Abstract

Generally applicable laser Doppler anemometers have become commercially available and are now widely used for fluid flow studies. When used for high velocity measurements, e.g., in excess of 100 m/sec, laser Doppler anemometers usually comprise a high power argon-ion laser and a counter signal processor. A literature survey showed that most high speed LDA measurements have been carried out at Doppler frequencies much below the frequency capabilities of modern LDA frequency counters. This paper suggests that this might be due to the multiaxial-mode output of cw lasers employed for high speed velocity measurements. The theory is discussed and experimental investigations are described that verify the theoretical results. These results suggest the use of single-mode lasers for high speed velocity measurements. The multiaxial-mode output of cw lasers is also claimed to be responsible for signal-to-noise ratio differences between LDA signals obtained with the blue and green lines of argon-ion lasers. The differences are only observed, however, when broadband detection systems are employed. Consideration is also given to the use of photodetectors for high frequency LDA systems. It is shown that photomultipliers that permit high anode currents are advantageous in laser Doppler anemometry; they are essential when measurements are made at high Doppler frequencies. Their use permits available high power lasers to be employed for LDA measurements and the high and basically noise-free gain of photomultipliers still to be used.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Cherdron, F. Durst, J. H. Whitelaw, J. Fluid Mech. 84, 13 (1978).
    [CrossRef]
  2. N. E. Kozovinos, J. List, “Turbulence Measurements in a Two-Dimensional Buoyant Jet Using Laser-Doppler Velocimetry,” in Proceedings, LDA Symposium, Copenhagen (1975).
  3. F. Durst, A. K. Rastogi, “Theoretical and Experimental Investigations of Turbulent Flows with Separation,” in Turbulent Shear Flows I (Springer, Heidelberg, 1979).
    [CrossRef]
  4. R. J. Baker, P. Hutchinson, E. E. Khalil, J. H. Whitelaw, “Measurements of Three Velocity Components and Their Correlations in a Model Furnace With and Without Combustion,” in Proceedings, Fifteenth Combustion Symposium (1974), p. 555.
  5. J. B. Abbiss, “Photon Correlation Measurements in Supersonic Flows,” Royal Radar Establishment, United Kingdom, paper presented at the Electron-Optic Conference (1974).
  6. F. Durst, J. H. Whitelaw, Opto-electronics 5, 137 (1973).
    [CrossRef]
  7. B. Eliasson, R. Dändliker, Opt. Acta 21, 119 (1974).
    [CrossRef]
  8. F. Durst, K. F. Heiber, Opt. Acta 24, 43 (1977).
    [CrossRef]
  9. F. Durst, “Möglichkeiten genauer Volumenstrommessungen mittels Laser-Doppler-Messverfahren,” Third Physikalisch Technische Bundesanstalt Seminar, Report ME-13 (1977).
  10. J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
    [CrossRef]
  11. X. Bouis, B. Gautier, J. Haertic, J. P. Hancy, “Velocimetrie Laser dans un Ecoulement Supersonique,” Institut Franco-Allemand de Recherches de Saint Louis, ISL Report 3/74 (1974).
  12. B. Koch, H. J. Pfeifer, “Turbulence Diagnostics of Supersonic and Hypersonic Wakes Using cw-Laser Radiation,” Institut Franco-Allemand de Recherches de Saint Louis, Report ISL-N 13/68 (1968).
  13. H. J. Pfeifer, H. D. vom Stein, E. David, B. Koch, Z. Angew. Math. Phys. 19, 729 (1968).
    [CrossRef]
  14. F. A. Smith, A. E. Lennert, J. O. Hornkohl, “Velocity Measurements in Aerodynamic Wind Tunnel (IT) Using a Laser Doppler Velocimeter,” Arnold Engineering Development Center Report AECD-TR-165 (1972).
  15. W. D. Bachalo, D. A. Johnson, “Laser-Velocimetry and Holographic Interferometry Measurements in Transonic Flows,” in Laser Velocimetry and Particle Sizing, H. D. Thompson, W. H. Stevenson, Eds. (Hemisphere Publishing, Washington, D.C., 1979).
  16. K. L. Orloff, V. R. Corsiglia, J. C. Biggers, T. W. Ekstedt, “Investigating Complex Aerodynamic Flows with a Laser Velocimeter,” in Proceedings, LDA Symposium, Copenhagen (1975).
  17. A. Boutier, J. Lefevre, “Some Applications of Laser Anemometry in Wind Tunnels,” in Proceedings, LDA Symposium, Copenhagen (1975).
  18. W. J. Yanta, D. F. Gates, F. W. Brown, “The Use of a Laser-Doppler Velocimeter in Supersonic Flow,” AIAA Paper 71-287 (1971).
  19. W. J. Yanta, R. A. Smith, “Measurements of Turbulence-Transport Properties with a Laser-Doppler Anemometer,” AIAA Paper 73-169 (1973).
  20. F. Durst, A. Melling, J. H. Whitelaw, Principles and Practice of Laser-Doppler Anemometry (Academic, New York, 1976).
  21. J. W. Foreman, Appl. Opt. 6, 821 (1967).
    [CrossRef] [PubMed]
  22. M. J. Rudd, J. Sci. Instrum. 2, 000 (1968).
  23. F. Durst, W. H. Stevenson, Appl. Opt. 18, 516 (1979).
    [CrossRef] [PubMed]
  24. RCA Photomultiplier Manual, RCA Handbook.
  25. H. Melchior, “Sensitive High Speed Photodetectors for the Demodulation of Visible and Near Infrared Light,” Internal Report, Bell Laboratories, Murray Hill, N.J. 07974 (1973).
  26. D. Dopheide, F. Durst, “High Frequency Laser-Doppler Measurements Employing Multiaxial He–Ne and Argon Laser Beams,” Institut Franco-Allemand de Recherches de Saint-Louis, Report ISL-R 117/80 (1980).
  27. D. Dopheide, F. Durst, “Einfluss der Axialmoden von cw-Lasern auf Laser-Doppler-Messungen bei hohen Frequenzen,” report in preparation.

