Abstract

In homogeneous atmospheres, backscatter and extinction coefficients are commonly determined by the inversion of lidar signals by using the slope method, i.e., from a linear least-squares fit to the logarithm on the range-compensated lidar return. We investigate the accuracy of this method. A quantitative analysis is presented of the influence of white noise and atmospheric extinction on the accuracy of the slope method and on the maximum range of lidar systems. To meet this objective, we simulate lidar signals with extinction coefficients ranging from 10−3 km−1 to 10 km−1 with different signal-to-noise ratios. It is shown that the backscatter coefficient can be determined by using the slope method with an accuracy of better than ~ 10% if the extinction coefficient is smaller than 1 km−1 and the signal-to-noise ratio is better than ~ 1000. The accuracy in the calculated extinction coefficient is only better than ~ 10% if the extinction is larger than 1 km−1 and the signal-to-noise ratio is better than ~ 2000. If the atmospheric extinction coefficient is smaller than 0.1 km−1, then it is not possible to invert the extinction from lidar measurements with an accuracy of 10% or better unless the signal-to-noise ratio is unrealistically high.

© 1993 Optical Society of America

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References

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  1. R. T. H. Collis, “Lidar: a new atmospheric probe,” Q.J.R. Meterol. Soc. 92, 220–230 (1966).
    [Crossref]
  2. A. I. Carswell, J. D. Houston, W. R. McNeil, S. R. Pal, S. Sizgoric, “Remote probing by laser radar,” Can. Aeronaut. Space J. (December1972), pp. 335–336.
  3. C. Werner, “Slant range visibility determination from lidar signatures by the two-point method,” Opt. Laser Technol. (February1981), pp. 27–36.
    [Crossref]
  4. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
    [Crossref] [PubMed]
  5. J. A. Ferguson, D. H. Stephens, “Algorithm for inverting lidar returns,” Appl. Opt. 22, 3673–3675 (1983).
    [Crossref] [PubMed]
  6. R. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, New York, 1984).
  7. G. J. Kunz, “Effects of detector bandwidth reduction on lidar signal processing,” Rep. PHL 1977-31 (Physics and Electronics Laboratory, TNO-FEL, The Hague, 1977).
  8. G. J. Kunz, “Hidden errors in lidar signals,” in Proceedings of the Ninth International Laser Radar Conference, Ch. Werner, F. Köpp, eds. German Aerospace Establishment, Institute of Atmospheric Physics, München, 1979).
  9. G. J. Kunz, “Comparison of using logarithmic amplifiers or a high resolution A/D converters,” Rep. FEL-90-I148 (Physics and Electronics Laboratory, TNO-FEL, The Hague, 1990).

1983 (1)

1981 (2)

C. Werner, “Slant range visibility determination from lidar signatures by the two-point method,” Opt. Laser Technol. (February1981), pp. 27–36.
[Crossref]

J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
[Crossref] [PubMed]

1972 (1)

A. I. Carswell, J. D. Houston, W. R. McNeil, S. R. Pal, S. Sizgoric, “Remote probing by laser radar,” Can. Aeronaut. Space J. (December1972), pp. 335–336.

1966 (1)

R. T. H. Collis, “Lidar: a new atmospheric probe,” Q.J.R. Meterol. Soc. 92, 220–230 (1966).
[Crossref]

Carswell, A. I.

A. I. Carswell, J. D. Houston, W. R. McNeil, S. R. Pal, S. Sizgoric, “Remote probing by laser radar,” Can. Aeronaut. Space J. (December1972), pp. 335–336.

Collis, R. T. H.

R. T. H. Collis, “Lidar: a new atmospheric probe,” Q.J.R. Meterol. Soc. 92, 220–230 (1966).
[Crossref]

Ferguson, J. A.

Houston, J. D.

A. I. Carswell, J. D. Houston, W. R. McNeil, S. R. Pal, S. Sizgoric, “Remote probing by laser radar,” Can. Aeronaut. Space J. (December1972), pp. 335–336.

Klett, J. D.

Kunz, G. J.

G. J. Kunz, “Effects of detector bandwidth reduction on lidar signal processing,” Rep. PHL 1977-31 (Physics and Electronics Laboratory, TNO-FEL, The Hague, 1977).

G. J. Kunz, “Hidden errors in lidar signals,” in Proceedings of the Ninth International Laser Radar Conference, Ch. Werner, F. Köpp, eds. German Aerospace Establishment, Institute of Atmospheric Physics, München, 1979).

G. J. Kunz, “Comparison of using logarithmic amplifiers or a high resolution A/D converters,” Rep. FEL-90-I148 (Physics and Electronics Laboratory, TNO-FEL, The Hague, 1990).

McNeil, W. R.

