Abstract

It is shown that the performance of heterodyne Doppler lidar (HDL) can be improved by (i) at least one good realization for every single shot or (ii) several simultaneous good realizations for accumulation. Until now, several simultaneous independent realizations at high carrier-to-noise ratio (CNR) have been considered. At low CNR, noise may have a detrimental effect on the accumulation techniques. We determine the chances of getting “heavy” speckles in HDL signals from many receiver-detector units on a single-shot basis and several good realizations on a single-shot basis, which is required for an effective accumulation. The use of multiple receiver-detector units at low CNR is worthwhile in contexts such as space lidar, where optimized treatment is at a premium. We conclude on the effectiveness of many receiver-detector units in parallel in order to achieve simultaneous independent realizations at low CNR to improve the performance of HDL on a statistical basis.

© 2002 Optical Society of America

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References

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  1. R. M. Hardesty, “Measurement of range-resolved water-vapor concentration by coherent CO2 differential absorption,” NOAA Tech. Memo. ERL WPL- 118 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1984), pp. 45–47.
  2. W. A. Brewer, V. Wulfmeyer, R. M. Hardesty, B. J. Rye, “Combined wind and water-vapor measurements using the NOAA mini-MOPA Doppler lidar”, in Proceedings of the Nineteenth International Laser Radar Conference, 6–10 July 1998, Annapolis, Md., U. N. Singh, S. Ismail, G. K. Schwemmer, eds. (National Aeronautics and Space Administration, Washington D.C., 1998), pp. 565–568.
  3. P. Drobinski, R. A. Brown, P. H. Flamant, J. Pelon, “Evidence of organised large eddies by ground-based Doppler lidar, sonic anemometer and sodar,” Boundary-Layer Meteorol. 88, 343–361 (1998).
    [CrossRef]
  4. P. Drobinski, A. M. Dabas, C. Haeberli, P. H. Flamant, “On the small-scale dynamics of flow splitting in the Rhine valley during a shallow foehn event,” Boundary-Layer Meteorol. 99, 277–296 (2001).
    [CrossRef]
  5. D. Fink, S. N. Vodopia, “Coherent detection SNR of an array of detectors,” Appl. Opt. 15, 453–454 (1976).
    [CrossRef] [PubMed]
  6. K. P. Chan, D. K. Killinger, “Coherent summation of spatially distorted laser Doppler signals by using a two dimensional heterodyne detector array,” Opt. Lett. 17, 1237–1239 (1992).
    [CrossRef] [PubMed]
  7. 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]
  8. P. Gatt, T. P. Costello, D. A. Heimermann, D. C. Castellanos, A. R. Weeks, M. Stickley, “Coherent optical array receivers for the mitigation of atmospheric turbulence and speckle effects,” Appl. Opt. 35, 5999–6009 (1996).
    [CrossRef] [PubMed]
  9. P. Drobinski, P. H. Flamant, P. Salamitou, “Spectral diversity technique for heterodyne Doppler lidar that uses hard target returns,” Appl. Opt. 39, 376–385 (2000).
    [CrossRef]
  10. A. M. Dabas, P. H. Flamant, P. Salamitou, “Characterization of pulsed coherent Doppler lidar with the speckle effect,” Appl. Opt. 33, 6524–6532 (1994).
    [CrossRef] [PubMed]
  11. P. Drobinski, A. M. Dabas, P. Delville, P. H. Flamant, J. Pelon, R. M. Hardesty, “Refractive index structure parameter in the planetary boundary layer: a comparison of measurements taken by a 10.6-µm coherent lidar, a 0.9-µm scintillometer and in-situ sensors,” Appl. Opt. 38, 1648–1656 (1999).
    [CrossRef]
  12. G. Guérit, P. Drobinski, P. H. Flamant, B. Augère, “Analytical expressions of the transverse coherence properties for monostatic and bistatic lidar in presence of moderate atmospheric refractive index turbulence,” Appl. Opt. 40, 4275–4285 (2001).
    [CrossRef]
  13. 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]
  14. B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II. correlogram accumulation,” IEEE Trans. Geosci. Remote Sens. 31, 28–35 (1993).
    [CrossRef]
  15. R. G. 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]
  16. A. M. Dabas, “Semiempirical model for the reliability of a matched filter frequency estimator for Doppler lidar,” J. Atmos. Ocean Techol. 16, 19–28 (1999).
    [CrossRef]
  17. B. J. Rye, R. M. Hardesty, “Detection techniques for validating Doppler estimates in heterodyne lidar,” Appl. Opt. 36, 1940–1951 (1997).
    [CrossRef] [PubMed]
  18. J. W. Goodman, “Statistical properties of laser speckles patterns,” in Laser Speckles and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1984), pp. 51–58.
  19. J. H. Churnside, H. T. Yura, “Speckle statistics of atmospherically backscattered laser light,” Appl. Opt. 22, 2559–2565 (1983).
    [CrossRef] [PubMed]
  20. D. S. Zrnic, “Simulation of weatherlike Doppler spectra and signals,” J. Appl. Meteor. 14, 619–620 (1975).
    [CrossRef]
  21. 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]
  22. M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Inf. Theory 11, 100–107 (1968).
    [CrossRef]
  23. A. M. Dabas, P. Drobinski, P. H. Flamant, “Adaptative filters for frequency estimates of heterodyne Doppler lidar returns: recursive implementation and quality control,” J. Atmos. Oceanic Technol. 16, 361–372 (1999).
    [CrossRef]

