Abstract

The effect of random and deterministic pulse-shape uncertainties on the accuracy of the Fourier deconvolution algorithm for improving the resolution of long-pulse lidars is investigated theoretically and by computer simulations. Various cases of pulse uncertainties are considered including those that are typical of Doppler lidars. It is shown that the retrieval error is a consequence of two main effects. The first effect consists of a shift up or down (depending on the sign of the uncertainty integral area) of the lidar profile as a whole, proportionally to the ratio of the pulse uncertainty area to the true pulse area. The second effect consists of additional amplitude and phase distortions of the spectrum of the small-scale inhomogeneities of the lidar profile. The results obtained allow us to predict the order and the character of the possible distortions and to choose ways to reduce or prevent them.

© 1995 Optical Society of America

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  1. J. Gilbert, J. L. Lachambre, F. Rheault, R. Fortin, “Dynamics of the CO2atmospheric pressure laser with transverse pulse excitation,” Can. J. Phys. 50, 2523–2535 (1972).
    [CrossRef]
  2. M. R. Haris, D. V. Willetts, “Performance characteristics of a TE CO2laser with a long excitation pulse,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 5–7.
  3. R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, New York, 1984).
  4. P. W. Baker, “Atmospheric water vapor differential absorption measurements on vertical paths with a CO2lidar,” Appl. Opt. 22, 2257–2264 (1983).
    [CrossRef] [PubMed]
  5. M. J. Kavaya, R. T. Menzies, “Lidar aerosol backscattering measurements: systematic, modeling, and calibration error considerations,” Appl. Opt. 24, 3444–3453 (1985).
    [CrossRef] [PubMed]
  6. Y. Zhao, T. K. Lea, R. M. Schotland, “Correction function in the lidar equation and some techniques for incoherent CO2lidar data reduction,” Appl. Opt. 27, 2730–2740 (1988).
    [CrossRef] [PubMed]
  7. Y. Zhao, R. M. Hardesty, “Technique for correcting effects of long CO2laser pulses in aerosol-backscattered coherent lidar returns,” Appl. Opt. 27, 2719–2729 (1988).
    [CrossRef] [PubMed]
  8. L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Deconvolution techniques for improving the resolution of long-pulse lidars,” J. Opt. Soc. Am. A 10, 2296–2306 (1993).
    [CrossRef]
  9. L. L. Gurdev, D. V. Stoyanov, T. N. Dreischuh, “Inverse algorithm for increasing the resolution of pulsed lidars,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 284–287.
  10. T. N. Dreischuh, D. V. Stoyanov, L. L. Gurdev, “Statistical characteristics of Fourier-deconvolved NOAA 10.6-μm ground-based lidar data,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.
  11. D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.
  12. T. N. Dreischuh, L. L. Gurdev, D. V. Stoyanov, “Influence of the pulse-shape uncertainty on the accuracy of the inverse techniques for improving the resolution of long-pulse lidars,” in Optics as a Key to High Technology: 16th Congress of the International Commission for Optics, Gy. Akos, T. Lippeny, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 1060–1061 (1993).
  13. Ch. Werner, G. Wildgruber, J. Streicher, Representativity of Wind Measurement from Space, Final Report, European Space Agency Contract No. 8664/90/HGE-I (German Aerospace Research Establishment, Munich, 1991).

1993 (1)

1988 (2)

1985 (1)

1983 (1)

1972 (1)

J. Gilbert, J. L. Lachambre, F. Rheault, R. Fortin, “Dynamics of the CO2atmospheric pressure laser with transverse pulse excitation,” Can. J. Phys. 50, 2523–2535 (1972).
[CrossRef]

Baker, P. W.

Dreischuh, T.

D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

Dreischuh, T. N.

L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Deconvolution techniques for improving the resolution of long-pulse lidars,” J. Opt. Soc. Am. A 10, 2296–2306 (1993).
[CrossRef]

T. N. Dreischuh, L. L. Gurdev, D. V. Stoyanov, “Influence of the pulse-shape uncertainty on the accuracy of the inverse techniques for improving the resolution of long-pulse lidars,” in Optics as a Key to High Technology: 16th Congress of the International Commission for Optics, Gy. Akos, T. Lippeny, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 1060–1061 (1993).

T. N. Dreischuh, D. V. Stoyanov, L. L. Gurdev, “Statistical characteristics of Fourier-deconvolved NOAA 10.6-μm ground-based lidar data,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

L. L. Gurdev, D. V. Stoyanov, T. N. Dreischuh, “Inverse algorithm for increasing the resolution of pulsed lidars,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 284–287.

Fortin, R.

J. Gilbert, J. L. Lachambre, F. Rheault, R. Fortin, “Dynamics of the CO2atmospheric pressure laser with transverse pulse excitation,” Can. J. Phys. 50, 2523–2535 (1972).
[CrossRef]

Gilbert, J.