A. I. Carswell, J. D. Houston, W. R. McNeil, S. R. Pal, S. Sizgoric, “Remote probing by laser radar,” Can. Aeronaut. Space J. (December1972), pp. 335–336.

Measures, R.

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

Pal, S. R.

A. I. Carswell, J. D. Houston, W. R. McNeil, S. R. Pal, S. Sizgoric, “Remote probing by laser radar,” Can. Aeronaut. Space J. (December1972), pp. 335–336.

Sizgoric, S.

A. I. Carswell, J. D. Houston, W. R. McNeil, S. R. Pal, S. Sizgoric, “Remote probing by laser radar,” Can. Aeronaut. Space J. (December1972), pp. 335–336.

Stephens, D. H.

Werner, C.

C. Werner, “Slant range visibility determination from lidar signatures by the two-point method,” Opt. Laser Technol. (February1981), pp. 27–36.
[Crossref]

Appl. Opt. (2)

Can. Aeronaut. Space J. (1)

A. I. Carswell, J. D. Houston, W. R. McNeil, S. R. Pal, S. Sizgoric, “Remote probing by laser radar,” Can. Aeronaut. Space J. (December1972), pp. 335–336.

Opt. Laser Technol. (1)

C. Werner, “Slant range visibility determination from lidar signatures by the two-point method,” Opt. Laser Technol. (February1981), pp. 27–36.
[Crossref]

Q.J.R. Meterol. Soc. (1)

R. T. H. Collis, “Lidar: a new atmospheric probe,” Q.J.R. Meterol. Soc. 92, 220–230 (1966).
[Crossref]

Other (4)

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

G. J. Kunz, “Effects of detector bandwidth reduction on lidar signal processing,” Rep. PHL 1977-31 (Physics and Electronics Laboratory, TNO-FEL, The Hague, 1977).

G. J. Kunz, “Hidden errors in lidar signals,” in Proceedings of the Ninth International Laser Radar Conference, Ch. Werner, F. Köpp, eds. German Aerospace Establishment, Institute of Atmospheric Physics, München, 1979).

G. J. Kunz, “Comparison of using logarithmic amplifiers or a high resolution A/D converters,” Rep. FEL-90-I148 (Physics and Electronics Laboratory, TNO-FEL, The Hague, 1990).

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Figures (6)

Fig. 1
Fig. 1

Maximum range of a lidar system as a function of the signal-to-noise ratio at the starting point of full overlap of the laser beam and the field of view of the receiver of 50 m, for different values of the atmospheric extinction coefficient.

Fig. 2
Fig. 2

Signal strength calculated by the slope method versus the simulated signal strength at the starting point of full overlap of the laser beam and the field of view of the receiver. The signal strength is proportional to the backscatter. The calculations were made for atmospheric extinction coefficients of (a) 0.1 km−1 and (b) 10 km−1.

Fig. 3
Fig. 3

Relative error in the calculated backscatter (see text) versus the signal-to-noise ratio at the starting point of full overlap of the laser beam and the field of view of the receiver. The triangles indicate positive errors and the inverted triangles indicate negative errors. The calculations were made for atmospheric extinction coefficients of (a) 0.1 km−1 and (b) 10 km−1.

Fig. 4
Fig. 4

Averaged standard deviations in the calculated backscatter versus the simulated signal-to-noise ratio for five different values of the extinction coefficient.

Fig. 5
Fig. 5

Extinction coefficients calculated with the slope method (crosses) as a function of the signal-to-noise ratio at the starting of full overlap of the laser beam and the field of view of the receiver, for extinction coefficients of (a) 10−3, (b) 10−2, (c) 10−1, (d) 100, and (e) 101 km−1. The inverted triangles indicate a negative calculated extinction.

Fig. 6
Fig. 6

Standard deviation in the calculated extinction as provided by the slope method versus the signal-to-noise ratio at the crossover point, for five different values of the extinction coefficient.

Equations (12)

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P ( R ) = K β R 2 exp ( - 2 α R ) ,
ln [ P ( R ) R 2 ] = ln ( K β ) - 2 α R .
y ± δ y = ln [ K β ± δ ( K β ) ]
y ± δ y = ln ( K β ) + ln { 1 ± [ δ ( K β ) / K β ] } .
y ± δ y = ln ( K β ) ± [ δ ( K β ) / K β ] .
K β = exp ( y ) .
δ ( K β ) K β = δ y .
P n = K β R max 2 exp ( - 2 α R max ) ,
2 α R max + 2 ln ( R max ) = ln ( K β ) .
2 α d R max + 2 R max d α + 2 R max d R max = d α α .
α R max = 1 2 R max .
R max = ( K C A 2 e ) 1 / 3 ,

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