Abstract

Laser Doppler anemometry permits, in principle, the measurement of both magnitude and direction of components of a particle’s velocity vector. Most exiting anemometers, however, permit measurements only with a directional ambiguity of 180°, resulting in errors in certain flow fields. Available methods of eliminating the directional ambiguity of Laser Doppler anemometers are reviewed, covering frequency shifting of the incident and scattered light beams, the use of beams with different polarization properties, and employment of multicolor laser beams. The advantages and disadvantages of existing methods are summarized, and suggestions for alterations are made. Different techniques used to remove the pedestal of laser Doppler anemometer signals are also reviewed. Optical techniques should be employed in any advanced optical anemometer system to avoid dynamic range limitations by electronic bandpass filters. Suggestions are made for advanced optical anemometers employing multielement avalanche photodiodes that can be used for simultaneous measurements of two velocity components. These anemometers incorporate devices to sense the direction of the velocity components and to eliminate optically the pedestal of laser Doppler signals.

© 1974 Optical Society of America

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References

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  1. F. Durst, J. H. Whitelaw, Proc. Roy. Soc. London A324, 157 (1971).
  2. F. Durst, J. H. Whitelaw, J. Phys. E. 4, 804 (1971).
    [CrossRef]
  3. R. J. Goldstein, D. K. Kreid, “Fluid Velocity Measurement from Doppler-Shift of Scattered Laser Radiation,” University of Minnesota, Institute of Technology, Department of Mechanical Engineering, HTL-TR-85 (1968).
  4. Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
    [CrossRef]
  5. E. B. Denison, W. H. Stevenson, Rev. Sci. Instrum. 41, 1475 (1970).
    [CrossRef]
  6. M. K. Mazumder, Appl. Phys. Lett. 10, 462 (1970).
    [CrossRef]
  7. W. H. Stevenson, Appl. Opt. 9, 649 (1970).
    [CrossRef] [PubMed]
  8. T. Suzuki, R. Hioko, J. Opt. Soc. Am. 57, 1551 (1967).
    [CrossRef]
  9. H. Cummins, N. Knable, G. Gampel, Y. Yeh, Appl. Phys. Lett. 2 (3), (1963).
  10. Zenith Technical Notes: “Acousto-Optic Application of Calibrators and Frequence Shifters for Laser Velocimeters” (1971).
  11. C. F. Buhrer, D. Baird, E. M. Cowell, Appl. Phys. Lett. 1, 46 (1962).
    [CrossRef]
  12. J. P. Campell, W. H. Steier, IEEE J. Quantum Electron. QE-7, 450 (1971).
    [CrossRef]
  13. L. E. Drain, B. C. Moss, Opto-Electron.429 (April1972).
    [CrossRef]
  14. J. Oldengarm, A. H. van Krieken, H. J. Raterink, Opt. Laser Technol. 249 (1973).
  15. P. Debye, F. W. Sears, Proc. Nat. Acad. Sci. U.S. 18, 409 (1932).
    [CrossRef]
  16. R. Lucas, P. Biquard, J. Phys. Rad. 3, 464 (1932).
    [CrossRef]
  17. C. V. Raman, N. S. Nath, Proc. Indian Acad. Sci. A2, 406 (1935).
  18. G. W. Willard, J. Accoust. Soc. Am. 21, 101 (1949).
    [CrossRef]
  19. F. L. Crosswy, J. O. Hornkohl, A. E. Lennert, “Signal Characteristics and Signal Conditioning Electronics for a Vector Velocity Laser Velocimeter,” Project Squid NOOO 14-67-0226-0005, P 396 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).
  20. Precision Devices and Systems (UK): “Laser Anemometer Phase Modulator” (1974).
  21. W. H. Goethert, “Balanced Detection for the Dual Scatter Laser Doppler Velocimeter,” Arnold Engineering Development Center, Air Force Systems Command, AE DC-TR-71-70, Arnold Air Force Station, Tennessee (1971).
  22. P. D. Iten, R. Dändliker, Appl. Opt. 13, 286 (1974).
    [CrossRef] [PubMed]
  23. L. D. Ballard, W. S. Epstein, E. R. Smith, S. Edelman, J. Res. Nat. Bur. Stand. (U.S.) C. 73C, 3/4, July/September (1969).
  24. L. E. Drain: “Scheme for Sign Determination in Laser-Doppler Velocity or Displacement Measurements,” Materials Physics Division, A.E.R.E., Harwell (1969).
  25. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).
  26. H. J. Pfeifer, H. D. vom Stein, “Ein Verfahren zur Bestimung des Vorzeichens der Geschwindigkeit bei der Doppler-Differenzmethode,” Deutsch-Französisches Forschungsinstitut N17/71, Saint-Louis (1971).
  27. A. Müller, “Measurement of the Sign of a Velocity Component from the Phase Difference of the Two Heterodyne Signals,” EUROMECH-36, London (1972).
  28. Thermo Systems Incorporated, “Model 1094, LDV Signal Processor Counter Type” (1973).
  29. W. J. Hiller, G. E. A. Meier, “Zur Vorzeichenbestimmung der Geschwindigkeitskomponenten beim Laser-Doppler-Anemometer,” Max-Planck-Institut für Strömungsforschung, Göttingen (October1972).
  30. D. B. Brayton, H. T. Kalb, F. L. Crosswy, “A Two-Component, Dual-Scatter Laser Doppler Velocimeter with Frequency Burst Signal Readout,” Project Squid NOOO 14-67-0226-0005, P52 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