2001 (2)

P. Drobinski, A. M. Dabas, C. Haeberli, P. H. Flamant, “On the small-scale dynamics of flow splitting in the Rhine valley during a shallow foehn event,” Boundary-Layer Meteorol. 99, 277–296 (2001).
[CrossRef]

G. Guérit, P. Drobinski, P. H. Flamant, B. Augère, “Analytical expressions of the transverse coherence properties for monostatic and bistatic lidar in presence of moderate atmospheric refractive index turbulence,” Appl. Opt. 40, 4275–4285 (2001).
[CrossRef]

2000 (2)

1999 (3)

P. Drobinski, A. M. Dabas, P. Delville, P. H. Flamant, J. Pelon, R. M. Hardesty, “Refractive index structure parameter in the planetary boundary layer: a comparison of measurements taken by a 10.6-µm coherent lidar, a 0.9-µm scintillometer and in-situ sensors,” Appl. Opt. 38, 1648–1656 (1999).
[CrossRef]

A. M. Dabas, “Semiempirical model for the reliability of a matched filter frequency estimator for Doppler lidar,” J. Atmos. Ocean Techol. 16, 19–28 (1999).
[CrossRef]

A. M. Dabas, P. Drobinski, P. H. Flamant, “Adaptative filters for frequency estimates of heterodyne Doppler lidar returns: recursive implementation and quality control,” J. Atmos. Oceanic Technol. 16, 361–372 (1999).
[CrossRef]

1998 (1)

P. Drobinski, R. A. Brown, P. H. Flamant, J. Pelon, “Evidence of organised large eddies by ground-based Doppler lidar, sonic anemometer and sodar,” Boundary-Layer Meteorol. 88, 343–361 (1998).
[CrossRef]

1997 (2)

1996 (1)

1994 (2)

A. M. Dabas, P. H. Flamant, P. Salamitou, “Characterization of pulsed coherent Doppler lidar with the speckle effect,” Appl. Opt. 33, 6524–6532 (1994).
[CrossRef] [PubMed]

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 (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]

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II. correlogram accumulation,” IEEE Trans. Geosci. Remote Sens. 31, 28–35 (1993).
[CrossRef]

1992 (1)

1983 (1)

1976 (1)

1975 (1)

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

1968 (1)

M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Inf. Theory 11, 100–107 (1968).
[CrossRef]

Augère, B.

Brewer, W. A.

W. A. Brewer, V. Wulfmeyer, R. M. Hardesty, B. J. Rye, “Combined wind and water-vapor measurements using the NOAA mini-MOPA Doppler lidar”, in Proceedings of the Nineteenth International Laser Radar Conference, 6–10 July 1998, Annapolis, Md., U. N. Singh, S. Ismail, G. K. Schwemmer, eds. (National Aeronautics and Space Administration, Washington D.C., 1998), pp. 565–568.

Brown, R. A.

P. Drobinski, R. A. Brown, P. H. Flamant, J. Pelon, “Evidence of organised large eddies by ground-based Doppler lidar, sonic anemometer and sodar,” Boundary-Layer Meteorol. 88, 343–361 (1998).
[CrossRef]

Castellanos, D. C.

