Abstract

We propose a new beam-splitter system that makes it possible to use nonstabilized laser diodes for laser Doppler anemometry (LDA) systems by making the system wavelength independent. The beam splitter consists of two linear diffraction gratings that produce two parallel beams with a beam spacing that is wavelength dependent. This ensures passive wavelength compensation for the fringe spacing in the measurement volume. One can choose the distance between the two parallel beams by changing the distance between the two gratings, whereas the distance to the measurement volume can be designed by choice of a condensing lens with the proper focal length. This means that the system can be designed to have a desired fringe spacing in the measurement volume. The gratings are implemented as surface-relief holograms in photoresist, which makes it possible to mass produce the beam-splitter system at low cost through replication of the structure. The method for passive wavelength compensation for the fringe spacing is demonstrated both theoretically and experimentally.

© 2003 Optical Society of America

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  1. H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
  2. J. J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
  3. Y. Yeh, H. Z. Cummins, “Localized fluid measurements with and HeNe laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
  4. H. D. V. Stein, H. J. Pfeifer, “A Doppler difference method for velocity measurements,” Metrologia 5, 59–61 (1969).
  5. L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1981).
  6. F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1980).
  7. S. G. Hanson, “Broadening of the measured frequency spectrum in a differential laser anemometer due to interference plane gradients,” J. Phys. D 6, 164–171 (1973).
  8. P. C. Miles, “Geometry of the fringe field formed in the intersection of two Gaussian beams,” Appl. Opt. 23, 5887–5895 (1996).
  9. J. Czarske, “A miniaturized dual-fibre laser Doppler Sensor,” Meas. Sci. Technol. 12, 1191–1198 (2001).
  10. S. Damp, “Battery-driven miniature LDA-system with semiconductor laser diode,” in Selected Papers from the Fourth International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, R. J. Adrian, D. F. G. Durão, F. Durst, T. Asanuma, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, 1989), Sec. 5.4, pp. 1–6.
  11. F. Quercioli, A. Mannoni, B. Tiribilli, “Laser Doppler velocimetry with a compact disc pickup,” Appl. Opt. 37, 5932–5937 (1998).
  12. S. Bopp, F. Durst, R. Müller, A. Naqwi, C. Tropea, H. Weber, “Small laser-Doppler anemometers using semiconductor lasers and avalanche photodiodes,” in Applications of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst, J. H. Whitewater, eds. (Springer-Verlag, 1988), pp. 315–360.
  13. J. Schmidt, R. Völkel, W. Stork, J. T. Sheridan, J. Schwider, N. Streibl, F. Durst, “Diffractive beam splitter for laser Doppler velocimetry,” Opt. Lett. 17, 1240–1242 (1992).
  14. S. L. Kaufmann, F. D. Dorman, D. C. Bjorkquist, M. R. Finn, “Laser optical measuring device and method for stabilizing fringe pattern spacing,” U.S. patent4,948,257 (14August1990).
  15. C. Dam-Hansen, J. Stubager, L. Lindvold, L. Lading, “Compact and low cost holographic optical front ends for an industrial laser time-of-flight flowsensor,” in Proceedings of the Third International Congress and Exhibition on Optoelectronics, Optical Sensors and Measuring Techniques (ACS Organisations GmbH, Erfurt, Germany, 1998), pp. 7–10.

2001 (1)

J. Czarske, “A miniaturized dual-fibre laser Doppler Sensor,” Meas. Sci. Technol. 12, 1191–1198 (2001).

1998 (1)

1996 (1)

P. C. Miles, “Geometry of the fringe field formed in the intersection of two Gaussian beams,” Appl. Opt. 23, 5887–5895 (1996).

1992 (1)

1973 (1)

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

1969 (1)

H. D. V. Stein, H. J. Pfeifer, “A Doppler difference method for velocity measurements,” Metrologia 5, 59–61 (1969).

1965 (1)

J. J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).

1964 (2)

Y. Yeh, H. Z. Cummins, “Localized fluid measurements with and HeNe laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).

Bjorkquist, D. C.

S. L. Kaufmann, F. D. Dorman, D. C. Bjorkquist, M. R. Finn, “Laser optical measuring device and method for stabilizing fringe pattern spacing,” U.S. patent4,948,257 (14August1990).

Bopp, S.

S. Bopp, F. Durst, R. Müller, A. Naqwi, C. Tropea, H. Weber, “Small laser-Doppler anemometers using semiconductor lasers and avalanche photodiodes,” in Applications of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst, J. H. Whitewater, eds. (Springer-Verlag, 1988), pp. 315–360.

Cummins, H. Z.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).

Y. Yeh, H. Z. Cummins, “Localized fluid measurements with and HeNe laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).

Czarske, J.

J. Czarske, “A miniaturized dual-fibre laser Doppler Sensor,” Meas. Sci. Technol. 12, 1191–1198 (2001).

Dam-Hansen, C.