1974 (1)

1973 (1)

J. Oldengarm, A. H. van Krieken, H. J. Raterink, Opt. Laser Technol. 249 (1973).

1972 (1)

L. E. Drain, B. C. Moss, Opto-Electron.429 (April1972).
[CrossRef]

1971 (3)

J. P. Campell, W. H. Steier, IEEE J. Quantum Electron. QE-7, 450 (1971).
[CrossRef]

F. Durst, J. H. Whitelaw, Proc. Roy. Soc. London A324, 157 (1971).

F. Durst, J. H. Whitelaw, J. Phys. E. 4, 804 (1971).
[CrossRef]

1970 (3)

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

M. K. Mazumder, Appl. Phys. Lett. 10, 462 (1970).
[CrossRef]

W. H. Stevenson, Appl. Opt. 9, 649 (1970).
[CrossRef] [PubMed]

1969 (1)

L. D. Ballard, W. S. Epstein, E. R. Smith, S. Edelman, J. Res. Nat. Bur. Stand. (U.S.) C. 73C, 3/4, July/September (1969).

1967 (1)

1964 (1)

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

1963 (1)

H. Cummins, N. Knable, G. Gampel, Y. Yeh, Appl. Phys. Lett. 2 (3), (1963).

1962 (1)

C. F. Buhrer, D. Baird, E. M. Cowell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

1949 (1)

G. W. Willard, J. Accoust. Soc. Am. 21, 101 (1949).
[CrossRef]

1935 (1)

C. V. Raman, N. S. Nath, Proc. Indian Acad. Sci. A2, 406 (1935).

1932 (2)

P. Debye, F. W. Sears, Proc. Nat. Acad. Sci. U.S. 18, 409 (1932).
[CrossRef]

R. Lucas, P. Biquard, J. Phys. Rad. 3, 464 (1932).
[CrossRef]

Baird, D.

C. F. Buhrer, D. Baird, E. M. Cowell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

Ballard, L. D.

L. D. Ballard, W. S. Epstein, E. R. Smith, S. Edelman, J. Res. Nat. Bur. Stand. (U.S.) C. 73C, 3/4, July/September (1969).

Biquard, P.

R. Lucas, P. Biquard, J. Phys. Rad. 3, 464 (1932).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Brayton, D. B.

D. B. Brayton, H. T. Kalb, F. L. Crosswy, “A Two-Component, Dual-Scatter Laser Doppler Velocimeter with Frequency Burst Signal Readout,” Project Squid NOOO 14-67-0226-0005, P52 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

Buhrer, C. F.