Chan, K. P.

Churnside, J. H.

Costello, T. P.

Dabas, A.

Dabas, A. M.

P. Drobinski, A. M. Dabas, C. Haeberli, P. H. Flamant, “On the small-scale dynamics of flow splitting in the Rhine valley during a shallow foehn event,” Boundary-Layer Meteorol. 99, 277–296 (2001).
[CrossRef]

A. M. Dabas, P. Drobinski, P. H. Flamant, “Adaptative filters for frequency estimates of heterodyne Doppler lidar returns: recursive implementation and quality control,” J. Atmos. Oceanic Technol. 16, 361–372 (1999).
[CrossRef]

P. Drobinski, A. M. Dabas, P. Delville, P. H. Flamant, J. Pelon, R. M. Hardesty, “Refractive index structure parameter in the planetary boundary layer: a comparison of measurements taken by a 10.6-µm coherent lidar, a 0.9-µm scintillometer and in-situ sensors,” Appl. Opt. 38, 1648–1656 (1999).
[CrossRef]

A. M. Dabas, “Semiempirical model for the reliability of a matched filter frequency estimator for Doppler lidar,” J. Atmos. Ocean Techol. 16, 19–28 (1999).
[CrossRef]

A. M. Dabas, P. H. Flamant, P. Salamitou, “Characterization of pulsed coherent Doppler lidar with the speckle effect,” Appl. Opt. 33, 6524–6532 (1994).
[CrossRef] [PubMed]

Delaval, A.

Delville, P.

Drobinski, P.

P. Drobinski, A. M. Dabas, C. Haeberli, P. H. Flamant, “On the small-scale dynamics of flow splitting in the Rhine valley during a shallow foehn event,” Boundary-Layer Meteorol. 99, 277–296 (2001).
[CrossRef]

G. Guérit, P. Drobinski, P. H. Flamant, B. Augère, “Analytical expressions of the transverse coherence properties for monostatic and bistatic lidar in presence of moderate atmospheric refractive index turbulence,” Appl. Opt. 40, 4275–4285 (2001).
[CrossRef]

P. Drobinski, P. H. Flamant, P. Salamitou, “Spectral diversity technique for heterodyne Doppler lidar that uses hard target returns,” Appl. Opt. 39, 376–385 (2000).
[CrossRef]

A. M. Dabas, P. Drobinski, P. H. Flamant, “Adaptative filters for frequency estimates of heterodyne Doppler lidar returns: recursive implementation and quality control,” J. Atmos. Oceanic Technol. 16, 361–372 (1999).
[CrossRef]

P. Drobinski, A. M. Dabas, P. Delville, P. H. Flamant, J. Pelon, R. M. Hardesty, “Refractive index structure parameter in the planetary boundary layer: a comparison of measurements taken by a 10.6-µm coherent lidar, a 0.9-µm scintillometer and in-situ sensors,” Appl. Opt. 38, 1648–1656 (1999).
[CrossRef]

P. Drobinski, R. A. Brown, P. H. Flamant, J. Pelon, “Evidence of organised large eddies by ground-based Doppler lidar, sonic anemometer and sodar,” Boundary-Layer Meteorol. 88, 343–361 (1998).
[CrossRef]

Favreau, X.

Fink, D.

Flamant, P. H.

G. Guérit, P. Drobinski, P. H. Flamant, B. Augère, “Analytical expressions of the transverse coherence properties for monostatic and bistatic lidar in presence of moderate atmospheric refractive index turbulence,” Appl. Opt. 40, 4275–4285 (2001).
[CrossRef]

P. Drobinski, A. M. Dabas, C. Haeberli, P. H. Flamant, “On the small-scale dynamics of flow splitting in the Rhine valley during a shallow foehn event,” Boundary-Layer Meteorol. 99, 277–296 (2001).
[CrossRef]

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]

P. Drobinski, P. H. Flamant, P. Salamitou, “Spectral diversity technique for heterodyne Doppler lidar that uses hard target returns,” Appl. Opt. 39, 376–385 (2000).
[CrossRef]

