Abstract

The edge technique has been used in simple laboratory experiments to demonstrate velocity measurements with an experimental error, standard deviation, as small as 12 cm/s, which represents a Doppler-shift measurement accuracy of 8 parts in 1010 of the laser frequency. An edge filter with a spectral width 140 times larger than the measurement accuracy achieved is used. The measurements are made in the presence of short-term frequency drifts equivalent to velocities of 5 to 10 m/s, which are eliminated by the differential frequency measurement used in the edge technique. Long-term frequency drifts are compensated for by servo locking the edge to the laser frequency. High accuracy is achieved for a range of locations on the edge from 0.33 to 4.5 fringe half-widths (half-width at half-maximum), a dynamic range greater than 500 times the measurement accuracy.

© 1994 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. R. J. Goldstein, W. F. Hagen, “Turbulent flow measurements utilizing the Doppler shift of scattered laser radiation,” Phys. Fluids 10, 1349–1352 (1967).
    [CrossRef]
  4. M. Rudd, “A new theoretical model for the laser Doppler-meter,” J. Phys. E 2, 55–58 (1969).
    [CrossRef]
  5. M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. L. M. Barker, R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  18. S. R. Drayson, “Rapid computation of the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 16, 611–614 (1976).
    [CrossRef]
  19. J. Humliček, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Trans. 21, 309–313 (1979).
    [CrossRef]
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    [CrossRef]

1992 (1)

1991 (1)

1988 (1)

1985 (1)

1982 (1)

J. Humilček, “Optimized computation of the Voigt and complex probability functions,” J. Quant. Spectrosc. Radiat. Transfer 27, 437–444 (1982).
[CrossRef]

1979 (1)

J. Humliček, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Trans. 21, 309–313 (1979).
[CrossRef]

1976 (1)

S. R. Drayson, “Rapid computation of the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 16, 611–614 (1976).
[CrossRef]

1972 (1)

L. M. Barker, R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
[CrossRef]

1971 (1)

D. M. Paul, D. A. Jackson, “Rapid velocity sensor using a static confocal Fabry–Perot and a single frequency argon laser,” J. Phys. E 4, 170–177 (1971).
[CrossRef]

1970 (1)

1969 (1)

M. Rudd, “A new theoretical model for the laser Doppler-meter,” J. Phys. E 2, 55–58 (1969).
[CrossRef]

1968 (1)

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[CrossRef]

1967 (2)

R. J. Goldstein, W. F. Hagen, “Turbulent flow measurements utilizing the Doppler shift of scattered laser radiation,” Phys. Fluids 10, 1349–1352 (1967).
[CrossRef]

G. Hernandez, “Analytical description of a Fabry–Perot photoelectric spectrometer,” Appl. Opt. 5, 1745–1748 (1967).
[CrossRef]

1965 (1)

J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

1964 (1)

Y. Yeh, H. Z. Cummins, “Localized fluid flow measurements with a He–Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[CrossRef]

1963 (1)

F. Bayer-Helms, “Analyse von Linienprofilen. I. Grundlagen und Messeinrichtungen,” Z. Agnew. Phys. 15, 330–338 (1963).

Barker, L. M.

L. M. Barker, R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
[CrossRef]

Bayer-Helms, F.

F. Bayer-Helms, “Analyse von Linienprofilen. I. Grundlagen und Messeinrichtungen,” Z. Agnew. Phys. 15, 330–338 (1963).

Behar, G.

Bloom, S. H.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 7, pp. 323–329.

Cummins, H. Z.

Y. Yeh, H. Z. Cummins, “Localized fluid flow measurements with a He–Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[CrossRef]

Drain, L. E.

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

Drayson, S. R.

S. R. Drayson, “Rapid computation of the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 16, 611–614 (1976).
[CrossRef]

Foreman, J. W.

J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

Gentry, B. M.

C. L. Korb, B. M. Gentry, C. Y. Weng, “Edge technique: theory and application to the lidar measurement of atmospheric wind,” Appl. Opt. 31, 4202–4213 (1992).
[CrossRef] [PubMed]

C. L. Korb, B. M. Gentry, “New Doppler lidar methods for atmospheric wind measurements: the edge technique,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 322–324.

George, E. W.

J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

Gidon, S.

Goldstein, R. J.

R. J. Goldstein, W. F. Hagen, “Turbulent flow measurements utilizing the Doppler shift of scattered laser radiation,” Phys. Fluids 10, 1349–1352 (1967).
[CrossRef]

Hagen, W. F.

R. J. Goldstein, W. F. Hagen, “Turbulent flow measurements utilizing the Doppler shift of scattered laser radiation,” Phys. Fluids 10, 1349–1352 (1967).
[CrossRef]

Hernandez, G.

Hollenbach, R. E.

L. M. Barker, R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
[CrossRef]

Huffaker, R. M.

Humilcek, J.

J. Humilček, “Optimized computation of the Voigt and complex probability functions,” J. Quant. Spectrosc. Radiat. Transfer 27, 437–444 (1982).
[CrossRef]

Humlicek, J.

J. Humliček, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Trans. 21, 309–313 (1979).
[CrossRef]

Jackson, D. A.

