Abstract

Laser Doppler anemometry is a method for absolute velocity measurements that is based on a Mach–Zehnder interferometer arrangement and usually employs transverse fundamental-mode lasers. We employed inexpensive and powerful broad-area laser diodes and investigated ways in which an interference fringe system is influenced by the spatial coherence properties of a multimode beam. It was demonstrated that, owing to poor spatial coherence of the beam, interference is suppressed in the marginal regions of the intersection volume. Based on these results, a sensor for highly spatially resolved velocity measurements can be built. The inherent astigmatism of the broad-area diode is corrected by an arrangement of two crossed cylindrical lenses. An interference fringe system of length 200 μm and a relative variation in fringe-spacing of only 0.22% were demonstrated with light emitted from a broad-area laser diode with a 100 μm × 1 μm emitter size. Based on this principle a powerful, simple, and robust laser Doppler sensor has been achieved. Highly spatially resolved measurements of a boundary layer flow are presented.

© 2005 Optical Society of America

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References

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  1. L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).
  2. H. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
    [CrossRef]
  3. L. Büttner, “Untersuchung neuartiger Laser-Doppler-Verfahren zur hochauflösenden Geschwindigkeitsmessung,” Ph.D. dissertation (University of Hanover, Göttingen, Germany, 2004).
  4. S. Hanson, “Broadening of the measured frequency spectrum in a differential laser anemometer due to interference plane gradients,” Appl. Phys. 6, 164–171 (1973).
  5. P. Miles, P. Witze, “Evaluation of the Gaussian beam model for prediction of LDV fringe fields,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July, 1996.
  6. L. Büttner, J. Czarske, “A multimode-fibre laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
    [CrossRef]
  7. L. Büttner, J. Czarske, “Multimode laser Doppler anemometer for turbulence measurements with high spatial resolution,” presented at the 4th American Society of Mechanical Engineers/Japan Society of Mechanical Engineers Joint Fluids Engineering Conference, Honolulu, Hawaii, 6–11 July 2003.
  8. L. Büttner, J. Czarske, “Multimode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers,” Exp. Fluids 36, 214–216 (2004).
    [CrossRef]
  9. M. Haag, M. Brandner, “Diode lasers—an innovative tool for production,” p. 36,LaserOpto 03/2000; http://www.photonik.de/ .
  10. P. Peuser, N. P. Schmitt, Diodengepumpte Festkörperlaser (Springer–Verlag, Berlin, 1995).
    [CrossRef]
  11. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
    [CrossRef]
  12. 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]
  13. P. C. Miles, P. O. Witze, “Fringe field quantification in an LDV probe volume by use of a magnified image,” Exp. Fluids 16, 330–335 (1994).
    [CrossRef]
  14. 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 Ninth International Int. Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July, 1998.
  15. Linos Photonics, Göttingen/Germany, product catalog http://www.linos-photonics.com/ , (2003).
  16. H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1987).

2004 (1)

L. Büttner, J. Czarske, “Multimode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers,” Exp. Fluids 36, 214–216 (2004).
[CrossRef]

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 (1)

L. Büttner, J. Czarske, “A multimode-fibre laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
[CrossRef]

1994 (1)

P. C. Miles, P. O. Witze, “Fringe field quantification in an LDV probe volume by use of a magnified image,” Exp. Fluids 16, 330–335 (1994).
[CrossRef]

1973 (1)

S. Hanson, “Broadening of the measured frequency spectrum in a differential laser anemometer due to interference plane gradients,” Appl. Phys. 6, 164–171 (1973).

Albrecht, H.

H. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

Borys, M.

H. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

Büttner, L.

L. Büttner, J. Czarske, “Multimode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers,” Exp. Fluids 36, 214–216 (2004).
[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, J. Czarske, “A multimode-fibre laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
[CrossRef]

L. Büttner, “Untersuchung neuartiger Laser-Doppler-Verfahren zur hochauflösenden Geschwindigkeitsmessung,” Ph.D. dissertation (University of Hanover, Göttingen, Germany, 2004).

L. Büttner, J. Czarske, “Multimode laser Doppler anemometer for turbulence measurements with high spatial resolution,” presented at the 4th American Society of Mechanical Engineers/Japan Society of Mechanical Engineers Joint Fluids Engineering Conference, Honolulu, Hawaii, 6–11 July 2003.

Czarske, J.

L. Büttner, J. Czarske, “Multimode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers,” Exp. Fluids 36, 214–216 (2004).
[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, J. Czarske, “A multimode-fibre laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
[CrossRef]

L. Büttner, J. Czarske, “Multimode laser Doppler anemometer for turbulence measurements with high spatial resolution,” presented at the 4th American Society of Mechanical Engineers/Japan Society of Mechanical Engineers Joint Fluids Engineering Conference, Honolulu, Hawaii, 6–11 July 2003.

Damaschke, N.

H. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

Drain, L. E.

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

Hanson, S.

S. Hanson, “Broadening of the measured frequency spectrum in a differential laser anemometer due to interference plane gradients,” Appl. Phys. 6, 164–171 (1973).

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 Ninth International Int. Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July, 1998.

Miles, P.

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

Miles, P. C.

