Abstract

Simple formulas for the standard deviation that is available from Doppler velocity estimators through the use of direct-detection frequency discriminators for targets spread in range are derived and contrasted with the fundamental limits provided by the Cramer–Rao bounds for both direct-detection and heterodyne systems. The structures of these formulas is sufficiently similar to facilitate a meaningful comparison among the different systems and to provide a basis for the evaluation of experimental performance.

© 1995 Optical Society of America

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References

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  1. D. Rees, I. S. McDermid, “Doppler lidar atmospheric wind sensor: reevaluation of a 355-nm incoherent Doppler lidar,” Appl. Opt. 29, 4133–4144 (1990).
    [CrossRef] [PubMed]
  2. M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
    [CrossRef]
  3. S. H. Bloom, R. Kremer, P. A. Searcy, M. Rivers, J. Menders, E. Korevar, “Long-range, noncoherent laser Doppler velocimeter,” Opt. Lett. 16, 1794–1796 (1991).
    [CrossRef] [PubMed]
  4. 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]
  5. R. T. Menzies, “Doppler lidar atmospheric wind sensors: a comparitive performance evaluation for global measurement applications from Earth orbit,” Appl. Opt. 25, 2546–2553 (1986).
    [CrossRef] [PubMed]
  6. B. J. Rye, “Doppler lidar estimation algorithms,” presented at the Optical Society of America Annual Meeting, Dallas, Tex., 3 October 1994.
  7. B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in Doppler lidar. I: incoherent spectral accumulation and the Cramer–Rao bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
    [CrossRef]
  8. R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar/lidar,” J. Atmos. Ocean. Technol. 11, 1217–1230 (1994).
    [CrossRef]
  9. M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Info. Theory, IT-11, 100–107 (1965).
    [CrossRef]
  10. R. G. Frehlich, “Cramer–Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals,” IEEE Trans. Geosci. Remote Sensing 31, 1123–1131 (1993).
    [CrossRef]
  11. B. J. Rye, R. M. Hardesty, “Cramer–Rao lower bound-limited Doppler estimation using discrimination,” in Proceedings of the Seventh Conference on Coherent Laser Radar Applications and Technology, P. H. Flanant, ed. (Centre National de la Recherche Scientifique, Palaiseau, France, 1990), pp. 217–220.
  12. R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Performance of a 2-μm coherent Doppler lidar for wind measurements,” J. Atmos. Ocean. Technol. 11, 1517–1528 (1994).
    [CrossRef]

1994 (2)

R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar/lidar,” J. Atmos. Ocean. Technol. 11, 1217–1230 (1994).
[CrossRef]

R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Performance of a 2-μm coherent Doppler lidar for wind measurements,” J. Atmos. Ocean. Technol. 11, 1517–1528 (1994).
[CrossRef]

1993 (2)

R. G. Frehlich, “Cramer–Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals,” IEEE Trans. Geosci. Remote Sensing 31, 1123–1131 (1993).
[CrossRef]

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in Doppler lidar. I: incoherent spectral accumulation and the Cramer–Rao bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
[CrossRef]

1992 (1)

1991 (1)

1990 (1)

1989 (1)

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

1986 (1)

1965 (1)

M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Info. Theory, IT-11, 100–107 (1965).
[CrossRef]

Bloom, S. H.

Chanin, M. L.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Frehlich, R. G.

R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar/lidar,” J. Atmos. Ocean. Technol. 11, 1217–1230 (1994).
[CrossRef]

R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Performance of a 2-μm coherent Doppler lidar for wind measurements,” J. Atmos. Ocean. Technol. 11, 1517–1528 (1994).
[CrossRef]

R. G. Frehlich, “Cramer–Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals,” IEEE Trans. Geosci. Remote Sensing 31, 1123–1131 (1993).
[CrossRef]

Garnier, A.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Gentry, B. M.

Hannon, S. M.

R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Performance of a 2-μm coherent Doppler lidar for wind measurements,” J. Atmos. Ocean. Technol. 11, 1517–1528 (1994).
[CrossRef]

Hardesty, R. M.

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in Doppler lidar. I: incoherent spectral accumulation and the Cramer–Rao bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
[CrossRef]

B. J. Rye, R. M. Hardesty, “Cramer–Rao lower bound-limited Doppler estimation using discrimination,” in Proceedings of the Seventh Conference on Coherent Laser Radar Applications and Technology, P. H. Flanant, ed. (Centre National de la Recherche Scientifique, Palaiseau, France, 1990), pp. 217–220.

Hauchecorne, A.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Henderson, S. W.

R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Performance of a 2-μm coherent Doppler lidar for wind measurements,” J. Atmos. Ocean. Technol. 11, 1517–1528 (1994).
[CrossRef]

Korb, C. L.

