Abstract

The equations for performance evaluation of the laser time-of-flight velocimeter (LTV) for atmospheric wind-speed measurement with single-particle digital-correlation analysis have been derived theoretically. Using an inverse power law for aerosol-size distribution and a simple expression for backscatter-differential cross section, the minimum-detectable number of signal photon counts, the photon-count distribution of signal particles, and the scaling law for LTV measurement rate are expressed in terms of correlator settings and parameters of a Gaussian laser beam. It is shown, both theoretically and experimentally, that these equations can be used to evaluate the system performance and assess the potential usefulness of the single-particle LTV.

© 1982 Optical Society of America

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References

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  1. J. W. Bilbro, “Atmospheric laser Doppler velocimetry: an overview,” Opt. Eng. 19, 533–542 (1980).
    [Crossref]
  2. K. G. Bartlett and C. Y. She, “Remote measurement of wind speed using a dual backscatter laser Doppler velocimeter,” Appl. Opt. 15, 1980–1983 (1976).
    [Crossref] [PubMed]
  3. K. G. Bartlett and C. Y. She, “Single-particle correlated time-of-flight velocimeter for remote wind-speed measurement,” Opt. Lett. 1, 175–177 (1977).
    [Crossref] [PubMed]
  4. L. Lading, A. S. Jensen, C. Fog, and H. Andersen, “Time-of-flight laser anemometer for velocity measurements in the atmosphere,” Appl. Opt. 17, 1486–1488 (1978).
    [Crossref]
  5. F. Durst, B. Howe, and G. Richter, “Long range LDA wind velocity measurements using visible laser radiation,” in Proceedings of the Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), Paper 3.
  6. L. Danielsson, “Experiments with laser-fringe velocity measurements over large distances in the atmosphere,” in Proceedings of Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), paper 4.
  7. K. G. Bartlett and C. Y. She, “Single-particle correlation techniques for remote measurement of wind speed: aerosol condition and measurement rate,” J. Opt. Soc. Am. 69, 455–459 (1979).
    [Crossref]
  8. L. Elterman, “Relationships between vertical attenuation and surface meteorological range,” Appl. Opt. 9, 1804–1810 (1970).
    [Crossref] [PubMed]
  9. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 129–139.
  10. A. J. Hughes and E. R. Pike, “Remote measurement of wind speed by laser Doppler systems,” Appl. Opt. 12, 597–601 (1973).
    [Crossref] [PubMed]
  11. W. Wiscombe and A. Mugnai, “Exact calculations of scattering from moderately-nonspherical Tn-particles: comparisons with equivalent spheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 141–152.
    [Crossref]
  12. S. Twomey, Atmospheric Aerosols (Elsevier, Amsterdam, 1977), p. 7.
  13. C. J. Oliver, “Correlation techniques,” in Photon Correlation and Light Beating Spectroscopy, Proceedings of NATO ASI, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1974), pp. 151–223.
  14. C. Y. She, “Individual particle scattering and single-burst digital correlation for remote atmospheric wind measurements,” Opt. Acta 26, 645–657 (1979).
    [Crossref]
  15. E. E. Hindman, R. D. Horn, and W. G. Finnegan, “Generation and characterization of aerosol particles,” in Light Absorption by Aerosol Particles, H. E. Gerber and E. E. Hindman, eds. (Spectrum, Hampton, Va., in press).
  16. C. Y. She, “Photon-burst correlation for detection and speed measurement of individual particles,” in Proceedings of Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), paper 20.
  17. C. L. Pan, J. V. Prodan, W. M. Fairbank, and C. Y. She, “Detection of individual atoms in helium buffer gas and observation of their real-time motion,” Opt. Lett. 5, 459–461 (1980).
    [Crossref] [PubMed]

1980 (2)

1979 (2)

K. G. Bartlett and C. Y. She, “Single-particle correlation techniques for remote measurement of wind speed: aerosol condition and measurement rate,” J. Opt. Soc. Am. 69, 455–459 (1979).
[Crossref]

C. Y. She, “Individual particle scattering and single-burst digital correlation for remote atmospheric wind measurements,” Opt. Acta 26, 645–657 (1979).
[Crossref]

1978 (1)

1977 (1)

1976 (1)

1973 (1)

1970 (1)

Andersen, H.

Bartlett, K. G.

Bilbro, J. W.

J. W. Bilbro, “Atmospheric laser Doppler velocimetry: an overview,” Opt. Eng. 19, 533–542 (1980).
[Crossref]

Danielsson, L.