P. C. Miles, P. O. Witze, “Fringe field quantification in an LDV probe volume by use of a magnified image,” Exp. Fluids 16, 330–335 (1994).
[CrossRef]

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]

Peuser, P.

P. Peuser, N. P. Schmitt, Diodengepumpte Festkörperlaser (Springer–Verlag, Berlin, 1995).
[CrossRef]

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]

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Schlichting, H.

H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1987).

Schmitt, N. P.

P. Peuser, N. P. Schmitt, Diodengepumpte Festkörperlaser (Springer–Verlag, Berlin, 1995).
[CrossRef]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

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 Ninth International Int. Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July, 1998.

Tropea, C.

H. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

Witze, P.

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

Witze, P. O.

P. C. Miles, P. O. Witze, “Fringe field quantification in an LDV probe volume by use of a magnified image,” Exp. Fluids 16, 330–335 (1994).
[CrossRef]

Appl. Phys. (1)

S. Hanson, “Broadening of the measured frequency spectrum in a differential laser anemometer due to interference plane gradients,” Appl. Phys. 6, 164–171 (1973).

Exp. Fluids (2)

L. Büttner, J. Czarske, “Multimode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers,” Exp. Fluids 36, 214–216 (2004).
[CrossRef]

P. C. Miles, P. O. Witze, “Fringe field quantification in an LDV probe volume by use of a magnified image,” Exp. Fluids 16, 330–335 (1994).
[CrossRef]

Meas. Sci. Technol. (2)

L. Büttner, J. Czarske, “A multimode-fibre laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
[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]

Other (11)

L. Büttner, J. Czarske, “Multimode laser Doppler anemometer for turbulence measurements with high spatial resolution,” presented at the 4th American Society of Mechanical Engineers/Japan Society of Mechanical Engineers Joint Fluids Engineering Conference, Honolulu, Hawaii, 6–11 July 2003.

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 Ninth International Int. Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July, 1998.

Linos Photonics, Göttingen/Germany, product catalog http://www.linos-photonics.com/ , (2003).

H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1987).

M. Haag, M. Brandner, “Diode lasers—an innovative tool for production,” p. 36,LaserOpto 03/2000; http://www.photonik.de/ .

P. Peuser, N. P. Schmitt, Diodengepumpte Festkörperlaser (Springer–Verlag, Berlin, 1995).
[CrossRef]

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

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

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

H. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser-Doppler and Phase-Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

L. Büttner, “Untersuchung neuartiger Laser-Doppler-Verfahren zur hochauflösenden Geschwindigkeitsmessung,” Ph.D. dissertation (University of Hanover, Göttingen, Germany, 2004).

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Figures (10)

Fig. 1
Fig. 1

Analogy of the laser Doppler anemometer setup to that of a Mach–Zehnder interferometer and influence of spatial coherence on the interference fringe system. For explanations see the text.

Fig. 2
Fig. 2

Correction of the astigmatism of the broad-area laser diode by means of two crossed cylindrical lenses. Shown are the caustic curves for the two transverse directions, perpendicular (horizontal) and parallel (vertical), to the p–n-junction simulated with the ABCD matrix formalism.

Fig. 3
Fig. 3

Burst signals from a particle passing through the center of the measurement volume (a) in the time domain and (b) in the frequency domain. An interference contrast close to 1 can be obtained even for low spatially coherent light.

Fig. 4
Fig. 4

Dependence of the interference contrast along optical axis z on various operation currents of the laser diode. At 450 mA the laser operates below threshold. For small currents above threshold, parasitic side peaks occur, which vanish successively for increasing diode current.

Fig. 5
Fig. 5

Reduction of the effective length of the measurement volume with increasing diode current.

Fig. 6
Fig. 6

Dependence of beam-quality factor M2 on the laser-diode current. The beam quality worsens with increasing current because of the rising number of excited transverse modes.

Fig. 7
Fig. 7

Burst signals from a position of a side peak for two diode currents.

Fig. 8
Fig. 8

Variation of fringe spacing throughout the measurement volume. A low variation of 0.22% and a high spatial resolution (200-μm length of the central peak) are achieved at the same time.

Fig. 9
Fig. 9

Dependence of the degree of turbulence of the free wind tunnel stream in the center of the test section on the free stream’s velocity.

Fig. 10
Fig. 10

Measured boundary layer flow at a glass plate that is positioned at z = 0. The velocity profile agrees well with the theoretical solution, the Blasius velocity profile, which is shown as a solid curve.

Equations (8)

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γ ( r 1 , r 2 ) = E * ( r 1 ) E ( r 2 ) [ E ( r 1 ) 2 E ( r 1 ) 2 ] 1 / 2 , 0 γ ( r 1 , r 2 ) 1.
r 1 = ( - Δ x , 0 , 0 ) T ,             r 2 = ( Δ x , 0 , 0 ) T .
V = V ( z ) = γ ( r 1 , r 2 ) = γ ( 2 Δ x ) = γ ( 2 z tan θ ) .
V = I Max - I Min I Max + I Min ,
w 0 , real × α real = M 2 ( λ / π ) .
w ( z ) = w 0 { 1 + [ M 2 ( z - z 0 ) z R ] 2 } 1 / 2 ,
M 2 = 2 m + 1.
Δ v v = | Δ f f | + | Δ d d | .

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