1979 (1)

1978 (1)

W. Cherdron, F. Durst, J. H. Whitelaw, J. Fluid Mech. 84, 13 (1978).
[CrossRef]

1977 (1)

F. Durst, K. F. Heiber, Opt. Acta 24, 43 (1977).
[CrossRef]

1974 (1)

B. Eliasson, R. Dändliker, Opt. Acta 21, 119 (1974).
[CrossRef]

1973 (1)

F. Durst, J. H. Whitelaw, Opto-electronics 5, 137 (1973).
[CrossRef]

1972 (1)

J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
[CrossRef]

1968 (2)

H. J. Pfeifer, H. D. vom Stein, E. David, B. Koch, Z. Angew. Math. Phys. 19, 729 (1968).
[CrossRef]

M. J. Rudd, J. Sci. Instrum. 2, 000 (1968).

1967 (1)

Abbiss, J. B.

J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
[CrossRef]

J. B. Abbiss, “Photon Correlation Measurements in Supersonic Flows,” Royal Radar Establishment, United Kingdom, paper presented at the Electron-Optic Conference (1974).

Bachalo, W. D.

W. D. Bachalo, D. A. Johnson, “Laser-Velocimetry and Holographic Interferometry Measurements in Transonic Flows,” in Laser Velocimetry and Particle Sizing, H. D. Thompson, W. H. Stevenson, Eds. (Hemisphere Publishing, Washington, D.C., 1979).

Baker, R. J.

R. J. Baker, P. Hutchinson, E. E. Khalil, J. H. Whitelaw, “Measurements of Three Velocity Components and Their Correlations in a Model Furnace With and Without Combustion,” in Proceedings, Fifteenth Combustion Symposium (1974), p. 555.

Biggers, J. C.

K. L. Orloff, V. R. Corsiglia, J. C. Biggers, T. W. Ekstedt, “Investigating Complex Aerodynamic Flows with a Laser Velocimeter,” in Proceedings, LDA Symposium, Copenhagen (1975).

Bouis, X.