C. F. Buhrer, D. Baird, E. M. Cowell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

Campell, J. P.

J. P. Campell, W. H. Steier, IEEE J. Quantum Electron. QE-7, 450 (1971).
[CrossRef]

Cowell, E. M.

C. F. Buhrer, D. Baird, E. M. Cowell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

Crosswy, F. L.

D. B. Brayton, H. T. Kalb, F. L. Crosswy, “A Two-Component, Dual-Scatter Laser Doppler Velocimeter with Frequency Burst Signal Readout,” Project Squid NOOO 14-67-0226-0005, P52 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

F. L. Crosswy, J. O. Hornkohl, A. E. Lennert, “Signal Characteristics and Signal Conditioning Electronics for a Vector Velocity Laser Velocimeter,” Project Squid NOOO 14-67-0226-0005, P 396 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

Cummins, H.

H. Cummins, N. Knable, G. Gampel, Y. Yeh, Appl. Phys. Lett. 2 (3), (1963).

Cummins, H. Z.

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

Dändliker, R.

Debye, P.

P. Debye, F. W. Sears, Proc. Nat. Acad. Sci. U.S. 18, 409 (1932).
[CrossRef]

Denison, E. B.

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

Drain, L. E.

L. E. Drain, B. C. Moss, Opto-Electron.429 (April1972).
[CrossRef]

L. E. Drain: “Scheme for Sign Determination in Laser-Doppler Velocity or Displacement Measurements,” Materials Physics Division, A.E.R.E., Harwell (1969).

Durst, F.

F. Durst, J. H. Whitelaw, Proc. Roy. Soc. London A324, 157 (1971).

F. Durst, J. H. Whitelaw, J. Phys. E. 4, 804 (1971).
[CrossRef]

Edelman, S.

L. D. Ballard, W. S. Epstein, E. R. Smith, S. Edelman, J. Res. Nat. Bur. Stand. (U.S.) C. 73C, 3/4, July/September (1969).

Epstein, W. S.

L. D. Ballard, W. S. Epstein, E. R. Smith, S. Edelman, J. Res. Nat. Bur. Stand. (U.S.) C. 73C, 3/4, July/September (1969).

Gampel, G.

H. Cummins, N. Knable, G. Gampel, Y. Yeh, Appl. Phys. Lett. 2 (3), (1963).

Goethert, W. H.

W. H. Goethert, “Balanced Detection for the Dual Scatter Laser Doppler Velocimeter,” Arnold Engineering Development Center, Air Force Systems Command, AE DC-TR-71-70, Arnold Air Force Station, Tennessee (1971).

Goldstein, R. J.

R. J. Goldstein, D. K. Kreid, “Fluid Velocity Measurement from Doppler-Shift of Scattered Laser Radiation,” University of Minnesota, Institute of Technology, Department of Mechanical Engineering, HTL-TR-85 (1968).

Hiller, W. J.

W. J. Hiller, G. E. A. Meier, “Zur Vorzeichenbestimmung der Geschwindigkeitskomponenten beim Laser-Doppler-Anemometer,” Max-Planck-Institut für Strömungsforschung, Göttingen (October1972).

Hioko, R.

Hornkohl, J. O.

F. L. Crosswy, J. O. Hornkohl, A. E. Lennert, “Signal Characteristics and Signal Conditioning Electronics for a Vector Velocity Laser Velocimeter,” Project Squid NOOO 14-67-0226-0005, P 396 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

Iten, P. D.

Kalb, H. T.

D. B. Brayton, H. T. Kalb, F. L. Crosswy, “A Two-Component, Dual-Scatter Laser Doppler Velocimeter with Frequency Burst Signal Readout,” Project Squid NOOO 14-67-0226-0005, P52 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

Knable, N.

H. Cummins, N. Knable, G. Gampel, Y. Yeh, Appl. Phys. Lett. 2 (3), (1963).

Kreid, D. K.

R. J. Goldstein, D. K. Kreid, “Fluid Velocity Measurement from Doppler-Shift of Scattered Laser Radiation,” University of Minnesota, Institute of Technology, Department of Mechanical Engineering, HTL-TR-85 (1968).

