Abstract

We report a novel laser-Doppler velocity profile sensor for microfluidic and nanofluidic applications and turbulence research. The sensor’s design is based on wavelength-division multiplexing. The high dispersion of a diffractive lens is used to generate a measurement volume with convergent and divergent interference fringes by means of two laser wavelengths. Evaluation of the scattered light from tracers allows velocity gradients to be measured in flows with submicrometer spatial resolution inside a measurement volume of 700-µm length. Using diffraction optics and fiber optics, we achieved a miniaturized and robust velocity profile sensor for highly resolved velocity measurements.

© 2005 Optical Society of America

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  1. M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
    [CrossRef]
  2. R. Bayt, A. Ayon, K. Breuer, “A performance evaluation of MEMS-bases micronozzles,” paper AIAA-97-3169, presented at the 33rd Joint Propulsion Conference, Seattle, Wash., 7–9 July 1997 (American Institute for Aeronautics and Astronautics, Reston, Va., 1997).
  3. A. A. Naqwi, W. C. Reynolds, “Measurement of turbulent wall velocity gradients using cylindrical waves of laser light,” Exp. Fluids 10, 257–266 (1991).
    [CrossRef]
  4. A. A. Naqwi, W. C. Reynolds, L. W. Carr, “Dual cylindrical wave laser-Doppler method for measurement of wall shear stress,” in Laser Anemometry in Fluid Mechanics, R. J. Adrian, D. F. G. Durão, F. Durst, H. Mishima, J. H. Whitelaw, eds. (LADOAN—Instituto Superior Técnico, Lisbon, Portugal, 1984), pp. 105–122.
  5. H. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer-Verlag, Berlin, 2002).
  6. J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
    [CrossRef]
  7. L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.
  8. D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fibre optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
    [CrossRef]
  9. M. Stieglmeier, C. Tropea, “Mobile fiber-optic laser Doppler anemometer,” Appl. Opt. 31, 4096–4105 (1992).
    [CrossRef] [PubMed]
  10. J. Czarske, “A miniaturised double-core fibre laser Doppler sensor,” Meas. Sci. Technol. 12, 1191–1198 (2001).
    [CrossRef]
  11. P. Miles, P. Witze, “Evaluation of the Gaussian beam model for prediction of LDV fringe fields,” presented at the 8th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July, 1996.
  12. E. B. Li, A. K. Tieu, “Analysis of the three-dimensional fringe pattern formed by the interference of ideal and astigmatic Gaussian beams,” presented at the 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July, 1998.
  13. S. Sinzinger, J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, Weinheim, Germany, 2003).
    [CrossRef]
  14. L. Büttner, J. Czarske, “Passive directional discrimination in laser Doppler anemometry by the two-wavelength quadrature homodyne technique,” Appl. Opt. 42, 3843–3852 (2003).
    [CrossRef]

2003 (1)

2002 (1)

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

2001 (2)

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

J. Czarske, “A miniaturised double-core fibre laser Doppler sensor,” Meas. Sci. Technol. 12, 1191–1198 (2001).
[CrossRef]

1992 (1)

1991 (1)

A. A. Naqwi, W. C. Reynolds, “Measurement of turbulent wall velocity gradients using cylindrical waves of laser light,” Exp. Fluids 10, 257–266 (1991).
[CrossRef]

1984 (1)

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fibre optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Albrecht, H.

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

Ayon, A.

R. Bayt, A. Ayon, K. Breuer, “A performance evaluation of MEMS-bases micronozzles,” paper AIAA-97-3169, presented at the 33rd Joint Propulsion Conference, Seattle, Wash., 7–9 July 1997 (American Institute for Aeronautics and Astronautics, Reston, Va., 1997).

Bayt, R.

R. Bayt, A. Ayon, K. Breuer, “A performance evaluation of MEMS-bases micronozzles,” paper AIAA-97-3169, presented at the 33rd Joint Propulsion Conference, Seattle, Wash., 7–9 July 1997 (American Institute for Aeronautics and Astronautics, Reston, Va., 1997).

Becker, S.

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Borys, M.

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

Breuer, K.