J. Gilbert, J. L. Lachambre, F. Rheault, R. Fortin, “Dynamics of the CO2atmospheric pressure laser with transverse pulse excitation,” Can. J. Phys. 50, 2523–2535 (1972).
[CrossRef]

Gurdev, L.

D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

Gurdev, L. L.

L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Deconvolution techniques for improving the resolution of long-pulse lidars,” J. Opt. Soc. Am. A 10, 2296–2306 (1993).
[CrossRef]

T. N. Dreischuh, L. L. Gurdev, D. V. Stoyanov, “Influence of the pulse-shape uncertainty on the accuracy of the inverse techniques for improving the resolution of long-pulse lidars,” in Optics as a Key to High Technology: 16th Congress of the International Commission for Optics, Gy. Akos, T. Lippeny, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 1060–1061 (1993).

T. N. Dreischuh, D. V. Stoyanov, L. L. Gurdev, “Statistical characteristics of Fourier-deconvolved NOAA 10.6-μm ground-based lidar data,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

L. L. Gurdev, D. V. Stoyanov, T. N. Dreischuh, “Inverse algorithm for increasing the resolution of pulsed lidars,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 284–287.

Hardesty, R. M.

Haris, M. R.

M. R. Haris, D. V. Willetts, “Performance characteristics of a TE CO2laser with a long excitation pulse,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 5–7.

Kavaya, M. J.

Lachambre, J. L.

J. Gilbert, J. L. Lachambre, F. Rheault, R. Fortin, “Dynamics of the CO2atmospheric pressure laser with transverse pulse excitation,” Can. J. Phys. 50, 2523–2535 (1972).
[CrossRef]

Lea, T. K.

Measures, R. M.

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, New York, 1984).

Menzies, R. T.

Rahm, S.

D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

Rheault, F.

J. Gilbert, J. L. Lachambre, F. Rheault, R. Fortin, “Dynamics of the CO2atmospheric pressure laser with transverse pulse excitation,” Can. J. Phys. 50, 2523–2535 (1972).
[CrossRef]

Schotland, R. M.

Stoyanov, D.

D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

Stoyanov, D. V.

L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Deconvolution techniques for improving the resolution of long-pulse lidars,” J. Opt. Soc. Am. A 10, 2296–2306 (1993).
[CrossRef]

T. N. Dreischuh, L. L. Gurdev, D. V. Stoyanov, “Influence of the pulse-shape uncertainty on the accuracy of the inverse techniques for improving the resolution of long-pulse lidars,” in Optics as a Key to High Technology: 16th Congress of the International Commission for Optics, Gy. Akos, T. Lippeny, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 1060–1061 (1993).

T. N. Dreischuh, D. V. Stoyanov, L. L. Gurdev, “Statistical characteristics of Fourier-deconvolved NOAA 10.6-μm ground-based lidar data,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

L. L. Gurdev, D. V. Stoyanov, T. N. Dreischuh, “Inverse algorithm for increasing the resolution of pulsed lidars,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 284–287.

Streicher, J.

Ch. Werner, G. Wildgruber, J. Streicher, Representativity of Wind Measurement from Space, Final Report, European Space Agency Contract No. 8664/90/HGE-I (German Aerospace Research Establishment, Munich, 1991).

D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

Werner, Ch.

D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

Ch. Werner, G. Wildgruber, J. Streicher, Representativity of Wind Measurement from Space, Final Report, European Space Agency Contract No. 8664/90/HGE-I (German Aerospace Research Establishment, Munich, 1991).

Wildgruber, G.

Ch. Werner, G. Wildgruber, J. Streicher, Representativity of Wind Measurement from Space, Final Report, European Space Agency Contract No. 8664/90/HGE-I (German Aerospace Research Establishment, Munich, 1991).

D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

Willetts, D. V.

M. R. Haris, D. V. Willetts, “Performance characteristics of a TE CO2laser with a long excitation pulse,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 5–7.

Zhao, Y.

Appl. Opt. (4)

Can. J. Phys. (1)

J. Gilbert, J. L. Lachambre, F. Rheault, R. Fortin, “Dynamics of the CO2atmospheric pressure laser with transverse pulse excitation,” Can. J. Phys. 50, 2523–2535 (1972).
[CrossRef]

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

Other (7)

M. R. Haris, D. V. Willetts, “Performance characteristics of a TE CO2laser with a long excitation pulse,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 5–7.

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, New York, 1984).

L. L. Gurdev, D. V. Stoyanov, T. N. Dreischuh, “Inverse algorithm for increasing the resolution of pulsed lidars,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 284–287.