X. Bouis, B. Gautier, J. Haertic, J. P. Hancy, “Velocimetrie Laser dans un Ecoulement Supersonique,” Institut Franco-Allemand de Recherches de Saint Louis, ISL Report 3/74 (1974).

Boutier, A.

A. Boutier, J. Lefevre, “Some Applications of Laser Anemometry in Wind Tunnels,” in Proceedings, LDA Symposium, Copenhagen (1975).

Brown, F. W.

W. J. Yanta, D. F. Gates, F. W. Brown, “The Use of a Laser-Doppler Velocimeter in Supersonic Flow,” AIAA Paper 71-287 (1971).

Cherdron, W.

W. Cherdron, F. Durst, J. H. Whitelaw, J. Fluid Mech. 84, 13 (1978).
[CrossRef]

Chubb, T. W.

J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
[CrossRef]

Corsiglia, V. R.

K. L. Orloff, V. R. Corsiglia, J. C. Biggers, T. W. Ekstedt, “Investigating Complex Aerodynamic Flows with a Laser Velocimeter,” in Proceedings, LDA Symposium, Copenhagen (1975).

Dändliker, R.

B. Eliasson, R. Dändliker, Opt. Acta 21, 119 (1974).
[CrossRef]

David, E.

H. J. Pfeifer, H. D. vom Stein, E. David, B. Koch, Z. Angew. Math. Phys. 19, 729 (1968).
[CrossRef]

Dopheide, D.

D. Dopheide, F. Durst, “High Frequency Laser-Doppler Measurements Employing Multiaxial He–Ne and Argon Laser Beams,” Institut Franco-Allemand de Recherches de Saint-Louis, Report ISL-R 117/80 (1980).

D. Dopheide, F. Durst, “Einfluss der Axialmoden von cw-Lasern auf Laser-Doppler-Messungen bei hohen Frequenzen,” report in preparation.

Durst, F.

F. Durst, W. H. Stevenson, Appl. Opt. 18, 516 (1979).
[CrossRef] [PubMed]

W. Cherdron, F. Durst, J. H. Whitelaw, J. Fluid Mech. 84, 13 (1978).
[CrossRef]

F. Durst, K. F. Heiber, Opt. Acta 24, 43 (1977).
[CrossRef]

F. Durst, J. H. Whitelaw, Opto-electronics 5, 137 (1973).
[CrossRef]

F. Durst, A. K. Rastogi, “Theoretical and Experimental Investigations of Turbulent Flows with Separation,” in Turbulent Shear Flows I (Springer, Heidelberg, 1979).
[CrossRef]

D. Dopheide, F. Durst, “Einfluss der Axialmoden von cw-Lasern auf Laser-Doppler-Messungen bei hohen Frequenzen,” report in preparation.

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

D. Dopheide, F. Durst, “High Frequency Laser-Doppler Measurements Employing Multiaxial He–Ne and Argon Laser Beams,” Institut Franco-Allemand de Recherches de Saint-Louis, Report ISL-R 117/80 (1980).

F. Durst, “Möglichkeiten genauer Volumenstrommessungen mittels Laser-Doppler-Messverfahren,” Third Physikalisch Technische Bundesanstalt Seminar, Report ME-13 (1977).

Ekstedt, T. W.

K. L. Orloff, V. R. Corsiglia, J. C. Biggers, T. W. Ekstedt, “Investigating Complex Aerodynamic Flows with a Laser Velocimeter,” in Proceedings, LDA Symposium, Copenhagen (1975).

Eliasson, B.

B. Eliasson, R. Dändliker, Opt. Acta 21, 119 (1974).
[CrossRef]

Foreman, J. W.

Gates, D. F.

W. J. Yanta, D. F. Gates, F. W. Brown, “The Use of a Laser-Doppler Velocimeter in Supersonic Flow,” AIAA Paper 71-287 (1971).

Gautier, B.

X. Bouis, B. Gautier, J. Haertic, J. P. Hancy, “Velocimetrie Laser dans un Ecoulement Supersonique,” Institut Franco-Allemand de Recherches de Saint Louis, ISL Report 3/74 (1974).

Haertic, J.

