Abstract

Real-time measurement capability of a frequency-modulated filtered light-scattering- (FM FLS) Doppler velocimeter has been demonstrated. Doppler-shifted light from a frequency-modulated Ti:sapphire laser scattered from a supersonic flow is imaged through a potassium vapor cell and is detected by FM spectroscopy. The FM signal is used in closed-loop feedback control of the laser frequency to lock the Doppler-shifted scattered light to the resonance frequency of the filter. The difference between the filter resonance frequency and the laser frequency when the scattered light is frequency locked to the filter resonance is the flow-induced Doppler shift. Changes in flow velocity are tracked by changes in laser frequency, which is subsequently measured to obtain the Doppler shift. The frequency-locking capability of the technique was achieved with use of a simple analog controller. The random Doppler shift measurement errors (2σ) were approximately 20 MHz, which correspond to velocity measurement errors for the real-time measurement of less than 3% in a 10-Hz bandwidth.

© 1998 Optical Society of America

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References

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  1. J. H. Grinstead, N. D. Finkelstein, W. R. Lempert, “Doppler velocimetry in a supersonic jet by use of frequency-modulated filtered light scattering,” Opt. Lett. 22, 331–333 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1997 (1)

1996 (3)

M. W. Smith, G. B. Northam, “Application of absorption filter planar Doppler velocimetry to sonic and supersonic jets,” AIAA J. 34, 434–441 (1996).
[CrossRef]

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

S. W. North, X. S. Zheng, R. Fei, G. H. Hall, “Line shape analysis of Doppler-broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

1993 (1)

1992 (2)

1970 (1)

1967 (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]

1964 (1)

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

Arie, A.

Bortz, M. L.

Byer, R. L.

Cummins, H. Z.

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

Fei, R.

S. W. North, X. S. Zheng, R. Fei, G. H. Hall, “Line shape analysis of Doppler-broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Finch, A

N. D. Finkelstein, J Gambogi, W. R. Lempert, R. B. Miles, G. A. Rines, A Finch, R. A. Schwartz, “Development of a tunable single-frequency ultraviolet laser source for UV filtered Rayleigh scattering,” paper 94-0492 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

Finkelstein, N. D.

J. H. Grinstead, N. D. Finkelstein, W. R. Lempert, “Doppler velocimetry in a supersonic jet by use of frequency-modulated filtered light scattering,” Opt. Lett. 22, 331–333 (1997).
[CrossRef] [PubMed]

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

N. D. Finkelstein, J Gambogi, W. R. Lempert, R. B. Miles, G. A. Rines, A Finch, R. A. Schwartz, “Development of a tunable single-frequency ultraviolet laser source for UV filtered Rayleigh scattering,” paper 94-0492 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

Forkey, J. N.

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

Gambogi, J

N. D. Finkelstein, J Gambogi, W. R. Lempert, R. B. Miles, G. A. Rines, A Finch, R. A. Schwartz, “Development of a tunable single-frequency ultraviolet laser source for UV filtered Rayleigh scattering,” paper 94-0492 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

Gentry, B. M.

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]

Grinstead, J. H.

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]

Hall, G. H.

S. W. North, X. S. Zheng, R. Fei, G. H. Hall, “Line shape analysis of Doppler-broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Horta, L. G.

M. Q. Phan, L. G. Horta, J. N. Juang, R. W. Longman, “Identification of linear systems by an asymptotically stable observer,” NASA Tech. paper 3164 (NASA Langley Research Center, Hampton Va., 1992).

Huffaker, R. M.

Jefer, M. M.

Juang, J. N.

M. Q. Phan, L. G. Horta, J. N. Juang, R. W. Longman, “Identification of linear systems by an asymptotically stable observer,” NASA Tech. paper 3164 (NASA Langley Research Center, Hampton Va., 1992).

Korb, C. L.

Lempert, W. R.

J. H. Grinstead, N. D. Finkelstein, W. R. Lempert, “Doppler velocimetry in a supersonic jet by use of frequency-modulated filtered light scattering,” Opt. Lett. 22, 331–333 (1997).
[CrossRef] [PubMed]

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

N. D. Finkelstein, J Gambogi, W. R. Lempert, R. B. Miles, G. A. Rines, A Finch, R. A. Schwartz, “Development of a tunable single-frequency ultraviolet laser source for UV filtered Rayleigh scattering,” paper 94-0492 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

Longman, R. W.

M. Q. Phan, L. G. Horta, J. N. Juang, R. W. Longman, “Identification of linear systems by an asymptotically stable observer,” NASA Tech. paper 3164 (NASA Langley Research Center, Hampton Va., 1992).

Miles, R. B.

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

N. D. Finkelstein, J Gambogi, W. R. Lempert, R. B. Miles, G. A. Rines, A Finch, R. A. Schwartz, “Development of a tunable single-frequency ultraviolet laser source for UV filtered Rayleigh scattering,” paper 94-0492 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

North, S. W.

S. W. North, X. S. Zheng, R. Fei, G. H. Hall, “Line shape analysis of Doppler-broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Northam, G. B.

M. W. Smith, G. B. Northam, “Application of absorption filter planar Doppler velocimetry to sonic and supersonic jets,” AIAA J. 34, 434–441 (1996).
[CrossRef]

Phan, M. Q.

M. Q. Phan, L. G. Horta, J. N. Juang, R. W. Longman, “Identification of linear systems by an asymptotically stable observer,” NASA Tech. paper 3164 (NASA Langley Research Center, Hampton Va., 1992).