L. Danielsson, “Experiments with laser-fringe velocity measurements over large distances in the atmosphere,” in Proceedings of Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), paper 4.

Durst, F.

F. Durst, B. Howe, and G. Richter, “Long range LDA wind velocity measurements using visible laser radiation,” in Proceedings of the Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), Paper 3.

Elterman, L.

Fairbank, W. M.

Finnegan, W. G.

E. E. Hindman, R. D. Horn, and W. G. Finnegan, “Generation and characterization of aerosol particles,” in Light Absorption by Aerosol Particles, H. E. Gerber and E. E. Hindman, eds. (Spectrum, Hampton, Va., in press).

Fog, C.

Hindman, E. E.

E. E. Hindman, R. D. Horn, and W. G. Finnegan, “Generation and characterization of aerosol particles,” in Light Absorption by Aerosol Particles, H. E. Gerber and E. E. Hindman, eds. (Spectrum, Hampton, Va., in press).

Horn, R. D.

E. E. Hindman, R. D. Horn, and W. G. Finnegan, “Generation and characterization of aerosol particles,” in Light Absorption by Aerosol Particles, H. E. Gerber and E. E. Hindman, eds. (Spectrum, Hampton, Va., in press).

Howe, B.

F. Durst, B. Howe, and G. Richter, “Long range LDA wind velocity measurements using visible laser radiation,” in Proceedings of the Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), Paper 3.

Hughes, A. J.

Jensen, A. S.

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 129–139.

Lading, L.

Mugnai, A.

W. Wiscombe and A. Mugnai, “Exact calculations of scattering from moderately-nonspherical Tn-particles: comparisons with equivalent spheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 141–152.
[Crossref]

Oliver, C. J.

C. J. Oliver, “Correlation techniques,” in Photon Correlation and Light Beating Spectroscopy, Proceedings of NATO ASI, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1974), pp. 151–223.

Pan, C. L.

Pike, E. R.

Prodan, J. V.

Richter, G.

F. Durst, B. Howe, and G. Richter, “Long range LDA wind velocity measurements using visible laser radiation,” in Proceedings of the Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), Paper 3.

She, C. Y.

Twomey, S.

S. Twomey, Atmospheric Aerosols (Elsevier, Amsterdam, 1977), p. 7.

Wiscombe, W.

W. Wiscombe and A. Mugnai, “Exact calculations of scattering from moderately-nonspherical Tn-particles: comparisons with equivalent spheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 141–152.
[Crossref]

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

C. Y. She, “Individual particle scattering and single-burst digital correlation for remote atmospheric wind measurements,” Opt. Acta 26, 645–657 (1979).
[Crossref]

Opt. Eng. (1)

J. W. Bilbro, “Atmospheric laser Doppler velocimetry: an overview,” Opt. Eng. 19, 533–542 (1980).
[Crossref]

Opt. Lett. (2)

Other (8)

E. E. Hindman, R. D. Horn, and W. G. Finnegan, “Generation and characterization of aerosol particles,” in Light Absorption by Aerosol Particles, H. E. Gerber and E. E. Hindman, eds. (Spectrum, Hampton, Va., in press).

C. Y. She, “Photon-burst correlation for detection and speed measurement of individual particles,” in Proceedings of Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), paper 20.

F. Durst, B. Howe, and G. Richter, “Long range LDA wind velocity measurements using visible laser radiation,” in Proceedings of the Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), Paper 3.

L. Danielsson, “Experiments with laser-fringe velocity measurements over large distances in the atmosphere,” in Proceedings of Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, W. T. Mayo and A. E. Smart, eds. (Joint Institute for Aeronautics and Acoustics, Stanford, Calif., 1980), paper 4.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 129–139.

W. Wiscombe and A. Mugnai, “Exact calculations of scattering from moderately-nonspherical Tn-particles: comparisons with equivalent spheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 141–152.
[Crossref]

S. Twomey, Atmospheric Aerosols (Elsevier, Amsterdam, 1977), p. 7.

C. J. Oliver, “Correlation techniques,” in Photon Correlation and Light Beating Spectroscopy, Proceedings of NATO ASI, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1974), pp. 151–223.

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Figures (5)

Fig. 1
Fig. 1

Experimental arrangement: A, laser and transmitting optics; B, photomultiplier tube and receiving optics; C, digital correlator and computer.

Fig. 2
Fig. 2

Scaling law of the laboratory correlation experiments. The LTV measurement rate F is plotted as a function of experimental parameters, such as laser power P0 and detector range R. The slope of this plot yields the power of the aerosol-size distribution, β = 4.332 ± 0.258.