X. Bouis, B. Gautier, J. Haertic, J. P. Hancy, “Velocimetrie Laser dans un Ecoulement Supersonique,” Institut Franco-Allemand de Recherches de Saint Louis, ISL Report 3/74 (1974).

Hancy, J. P.

X. Bouis, B. Gautier, J. Haertic, J. P. Hancy, “Velocimetrie Laser dans un Ecoulement Supersonique,” Institut Franco-Allemand de Recherches de Saint Louis, ISL Report 3/74 (1974).

Heiber, K. F.

F. Durst, K. F. Heiber, Opt. Acta 24, 43 (1977).
[CrossRef]

Hornkohl, J. O.

F. A. Smith, A. E. Lennert, J. O. Hornkohl, “Velocity Measurements in Aerodynamic Wind Tunnel (IT) Using a Laser Doppler Velocimeter,” Arnold Engineering Development Center Report AECD-TR-165 (1972).

Hutchinson, P.

R. J. Baker, P. Hutchinson, E. E. Khalil, J. H. Whitelaw, “Measurements of Three Velocity Components and Their Correlations in a Model Furnace With and Without Combustion,” in Proceedings, Fifteenth Combustion Symposium (1974), p. 555.

Johnson, D. A.

W. D. Bachalo, D. A. Johnson, “Laser-Velocimetry and Holographic Interferometry Measurements in Transonic Flows,” in Laser Velocimetry and Particle Sizing, H. D. Thompson, W. H. Stevenson, Eds. (Hemisphere Publishing, Washington, D.C., 1979).

Khalil, E. E.

R. J. Baker, P. Hutchinson, E. E. Khalil, J. H. Whitelaw, “Measurements of Three Velocity Components and Their Correlations in a Model Furnace With and Without Combustion,” in Proceedings, Fifteenth Combustion Symposium (1974), p. 555.

Koch, B.

H. J. Pfeifer, H. D. vom Stein, E. David, B. Koch, Z. Angew. Math. Phys. 19, 729 (1968).
[CrossRef]

B. Koch, H. J. Pfeifer, “Turbulence Diagnostics of Supersonic and Hypersonic Wakes Using cw-Laser Radiation,” Institut Franco-Allemand de Recherches de Saint Louis, Report ISL-N 13/68 (1968).

Kozovinos, N. E.

N. E. Kozovinos, J. List, “Turbulence Measurements in a Two-Dimensional Buoyant Jet Using Laser-Doppler Velocimetry,” in Proceedings, LDA Symposium, Copenhagen (1975).

Lefevre, J.

A. Boutier, J. Lefevre, “Some Applications of Laser Anemometry in Wind Tunnels,” in Proceedings, LDA Symposium, Copenhagen (1975).

Lennert, A. E.

F. A. Smith, A. E. Lennert, J. O. Hornkohl, “Velocity Measurements in Aerodynamic Wind Tunnel (IT) Using a Laser Doppler Velocimeter,” Arnold Engineering Development Center Report AECD-TR-165 (1972).

List, J.

N. E. Kozovinos, J. List, “Turbulence Measurements in a Two-Dimensional Buoyant Jet Using Laser-Doppler Velocimetry,” in Proceedings, LDA Symposium, Copenhagen (1975).

Melchior, H.

H. Melchior, “Sensitive High Speed Photodetectors for the Demodulation of Visible and Near Infrared Light,” Internal Report, Bell Laboratories, Murray Hill, N.J. 07974 (1973).

Melling, A.

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

Mundell, A. R. G.

J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
[CrossRef]

Oliver, C. J.

J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
[CrossRef]

Orloff, K. L.

K. L. Orloff, V. R. Corsiglia, J. C. Biggers, T. W. Ekstedt, “Investigating Complex Aerodynamic Flows with a Laser Velocimeter,” in Proceedings, LDA Symposium, Copenhagen (1975).

Pfeifer, H. J.

H. J. Pfeifer, H. D. vom Stein, E. David, B. Koch, Z. Angew. Math. Phys. 19, 729 (1968).
[CrossRef]

B. Koch, H. J. Pfeifer, “Turbulence Diagnostics of Supersonic and Hypersonic Wakes Using cw-Laser Radiation,” Institut Franco-Allemand de Recherches de Saint Louis, Report ISL-N 13/68 (1968).

