Abstract

A laser velocimeter system using three frequency-modulated light beams and one detector for measurement of the instantaneous velocity vector in reversing flow is considered. An analysis of the scattering and detection processes by means of the Mie and optical mixing theories is outlined. A system proposed for gravity wave studies uses an argon-ion laser and three Bragg cells as a source and a photomultiplier detector of the light backscattered from 0.2-μm-diameter spheres, introduced into the flow in a low concentration, and can measure local velocity vectors of magnitude between 0.1 m/sec and 3.0 m/sec, with turbulent fluctuations of 1% or greater intensity.

© 1973 Optical Society of America

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References

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  1. Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
    [CrossRef]
  2. E. B. Denison, W. H. Stevenson, Rev. Sci. Instrum. 41, 1475 (1970).
    [CrossRef]
  3. R. J. Goldstein, W. Hagen, Phys. Fluids 10, 1349 (1967).
    [CrossRef]
  4. R. M. Huffaker, Appl. Opt. 9, 1026 (1970).
    [CrossRef] [PubMed]
  5. R. J. Goldstein, R. J. Adrian, Rev. Sci. Instrum. 42, 1317 (1971).
    [CrossRef]
  6. J. B. Morton, W. H. Clark, J. Phys. E: Sci. Instrum. 4, 809 (1971).
    [CrossRef]
  7. M. J. Rudd, J. Phys. E. 2, 55 (1969).
    [CrossRef]
  8. C. P. Wang, Appl. Phys. Lett. 18, 522 (1971).
    [CrossRef]
  9. C. P. Wang, Appl. Phys. Lett. 20, 339 (1972).
    [CrossRef]
  10. R. J. Adrian, R. J. Goldstein, J. Phys. E: Sci. Instrum. 4, 505 (1971).
    [CrossRef]
  11. J. C. Owens, Proc. IEEE 57, 530 (1969).
    [CrossRef]
  12. C. Moller, Theory of Relativity (Oxford U. P., London, 1952), Sec. 5, 26.
  13. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), Sect. 13.5.
  14. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  15. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 10.
  16. H. Z. Cummins, H. L. Swinney, in Progress in Optics, (North-Holland, Amsterdam, 1970), Vol. 8, p. 135.
    [CrossRef]
  17. W. Feller, Introduction to Probability Theory and Its Applications (Wiley, New York, 1966), Vol. 2, p. 255.
  18. K. E. Rieckhoff, Appl. Phys. Lett. 9, 87 (1966).
    [CrossRef]
  19. R. H. Cole, Underwater Explosions (Dover, New York, 1965), Chap. 2.
  20. G. C. Cachier, J. Acoust. Soc. Am. 49, 974 (1971).
    [CrossRef]
  21. G. L. Clarke, H. R. James, J. Opt. Soc. Am. 29, 43 (1939).
    [CrossRef]
  22. N. G. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968).
  23. J. C. Angus, D. L. Morrow, J. W. Dunning, M. J. French, Ind. Eng. Chem. 61(2), 8 (1969).
    [CrossRef]
  24. Available from Dow Chemical Co., Midland, Mich.
  25. R. B. Penndorf, “New Tables of Mie Scattering Functions for Spherical Particles,” Geophys. Res. Paper 45, Part 6, Table A.10.
  26. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), Fig. 13.11.
  27. R. Adrian, J. Phys. E: Sci. Instrum. 5, 91 (1972).
    [CrossRef]

1972 (2)

C. P. Wang, Appl. Phys. Lett. 20, 339 (1972).
[CrossRef]

R. Adrian, J. Phys. E: Sci. Instrum. 5, 91 (1972).
[CrossRef]

1971 (5)

C. P. Wang, Appl. Phys. Lett. 18, 522 (1971).
[CrossRef]

R. J. Adrian, R. J. Goldstein, J. Phys. E: Sci. Instrum. 4, 505 (1971).
[CrossRef]

R. J. Goldstein, R. J. Adrian, Rev. Sci. Instrum. 42, 1317 (1971).
[CrossRef]

J. B. Morton, W. H. Clark, J. Phys. E: Sci. Instrum. 4, 809 (1971).
[CrossRef]

G. C. Cachier, J. Acoust. Soc. Am. 49, 974 (1971).
[CrossRef]

1970 (2)

E. B. Denison, W. H. Stevenson, Rev. Sci. Instrum. 41, 1475 (1970).
[CrossRef]

R. M. Huffaker, Appl. Opt. 9, 1026 (1970).
[CrossRef] [PubMed]

1969 (3)