Lennert, A. E.

F. L. Crosswy, J. O. Hornkohl, A. E. Lennert, “Signal Characteristics and Signal Conditioning Electronics for a Vector Velocity Laser Velocimeter,” Project Squid NOOO 14-67-0226-0005, P 396 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

Lucas, R.

R. Lucas, P. Biquard, J. Phys. Rad. 3, 464 (1932).
[CrossRef]

Mazumder, M. K.

M. K. Mazumder, Appl. Phys. Lett. 10, 462 (1970).
[CrossRef]

Meier, G. E. A.

W. J. Hiller, G. E. A. Meier, “Zur Vorzeichenbestimmung der Geschwindigkeitskomponenten beim Laser-Doppler-Anemometer,” Max-Planck-Institut für Strömungsforschung, Göttingen (October1972).

Moss, B. C.

L. E. Drain, B. C. Moss, Opto-Electron.429 (April1972).
[CrossRef]

Müller, A.

A. Müller, “Measurement of the Sign of a Velocity Component from the Phase Difference of the Two Heterodyne Signals,” EUROMECH-36, London (1972).

Nath, N. S.

C. V. Raman, N. S. Nath, Proc. Indian Acad. Sci. A2, 406 (1935).

Oldengarm, J.

J. Oldengarm, A. H. van Krieken, H. J. Raterink, Opt. Laser Technol. 249 (1973).

Pfeifer, H. J.

H. J. Pfeifer, H. D. vom Stein, “Ein Verfahren zur Bestimung des Vorzeichens der Geschwindigkeit bei der Doppler-Differenzmethode,” Deutsch-Französisches Forschungsinstitut N17/71, Saint-Louis (1971).

Raman, C. V.

C. V. Raman, N. S. Nath, Proc. Indian Acad. Sci. A2, 406 (1935).

Raterink, H. J.

J. Oldengarm, A. H. van Krieken, H. J. Raterink, Opt. Laser Technol. 249 (1973).

Sears, F. W.

P. Debye, F. W. Sears, Proc. Nat. Acad. Sci. U.S. 18, 409 (1932).
[CrossRef]

Smith, E. R.

L. D. Ballard, W. S. Epstein, E. R. Smith, S. Edelman, J. Res. Nat. Bur. Stand. (U.S.) C. 73C, 3/4, July/September (1969).

Steier, W. H.

J. P. Campell, W. H. Steier, IEEE J. Quantum Electron. QE-7, 450 (1971).
[CrossRef]

Stevenson, W. H.

W. H. Stevenson, Appl. Opt. 9, 649 (1970).
[CrossRef] [PubMed]

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

Suzuki, T.

van Krieken, A. H.

J. Oldengarm, A. H. van Krieken, H. J. Raterink, Opt. Laser Technol. 249 (1973).

vom Stein, H. D.

H. J. Pfeifer, H. D. vom Stein, “Ein Verfahren zur Bestimung des Vorzeichens der Geschwindigkeit bei der Doppler-Differenzmethode,” Deutsch-Französisches Forschungsinstitut N17/71, Saint-Louis (1971).

Whitelaw, J. H.

F. Durst, J. H. Whitelaw, J. Phys. E. 4, 804 (1971).
[CrossRef]

F. Durst, J. H. Whitelaw, Proc. Roy. Soc. London A324, 157 (1971).

Willard, G. W.

G. W. Willard, J. Accoust. Soc. Am. 21, 101 (1949).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Yeh, Y.

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

H. Cummins, N. Knable, G. Gampel, Y. Yeh, Appl. Phys. Lett. 2 (3), (1963).

Appl. Opt. (2)

Appl. Phys. Lett. (4)

M. K. Mazumder, Appl. Phys. Lett. 10, 462 (1970).
[CrossRef]

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

H. Cummins, N. Knable, G. Gampel, Y. Yeh, Appl. Phys. Lett. 2 (3), (1963).

C. F. Buhrer, D. Baird, E. M. Cowell, Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. P. Campell, W. H. Steier, IEEE J. Quantum Electron. QE-7, 450 (1971).
[CrossRef]