Pike, E. R.

J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
[CrossRef]

Rastogi, A. K.

F. Durst, A. K. Rastogi, “Theoretical and Experimental Investigations of Turbulent Flows with Separation,” in Turbulent Shear Flows I (Springer, Heidelberg, 1979).
[CrossRef]

Rudd, M. J.

M. J. Rudd, J. Sci. Instrum. 2, 000 (1968).

Sharpe, P. R.

J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
[CrossRef]

Smith, F. A.

F. A. Smith, A. E. Lennert, J. O. Hornkohl, “Velocity Measurements in Aerodynamic Wind Tunnel (IT) Using a Laser Doppler Velocimeter,” Arnold Engineering Development Center Report AECD-TR-165 (1972).

Smith, R. A.

W. J. Yanta, R. A. Smith, “Measurements of Turbulence-Transport Properties with a Laser-Doppler Anemometer,” AIAA Paper 73-169 (1973).

Stevenson, W. H.

vom Stein, H. D.

H. J. Pfeifer, H. D. vom Stein, E. David, B. Koch, Z. Angew. Math. Phys. 19, 729 (1968).
[CrossRef]

Whitelaw, J. H.

W. Cherdron, F. Durst, J. H. Whitelaw, J. Fluid Mech. 84, 13 (1978).
[CrossRef]

F. Durst, J. H. Whitelaw, Opto-electronics 5, 137 (1973).
[CrossRef]

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

R. J. Baker, P. Hutchinson, E. E. Khalil, J. H. Whitelaw, “Measurements of Three Velocity Components and Their Correlations in a Model Furnace With and Without Combustion,” in Proceedings, Fifteenth Combustion Symposium (1974), p. 555.

Yanta, W. J.

W. J. Yanta, R. A. Smith, “Measurements of Turbulence-Transport Properties with a Laser-Doppler Anemometer,” AIAA Paper 73-169 (1973).

W. J. Yanta, D. F. Gates, F. W. Brown, “The Use of a Laser-Doppler Velocimeter in Supersonic Flow,” AIAA Paper 71-287 (1971).

Appl. Opt. (2)

J. Fluid Mech. (1)

W. Cherdron, F. Durst, J. H. Whitelaw, J. Fluid Mech. 84, 13 (1978).
[CrossRef]

J. Phys. D (1)

J. B. Abbiss, T. W. Chubb, A. R. G. Mundell, P. R. Sharpe, C. J. Oliver, E. R. Pike, J. Phys. D: 5, 100 (1972).
[CrossRef]

J. Sci. Instrum. (1)

M. J. Rudd, J. Sci. Instrum. 2, 000 (1968).

Opt. Acta (2)

B. Eliasson, R. Dändliker, Opt. Acta 21, 119 (1974).
[CrossRef]

F. Durst, K. F. Heiber, Opt. Acta 24, 43 (1977).
[CrossRef]

Opto-electronics (1)

F. Durst, J. H. Whitelaw, Opto-electronics 5, 137 (1973).
[CrossRef]

Z. Angew. Math. Phys. (1)

H. J. Pfeifer, H. D. vom Stein, E. David, B. Koch, Z. Angew. Math. Phys. 19, 729 (1968).
[CrossRef]

Other (18)

F. A. Smith, A. E. Lennert, J. O. Hornkohl, “Velocity Measurements in Aerodynamic Wind Tunnel (IT) Using a Laser Doppler Velocimeter,” Arnold Engineering Development Center Report AECD-TR-165 (1972).

W. D. Bachalo, D. A. Johnson, “Laser-Velocimetry and Holographic Interferometry Measurements in Transonic Flows,” in Laser Velocimetry and Particle Sizing, H. D. Thompson, W. H. Stevenson, Eds. (Hemisphere Publishing, Washington, D.C., 1979).