J. C. Angus, D. L. Morrow, J. W. Dunning, M. J. French, Ind. Eng. Chem. 61(2), 8 (1969).
[CrossRef]

M. J. Rudd, J. Phys. E. 2, 55 (1969).
[CrossRef]

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

1967 (1)

R. J. Goldstein, W. Hagen, Phys. Fluids 10, 1349 (1967).
[CrossRef]

1966 (1)

K. E. Rieckhoff, Appl. Phys. Lett. 9, 87 (1966).
[CrossRef]

1964 (1)

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

1939 (1)

Adrian, R.

R. Adrian, J. Phys. E: Sci. Instrum. 5, 91 (1972).
[CrossRef]

Adrian, R. J.

R. J. Adrian, R. J. Goldstein, J. Phys. E: Sci. Instrum. 4, 505 (1971).
[CrossRef]

R. J. Goldstein, R. J. Adrian, Rev. Sci. Instrum. 42, 1317 (1971).
[CrossRef]

Angus, J. C.

J. C. Angus, D. L. Morrow, J. W. Dunning, M. J. French, Ind. Eng. Chem. 61(2), 8 (1969).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), Sect. 13.5.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), Fig. 13.11.

Cachier, G. C.

G. C. Cachier, J. Acoust. Soc. Am. 49, 974 (1971).
[CrossRef]

Clark, W. H.

J. B. Morton, W. H. Clark, J. Phys. E: Sci. Instrum. 4, 809 (1971).
[CrossRef]

Clarke, G. L.

Cole, R. H.

R. H. Cole, Underwater Explosions (Dover, New York, 1965), Chap. 2.

Cummins, H. Z.

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

H. Z. Cummins, H. L. Swinney, in Progress in Optics, (North-Holland, Amsterdam, 1970), Vol. 8, p. 135.
[CrossRef]

Denison, E. B.

E. B. Denison, W. H. Stevenson, Rev. Sci. Instrum. 41, 1475 (1970).
[CrossRef]

Dunning, J. W.

J. C. Angus, D. L. Morrow, J. W. Dunning, M. J. French, Ind. Eng. Chem. 61(2), 8 (1969).
[CrossRef]

Feller, W.

W. Feller, Introduction to Probability Theory and Its Applications (Wiley, New York, 1966), Vol. 2, p. 255.

French, M. J.

J. C. Angus, D. L. Morrow, J. W. Dunning, M. J. French, Ind. Eng. Chem. 61(2), 8 (1969).
[CrossRef]

Goldstein, R. J.

R. J. Adrian, R. J. Goldstein, J. Phys. E: Sci. Instrum. 4, 505 (1971).
[CrossRef]

R. J. Goldstein, R. J. Adrian, Rev. Sci. Instrum. 42, 1317 (1971).
[CrossRef]

R. J. Goldstein, W. Hagen, Phys. Fluids 10, 1349 (1967).
[CrossRef]

Hagen, W.

R. J. Goldstein, W. Hagen, Phys. Fluids 10, 1349 (1967).
[CrossRef]

Huffaker, R. M.

James, H. R.

Jerlov, N. G.

N. G. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968).

Moller, C.

C. Moller, Theory of Relativity (Oxford U. P., London, 1952), Sec. 5, 26.

Morrow, D. L.

J. C. Angus, D. L. Morrow, J. W. Dunning, M. J. French, Ind. Eng. Chem. 61(2), 8 (1969).
[CrossRef]

Morton, J. B.

J. B. Morton, W. H. Clark, J. Phys. E: Sci. Instrum. 4, 809 (1971).
[CrossRef]

Owens, J. C.

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

Penndorf, R. B.

R. B. Penndorf, “New Tables of Mie Scattering Functions for Spherical Particles,” Geophys. Res. Paper 45, Part 6, Table A.10.

Rieckhoff, K. E.

K. E. Rieckhoff, Appl. Phys. Lett. 9, 87 (1966).
[CrossRef]

Rudd, M. J.

M. J. Rudd, J. Phys. E. 2, 55 (1969).
[CrossRef]

Stevenson, W. H.

E. B. Denison, W. H. Stevenson, Rev. Sci. Instrum. 41, 1475 (1970).
[CrossRef]

Swinney, H. L.

H. Z. Cummins, H. L. Swinney, in Progress in Optics, (North-Holland, Amsterdam, 1970), Vol. 8, p. 135.
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 10.

