Abstract

A formula that can analyze the laser Doppler velocimeter spectrum was derived. The formula showed good agreement with computational experimental results. The use of a Fourier transform lens as detection optics was proposed and was found to be independent of the displacement of the object along the direction parallel to the optical axis. An experimental method was also proposed that can make the simultaneous measurement of velocity and displacement possible simply by adding a second detector. By using two detectors, not only can displacement of the surface be measured, but also the results of the speed measurement can be compensated for.

© 1997 Optical Society of America

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References

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  1. F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, London, 1976).
  2. M. Reynolds, V. Toal, “An interferometric linear in-plane position transducer,” Opt. Technol. 24, 59–65 (1992).
    [Crossref]
  3. A. E. Smart, C. J. Moore, “Aero-engine applications of laser anemometry,” AIAA J. 14, 363–370 (1976).
    [Crossref]
  4. J. B. Cole, M. D. Swords, “Laser Doppler anemometry in an engine,” Appl. Opt. 18, 1539–1545 (1979).
    [Crossref] [PubMed]
  5. R. G. W. Brown, J. G. Burnett, J. Mansbridge, C. I. Moir, B. S. Lowans, “Miniature, solid state photon correlation laser Doppler velocimetry,” Appl. Opt. 29, 3291–3302 (1990).
    [Crossref] [PubMed]
  6. H. W. Jetink, F. F. M. de Mul, H. E. Suichies, J. G. Aarnoudse, J. Greve, “Small laser Doppler velocimeter based on the self-mixing effect in a diode laser,” Appl. Opt. 27, 379–385 (1988).
    [Crossref]
  7. J. Schmidt, R. Völkel, W. Stork, J. T. Sheridan, J. Schwider, N. Streibl, F. Drust, “Diffractive beam splitter for laser Doppler velocimetry,” Opt. Lett. 17, 1240–1242 (1992).
    [Crossref] [PubMed]
  8. W. Stork, K. D. Müller-Glaser, J. Schmidt, A. Wagner, H. Yajima, “Miniaturized laser-Doppler-velocimeter using microoptic elements,” in Micro System Technologies 94, H. Reichl, A. Heuberger, eds. (VDE-Verlag, Berlin, 1994), pp. 1081–1085.
  9. W. Stork, A. Wagner, J. Drescher, A. Kühnle, T. Matthä, K. D. Müller-Glaser, “Miniaturized Laser-Doppler Velocimeter for speed measurements of solid state surfaces,” in Proceedings of Sensor 95 (ACS Organisation GmbH, Nürmberg, 1995), pp. 601–606.
  10. A. Yariv, Optical Electronics (Holt-Saunders, New York, 1985) Chap. 2.
  11. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

1992 (2)

1990 (1)

1988 (1)

1979 (1)

1976 (1)

A. E. Smart, C. J. Moore, “Aero-engine applications of laser anemometry,” AIAA J. 14, 363–370 (1976).
[Crossref]

Aarnoudse, J. G.

Brown, R. G. W.

Burnett, J. G.

Cole, J. B.

de Mul, F. F. M.

Drescher, J.

W. Stork, A. Wagner, J. Drescher, A. Kühnle, T. Matthä, K. D. Müller-Glaser, “Miniaturized Laser-Doppler Velocimeter for speed measurements of solid state surfaces,” in Proceedings of Sensor 95 (ACS Organisation GmbH, Nürmberg, 1995), pp. 601–606.

Drust, F.

Durst, F.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, London, 1976).

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

Greve, J.

Jetink, H. W.

Kühnle, A.

W. Stork, A. Wagner, J. Drescher, A. Kühnle, T. Matthä, K. D. Müller-Glaser, “Miniaturized Laser-Doppler Velocimeter for speed measurements of solid state surfaces,” in Proceedings of Sensor 95 (ACS Organisation GmbH, Nürmberg, 1995), pp. 601–606.

Lowans, B. S.

Mansbridge, J.

Matthä, T.

W. Stork, A. Wagner, J. Drescher, A. Kühnle, T. Matthä, K. D. Müller-Glaser, “Miniaturized Laser-Doppler Velocimeter for speed measurements of solid state surfaces,” in Proceedings of Sensor 95 (ACS Organisation GmbH, Nürmberg, 1995), pp. 601–606.

Melling, A.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, London, 1976).

Moir, C. I.

Moore, C. J.

A. E. Smart, C. J. Moore, “Aero-engine applications of laser anemometry,” AIAA J. 14, 363–370 (1976).
[Crossref]

Müller-Glaser, K. D.

W. Stork, K. D. Müller-Glaser, J. Schmidt, A. Wagner, H. Yajima, “Miniaturized laser-Doppler-velocimeter using microoptic elements,” in Micro System Technologies 94, H. Reichl, A. Heuberger, eds. (VDE-Verlag, Berlin, 1994), pp. 1081–1085.

W. Stork, A. Wagner, J. Drescher, A. Kühnle, T. Matthä, K. D. Müller-Glaser, “Miniaturized Laser-Doppler Velocimeter for speed measurements of solid state surfaces,” in Proceedings of Sensor 95 (ACS Organisation GmbH, Nürmberg, 1995), pp. 601–606.

Reynolds, M.

M. Reynolds, V. Toal, “An interferometric linear in-plane position transducer,” Opt. Technol. 24, 59–65 (1992).
[Crossref]

Schmidt, J.