K. L. Orloff, V. R. Corsiglia, J. C. Biggers, T. W. Ekstedt, “Investigating Complex Aerodynamic Flows with a Laser Velocimeter,” in Proceedings, LDA Symposium, Copenhagen (1975).

A. Boutier, J. Lefevre, “Some Applications of Laser Anemometry in Wind Tunnels,” in Proceedings, LDA Symposium, Copenhagen (1975).

W. J. Yanta, D. F. Gates, F. W. Brown, “The Use of a Laser-Doppler Velocimeter in Supersonic Flow,” AIAA Paper 71-287 (1971).

W. J. Yanta, R. A. Smith, “Measurements of Turbulence-Transport Properties with a Laser-Doppler Anemometer,” AIAA Paper 73-169 (1973).

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

RCA Photomultiplier Manual, RCA Handbook.

H. Melchior, “Sensitive High Speed Photodetectors for the Demodulation of Visible and Near Infrared Light,” Internal Report, Bell Laboratories, Murray Hill, N.J. 07974 (1973).

D. Dopheide, F. Durst, “High Frequency Laser-Doppler Measurements Employing Multiaxial He–Ne and Argon Laser Beams,” Institut Franco-Allemand de Recherches de Saint-Louis, Report ISL-R 117/80 (1980).

D. Dopheide, F. Durst, “Einfluss der Axialmoden von cw-Lasern auf Laser-Doppler-Messungen bei hohen Frequenzen,” report in preparation.

F. Durst, “Möglichkeiten genauer Volumenstrommessungen mittels Laser-Doppler-Messverfahren,” Third Physikalisch Technische Bundesanstalt Seminar, Report ME-13 (1977).

X. Bouis, B. Gautier, J. Haertic, J. P. Hancy, “Velocimetrie Laser dans un Ecoulement Supersonique,” Institut Franco-Allemand de Recherches de Saint Louis, ISL Report 3/74 (1974).

B. Koch, H. J. Pfeifer, “Turbulence Diagnostics of Supersonic and Hypersonic Wakes Using cw-Laser Radiation,” Institut Franco-Allemand de Recherches de Saint Louis, Report ISL-N 13/68 (1968).

N. E. Kozovinos, J. List, “Turbulence Measurements in a Two-Dimensional Buoyant Jet Using Laser-Doppler Velocimetry,” in Proceedings, LDA Symposium, Copenhagen (1975).

F. Durst, A. K. Rastogi, “Theoretical and Experimental Investigations of Turbulent Flows with Separation,” in Turbulent Shear Flows I (Springer, Heidelberg, 1979).
[CrossRef]

R. J. Baker, P. Hutchinson, E. E. Khalil, J. H. Whitelaw, “Measurements of Three Velocity Components and Their Correlations in a Model Furnace With and Without Combustion,” in Proceedings, Fifteenth Combustion Symposium (1974), p. 555.

J. B. Abbiss, “Photon Correlation Measurements in Supersonic Flows,” Royal Radar Establishment, United Kingdom, paper presented at the Electron-Optic Conference (1974).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

Basic components of the LDA optical system.

Fig. 2
Fig. 2

Phase variations due to particle movement relative to incident wave and due to distance changes relative to photodetector.

Fig. 3
Fig. 3

Sketch of spectral distribution of energy of LDA signal components obtained from multiaxial-mode laser beams. (This sketch does not contain the experimentally observed amplitude differences of the various LDA frequency components.)

Fig. 4
Fig. 4

Separation of signal components in turbulent flows by means of low-pass filters.

Fig. 5
Fig. 5

Frequency restrictions imposed on laser Doppler measurements by multiaxial-mode radiation.

Fig. 6
Fig. 6

Angle restrictions imposed on laser Doppler optics by multiaxial-mode laser radiation.

Fig. 7
Fig. 7

Two-color LDA optics for measurement of two velocity components.

Fig. 8
Fig. 8

Block diagram of the optical system and signal processing equipment used in verification experiments.

Fig. 9
Fig. 9

LDA signal power spectrum obtained from a multimode He–Ne laser: axial-mode spacing 76 MHz; νD ≈ 20 MHz.