R. Bayt, A. Ayon, K. Breuer, “A performance evaluation of MEMS-bases micronozzles,” paper AIAA-97-3169, presented at the 33rd Joint Propulsion Conference, Seattle, Wash., 7–9 July 1997 (American Institute for Aeronautics and Astronautics, Reston, Va., 1997).

Büttner, L.

L. Büttner, J. Czarske, “Passive directional discrimination in laser Doppler anemometry by the two-wavelength quadrature homodyne technique,” Appl. Opt. 42, 3843–3852 (2003).
[CrossRef]

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Carr, L. W.

A. A. Naqwi, W. C. Reynolds, L. W. Carr, “Dual cylindrical wave laser-Doppler method for measurement of wall shear stress,” in Laser Anemometry in Fluid Mechanics, R. J. Adrian, D. F. G. Durão, F. Durst, H. Mishima, J. H. Whitelaw, eds. (LADOAN—Instituto Superior Técnico, Lisbon, Portugal, 1984), pp. 105–122.

Chan, R. K. Y.

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fibre optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Czarske, J.

L. Büttner, J. Czarske, “Passive directional discrimination in laser Doppler anemometry by the two-wavelength quadrature homodyne technique,” Appl. Opt. 42, 3843–3852 (2003).
[CrossRef]

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

J. Czarske, “A miniaturised double-core fibre laser Doppler sensor,” Meas. Sci. Technol. 12, 1191–1198 (2001).
[CrossRef]

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Damaschke, N.

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

Dopheide, D.

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Durst, F.

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Fischer, M.

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

Jackson, D. A.

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fibre optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Jahns, J.

S. Sinzinger, J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, Weinheim, Germany, 2003).
[CrossRef]

Jones, J. D. C.

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fibre optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Jovanovic, J.

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

Li, E. B.

E. B. Li, A. K. Tieu, “Analysis of the three-dimensional fringe pattern formed by the interference of ideal and astigmatic Gaussian beams,” presented at the 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July, 1998.

Lienhart, H.

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Miles, P.

P. Miles, P. Witze, “Evaluation of the Gaussian beam model for prediction of LDV fringe fields,” presented at the 8th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July, 1996.

Müller, H.

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Naqwi, A. A.

A. A. Naqwi, W. C. Reynolds, “Measurement of turbulent wall velocity gradients using cylindrical waves of laser light,” Exp. Fluids 10, 257–266 (1991).
[CrossRef]

A. A. Naqwi, W. C. Reynolds, L. W. Carr, “Dual cylindrical wave laser-Doppler method for measurement of wall shear stress,” in Laser Anemometry in Fluid Mechanics, R. J. Adrian, D. F. G. Durão, F. Durst, H. Mishima, J. H. Whitelaw, eds. (LADOAN—Instituto Superior Técnico, Lisbon, Portugal, 1984), pp. 105–122.

Razik, T.

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Reynolds, W. C.

A. A. Naqwi, W. C. Reynolds, “Measurement of turbulent wall velocity gradients using cylindrical waves of laser light,” Exp. Fluids 10, 257–266 (1991).
[CrossRef]

A. A. Naqwi, W. C. Reynolds, L. W. Carr, “Dual cylindrical wave laser-Doppler method for measurement of wall shear stress,” in Laser Anemometry in Fluid Mechanics, R. J. Adrian, D. F. G. Durão, F. Durst, H. Mishima, J. H. Whitelaw, eds. (LADOAN—Instituto Superior Técnico, Lisbon, Portugal, 1984), pp. 105–122.

Shirai, K.

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

Sinzinger, S.

S. Sinzinger, J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, Weinheim, Germany, 2003).
[CrossRef]

Stieglmeier, M.

Tieu, A. K.

E. B. Li, A. K. Tieu, “Analysis of the three-dimensional fringe pattern formed by the interference of ideal and astigmatic Gaussian beams,” presented at the 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July, 1998.

Tropea, C.

M. Stieglmeier, C. Tropea, “Mobile fiber-optic laser Doppler anemometer,” Appl. Opt. 31, 4096–4105 (1992).
[CrossRef] [PubMed]

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

Witze, P.

P. Miles, P. Witze, “Evaluation of the Gaussian beam model for prediction of LDV fringe fields,” presented at the 8th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July, 1996.