J. Accoust. Soc. Am. (1)

G. W. Willard, J. Accoust. Soc. Am. 21, 101 (1949).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E. (1)

F. Durst, J. H. Whitelaw, J. Phys. E. 4, 804 (1971).
[CrossRef]

J. Phys. Rad. (1)

R. Lucas, P. Biquard, J. Phys. Rad. 3, 464 (1932).
[CrossRef]

J. Res. Nat. Bur. Stand. (U.S.) C. (1)

L. D. Ballard, W. S. Epstein, E. R. Smith, S. Edelman, J. Res. Nat. Bur. Stand. (U.S.) C. 73C, 3/4, July/September (1969).

Opt. Laser Technol. (1)

J. Oldengarm, A. H. van Krieken, H. J. Raterink, Opt. Laser Technol. 249 (1973).

Opto-Electron. (1)

L. E. Drain, B. C. Moss, Opto-Electron.429 (April1972).
[CrossRef]

Proc. Indian Acad. Sci. (1)

C. V. Raman, N. S. Nath, Proc. Indian Acad. Sci. A2, 406 (1935).

Proc. Nat. Acad. Sci. U.S. (1)

P. Debye, F. W. Sears, Proc. Nat. Acad. Sci. U.S. 18, 409 (1932).
[CrossRef]

Proc. Roy. Soc. London (1)

F. Durst, J. H. Whitelaw, Proc. Roy. Soc. London A324, 157 (1971).

Rev. Sci. Instrum. (1)

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

Other (12)

R. J. Goldstein, D. K. Kreid, “Fluid Velocity Measurement from Doppler-Shift of Scattered Laser Radiation,” University of Minnesota, Institute of Technology, Department of Mechanical Engineering, HTL-TR-85 (1968).

Zenith Technical Notes: “Acousto-Optic Application of Calibrators and Frequence Shifters for Laser Velocimeters” (1971).

L. E. Drain: “Scheme for Sign Determination in Laser-Doppler Velocity or Displacement Measurements,” Materials Physics Division, A.E.R.E., Harwell (1969).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

H. J. Pfeifer, H. D. vom Stein, “Ein Verfahren zur Bestimung des Vorzeichens der Geschwindigkeit bei der Doppler-Differenzmethode,” Deutsch-Französisches Forschungsinstitut N17/71, Saint-Louis (1971).

A. Müller, “Measurement of the Sign of a Velocity Component from the Phase Difference of the Two Heterodyne Signals,” EUROMECH-36, London (1972).

Thermo Systems Incorporated, “Model 1094, LDV Signal Processor Counter Type” (1973).

W. J. Hiller, G. E. A. Meier, “Zur Vorzeichenbestimmung der Geschwindigkeitskomponenten beim Laser-Doppler-Anemometer,” Max-Planck-Institut für Strömungsforschung, Göttingen (October1972).

D. B. Brayton, H. T. Kalb, F. L. Crosswy, “A Two-Component, Dual-Scatter Laser Doppler Velocimeter with Frequency Burst Signal Readout,” Project Squid NOOO 14-67-0226-0005, P52 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

F. L. Crosswy, J. O. Hornkohl, A. E. Lennert, “Signal Characteristics and Signal Conditioning Electronics for a Vector Velocity Laser Velocimeter,” Project Squid NOOO 14-67-0226-0005, P 396 (School of Mechanical Engineering, Purdue University, Lafayette, Indiana, March1972).

Precision Devices and Systems (UK): “Laser Anemometer Phase Modulator” (1974).

W. H. Goethert, “Balanced Detection for the Dual Scatter Laser Doppler Velocimeter,” Arnold Engineering Development Center, Air Force Systems Command, AE DC-TR-71-70, Arnold Air Force Station, Tennessee (1971).

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Figures (20)

Fig. 1
Fig. 1

Conventional dual beam laser Doppler anemometers.

Fig. 2
Fig. 2

Error of mean and fluctuating velocity measurements due to direction ambiguity in LDA.