C. Dam-Hansen, J. Stubager, L. Lindvold, L. Lading, “Compact and low cost holographic optical front ends for an industrial laser time-of-flight flowsensor,” in Proceedings of the Third International Congress and Exhibition on Optoelectronics, Optical Sensors and Measuring Techniques (ACS Organisations GmbH, Erfurt, Germany, 1998), pp. 7–10.

Damp, S.

S. Damp, “Battery-driven miniature LDA-system with semiconductor laser diode,” in Selected Papers from the Fourth International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, R. J. Adrian, D. F. G. Durão, F. Durst, T. Asanuma, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, 1989), Sec. 5.4, pp. 1–6.

Dorman, F. D.

S. L. Kaufmann, F. D. Dorman, D. C. Bjorkquist, M. R. Finn, “Laser optical measuring device and method for stabilizing fringe pattern spacing,” U.S. patent4,948,257 (14August1990).

Drain, L. E.

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1981).

Durst, F.

J. Schmidt, R. Völkel, W. Stork, J. T. Sheridan, J. Schwider, N. Streibl, F. Durst, “Diffractive beam splitter for laser Doppler velocimetry,” Opt. Lett. 17, 1240–1242 (1992).

S. Bopp, F. Durst, R. Müller, A. Naqwi, C. Tropea, H. Weber, “Small laser-Doppler anemometers using semiconductor lasers and avalanche photodiodes,” in Applications of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst, J. H. Whitewater, eds. (Springer-Verlag, 1988), pp. 315–360.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1980).

Finn, M. R.

S. L. Kaufmann, F. D. Dorman, D. C. Bjorkquist, M. R. Finn, “Laser optical measuring device and method for stabilizing fringe pattern spacing,” U.S. patent4,948,257 (14August1990).

Foreman, J. J. W.

J. J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).

George, E. W.

J. J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).

Hanson, S. G.

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

Kaufmann, S. L.

S. L. Kaufmann, F. D. Dorman, D. C. Bjorkquist, M. R. Finn, “Laser optical measuring device and method for stabilizing fringe pattern spacing,” U.S. patent4,948,257 (14August1990).

Knable, N.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).

Lading, L.

C. Dam-Hansen, J. Stubager, L. Lindvold, L. Lading, “Compact and low cost holographic optical front ends for an industrial laser time-of-flight flowsensor,” in Proceedings of the Third International Congress and Exhibition on Optoelectronics, Optical Sensors and Measuring Techniques (ACS Organisations GmbH, Erfurt, Germany, 1998), pp. 7–10.

Lewis, R. D.

J. J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).

Lindvold, L.

C. Dam-Hansen, J. Stubager, L. Lindvold, L. Lading, “Compact and low cost holographic optical front ends for an industrial laser time-of-flight flowsensor,” in Proceedings of the Third International Congress and Exhibition on Optoelectronics, Optical Sensors and Measuring Techniques (ACS Organisations GmbH, Erfurt, Germany, 1998), pp. 7–10.

Mannoni, A.

Melling, A.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1980).

Miles, P. C.

P. C. Miles, “Geometry of the fringe field formed in the intersection of two Gaussian beams,” Appl. Opt. 23, 5887–5895 (1996).

Müller, R.

S. Bopp, F. Durst, R. Müller, A. Naqwi, C. Tropea, H. Weber, “Small laser-Doppler anemometers using semiconductor lasers and avalanche photodiodes,” in Applications of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst, J. H. Whitewater, eds. (Springer-Verlag, 1988), pp. 315–360.

Naqwi, A.

S. Bopp, F. Durst, R. Müller, A. Naqwi, C. Tropea, H. Weber, “Small laser-Doppler anemometers using semiconductor lasers and avalanche photodiodes,” in Applications of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst, J. H. Whitewater, eds. (Springer-Verlag, 1988), pp. 315–360.

Pfeifer, H. J.

H. D. V. Stein, H. J. Pfeifer, “A Doppler difference method for velocity measurements,” Metrologia 5, 59–61 (1969).

Quercioli, F.

Schmidt, J.

Schwider, J.

Sheridan, J. T.

Stein, H. D. V.

H. D. V. Stein, H. J. Pfeifer, “A Doppler difference method for velocity measurements,” Metrologia 5, 59–61 (1969).

Stork, W.

Streibl, N.

Stubager, J.

C. Dam-Hansen, J. Stubager, L. Lindvold, L. Lading, “Compact and low cost holographic optical front ends for an industrial laser time-of-flight flowsensor,” in Proceedings of the Third International Congress and Exhibition on Optoelectronics, Optical Sensors and Measuring Techniques (ACS Organisations GmbH, Erfurt, Germany, 1998), pp. 7–10.

Tiribilli, B.

Tropea, C.

S. Bopp, F. Durst, R. Müller, A. Naqwi, C. Tropea, H. Weber, “Small laser-Doppler anemometers using semiconductor lasers and avalanche photodiodes,” in Applications of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst, J. H. Whitewater, eds. (Springer-Verlag, 1988), pp. 315–360.