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

W. Stork, K. D. Müller-Glaser, J. Schmidt, A. Wagner, H. Yajima, “Miniaturized laser-Doppler-velocimeter using microoptic elements,” in Micro System Technologies 94, H. Reichl, A. Heuberger, eds. (VDE-Verlag, Berlin, 1994), pp. 1081–1085.

Schwider, J.

Sheridan, J. T.

Smart, A. E.

A. E. Smart, C. J. Moore, “Aero-engine applications of laser anemometry,” AIAA J. 14, 363–370 (1976).
[Crossref]

Stork, W.

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

W. Stork, K. D. Müller-Glaser, J. Schmidt, A. Wagner, H. Yajima, “Miniaturized laser-Doppler-velocimeter using microoptic elements,” in Micro System Technologies 94, H. Reichl, A. Heuberger, eds. (VDE-Verlag, Berlin, 1994), pp. 1081–1085.

W. Stork, A. Wagner, J. Drescher, A. Kühnle, T. Matthä, K. D. Müller-Glaser, “Miniaturized Laser-Doppler Velocimeter for speed measurements of solid state surfaces,” in Proceedings of Sensor 95 (ACS Organisation GmbH, Nürmberg, 1995), pp. 601–606.

Streibl, N.

Suichies, H. E.

Swords, M. D.

Toal, V.

M. Reynolds, V. Toal, “An interferometric linear in-plane position transducer,” Opt. Technol. 24, 59–65 (1992).
[Crossref]

Völkel, R.

Wagner, A.

W. Stork, A. Wagner, J. Drescher, A. Kühnle, T. Matthä, K. D. Müller-Glaser, “Miniaturized Laser-Doppler Velocimeter for speed measurements of solid state surfaces,” in Proceedings of Sensor 95 (ACS Organisation GmbH, Nürmberg, 1995), pp. 601–606.

W. Stork, K. D. Müller-Glaser, J. Schmidt, A. Wagner, H. Yajima, “Miniaturized laser-Doppler-velocimeter using microoptic elements,” in Micro System Technologies 94, H. Reichl, A. Heuberger, eds. (VDE-Verlag, Berlin, 1994), pp. 1081–1085.

Whitelaw, J. H.

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, London, 1976).

Yajima, H.

W. Stork, K. D. Müller-Glaser, J. Schmidt, A. Wagner, H. Yajima, “Miniaturized laser-Doppler-velocimeter using microoptic elements,” in Micro System Technologies 94, H. Reichl, A. Heuberger, eds. (VDE-Verlag, Berlin, 1994), pp. 1081–1085.

Yariv, A.

A. Yariv, Optical Electronics (Holt-Saunders, New York, 1985) Chap. 2.

AIAA J. (1)

A. E. Smart, C. J. Moore, “Aero-engine applications of laser anemometry,” AIAA J. 14, 363–370 (1976).
[Crossref]

Appl. Opt. (3)

Opt. Lett. (1)

Opt. Technol. (1)

M. Reynolds, V. Toal, “An interferometric linear in-plane position transducer,” Opt. Technol. 24, 59–65 (1992).
[Crossref]

Other (5)

F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, London, 1976).

W. Stork, K. D. Müller-Glaser, J. Schmidt, A. Wagner, H. Yajima, “Miniaturized laser-Doppler-velocimeter using microoptic elements,” in Micro System Technologies 94, H. Reichl, A. Heuberger, eds. (VDE-Verlag, Berlin, 1994), pp. 1081–1085.

W. Stork, A. Wagner, J. Drescher, A. Kühnle, T. Matthä, K. D. Müller-Glaser, “Miniaturized Laser-Doppler Velocimeter for speed measurements of solid state surfaces,” in Proceedings of Sensor 95 (ACS Organisation GmbH, Nürmberg, 1995), pp. 601–606.

A. Yariv, Optical Electronics (Holt-Saunders, New York, 1985) Chap. 2.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

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Figures (8)

Fig. 1
Fig. 1

Principle of laser Doppler velocimetry.

Fig. 2
Fig. 2

Schematic of the detection component of the LDV.

Fig. 3
Fig. 3

Detection scheme of the LDV (Fresnel transform).

Fig. 4
Fig. 4

LDV spectra for the different displacements.

Fig. 5
Fig. 5

Relation between the peak frequencies and displacements.

Fig. 6
Fig. 6

Detection scheme that is insensitive to the displacement.

Fig. 7
Fig. 7

LDV spectra obtained by the computational experiments.

Fig. 8
Fig. 8

Ratio of the peak frequencies obtained by two detectors as a function of the displacement.

Equations (15)

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Rξ; τ=Iξ;02+JAξ; τ2,
JAξ; τ=Aξ; 0 A*ξ; τ.
Sξ; f=FTτJAξ; τ2,
Aξ; t= Ubxax-vτα expjβξ-x2dx,=expjβξ2  gxax-vτexpj2βξxdx,
gx=αUbxexpjβx2.
JAξ; τ=Aξ; 0A*ξ; τ= gx1ax1exp-j2βξx1g*x2×a*x2-vτexpj2βξx2dx1dx2.
 ax1a*x2-vτdx1dx2= δx1-x2+vτdx1dx2.
JAξ; τ= gxg*x1+vτdx1 expj2βξvτ
=Pgvτexpj2βξvτ,
Pgvτ= gx1g*x1+vτdx1.
Sf=FTτPgvτ2.
Sfv=1v2 g˜fv2g˜fv2,
Aξ; t= Ubxax-vτexpj2βξxdx.
Sfv=1v2 Ũbfv2Ũbfv2.
Ubx= Ub0Xexpjβx-X2dX=Ub0xhx,

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