Fig. 3
Fig. 3

Rotating disk grating in LDA. (a) Direction sensitive LDA; (b) optical frequency shifting with a moving grating; (c) radial disk grating; (d) optical arrangement of LDA using rotating disk grating.

Fig. 4
Fig. 4

Rotating cylindrical grating in LDA.

Fig. 5
Fig. 5

Acoustooptic frequency shifting of light. (a) Specifications of an acoustooptic cell; (b) two-cell arrangement.

Fig. 6
Fig. 6

Electrooptic method of light frequency shifting, (a) Litium- niobate-crystal (LiO3Nb); (b) electric field distribution in the crystal (I) top and bottom electrodes at zero, (II) ⅛ period later; (c) experimental arrangement.

Fig. 7
Fig. 7

Specifications of electrooptic cells. (a) Arrangement of polarizers, quarter waveplates, and electrooptic cells for single sideband suppressed carrier modulation; (b) distribution of intensity in the sidebands for the four-cell (III) sequence; (c) single sideband conversion efficiency for multicell electrooptic devices with the orientation of the cells advancing in steps of π/2N (I) or π/N (II). Note: The number 5 on the ordinate of (c) should be replaced by 50.

Fig. 8
Fig. 8

Optical arrangement for Doppler beating, using electrooptic cells, (a) Experimental arrangement for Doppler beating with frequency shifting of the reference beam using double passage through the electrooptic cells; (b) Doppler beat spectrum with frequency shifting by 1 MHz by two KD*P cells, showing residual signals from the carrier and unwanted sideband.

Fig. 9
Fig. 9

Direction sensitive interferometer, employing polarized light and electronic frequency shifting.

Fig. 10
Fig. 10

Employment of polarized light in LDA for direction sensing. (a) Optical arrangement; (b) polarization direction of the two beams; (c) fringe patterns; (d) signals generated by a particle moving from left to right; (e) signals generated by a particle moving from right to left; (f) subtraction of the two signals (AB).

Fig. 11
Fig. 11

Optical setting for a multicolor laser Doppler anemometer. (a) Optical arrangement; (b) fringe patterns in the probe volume; (c) a four-mode LDV fringe pattern.

Fig. 12
Fig. 12

Doppler frequency produced by scattering particles, (a) Signal produced by a single particle; (b) frequency spectrum of signal (a); (c) frequency spectrum of two scattering particles; (d) constant frequency shifting of (c).

Fig. 13
Fig. 13

Interference of pedestal with Doppler shifted frequency spectrum (observed at ⅙ dia downstream of a free jet with the fringe system of the LDV set at 85° WRT the main flow direction) (θ = 10°, N = 75, Ncr = 7).

Fig. 14
Fig. 14

Dependence of on shifting frequency and the number of fringes in the probe volume.

Fig. 15
Fig. 15

Pedestal removal by optical methods. (a) Optical arrangement for pedestal removing; (b) detected signal of the two photodiodes; (c) resulting symmetrical signal.

Fig. 16
Fig. 16

Two-dimensional LDA, employing three polarized light beams. (a) Optical arrangement of a 2-D laser Doppler velocimeter using three polarized light beams30; (b) polarization plane of the three beams; (c) two imposed fringe patterns within the probe volume; (d) orientation of fringe pattern and measured velocity plane.

Fig. 17
Fig. 17

Two-dimensional vector LDA, employing a 2-D Bragg cell, (a) Optical arrangement; (b) possible beam and frequency combination using a 2-D Bragg cell; (c) polarization plane of the four beams.

Fig. 18
Fig. 18

One beam LDA for 1-D vector velocity measurement.

Fig. 19
Fig. 19

Direction sensitive LDA, employing two Bragg cells.

Fig. 20
Fig. 20

Compact optical unit, employing polarized light, for vector velocity measurements.