D. M. Paul, D. A. Jackson, “Rapid velocity sensor using a static confocal Fabry–Perot and a single frequency argon laser,” J. Phys. E 4, 170–177 (1971).
[CrossRef]

Korb, C. L.

C. L. Korb, B. M. Gentry, C. Y. Weng, “Edge technique: theory and application to the lidar measurement of atmospheric wind,” Appl. Opt. 31, 4202–4213 (1992).
[CrossRef] [PubMed]

C. L. Korb, B. M. Gentry, “New Doppler lidar methods for atmospheric wind measurements: the edge technique,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 322–324.

Korevaar, E.

Kremer, R.

Lewis, R. D.

J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

Menders, J.

Paul, D. M.

D. M. Paul, D. A. Jackson, “Rapid velocity sensor using a static confocal Fabry–Perot and a single frequency argon laser,” J. Phys. E 4, 170–177 (1971).
[CrossRef]

Rivers, M.

Rudd, M.

M. Rudd, “A new theoretical model for the laser Doppler-meter,” J. Phys. E 2, 55–58 (1969).
[CrossRef]

Searcy, P. A.

Teich, M. C.

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[CrossRef]

Weng, C. Y.

Wilksch, P. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 7, pp. 323–329.

Yeh, Y.

Y. Yeh, H. Z. Cummins, “Localized fluid flow measurements with a He–Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (2)

Y. Yeh, H. Z. Cummins, “Localized fluid flow measurements with a He–Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[CrossRef]

J. W. Foreman, E. W. George, R. D. Lewis, “Measurement of localized flow velocities in gases with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

J. Appl. Phys. (1)

L. M. Barker, R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
[CrossRef]

J. Phys. E (2)

D. M. Paul, D. A. Jackson, “Rapid velocity sensor using a static confocal Fabry–Perot and a single frequency argon laser,” J. Phys. E 4, 170–177 (1971).
[CrossRef]

M. Rudd, “A new theoretical model for the laser Doppler-meter,” J. Phys. E 2, 55–58 (1969).
[CrossRef]

J. Quant. Spectrosc. Radiat. Trans. (1)

J. Humliček, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Trans. 21, 309–313 (1979).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

J. Humilček, “Optimized computation of the Voigt and complex probability functions,” J. Quant. Spectrosc. Radiat. Transfer 27, 437–444 (1982).
[CrossRef]

S. R. Drayson, “Rapid computation of the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 16, 611–614 (1976).
[CrossRef]

Opt. Lett. (1)

Phys. Fluids (1)

R. J. Goldstein, W. F. Hagen, “Turbulent flow measurements utilizing the Doppler shift of scattered laser radiation,” Phys. Fluids 10, 1349–1352 (1967).
[CrossRef]

Proc. IEEE (1)

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[CrossRef]

Z. Agnew. Phys. (1)

F. Bayer-Helms, “Analyse von Linienprofilen. I. Grundlagen und Messeinrichtungen,” Z. Agnew. Phys. 15, 330–338 (1963).

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 7, pp. 323–329.

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

C. L. Korb, B. M. Gentry, “New Doppler lidar methods for atmospheric wind measurements: the edge technique,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 322–324.

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Figures (6)

Fig. 1
Fig. 1

Spectral response of a high-resolution optical filter as a function of frequency in units of the filter half-width α. The locations of the outgoing and the backscattered laser frequencies, νOUT and νRET, respectively, are shown on the edge of the filter. A small Doppler shift ΔνDOP produces a large change in measured signal ΔT.

Fig. 2
Fig. 2

Normalized edge signal, measured for the outgoing and the backscattered laser signals by splitting the incoming beam with a beam splitter (BS) into edge detector (EDGE DET.) and the energy-monitor detector (EM DET.) channels.

Fig. 3
Fig. 3

Optical system used in the laser velocimeter experiments.

Fig. 4
Fig. 4

Frequency drift of the étalon measured as a function of time. The drift is measured by servo locking the étalon to the laser and converting the accumulated error voltage to frequency units. Drift is shown on the left axis in wave numbers and on the right axis in equivalent velocity units.

Fig. 5
Fig. 5

Oscilloscope trace of the EDGE DET. and the EM DET. signals. The reference (REF) and the target channels are alternately passed by the chopper.

Fig. 6
Fig. 6

Typical velocity measurements showing a comparison of the laser-measured and the known target velocities. The solid line is the best-fit line obtained from a least-squares fit to the 200 measured points. The slope of the line is 0.99, and the standard deviation is 0.188 m/s.

Tables (1)

Tables Icon

Table 1 Summary of Analysis of Velocity Measurements Taken at Different Locations on the Edgea

Equations (6)

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

I N ( ν ) = I EDGE I EM = C F ( ν ) ,
C = G η τ G 0 η 0 τ 0 ,
v = c 2 ν [ I N ( ν + Δ ν ) - I N ( ν ) C β ( ν , ν + Δ ν ) ] ,
Θ = 1 v Δ I N I N ,
= Δ I Θ .
F = ( 1 - L 1 - R ) 2 1 1 + 4 R ( 1 - R 2 ) sin 2 ( δ 2 ) ,

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