Fig. 3
Fig. 3

Total average count rate that is due to particle and molecular scattering, d n ¯/dt, is plotted as a function of experimental parameters.

Fig. 4
Fig. 4

Measured photon-count distribution together with a calculated Poisson distribution with measured average of 0.4334 count/sample, τ0 = 135 μsec, and P0 = 1 W. The number of samples with n photon counts, N(n), is plotted versus photon counts n in a sample time τ0. The difference between the measured distribution and the calculated Poisson distribution represents the photon-count distribution of the signal particles.

Fig. 5
Fig. 5

Photon-count distribution N(n) of signal particles obtained from data in Fig. 4 plotted as a function of photon counts per sample n divided by γ, which contains experimental parameters, for nns = 12. ns is the minimum detectable burst count. The slope of the plot yields the power of the aerosol size distribution, β = 4.54 ± 0.35.

Tables (3)

Tables Icon

Table 1 Minimum Signal Count ns and Expected Clip Count Due to Noise En(Tc) for Given Values of Average Count per Sample (d n ¯/dt)τ0

Tables Icon

Table 2 Parameters Associated with the Acceptance Criterion of the Correlation Experiments

Tables Icon

Table 3 Comparison of Total Number of Measurements in Correlation Experiments with Total Number of Signal Particles in Photon-Count Distribution

Equations (17)

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{ 2 P 0 π ρ 2 exp [ - 2 ( x 2 + y 2 ) / ρ 2 ] } σ ( r ) A R 2 ,
n = 2 π σ ( r ) A h ν 1 v η P 0 ρ R 2 exp ( - 2 y 2 / ρ 2 ) ,
d n ¯ d t = η P dc h ν = n l h ν - l / 2 l / 2 - l / 2 l / 2 d x d y × 0 d N d r d r { 2 P 0 π ρ 2 exp [ - 2 ( x 2 + y 2 ) / ρ 2 ] } σ ( r ) A R 2 + d n ¯ r d t = η h ν A R 2 P 0 l 0 σ ( r ) d N d r d r + d n ¯ r d t = 1 η p [ η h ν A R 2 P 0 l 0 σ ( r ) d N d r d r ] ,
n = C - exp [ - 2 ( v t / ρ ) 2 ] d t = C π 2 ρ v ,
C = ( κ + 1 ) τ 0 exp [ ½ ( m - 1 ) 2 ( v τ 0 / ρ ) 2 ] .
n s = π 2 ( κ + 1 ) ( ρ v τ 0 ) exp [ 1 2 ( v τ 0 ρ ) 2 ( m - 1 ) 2 ] .
F = l v - l / 2 l / 2 d y r s d N d r d r .
r s - 2 = γ n s exp ( - 2 y 2 / ρ 2 ) , d n ¯ d t = l c 0 η p ( β - 3 ) 0 β - 3 ( K 0 A h ν η P 0 R 2 ) ,
F v ρ = π ( l c 0 ) ( β - 1 ) 3 / 2 ( γ n s ) ( β - 1 ) / 2 ,
γ ( 2 π K 0 A h ν ) 1 v ( η P 0 ρ R 2 ) .
n = 1 v ( 2 π K 0 A h ν η P 0 ρ R 2 ) r 2 exp ( - 2 y 2 / ρ 2 ) γ r 2 exp ( - 2 y 2 / ρ 2 )
p ( r 2 , y ) = p ( r 2 ) p ( y ) = β - 1 2 0 2 ( r 2 0 2 ) - ( β + 1 ) / 2 ( 1 l ) .
p ( n , y ) = 1 γ l β - 1 2 0 2 ( n 0 2 γ ) - ( β + 1 ) / 2 exp [ - ( β - 1 ) y 2 / ρ 2 ] .
p ( n ) = ρ [ π ( β - 1 ) ] 1 / 2 2 l ( γ 0 2 ) ( β - 1 ) / 2 n - ( β + 1 ) / 2 .
N ( n ) = ( c 0 β - 1 0 - ( β - 1 ) ) ( l l v T p ) p ( n )
N ( n ) = π c 0 l v ρ T p 2 β - 1 γ ( n γ ) - ( β + 1 ) / 2 ,
F = 1 T p n s N ( n ) d n = ( v ρ ) π l c 0 ( β - 1 ) 3 / 2 ( γ n s ) ( β - 1 ) / 2 .