P. Drobinski, A. M. Dabas, P. Delville, P. H. Flamant, J. Pelon, R. M. Hardesty, “Refractive index structure parameter in the planetary boundary layer: a comparison of measurements taken by a 10.6-µm coherent lidar, a 0.9-µm scintillometer and in-situ sensors,” Appl. Opt. 38, 1648–1656 (1999).
[CrossRef]

A. M. Dabas, P. Drobinski, P. H. Flamant, “Adaptative filters for frequency estimates of heterodyne Doppler lidar returns: recursive implementation and quality control,” J. Atmos. Oceanic Technol. 16, 361–372 (1999).
[CrossRef]

P. Drobinski, R. A. Brown, P. H. Flamant, J. Pelon, “Evidence of organised large eddies by ground-based Doppler lidar, sonic anemometer and sodar,” Boundary-Layer Meteorol. 88, 343–361 (1998).
[CrossRef]

A. M. Dabas, P. H. Flamant, P. Salamitou, “Characterization of pulsed coherent Doppler lidar with the speckle effect,” Appl. Opt. 33, 6524–6532 (1994).
[CrossRef] [PubMed]

Frehlich, R. G.

R. G. 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]

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]

Gatt, P.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckles patterns,” in Laser Speckles and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1984), pp. 51–58.

Guérit, G.

Haeberli, C.

P. Drobinski, A. M. Dabas, C. Haeberli, P. H. Flamant, “On the small-scale dynamics of flow splitting in the Rhine valley during a shallow foehn event,” Boundary-Layer Meteorol. 99, 277–296 (2001).
[CrossRef]

Hannon, S. M.

Hardesty, R. M.

P. Drobinski, A. M. Dabas, P. Delville, P. H. Flamant, J. Pelon, R. M. Hardesty, “Refractive index structure parameter in the planetary boundary layer: a comparison of measurements taken by a 10.6-µm coherent lidar, a 0.9-µm scintillometer and in-situ sensors,” Appl. Opt. 38, 1648–1656 (1999).
[CrossRef]

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. II. correlogram accumulation,” IEEE Trans. Geosci. Remote Sens. 31, 28–35 (1993).
[CrossRef]

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]

W. A. Brewer, V. Wulfmeyer, R. M. Hardesty, B. J. Rye, “Combined wind and water-vapor measurements using the NOAA mini-MOPA Doppler lidar”, in Proceedings of the Nineteenth International Laser Radar Conference, 6–10 July 1998, Annapolis, Md., U. N. Singh, S. Ismail, G. K. Schwemmer, eds. (National Aeronautics and Space Administration, Washington D.C., 1998), pp. 565–568.

R. M. Hardesty, “Measurement of range-resolved water-vapor concentration by coherent CO2 differential absorption,” NOAA Tech. Memo. ERL WPL- 118 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1984), pp. 45–47.

Heimermann, D. A.

Henderson, S. W.

Killinger, D. K.

Levin, M. J.

M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Inf. Theory 11, 100–107 (1968).
[CrossRef]

Pelon, J.

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. II. correlogram accumulation,” IEEE Trans. Geosci. Remote Sens. 31, 28–35 (1993).
[CrossRef]

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]

W. A. Brewer, V. Wulfmeyer, R. M. Hardesty, B. J. Rye, “Combined wind and water-vapor measurements using the NOAA mini-MOPA Doppler lidar”, in Proceedings of the Nineteenth International Laser Radar Conference, 6–10 July 1998, Annapolis, Md., U. N. Singh, S. Ismail, G. K. Schwemmer, eds. (National Aeronautics and Space Administration, Washington D.C., 1998), pp. 565–568.

Salamitou, P.

Stickley, M.

Vodopia, S. N.

Weeks, A. R.

Wulfmeyer, V.

W. A. Brewer, V. Wulfmeyer, R. M. Hardesty, B. J. Rye, “Combined wind and water-vapor measurements using the NOAA mini-MOPA Doppler lidar”, in Proceedings of the Nineteenth International Laser Radar Conference, 6–10 July 1998, Annapolis, Md., U. N. Singh, S. Ismail, G. K. Schwemmer, eds. (National Aeronautics and Space Administration, Washington D.C., 1998), pp. 565–568.

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]

Yura, H. T.

Zrnic, D. S.

