Abstract

A method is presented for analysis of the relationship of the velocity measuring uncertainty and the system parameters of laser Doppler velocimeters. The method permits optimization of the laser Doppler system to minimize the uncertainty of fluid velocity measurements.

© 1996 Optical Society of America

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References

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  1. L. Drain, The Laser Doppler Technique (Wiley, Chichester, UK, 1986).
  2. W. George, in Laser Doppler Velocimetry, R. A. Adrian ed., SPIE Milestone Ser. 78, 135 (1993).
  3. F. Durst, J. Whitelaw, in Proceedings of Heat Transfer Conference (American Society of Mechanical Engineers, New York, 1972), p. 1.
  4. J. Czarske, H. Müller, Opt. Commun. 114, 223 (1995).
    [CrossRef]
  5. J. Czarske, “Verfahren zur Messung und Auswertung der Interferenzphase in der Laser-Doppler-Velocimetrie,” Fortschritt-Berichte Series 8, No. 530 (VDI, Düsseldorf, 1995).
  6. G. Seber, Linear Regression Analysis (Wiley, New York, 1977), p. 193.
  7. D. Rife, R. Boorstyn, IEEE Trans. Inf. Theory 20, 591 (1974).
    [CrossRef]
  8. L. Lading, T. Jorgensen, J. Opt. Soc. Am. A 7, 1324 (1990).
    [CrossRef]

1995 (1)

J. Czarske, H. Müller, Opt. Commun. 114, 223 (1995).
[CrossRef]

1990 (1)

1974 (1)

D. Rife, R. Boorstyn, IEEE Trans. Inf. Theory 20, 591 (1974).
[CrossRef]

Boorstyn, R.

D. Rife, R. Boorstyn, IEEE Trans. Inf. Theory 20, 591 (1974).
[CrossRef]

Czarske, J.

J. Czarske, H. Müller, Opt. Commun. 114, 223 (1995).
[CrossRef]

J. Czarske, “Verfahren zur Messung und Auswertung der Interferenzphase in der Laser-Doppler-Velocimetrie,” Fortschritt-Berichte Series 8, No. 530 (VDI, Düsseldorf, 1995).

Drain, L.

L. Drain, The Laser Doppler Technique (Wiley, Chichester, UK, 1986).

Durst, F.

F. Durst, J. Whitelaw, in Proceedings of Heat Transfer Conference (American Society of Mechanical Engineers, New York, 1972), p. 1.

George, W.

W. George, in Laser Doppler Velocimetry, R. A. Adrian ed., SPIE Milestone Ser. 78, 135 (1993).

Jorgensen, T.

Lading, L.

Müller, H.

J. Czarske, H. Müller, Opt. Commun. 114, 223 (1995).
[CrossRef]

Rife, D.

D. Rife, R. Boorstyn, IEEE Trans. Inf. Theory 20, 591 (1974).
[CrossRef]

Seber, G.

G. Seber, Linear Regression Analysis (Wiley, New York, 1977), p. 193.

Whitelaw, J.

F. Durst, J. Whitelaw, in Proceedings of Heat Transfer Conference (American Society of Mechanical Engineers, New York, 1972), p. 1.

IEEE Trans. Inf. Theory (1)

D. Rife, R. Boorstyn, IEEE Trans. Inf. Theory 20, 591 (1974).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

J. Czarske, H. Müller, Opt. Commun. 114, 223 (1995).
[CrossRef]

Other (5)

J. Czarske, “Verfahren zur Messung und Auswertung der Interferenzphase in der Laser-Doppler-Velocimetrie,” Fortschritt-Berichte Series 8, No. 530 (VDI, Düsseldorf, 1995).

G. Seber, Linear Regression Analysis (Wiley, New York, 1977), p. 193.

L. Drain, The Laser Doppler Technique (Wiley, Chichester, UK, 1986).

W. George, in Laser Doppler Velocimetry, R. A. Adrian ed., SPIE Milestone Ser. 78, 135 (1993).

F. Durst, J. Whitelaw, in Proceedings of Heat Transfer Conference (American Society of Mechanical Engineers, New York, 1972), p. 1.

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Figures (4)

Fig. 1
Fig. 1

Illustration of the diametrical relationship of the SNR and the signal duration to the measuring volume diameter, assuming constant laser power and sampling frequency. Left, a small diameter yields a high SNR and hence a low phase uncertainty, but the number of phase values is small. Right, a large diameter results in a large signal duration and hence a great number of phase values, but the SNR is small, so a high phase uncertainty results.

Fig. 2
Fig. 2

Center frequency standard deviation as an exemplary function of the measuring volume diameter.

Fig. 3
Fig. 3

Mismatching of the Gaussian weighting function exp[−(2t/τ)2] for conventional LDV systems and the calculation function t2 of the frequency estimation procedure.

Fig. 4
Fig. 4

Comparison between the conventional LDV system and a proposed two-focus LDV system: Two phase error bars at the limits of the measuring volume illustrate the reduction of the center frequency uncertainty Δ〈ω̂〉 for the two-focus LDV system.

Equations (3)

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ϕ M ( t ) = ( 2 π v 0 / d ) t + ϕ N ( t ) ,
Δ ω ^ = Δ ϕ min [ i = - ( N - 1 ) / 2 ( N - 1 ) / 2 t i 2 w i ] 1 / 2 ,
Δ ϕ M ( t ) = [ c 1 + c 2 S ( t ) ] 1 / 2 / S ( t ) ,

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