Tables (2)

Tables Icon

Table I Comparison of Different Methods of Direction Sensing in LDV

Tables Icon

Table II Comparison of Different Methods of Pedestal Removing

Equations (40)

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

f D = f S + 1 / λ ( { k 1 } i { k 2 } i ) { U } i .
A ( x 1 , t ) = 1 + cos [ ( 2 π / d ) ( x 1 υ g t ) ] .
ψ ( x 2 , t ) = exp ( i 2 π f 0 t ) { δ ( x 2 ) + 1 2 exp [ i ( 2 π / d ) υ g t ] × δ ( x 2 + 2 π d ) + 1 2 exp [ i ( 2 π / d ) υ g t ] δ ( x 2 2 π d ) } .
f D = N D · υ g / d + ( { k 1 } i { k 2 } i ) { U } i · 1 λ ,
f D = 1 λ { U } i [ { l } i { k } i ] = 1 λ { U } i { n } i .
f D = 1 λ V g · 2 · sin θ / 2 · cos θ / 2 = 1 λ V g · sin θ .
sin θ = ( N D · λ ) / d ,
f D = N D · ( υ g / d ) .
N total = ( 2 π · r g ) / d ,
f D = N D · [ ( υ g · N total ) / ( 2 π · r g ) ] .
ω = υ g / ( 2 π r g ) .
f D = N D · ω · N total .
f s = υ g / d = r ω / K r = ω / K .
θ t θ i = m λ / d .
sin θ B = 1 2 ( λ / Λ ) .
L Λ 2 / λ
Δ θ = ( λ / υ u ) ( f s 1 f s 2 ) .
E x = E 0 cos 2 π f 0 t , E y = E 0 sin 2 π f 0 t .
E x = E 0 cos [ 2 π f 0 t + 1 2 δ cos ( 2 π f s t ) ] , E y = E 0 sin [ 2 π f 0 t 1 2 δ cos ( 2 π f s t ) ] .
{ E 1 x = A 1 cos 2 π f 0 t · cos π / 4 , E 1 y = A 1 cos 2 π f 0 t · sin π / 4 ,
E 2 x = A 2 cos ( 2 π f 0 t + φ ) , E 2 y = A 2 cos ( 2 π f 0 t + φ + π / 2 ) .
J ( 12 ) x = ( E 1 x · E 2 x ) ¯ = 2 4 A 1 A 2 cos φ , J ( 12 ) y = ( E 1 y · E 2 y ) ¯ = 2 4 A 1 A 2 cos ( φ + π / 2 ) .
Δ x i = λ i / ( 2 sin θ / 2 ) , i = 1,2 n .
f D i = ( 2 υ sin θ / 2 ) / λ i , i = 1,2 n .
x ( t ) = A p exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } + A s exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } cos 2 π f D t ,
f D = υ / d = ( 2 υ sin θ / 2 ) / λ
1 τ = f D N = f D · λ 2 b 0 tan θ / 2 .
X ( f ) = ( A p 2 ) ( π 2 ) 1 / 2 exp { [ π f τ 2 ( 2 ) 1 / 2 ] 2 } + ( A s τ 4 ) ( π 2 ) 1 / 2 ( exp { [ π ( f + f D ) τ 2 ( 2 ) 1 / 2 ] 2 } + exp { [ π ( f f D ) τ 2 ( 2 ) 1 / 2 ] 2 } ) .
( f D ) min e / ( 2 τ max ) ,
f D min
f D max
f D min and f D max : f D min ( e / 2 N ) f D max .
f D min 0.14 f D max .
cos φ = ( U / U ) ( N cr / N ) .
cos ϕ = ( U / U ) ( N cr / N ) ( f s / f D 0 ) ,
f D 0 = ( 2 U sin θ / 2 ) / λ .
f s / f D 0 .
x 1 ( t ) = A p exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } + A s exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } cos ( 2 π f D t ) ,
x 2 ( t ) = A p exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } + A s exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } cos ( 2 π f D t + π ) = A p exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } A s exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } · cos ( 2 π f D t ) .
x t = x 1 ( t ) x 2 ( t ) = 2 A s exp { [ 2 ( 2 ) 1 / 2 ( t t 0 ) / τ ] 2 } cos ( 2 π f D t ) .

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