

Hess, C. F.

C. F. Hess and 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. Durão, F. Durst, M. V. Heitor, M. Maeda, and J. H. Whitelaw, eds. (Springer-Verlag, 1993), pp. 131–144.

Kser, J.

J. Rheims, J. Kser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

Lettington, A. H.

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

Martin, W. W.

A. Brankovic, I. G. Currie, and W. W. Martin, “Laser Doppler measurements of bubble dynamics,” Phys. Fluids 27, 348–355 (1984).
[CrossRef]

Masumura, A.

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der physik 330, 377–445 (1908).

Nobach, H.

Rheims, J.

J. Rheims, J. Kser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

Schäfer, W.

W. Schäfer, “Time-shift technique for particle characterization in sprays,” PhD Thesis (Technical University of Darmstadt, Institute for Fluid Mechanics and Aerodynamics, 2013).

Semiat, R.

R. Semiat and A. E. Dukler, “Simultaneous measurement of size and velocity of bubbles or drops: a new optical technique,” AIChE J. 27, 148–159 (1981).
[CrossRef]

Semidetnov, N.

N. Damaschke, H. Nobach, N. Semidetnov, and C. Tropea, “Optical particle sizing in backscatter,” Appl. Opt. 41, 5713–5727 (2002).
[CrossRef]

N. Semidetnov, “Investigation of laser Doppler anemometer as instrument for two-phase flow measurements,” (in Russian) Ph.D. thesis (Leningrad Institute for Precision Mechanics and Optics, 1985).

Tropea, C.

C. Tropea, “Optical particle characterization in flows,” Annu. Rev. Fluid Mech. 43, 399–426 (2011).
[CrossRef]

N. Damaschke, H. Nobach, N. Semidetnov, and C. Tropea, “Optical particle sizing in backscatter,” Appl. Opt. 41, 5713–5727 (2002).
[CrossRef]

H.-E. Albrecht, N. Damaschke, M. Borys, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2002), p. 738.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Courier Dover, 1957).

Varty, R. L.

P. Y. W. Yu and R. L. Varty, “Laser-Doppler measurement of the velocity and diameter of bubbles using the triple-peak technique,” Int. J. Multiphase Flow 14, 765–776 (1988).
[CrossRef]

Waterman, D. R.

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

Wood, C. P.

C. F. Hess and 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. Durão, F. Durst, M. V. Heitor, M. Maeda, and J. H. Whitelaw, eds. (Springer-Verlag, 1993), pp. 131–144.

Wriedt, T.

J. Rheims, J. Kser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

Yu, P. Y. W.

P. Y. W. Yu and R. L. Varty, “Laser-Doppler measurement of the velocity and diameter of bubbles using the triple-peak technique,” Int. J. Multiphase Flow 14, 765–776 (1988).
[CrossRef]

AIChE J. (1)

R. Semiat and A. E. Dukler, “Simultaneous measurement of size and velocity of bubbles or drops: a new optical technique,” AIChE J. 27, 148–159 (1981).
[CrossRef]

Annalen der physik (2)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Annalen der physik 335, 57–136 (1909).

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der physik 330, 377–445 (1908).

Annu. Rev. Fluid Mech. (1)

C. Tropea, “Optical particle characterization in flows,” Annu. Rev. Fluid Mech. 43, 399–426 (2011).
[CrossRef]

Appl. Opt. (4)

Int. J. Multiphase Flow (1)

P. Y. W. Yu and R. L. Varty, “Laser-Doppler measurement of the velocity and diameter of bubbles using the triple-peak technique,” Int. J. Multiphase Flow 14, 765–776 (1988).
[CrossRef]

Meas. Sci. Technol. (2)

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

J. Rheims, J. Kser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

Phys. Fluids (1)

A. Brankovic, I. G. Currie, and W. W. Martin, “Laser Doppler measurements of bubble dynamics,” Phys. Fluids 27, 348–355 (1984).
[CrossRef]

Other (7)

H.-E. Albrecht, N. Damaschke, M. Borys, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2002), p. 738.

N. Semidetnov, “Investigation of laser Doppler anemometer as instrument for two-phase flow measurements,” (in Russian) Ph.D. thesis (Leningrad Institute for Precision Mechanics and Optics, 1985).

C. F. Hess and 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. Durão, F. Durst, M. V. Heitor, M. Maeda, and J. H. Whitelaw, eds. (Springer-Verlag, 1993), pp. 131–144.

http://www.dow.com/optim/optim-advantage/physical-properties/refractive.htm .