Völkel, R.

Weber, H.

S. Bopp, F. Durst, R. Müller, A. Naqwi, C. Tropea, H. Weber, “Small laser-Doppler anemometers using semiconductor lasers and avalanche photodiodes,” in Applications of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst, J. H. Whitewater, eds. (Springer-Verlag, 1988), pp. 315–360.

Whitelaw, J. H.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1980).

Yeh, Y.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).

Y. Yeh, H. Z. Cummins, “Localized fluid measurements with and HeNe laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).

Appl. Opt. (2)

P. C. Miles, “Geometry of the fringe field formed in the intersection of two Gaussian beams,” Appl. Opt. 23, 5887–5895 (1996).

F. Quercioli, A. Mannoni, B. Tiribilli, “Laser Doppler velocimetry with a compact disc pickup,” Appl. Opt. 37, 5932–5937 (1998).

Appl. Phys. Lett. (2)

J. J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).

Y. Yeh, H. Z. Cummins, “Localized fluid measurements with and HeNe laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).

J. Phys. D (1)

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

Meas. Sci. Technol. (1)

J. Czarske, “A miniaturized dual-fibre laser Doppler Sensor,” Meas. Sci. Technol. 12, 1191–1198 (2001).

Metrologia (1)

H. D. V. Stein, H. J. Pfeifer, “A Doppler difference method for velocity measurements,” Metrologia 5, 59–61 (1969).

Opt. Lett. (1)

Phys. Rev. Lett. (1)

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).

Other (6)

S. Damp, “Battery-driven miniature LDA-system with semiconductor laser diode,” in Selected Papers from the Fourth International Symposium on Applications of Laser-Doppler Anemometry to Fluid Mechanics, R. J. Adrian, D. F. G. Durão, F. Durst, T. Asanuma, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, 1989), Sec. 5.4, pp. 1–6.

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1981).

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1980).

S. L. Kaufmann, F. D. Dorman, D. C. Bjorkquist, M. R. Finn, “Laser optical measuring device and method for stabilizing fringe pattern spacing,” U.S. patent4,948,257 (14August1990).

C. Dam-Hansen, J. Stubager, L. Lindvold, L. Lading, “Compact and low cost holographic optical front ends for an industrial laser time-of-flight flowsensor,” in Proceedings of the Third International Congress and Exhibition on Optoelectronics, Optical Sensors and Measuring Techniques (ACS Organisations GmbH, Erfurt, Germany, 1998), pp. 7–10.

S. Bopp, F. Durst, R. Müller, A. Naqwi, C. Tropea, H. Weber, “Small laser-Doppler anemometers using semiconductor lasers and avalanche photodiodes,” in Applications of Laser Anemometry to Fluid Mechanics, R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst, J. H. Whitewater, eds. (Springer-Verlag, 1988), pp. 315–360.

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Figures (8)

Fig. 1
Fig. 1

Two ways to produce two parallel beams by use of two diffraction gratings as a beam splitter: (a) a common approach, (b) the new proposed configuration. The dashed lines illustrate beam splitting for a higher wavelength.

Fig. 2
Fig. 2

LDA system based on a beam splitter consisting of diffractive optical elements.

Fig. 3
Fig. 3

Change in fringe spacing as a function of wavelength compared with that of an uncompensated (conventional) LDA system.

Fig. 4
Fig. 4

Change in fringe spacing caused by temperature fluctuations of the gratings. The operation wavelength is assumed to be constant.

Fig. 5
Fig. 5

Measurement error caused by turning of the fringes as the wavelength is varied.

Fig. 6
Fig. 6

Optimum ratio of the distance between the two gratings and the distance between the two parallel beams for the beam splitter.

Fig. 7
Fig. 7

Possible way to implement the beam splitter in a LDA system with a detection system consisting of a lens and a photodiode. Constructing substrates with one grating and one mirror simplifies the alignment of the system.

Fig. 8
Fig. 8

Measured fringe period in the cross section of the measurement volume. The wavelength was varied by use of a tunable laser diode. The error bars show the standard deviations of the measurements for the various wavelengths.

Equations (13)

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Λ= λ2 sinθ/2,
θ2=arcsinλΛ1-sin θ1,
Δθ2= 11-λ/Λ1-sin θ121/2×1Λ1 Δλ- λΛ12 ΔΛ1.
Δd= sin θ2 sin Δθ2cos θ2 cos Δθ2-sin θ2 sin Δθ2 d,
Δd= sin Δθ2cos Δθ2-sin Δθ2 dΔθ2d,
θm1=arctandres/2f
θm2=arctandres/2+Δdf,
Λm= λ+Δλ2 sinθm1+θm2/2.
ΔΛ1=αΔTΛ1,
Δϕ=Δθm2/2,
Δvv=1- 1cos Δϕ,
Λm λ+Δλdres+Δd λ+Δλdres+ 11-λ/Λ1-sin θ121/2 dΔλ/Λ1,
ddres= cos θ2sin θ1+sin θ2.

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