Korevar, E.

Kremer, R.

Levin, M. J.

M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Info. Theory, IT-11, 100–107 (1965).
[CrossRef]

McDermid, I. S.

Menders, J.

Menzies, R. T.

Porteneuve, J.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Rees, D.

Rivers, M.

Rye, B. J.

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in Doppler lidar. I: incoherent spectral accumulation and the Cramer–Rao bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
[CrossRef]

B. J. Rye, R. M. Hardesty, “Cramer–Rao lower bound-limited Doppler estimation using discrimination,” in Proceedings of the Seventh Conference on Coherent Laser Radar Applications and Technology, P. H. Flanant, ed. (Centre National de la Recherche Scientifique, Palaiseau, France, 1990), pp. 217–220.

B. J. Rye, “Doppler lidar estimation algorithms,” presented at the Optical Society of America Annual Meeting, Dallas, Tex., 3 October 1994.

Searcy, P. A.

Weng, C. Y.

Yadlowsky, M. J.

R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar/lidar,” J. Atmos. Ocean. Technol. 11, 1217–1230 (1994).
[CrossRef]

Appl. Opt. (3)

Geophys. Res. Lett. (1)

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (1)

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in Doppler lidar. I: incoherent spectral accumulation and the Cramer–Rao bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (1)

R. G. Frehlich, “Cramer–Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals,” IEEE Trans. Geosci. Remote Sensing 31, 1123–1131 (1993).
[CrossRef]

IEEE Trans. Info. Theory (1)

M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Info. Theory, IT-11, 100–107 (1965).
[CrossRef]

J. Atmos. Ocean. Technol. (2)

R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Performance of a 2-μm coherent Doppler lidar for wind measurements,” J. Atmos. Ocean. Technol. 11, 1517–1528 (1994).
[CrossRef]

R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar/lidar,” J. Atmos. Ocean. Technol. 11, 1217–1230 (1994).
[CrossRef]

Opt. Lett. (1)

Other (2)

B. J. Rye, R. M. Hardesty, “Cramer–Rao lower bound-limited Doppler estimation using discrimination,” in Proceedings of the Seventh Conference on Coherent Laser Radar Applications and Technology, P. H. Flanant, ed. (Centre National de la Recherche Scientifique, Palaiseau, France, 1990), pp. 217–220.

B. J. Rye, “Doppler lidar estimation algorithms,” presented at the Optical Society of America Annual Meeting, Dallas, Tex., 3 October 1994.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagrams of the transmission profiles for the discriminators considered in the text. (a) the double-edge discriminator, and (b) the separated-channel discriminator with a rectangular profile.

Fig. 2
Fig. 2

Plots of the precision measurements of a separated-channel discriminator. The ordinates show the ratio σchFP [see Eq. (1) and approximation (6)] for equal signal bandwidths F 2 from molecular backscatter and equal detected photocounts (τch = τFP). The absiccas show the window separation F c as a fraction of F 2. The graphs were plotted for a constant value of ΔF/F 2 with β, s ¯ 1 , and s ¯ 2 calculated through the integration of the Gaussian-signal spectrum N(F). The dashed curves indicate Lorentzian windows, and the solid curves, rectangular windows. The windows are not permitted to overlap, so, where F c < ΔF, the lower-frequency limit of the window has been set to 0. Curve (i) shows ΔF/F 2 = 10,000 [equivalent to the result from approximation (6)], curve (ii) shows ΔF/F 2 = 0.1, and curve (iii) shows ΔF/F 2 = 1.

Fig. 3
Fig. 3

Plots of the standard deviations σ of Doppler frequency estimates as functions of the available photocount N pc with the receiver-transmission loss terms τ neglected. Frequency shifts are expressed as radial wind velocities, with F 2 = 1 m/s, F s = 50 m/s (aerosol backscatter), and F 2 = 300 m/s (molecular backscatter).

Equations (6)

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σ FP = λ 2 F 2 ( τ FP N pc ) 1 / 2 ,
σ het λ 2 F 2 ( τ het N pc ) 1 / 2 1 [ g ( α ) ] 1 / 2 , g ( α ) = α - + x 2 exp ( - x 2 ) d x [ 1 + ( 2 π ) 1 / 2 α exp ( - x 2 / 2 ) ] 2 .
σ discr = λ 2 1 β σ ( S ) λ 2 γ β ( N ¯ 1 + N ¯ 2 ) 1 / 2 .
s ¯ = 2 F s F s F N ( F ) d F F s N ( F ) d F = 2 F s F ¯ m * ,
σ de λ 2 γ F s ( 2 τ de N pc ) 1 / 2 .
σ ch λ 2 π 2 F 2 ( τ ch N pc ) 1 / 2 ,

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