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

Appl. Opt. (10)

D. Fink, S. N. Vodopia, “Coherent detection SNR of an array of detectors,” Appl. Opt. 15, 453–454 (1976).
[CrossRef] [PubMed]

J. H. Churnside, H. T. Yura, “Speckle statistics of atmospherically backscattered laser light,” Appl. Opt. 22, 2559–2565 (1983).
[CrossRef] [PubMed]

A. M. Dabas, P. H. Flamant, P. Salamitou, “Characterization of pulsed coherent Doppler lidar with the speckle effect,” Appl. Opt. 33, 6524–6532 (1994).
[CrossRef] [PubMed]

R. G. 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]

P. Drobinski, P. H. Flamant, P. Salamitou, “Spectral diversity technique for heterodyne Doppler lidar that uses hard target returns,” Appl. Opt. 39, 376–385 (2000).
[CrossRef]

P. Gatt, T. P. Costello, D. A. Heimermann, D. C. Castellanos, A. R. Weeks, M. Stickley, “Coherent optical array receivers for the mitigation of atmospheric turbulence and speckle effects,” Appl. Opt. 35, 5999–6009 (1996).
[CrossRef] [PubMed]

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

P. Drobinski, A. M. Dabas, P. Delville, P. H. Flamant, J. Pelon, R. M. Hardesty, “Refractive index structure parameter in the planetary boundary layer: a comparison of measurements taken by a 10.6-µm coherent lidar, a 0.9-µm scintillometer and in-situ sensors,” Appl. Opt. 38, 1648–1656 (1999).
[CrossRef]

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]

G. Guérit, P. Drobinski, P. H. Flamant, B. Augère, “Analytical expressions of the transverse coherence properties for monostatic and bistatic lidar in presence of moderate atmospheric refractive index turbulence,” Appl. Opt. 40, 4275–4285 (2001).
[CrossRef]

Boundary-Layer Meteorol. (2)

P. Drobinski, R. A. Brown, P. H. Flamant, J. Pelon, “Evidence of organised large eddies by ground-based Doppler lidar, sonic anemometer and sodar,” Boundary-Layer Meteorol. 88, 343–361 (1998).
[CrossRef]

P. Drobinski, A. M. Dabas, C. Haeberli, P. H. Flamant, “On the small-scale dynamics of flow splitting in the Rhine valley during a shallow foehn event,” Boundary-Layer Meteorol. 99, 277–296 (2001).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (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]

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II. correlogram accumulation,” IEEE Trans. Geosci. Remote Sens. 31, 28–35 (1993).
[CrossRef]

IEEE Trans. Inf. Theory (1)

M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Inf. Theory 11, 100–107 (1968).
[CrossRef]

J. Appl. Meteor. (1)

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

J. Atmos. Ocean Techol. (1)

A. M. Dabas, “Semiempirical model for the reliability of a matched filter frequency estimator for Doppler lidar,” J. Atmos. Ocean Techol. 16, 19–28 (1999).
[CrossRef]

J. Atmos. Oceanic Technol. (2)

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]

A. M. Dabas, P. Drobinski, P. H. Flamant, “Adaptative filters for frequency estimates of heterodyne Doppler lidar returns: recursive implementation and quality control,” J. Atmos. Oceanic Technol. 16, 361–372 (1999).
[CrossRef]

Opt. Lett. (1)

Other (3)

R. M. Hardesty, “Measurement of range-resolved water-vapor concentration by coherent CO2 differential absorption,” NOAA Tech. Memo. ERL WPL- 118 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1984), pp. 45–47.

W. A. Brewer, V. Wulfmeyer, R. M. Hardesty, B. J. Rye, “Combined wind and water-vapor measurements using the NOAA mini-MOPA Doppler lidar”, in Proceedings of the Nineteenth International Laser Radar Conference, 6–10 July 1998, Annapolis, Md., U. N. Singh, S. Ismail, G. K. Schwemmer, eds. (National Aeronautics and Space Administration, Washington D.C., 1998), pp. 565–568.

J. W. Goodman, “Statistical properties of laser speckles patterns,” in Laser Speckles and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1984), pp. 51–58.

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Figures (9)

Fig. 1
Fig. 1

Scheme of a one-transmitter-to-one-receiver HDL (panel A) and a scheme of a one-transmitter-to-many receivers HDL (panel B).