Wang, C. P.

C. P. Wang, Appl. Phys. Lett. 20, 339 (1972).
[CrossRef]

C. P. Wang, Appl. Phys. Lett. 18, 522 (1971).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), Fig. 13.11.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), Sect. 13.5.

Yeh, Y.

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

C. P. Wang, Appl. Phys. Lett. 18, 522 (1971).
[CrossRef]

C. P. Wang, Appl. Phys. Lett. 20, 339 (1972).
[CrossRef]

K. E. Rieckhoff, Appl. Phys. Lett. 9, 87 (1966).
[CrossRef]

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Ind. Eng. Chem. (1)

J. C. Angus, D. L. Morrow, J. W. Dunning, M. J. French, Ind. Eng. Chem. 61(2), 8 (1969).
[CrossRef]

J. Acoust. Soc. Am. (1)

G. C. Cachier, J. Acoust. Soc. Am. 49, 974 (1971).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E. (1)

M. J. Rudd, J. Phys. E. 2, 55 (1969).
[CrossRef]

J. Phys. E: Sci. Instrum. (3)

J. B. Morton, W. H. Clark, J. Phys. E: Sci. Instrum. 4, 809 (1971).
[CrossRef]

R. J. Adrian, R. J. Goldstein, J. Phys. E: Sci. Instrum. 4, 505 (1971).
[CrossRef]

R. Adrian, J. Phys. E: Sci. Instrum. 5, 91 (1972).
[CrossRef]

Phys. Fluids (1)

R. J. Goldstein, W. Hagen, Phys. Fluids 10, 1349 (1967).
[CrossRef]

Proc. IEEE (1)

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

Rev. Sci. Instrum. (2)

R. J. Goldstein, R. J. Adrian, Rev. Sci. Instrum. 42, 1317 (1971).
[CrossRef]

E. B. Denison, W. H. Stevenson, Rev. Sci. Instrum. 41, 1475 (1970).
[CrossRef]

Other (11)

R. H. Cole, Underwater Explosions (Dover, New York, 1965), Chap. 2.

C. Moller, Theory of Relativity (Oxford U. P., London, 1952), Sec. 5, 26.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), Sect. 13.5.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 10.

H. Z. Cummins, H. L. Swinney, in Progress in Optics, (North-Holland, Amsterdam, 1970), Vol. 8, p. 135.
[CrossRef]

W. Feller, Introduction to Probability Theory and Its Applications (Wiley, New York, 1966), Vol. 2, p. 255.

N. G. Jerlov, Optical Oceanography (Elsevier, Amsterdam, 1968).

Available from Dow Chemical Co., Midland, Mich.

R. B. Penndorf, “New Tables of Mie Scattering Functions for Spherical Particles,” Geophys. Res. Paper 45, Part 6, Table A.10.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965), Fig. 13.11.

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Figures (5)

Fig. 1
Fig. 1

Schematic view of proposed laser Doppler velocimeter.

Fig. 2
Fig. 2

Frequency spectrum of detector photocurrent.

Fig. 3
Fig. 3

Interference fringe pattern formation.

Fig. 4
Fig. 4

Integrated optical system.

Fig. 5
Fig. 5

Block diagram of signal processing system.

Equations (9)

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ν α D = ν α ( U s - U α ) · v / C F ,
ν M 1 = ν + ν ( U 1 - U 2 ) · v / C F ,
ν M 2 = ν + ν ( U 1 - U 3 ) · v / C F ,
ν M 3 = ( ν - ν ) + ν ( U 2 - U 3 ) · v / C F ,
E m , α δ = ( γ { S γ δ [ ( U s - U α ) , D m ] } [ E γ ( r m , t ) ] α ) [ exp ( i k α R ) / i k α R ] · exp { i [ 2 π ν α t + ( 2 π ν α t / C F ) ( U s - U α ) · v m ( t ) + Ψ m α ] } .
P = P N + P O + P C + P M + P A + P B .
ν B = ν + ( ν / C F ) [ ( U s - U 2 ) · ( v m - v m ) + ( U 1 - U 2 ) · v m ] .
P M / P B N / [ N ( N - 1 ) / ( A Ω B / λ 2 ) ] = Ω d A m m / ( N - 1 ) λ 2 Ω d D 4 / 3 V 2 / 9 / N 2 / 9 ( N - 1 ) λ 2 ,
ν F = ( 2 v sin χ / λ F ) ,

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