Fig. 10
Fig. 10

LDA signal power spectrum obtained from a He–Ne laser with axial-mode spacing of 76 MHz: (a) νD ≈ 11 MHz; (b) fD ≈ 24 MHz; (c) νD ≈ 31 MHz.

Fig. 11
Fig. 11

LDA signal: νD ≈ 5 MHz; modulation frequency ν1 = 76 MHz; sweep time 50 nsec/div; vertical sensitivity 50 mV/div.

Fig. 12
Fig. 12

LDA signal: νD ≈ 11 MHz; modulation frequency ν2 = 152 MHz; sweep time 20 nsec/div; vertical sensitivity 50 mV/div.

Fig. 13
Fig. 13

LDA signal: νD ≈ 25 MHz; modulation frequency ν3 = 228 MHz; sweep time 10 nsec/div; vertical sensitivity 50 mV/div.

Fig. 14
Fig. 14

Single-mode laser radiation with two-color laser beam with specially designed Fabry-Perot etalons: (a) spectral distribution of two-color laser radiation; (b) transmission vs frequency of Fabry-Perot etalons; (c) single-mode radiation with two-color laser beams.

Fig. 15
Fig. 15

Equivalent circuit diagram suggested by Durst and Heiber8 to study SNRs of LDA signals detected with various photodetectors.

Fig. 16
Fig. 16

Signal-to-noise ratio for different photodetectors as a function of detected scattered light power for (iA)max = 10−3 A for the photomultiplier.

Fig. 17
Fig. 17

Signal-to-noise ratio for different photodetectors as a function of detected scattered light power for (iA)max = 10−5 A for the photomultiplier.

Fig. 18
Fig. 18

LDA signal obtained from a multimode Ar-ion laser using a broadband detection system with a bandwidth of 450 MHz. νD ≈ 18 MHz. All beat frequencies below 450 MHz are detected. Signal appears to be very noisy. Sweep time is 20 nsec/div; vertical sensitivity is 50 mV/div.