Fig. 2
Fig. 2

Number M of speckles computed from Zrnic HDL signals (dots) as a function of Ω = Nw s T s , where w s ranges between 0.001 F s and 0.1 F s and N ranges between 5 and 500. The solid line corresponds to Eq. (6).

Fig. 3
Fig. 3

Scatterplot of log-likelihood difference (T) versus frequency estimate of the atmospheric echo for Zrnic HDL signal [f s = 0, Ω = 0.64 (w s = 0.02 F s , N = 32), Φ = 10 (N = 32, CNR = -5 dB)] with a perfectly matched filter.

Fig. 4
Fig. 4

Threshold value T th as a function of Φ = N × CNR for various values of Ω and for a probability of false-alarm P FA = 1%.

Fig. 5
Fig. 5

Performance of the statistical test as a function of Φ for a perfectly matched filter and a probability of false-alarm P FA = 1%. They correspond to 5000 simulated HDL signals. Panels A and C correspond to Ω = 0.64 (i.e., N = 32 and w s = 0.02 F s ); panels B and D correspond to Ω = 3.20 (i.e., N = 32 and w s = 0.1 F s ). Panels A and B indicate good-detection (i.e., validation of good measurements) probability. Panels C and D indicate validation rate (number of validated measurements over total number, dotted line) and reliability before (solid line) and after (dashed line) quality control.

Fig. 6
Fig. 6

Probability of good detection as a function of Φ for P FA = 1% and Ω = 0.64 (solid line) and Ω = 3.20 (dashed line). Panel B is a zoom of the two curves with x axis ranging between Φ = 10 and Φ = 100 and y axis ranging between 90% and 100%.

Fig. 7
Fig. 7

PDFs of the noise power (dashed line) and the HDL signal power (solid line) as a function of p/〈p〉 for (Φ; Ω) = (35; 0.07) (i.e., for N = 70, w s = 0.001 F s , and CNR = 3 dB) (panel A); (Φ; Ω) = (35; 2.81) (i.e., for N = 70, w s = 0.04 F s , and CNR = 3 dB) (panel B); (Φ; Ω) = (14; 0.07) (i.e., for N = 70, w s = 0.001 F s and CNR = -7 dB) (panel C); (Φ; Ω) = (14; 2.81) (i.e., for N = 70, w s = 0.04 F s , and CNR = -7 dB) (panel D).

Fig. 8
Fig. 8

Probability Xrq of good detection of the atmospheric echo as a function of Φ for different values of (q; r), for P FA = 1% and Ω = 0.64. Panels A, B, and C correspond to q = 1, 2 and 5, respectively.

Fig. 9
Fig. 9

Same as Fig. 8 for Ω = 3.20.

Equations (23)

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Xrq=qrXq1-Xr-q.
Xrq=k=qrkrXk1-Xr-k.
probp= pp-1Γexp-pp,
1=1MCNR1+CNR2+1N1-CNR1+CNR2,
M=N2j=1Nk=1N |γj-k|2-1.
MΩ=1+4πΩ21/2.
lnΛx, ΨN, Ψs=ni=1NxiΨNΨsfiΨfi-lnΨfiΨN,
lnΛx, ΨN, Ψs=ni=1NxiΨN-ni=1NxiΨfiT -ni=1NlnΨfiΨN.
0ΔPFAprobΔδdδ=PFA,
pˆ=1Nk=1N sk*sk.
=p¯2/σP2,
σpˆ2=1N2k=1Nm=1N Esk*sksm*sm-1N2k=1N Esk*sk2,
Esk*sksm*sm= Esk*skEsm*sm+ Esk*sm*Esksm+ Esk*smEsksm*- 2Esk*EskEsm* Esm.
Esk*sm=p¯γ m-k,
Esk= Esk*= Esm=Esm*-0,
Esksm=Esk*sm*=0.
σpˆ2=p¯2N2k=1Nm=1N|γk-m|2,
=N2k=1Nm=1N |γk-m|2-1.
|γk-m|2=α2|gk-m|2+1-α2δk-m+2α1-αg0δk-m,
α=CNR1+CNR.
|γk-m|2=α2gk-m|2+1-α2δk-m.
1=1MCNR1+CNR2+1N1-CNR1+CNR2,
M=N2k=1Nm=1N |gk-m|2-1

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