Appl. Opt. (2)

Exp. Fluids (1)

A. A. Naqwi, W. C. Reynolds, “Measurement of turbulent wall velocity gradients using cylindrical waves of laser light,” Exp. Fluids 10, 257–266 (1991).
[CrossRef]

J. Phys. E (1)

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fibre optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Meas. Sci. Technol. (2)

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

J. Czarske, “A miniaturised double-core fibre laser Doppler sensor,” Meas. Sci. Technol. 12, 1191–1198 (2001).
[CrossRef]

Phys. Fluids (1)

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

Other (7)

R. Bayt, A. Ayon, K. Breuer, “A performance evaluation of MEMS-bases micronozzles,” paper AIAA-97-3169, presented at the 33rd Joint Propulsion Conference, Seattle, Wash., 7–9 July 1997 (American Institute for Aeronautics and Astronautics, Reston, Va., 1997).

A. A. Naqwi, W. C. Reynolds, L. W. Carr, “Dual cylindrical wave laser-Doppler method for measurement of wall shear stress,” in Laser Anemometry in Fluid Mechanics, R. J. Adrian, D. F. G. Durão, F. Durst, H. Mishima, J. H. Whitelaw, eds. (LADOAN—Instituto Superior Técnico, Lisbon, Portugal, 1984), pp. 105–122.

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

P. Miles, P. Witze, “Evaluation of the Gaussian beam model for prediction of LDV fringe fields,” presented at the 8th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July, 1996.

E. B. Li, A. K. Tieu, “Analysis of the three-dimensional fringe pattern formed by the interference of ideal and astigmatic Gaussian beams,” presented at the 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July, 1998.

S. Sinzinger, J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, Weinheim, Germany, 2003).
[CrossRef]

L. Büttner, K. Shirai, T. Razik, J. Czarske, H. Müller, D. Dopheide, S. Becker, H. Lienhart, F. Durst, “Highly spatial resolved measurements of turbulent boundary layers by a laser Doppler velocity profile sensor,” presented at the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 12–15 July, 2004.

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Figures (8)

Fig. 1
Fig. 1

Schematic of the velocity profile sensor: Two (superposed) interference fringe systems are generated by means of two laser wavelengths, one with convex wave fronts that result in divergent fringes (top) and the other with concave wavefronts that result in convergent fringes (bottom).

Fig. 2
Fig. 2

Dispersion management for a velocity profile sensor employing fiber-optic and diffractive optical elements: crosses, beam waist positions of the infrared beams; pluses, beam waist positions of the red beams.

Fig. 3
Fig. 3

Wavelength dependence of the focal lengths of a refractive and a diffractive lens.

Fig. 4
Fig. 4

Experimental schematic of the velocity profile sensor with fiber optics and a diffractive lens.

Fig. 5
Fig. 5

Caustic curves about the measurement volume. The beam waists of the 825-nm beams are located before the measurement volume, generating divergent fringes, whereas the beam waists of the 658-nm beams are located behind, generating convergent fringes.

Fig. 6
Fig. 6

Normalized amplitudes of the fast Fourier transform Doppler peak. A satisfactory superposition of the individual interference fringe system occurs with an effective length of the measurement volume of 700 µm.

Fig. 7
Fig. 7

Top, convergent and divergent fringes d1,2(z) in the measurement volume; bottom, calibration function q(z) = d1(z)/d2(z).

Fig. 8
Fig. 8

Determination of the spatial resolution. In the center of the measurement a spatial resolution of ∼650 nm was achieved.

Tables (1)

Tables Icon

Table 1 Design Parameters for the Diffractive Lens Used in Our Experiments

Equations (5)

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q ( z ) = f 2 ( υ , z ) f 1 ( υ , z ) = υ / d 2 ( z ) υ / d 1 ( z ) = d 1 ( z ) d 2 ( z ) .
υ ( z ) = f 1 ( υ , z ) d 1 ( z ) = f 2 ( υ , z ) d 2 ( z ) .
f ( λ ) = R 2 0 / 2 λ ,
η ges = η I A I + η II A II A ges 69 % ,
η T = T 2 = [ 4 η Air η SiO 2 ( η Air + η SiO 2 ) 2 ] 2 93 % .

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