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

{ ε ( ξ, t ) } i = j = 1 M { [ E 0 ( t ) ] j } i exp { i [ k j ξ ω j t + ϕ j ( t ) ] } .
{ E 0 ( t ) } j = { E 0 } j = constant , and ϕ j ( t ) = constant = ϕ j .
Δ f M = c / 2 L ,
M = Δ F D Δ f M = Δ F D · ( 2 L ) c .
( ε s ) 1 = n = 1 M a 1 n ( t ) R p exp [ i ( π 2 R p λ n ω n t ϕ n ) ] ,
( ε s ) 2 = m = 1 M a 2 m ( t ) R p exp [ i ( π 2 R p λ m ω m t ϕ m ) ] .
ϕ j = ( ϕ j ) 0 2 π λ j { U p } i · { l k } i · t R p = ( R p ) 0 { U p } i · { k p } i · t ,
( ε s ) 1 = n = 1 M a 1 n R p ( exp i { 2 π λ n ( R p ) 0 ( ϕ n ) 0 ω n t 2 π λ n { U p } i · [ { l 1 } i { k p } i ] · t } ) ,
( ε s ) 2 = m = 1 M a 2 m R p ( exp i { 2 π λ m ( R p ) 0 ( ϕ m ) 0 ω m t 2 π λ m { U p } i · [ { l 2 } i { k p } i ] · t } ) .
I Q = 1 T 0 T { R [ ( ε s ) 1 ] + R [ ( ε s ) 2 ] } 2 d t ,
I Q = j = 1 M a 1 j 2 + a 2 j 2 R p 2 + n = 1 M m = 1 M a 1 n a 1 m + a 2 n a 2 m R p 2 × cos { 2 π ( R p ) 0 ( 1 λ m 1 λ n ) + [ ( ϕ m ) 0 ( ϕ m ) 0 ] + 2 π ( ν m ν n ) t } + n = 1 M m = 1 M a 1 n a 2 m R p 2 cos [ 2 π ( R p ) 0 ( 1 λ m 1 λ n ) + [ ( ϕ m ) 0 ( ϕ n ) 0 ] + 2 π t ( ( ν m ν n ) { U p } i { 1 λ m [ { k p } i { l 2 } i ] 1 λ n [ { k p } i { l 1 } i ] } ) ] .
λ = λ m = λ n , i . e . , ( ν m ν n ) 1 2 ( ν m + ν n ) .
I Q = j = 1 M a 1 j 2 + a 2 j 2 R p 2 + n = 1 M m = 1 M a 1 n a 1 m + a 2 n a 2 m R p 2 cos { [ ( ϕ m ) 0 ( ϕ n ) 0 ] + 2 π t ( ν m ν n ) } + n = 1 M m = 1 M a 1 n a 2 m R p 2 cos ( [ ( ϕ m ) 0 ( ϕ n ) 0 ] + 2 π t { ( ν m ν n ) + 1 λ { U p } i [ { l 2 } i { l 1 } i ] } ) .
{ n } i = { l 2 } i { l 1 } i
i a = const ( a 1 j 2 + a 2 j 2 ) R p 2 { 1 + a 1 j a 2 j ( a 1 j 2 + a 2 j 2 ) × cos [ 2 π t 1 λ { U p } i { n } i ] } .
i a = const ( j = 1 M a 1 j 2 + a 2 j 2 R p 2 + n = 1 M m = 1 M a 1 n a 1 m + a 2 n a 2 m R p 2 cos [ Δ ϕ m , n + 2 π t ( ν m ν n ) t ] + n = 1 M m = 1 M a 1 n a 2 m R p 2 cos { Δ ϕ m , n + 2 π [ ( ν m ν n ) + 1 λ { U p } i { n } i ] } ) .
( ν m ν n ) = ( m n ) c 2 L = Δ m n c 2 L .
ν s , Δ = | ± | Δ m n | c 2 L + 1 λ { U p } i { n } i | .
ν D = ν s , 0 = | 1 λ { U p } i { n } i | ,
ν s , 1 = | ± c 2 L + 1 λ { U p } i { n } i | ν s , 2 = | ± c 2 L + 1 λ { U p } i { n } i | .
S ( t ) = S 0 · exp [ ( t t i ) 2 Δ τ 2 ] · cos [ 2 π ν D ( t t i ) ] .
ν D B · ν s , 1
ν D = 1 λ { U p } i { n } i B c 2 L ( 1 + B ) .
ν ¯ D ( 1 + 3 T u ) B [ c 2 L ν ¯ D ( 1 + 3 T u ) ] ,
T u = Δ ν 2 ν D .
( ν ¯ D ) max = B · c 2 L ( 1 + B ) ( 1 + 3 T u ) .
( U ) max B · c λ 4 L sin ϕ ( 1 + B ) ( 1 + 3 T u ) ,
ν s , 1 = ν 1 ± ν D = { 96 MHz 56 MHz , ν s , 3 = ν 3 ± ν D = { 248 MHz 208 MHz , ν s , 2 = ν 2 ± ν D = { 172 MHz 132 MHz .
ν D = 1 λ { U p } i { n } i = 2 U sin φ λ ,
( ν D ) max = 1 2 ( ν m ν m 1 ) = 1 2 c 2 L .
Δ ν E Δ F D c 2 d ; Δ d c 2 Δ F D .
N · Δ ν E = ν b ν g and Δ E { ( Δ F D ) g ( Δ F D ) b .
SNR = i cath / [ 2 e ( i cath + i D ) Δ f + 4 k T × 1 R A ( 1 + R p a R A + 4 3 π 2 R p a R A Δ f 2 C A ) Δ f ] 1 / 2 ,
SNR = i cath δ K / [ 2 e i cath δ K + 1 δ K δ 1 × Δ f + 2 e i D Δ f + 4 k T 1 R A × ( 1 + R p a R A + 4 3 π 2 R p a R A Δ f 2 C 2 ) Δ f ] 1 / 2 ,
SNR = M i cath / [ 2 e i cath M 2 M x × Δ f + 2 e i D Δ f + 4 k T × 1 R A ( 1 + R p a R A + 4 3 π 2 R p a R A Δ f 2 C A ) Δ f ] 1 / 2 .

Metrics