Abstract

A 1.55-µm continuous-wave heterodyne Doppler lidar (HDL) with three receiver–detector units is used to validate experimentally the findings presented in the Guérit et al. companion paper [Appl. Opt. 41, 2232 (2002)] on the effectiveness of independent realizations to improve HDL performance (velocity or power estimates or both) at a low carrier-to-noise ratio (CNR). In fact, noise has a detrimental effect on the accumulation techniques, so in the Guérit et al. companion paper, the chances of getting “heavy” speckles in HDL signals from many receiver–detector units on a single- or several-shot basis are investigated theoretically and numerically with the Zrnic HDL model. The experimental results enable us to conclude there is a very good agreement (better than 95%) between the performance computed from actual HDL data and from the theoretical predictions.

© 2002 Optical Society of America

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References

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  1. G. Guérit, P. Drobinski, P. H. Flamant, J. P. Cariou, “Effectiveness of simultaneous independent realizations at low carrier-to-noise ratio to improve heterodyne Doppler lidar performance. Part I. Theory and numerical simulations,” Appl. Opt. 41, 2232–2239 (2002).
    [CrossRef] [PubMed]
  2. B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31, 16–27 (1993).
    [CrossRef]
  3. X. Favreau, A. Delaval, P. H. Flamant, A. Dabas, P. Delville, “Four-element receiver for pulsed 10-µm heterodyne Doppler lidar,” Appl. Opt. 39, 2441–2448 (2000).
    [CrossRef]
  4. D. S. Zrnic, “Simulation of weatherlike Doppler spectra and signals,” J. Appl. Meteorol. 14, 619–620 (1975).
    [CrossRef]
  5. B. J. Rye, R. M. Hardesty, “Detection techniques for validating Doppler estimates in heterodyne lidar,” Appl. Opt. 36, 1940–1951 (1997).
    [CrossRef] [PubMed]
  6. R. Frehlich, S. M. Hannon, S. W. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
    [CrossRef] [PubMed]
  7. R. G. Frehlich, M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Oceanic Technol. 11, 1217–1230 (1994).
    [CrossRef]
  8. J. W. Goodman, “Statistical properties of laser speckle patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Topics in Applied Physics Series, (Springer-Verlag, Berlin, 1975), pp. 51–58.
  9. G. M. Ancellet, R. T. Menzies, “Atmospheric correlation-time measurements and effects on coherent Doppler lidar,” J. Opt. Soc. Am. A 4, 367–373 (1987).
    [CrossRef]
  10. R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, “Characteristics of coherent lidar returns from calibration targets and aerosols,” Appl. Opt. 20, 3763–3769 (1981).
    [CrossRef] [PubMed]
  11. J. Y. Wang, “Lidar signal fluctuations caused by beam translation and scan,” Appl. Opt. 25, 2878–2885 (1986).
    [CrossRef] [PubMed]

2002 (1)

2000 (1)

1997 (2)

1994 (1)

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

1993 (1)

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

1987 (1)

1986 (1)

1981 (1)

1975 (1)

D. S. Zrnic, “Simulation of weatherlike Doppler spectra and signals,” J. Appl. Meteorol. 14, 619–620 (1975).
[CrossRef]

Ancellet, G. M.

Cariou, J. P.

Dabas, A.

Delaval, A.

Delville, P.

Drobinski, P.

Favreau, X.

Flamant, P. H.

Frehlich, R.

Frehlich, R. G.

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

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Topics in Applied Physics Series, (Springer-Verlag, Berlin, 1975), pp. 51–58.

Guérit, G.

Hannon, S. M.

Hardesty, R. M.

Henderson, S. W.

Keeler, R. J.

Menzies, R. T.

Post, M. J.

Richter, R. A.

Rye, B. J.

B. J. Rye, R. M. Hardesty, “Detection techniques for validating Doppler estimates in heterodyne lidar,” Appl. Opt. 36, 1940–1951 (1997).
[CrossRef] [PubMed]

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

Wang, J. Y.

Yadlowsky, M. J.

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

Zrnic, D. S.

D. S. Zrnic, “Simulation of weatherlike Doppler spectra and signals,” J. Appl. Meteorol. 14, 619–620 (1975).
[CrossRef]

Appl. Opt. (6)

IEEE Trans. Geosci. Remote Sens. (1)

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

J. Appl. Meteorol. (1)

D. S. Zrnic, “Simulation of weatherlike Doppler spectra and signals,” J. Appl. Meteorol. 14, 619–620 (1975).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

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

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

Other (1)

J. W. Goodman, “Statistical properties of laser speckle patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Topics in Applied Physics Series, (Springer-Verlag, Berlin, 1975), pp. 51–58.

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Figures (7)

Fig. 1
Fig. 1

Schematic of a one-to-many HDL [one transmitter to many (r) receivers].

Fig. 2
Fig. 2

Experimental setup. (a) 1.55-µm cw multireceiver HDL. (b) Receiving bloc made of three receiver–detector units [zoom of dashed box in (a).

Fig. 3
Fig. 3

Examples of signals and associated spectra, respectively, for various CNR values: (a) and (b) CNR = -5 dB, (c) and (d) CNR = -1 dB, (e) and (f) CNR = 11 dB.

Fig. 4
Fig. 4

Log–log plots of the number of speckle cells M in the atmospheric return as a function of the range gate ΔT = NT s for (a) CNR = -5 dB, (b) CNR = -1 dB, (c) CNR = 11 dB. The estimates of M as well as the experimental uncertainties are represented by error bars. The solid curves represent the fit between M 2 and ΔT 2. This leads to an approximate relation M1+ΔT2/τc2. The corresponding correlation time τ c and mean regression error Δ M are indicated.

Fig. 5
Fig. 5

Examples of simultaneous HDL signals from the three detectors for CNR = 11 dB.

Fig. 6
Fig. 6

Experimental results for CNR = -5 dB (the HDL spectral width w s = 0.002 × F s , i.e., 40 kHz) and probability of false alarm P FA = 1%: (a) threshold value T th (solid curve) and parameter Ω (dashed curve) as a function of Φ = N ×CNR, (b) probabilities X r ≥1, (c) X r ≥2 and (d) X 3 ≥3 as functions of Φ = N × CNR. Circles, case r = 1; squares, r = 2; triangles, r = 3. The probabilities are compared with those computed numerically from Zrnic synthetic HDL signals with similar characteristics when (q; r) = (1; 1) (solid curve) and by use of Eq. (2) when r ≠ 1 (dashed curves).

Fig. 7
Fig. 7

Same as Fig. 6 for CNR = -1 dB.

Tables (2)

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Table 1 Correlation Coefficients Cij between Two Simultaneous HDL Signals (s i , s j ) Delivered by the Three Receivers for Various CNRs, Estimated on 400 Shots a

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Table 2 Probability Xr q Computed from the Actual HDL Dataa

Equations (4)

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lnΛx, ΨN, Ψs=ni=1NxiΨN-ni=1NxiΨfi-ni=1NlnΨfiΨN,
Xrq=r!q!r-q!Xq1-Xr-q  binomial law, Xrq=k=qrXrk.
=p¯2/σpˆ2.
1=1MCNR1+CNR2+1N1-CNR1+CNR2,

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