Rines, G. A.

N. D. Finkelstein, J Gambogi, W. R. Lempert, R. B. Miles, G. A. Rines, A Finch, R. A. Schwartz, “Development of a tunable single-frequency ultraviolet laser source for UV filtered Rayleigh scattering,” paper 94-0492 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

Schwartz, R. A.

N. D. Finkelstein, J Gambogi, W. R. Lempert, R. B. Miles, G. A. Rines, A Finch, R. A. Schwartz, “Development of a tunable single-frequency ultraviolet laser source for UV filtered Rayleigh scattering,” paper 94-0492 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

Silver, J. A.

Smith, M. W.

M. W. Smith, G. B. Northam, “Application of absorption filter planar Doppler velocimetry to sonic and supersonic jets,” AIAA J. 34, 434–441 (1996).
[CrossRef]

Weng, C. Y.

Yeh, Y.

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

Zheng, X. S.

S. W. North, X. S. Zheng, R. Fei, G. H. Hall, “Line shape analysis of Doppler-broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

AIAA J. (2)

M. W. Smith, G. B. Northam, “Application of absorption filter planar Doppler velocimetry to sonic and supersonic jets,” AIAA J. 34, 434–441 (1996).
[CrossRef]

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

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

J. Chem. Phys. (1)

S. W. North, X. S. Zheng, R. Fei, G. H. Hall, “Line shape analysis of Doppler-broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Opt. Lett. (2)

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]

Other (2)

N. D. Finkelstein, J Gambogi, W. R. Lempert, R. B. Miles, G. A. Rines, A Finch, R. A. Schwartz, “Development of a tunable single-frequency ultraviolet laser source for UV filtered Rayleigh scattering,” paper 94-0492 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

M. Q. Phan, L. G. Horta, J. N. Juang, R. W. Longman, “Identification of linear systems by an asymptotically stable observer,” NASA Tech. paper 3164 (NASA Langley Research Center, Hampton Va., 1992).

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Figures (12)

Fig. 1
Fig. 1

Frequency-modulated filtered light-scattering velocimetry. Closed-loop control of the laser frequency with the FM signal as feedback locks the frequency of the Doppler-shifted scattering to the resonance frequency of the absorption filter. The difference between the incident laser and absorption filter frequencies is the Doppler shift.

Fig. 2
Fig. 2

Experimental configuration. PD, photodiode; PMT, photomultiplier tube; E/O, electro-optic.

Fig. 3
Fig. 3

Signal demodulation network for processing the scattered light signal photocurrent. E/O, electro-optic; LO, local oscillator; IF, intermediate frequency.

Fig. 4
Fig. 4

Doppler shift measurement geometry. V, jet velocity vector; i L , laser propagation vector; i s , scattering vector; D, nozzle exit diameter.

Fig. 5
Fig. 5

Single-pulse planar images of the atmospheric free jet showing the region of CO2 condensation: (a) near properly expanded, supply pressure ∼220 psi; (b) underexpanded, supply pressure ∼350 psi.

Fig. 6
Fig. 6

Direct and first-harmonic FM absorption spectra of the potassium vapor filter obtained with scattering from a target.

Fig. 7
Fig. 7

Variation of measured SNR of the FM spectrum with signal. The signal is proportional to 〈P s 〉/Δf. The slope of the line corresponds to photon shot noise. The data point with the circle results from the spectrum of Fig. 6.

Fig. 8
Fig. 8

Control loop for frequency-locking the Doppler-shifted scattered light frequency to the absorption resonance of the filter.

Fig. 9
Fig. 9

Bode diagram for the laser frequency controller.

Fig. 10
Fig. 10

FM spectra of potassium vapor filter obtained with scattering from the jet for two different supply pressures. The direct absorption spectrum of the reference cell is also shown. The points marked on the direct absorption spectrum refer to the laser frequency positions indicated in the lock-loop demonstration of Fig. 11.

Fig. 11
Fig. 11

Time history of (a) laser frequency relative to filter resonance, (b) controller output, and (c) error signal demonstrating the velocity-tracking capability of the closed-loop feedback system. Regions AD refer to the laser frequency positions on the direct absorption spectrum of Fig. 8. The supply pressure was decreased between B and C and increased between C and D. The velocity determined from the detuned laser frequency is indicated on the right-hand scale of (a).

Fig. 12
Fig. 12

Closed-loop velocity measurement uncertainty (2σ) as a function of FM SNR. The line is the FM signal-limited uncertainty calculated from Eq. (8). The points were evaluated from the data of Fig. 11.

Equations (8)

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P = η c τ ν LP L i   N i σ i = P s τ ν ,
Δ S FM = d S FM d ν ν 0 Δ ν ,
S FM = η h ν 0 P s Δ f   τ ν Q ν ,
Δ ν = Δ S FM η P s τ ν 0 / h ν 0 Δ f 1 | d Q / d ν | ν 0 .
Δ ν = 1 η P s / h ν 0 Δ f 1 / 2 τ ν 0 d Q d ν ν 0 - 1 .
SNR p = i s t 2 ¯ i sn 2 ¯ +   i b 2 ¯ ,
SNR = | Q | η h ν 0 P s Δ f 1 / 2 ,
Δ V = 2 C | Q | SNR τ ν 0 d Q d ν ν 0 - 1 .

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