H. C. van de Hulst, Light Scattering by Small Particles (Courier Dover, 1957).

E. Hecht, Optik (Oldenbourg, 2005).

W. Schäfer, “Time-shift technique for particle characterization in sprays,” PhD Thesis (Technical University of Darmstadt, Institute for Fluid Mechanics and Aerodynamics, 2013).

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Figures (14)

Fig. 1.
Fig. 1.

Schematic illustration of the scattering orders according to geometrical optics. Abbreviation: GP, glare point; p=0, reflection; p=1, first-order refraction; p=2, second-order refraction; p=3, third-order refraction; θi, incident point angle.

Fig. 2.
Fig. 2.

Basic principle of the TS technique in backscatter.

Fig. 3.
Fig. 3.

Characterization of the scattering field from spherical particles, according to scattering angle and relative refractive index. The lines demarcate appearance or disappearance of additional scattering orders, as summarized in Table 1.

Fig. 4.
Fig. 4.

Schematic illustration of one possibly optical configuration of the TS technique in backscatter with two detectors and one light source.

Fig. 5.
Fig. 5.

TS signals for a particle with m=1.34, 2w0=20μm, v=10m/s, and d=100μm in backscatter from two detectors with p=0, p=2.1, and p=2.2 for θS=155deg.

Fig. 6.
Fig. 6.

TS signals for a particle with m=1.34, 2w0=20μm, v=10m/s, and d=100μm in forward scattering from two detectors with p=0 and p=1 for θS=60deg.

Fig. 7.
Fig. 7.

α as a function of scattering angle, calculated for different relative refractive indexes.

Fig. 8.
Fig. 8.

γ as a function of scattering angle, calculated for different relative refractive indexes.

Fig. 9.
Fig. 9.

β as a function of scattering angle, calculated for different relative refractive indexes.

Fig. 10.
Fig. 10.

Numerical calculation for a forward scatter configuration with p=0 and p=1. Minimum particle-beam ratio as a function of scattering angle computed for different relative refractive indexes and polarization.

Fig. 11.
Fig. 11.

Particle size/diameter distribution of glass beads measured by direct imaging (black line) and by the TS technique (symbols).

Fig. 12.
Fig. 12.

Particle velocity distribution of glass beads measured by the TS technique.

Fig. 13.
Fig. 13.

Distributions of beta and gamma measured by the TS technique.

Fig. 14.
Fig. 14.

Relative refractive index distribution measured by the TS technique at wavelength of 405 nm and fit of measured data for water: 0.181*exp(((m1.34)/0.0303)2), ethanol: 0.182*exp(((m1.367)/0.0301)2), wg25: 0.155*exp(((m1.368)/0.0348)2).

Tables (2)

Tables Icon

Table 1. Key of Scattering Orders and Their Modes Presented in Fig. 3

Tables Icon

Table 2. Relative Refractive Indexes Measured with Time-Shift (Fig. 14) and Compared with Literature Values

Equations (14)

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I(z)=I0g(z,w0)vz=z/tS(t)=pApgp(vz(tt0(p)),w0),
Δs=FWHM{Apgp(vz(tt0(p)),w0)}=w0vz2ln(2),
Δt(p=a,p=b)=dvzf(m,θS)=t0(p=a)t0(p=b),
θc(p=1)=2arccos(1/m),
θrb(p=2)=π4arcsin[(1/m)(4m2)/3]+2arcsin[(4m2)/3],
θrb(p=3)=6arcsin[(1/m)(9m2)/8]2arcsin[(9m2)/8].
Δt00Δt11=dvzcosθS2dvzsinθi(p=1)=cosθS2sinθi(p=1)=α.
Δt220Δt210=d/2vz[cosθS2+sinθi(p=2.2)]d/2vz[cosθS2+sinθi(p=2.1)]=[cosθS2+sinθi(p=2.2)][cosθS2+sinθi(p=2.1)]=γ.
Δt2222Δt2121=dvzsinθi(p=2.2)dvzsinθi(p=2.1)=sinθi(p=2.2)sinθi(p=2.1)=β,
sinθi(p=2.1)=(cosθS2)(γ1βγ)
sinθi(p=2.2)=(cosθS2)(βγ1βγ),
m=sinθi(p=2.1)sin(π4θS4+θi(p=2.1)2)=sinθi(p=2.2)sin(π4θS4+θi(p=2.2)2).
FWHM=σ2ln(2)=w0vz2ln(2).
(dmin2w0)=ln(2)f(θS,m)(1+1+ln|Ap=a/Ap=b|ln(2)).

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