T. N. Dreischuh, D. V. Stoyanov, L. L. Gurdev, “Statistical characteristics of Fourier-deconvolved NOAA 10.6-μm ground-based lidar data,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

D. Stoyanov, L. Gurdev, T. Dreischuh, Ch. Werner, J. Streicher, S. Rahm, G. Wildgruber, “One approach to improve the resolution of Doppler lidars,” presented at the 7th Conference on Coherent Laser Radar Applications and Technology, Paris, July 19–23, 1993.

T. N. Dreischuh, L. L. Gurdev, D. V. Stoyanov, “Influence of the pulse-shape uncertainty on the accuracy of the inverse techniques for improving the resolution of long-pulse lidars,” in Optics as a Key to High Technology: 16th Congress of the International Commission for Optics, Gy. Akos, T. Lippeny, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 1060–1061 (1993).

Ch. Werner, G. Wildgruber, J. Streicher, Representativity of Wind Measurement from Space, Final Report, European Space Agency Contract No. 8664/90/HGE-I (German Aerospace Research Establishment, Munich, 1991).

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Figures (4)

Fig. 1
Fig. 1

Models of the original short-pulse lidar profile and (inset) of a laser pulse shape (with τ1 = 0.1 μs, τ2 = 2 μs, and χ = 0.2) as a functions of sample number.

Fig. 2
Fig. 2

(a) Original profile (dashed curve) and the profile restored by use of Fourier deconvolution (solid curve) in the case of parabolic uncertainty with A = 0.025 and τ0 = 12 μs; (b) obtained (solid curve) and estimated [Eq. (4), dashed curve] errors corresponding to the data of Fig. 2(a).

Fig. 3
Fig. 3

Original profile (dashed curve) and the profile restored for the case of the spike cut (solid curve); (b) obtained (solid curve) and estimated [relation (9), dashed curve] errors corresponding to the data of (a).

Fig. 4
Fig. 4

Relative error δ Φ ¯/Φ for the restored profile given in Fig. 3(a), compared with the value of ps/pR given by the dashed horizontal line.

Equations (18)

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F ( t ) = - S ( t - 2 z / c ) Φ ( z ) d z
Φ ( z c t / 2 ) = ( π c ) - 1 - [ F ˜ ( ω ) / S ˜ ( ω ) ] exp ( - j ω t ) d ω ,
δ Φ ( z = c t / 2 ) = Φ r ( z ) - Φ ( z ) = - ( π c ) - 1 - Φ ˜ ( ω ) f ˜ ( ω ) [ S ˜ ( ω ) + f ˜ ( ω ) ] - 1 × exp ( - j ω t ) d ω ,
S m * δ Φ = - f * Φ ,
δ Φ ( z = c t / 2 ) - p eff - 1 - Φ ( z ) f ( t - 2 z / c ) d z = - ( p un / p eff ) Φ ¯ ( t )
δ Φ ¯ ( t ) / Φ ( t ) p S / p R .
δ Φ ( z = c t / 2 ) = - ( π c ) - 1 ( J 1 + J 2 ) ,
J 1 = - Φ ˜ sm ( ω ) F ( ω ) exp ( - j ω t ) d ω ,
J 2 = - Φ ˜ 0 ( ω ) F ( ω ) exp ( - j ω t ) d ω ,
J 1 = - π c ( p S / p R ) Φ sm ( z = c t / 2 ) ,
J 2 = - π c [ p S / p R ( ω 0 ) ] { cos [ φ R ( ω 0 ) ] Φ 0 ( z = c t / 2 ) + 2 sin [ φ R ( ω 0 ) ] ( π c ) - 1 Im [ J a ( z = c t / 2 ) ] } ,
δ Φ ( z = c t / 2 ) ( p S / p R ) Φ sm ( z = c t / 2 ) + [ p S / p R ( ω 0 ) ] Φ 0 [ z - z sh ( ω 0 ) ] ,
δ Φ ( z = c t / 2 ) - ( p un / p eff ) Φ sm ( z = c t / 2 ) - F ( ω 0 ) Φ 0 [ z - z sh ( ω 0 ) ] ,
σ Φ ( z = c t / 2 ) = δ Φ ( z = c t / 2 ) 2 1 / 2 ( σ p un / σ eff ) Φ ¯ ( t ) ,
f ( ϑ ) = σ f ( ϑ ) f ˜ ( ϑ ) ,
δ Φ ( z = c t / 2 ) - ( p un / p eff ) { Φ sm ( z = c t / 2 ) + F r ( ω 0 ) Φ 0 [ z - z sh ( ω 0 ) ] } ,
σ = [ ( τ q τ c ) 1 / 2 / ( N 1 / 2 τ eff ) ] { Φ sm ( z = c t / 2 ) + F r ( ω 0 ) Φ 0 [ z - z sh ( ω 0 ) ] } ,
S ( ϑ ) = ϑ [ ( 2 e / τ 1 ) exp ( - ϑ 2 / τ 1 2 ) + ( χ e / τ 2 ) exp ( - ϑ / τ 2 ) ] / S p ,

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