Abstract

The technique of inverting a single-ended lidar return to obtain range-dependent atmospheric extinction coefficients requires an assumption concerning the relationship between the volumetric backscatter and extinction coefficients. By comparing the powers returned from a volume common to each of two lidars located at opposite ends of a propagation path the need for this relationship can be eliminated, and the extinction coefficient is determined as a function of position between the two lidars. If the lidars are calibrated, the backscatter coefficients and their relationship to extinction can then be determined as a function of position. We present measurements obtained with two lidars which were operated reciprocally over a slant path of ~1 km during reduced visibility conditions. The measured extinction and backscatter coefficients determined by this method provide the boundary value inputs to both the forward and reverse integration algorithms for inverting the single-ended lidar returns. The accuracies by which both single-ended integration schemes can reproduce the double-ended measurements are examined by allowing the ratio of backscatter to extinction coefficients to be either constant or varying with position between the two lidars as measured.

© 1988 Optical Society of America

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References

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  1. R. H. Kohl, “Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers,” J. Appl. Meteorol. 17, 1034 (1978).
    [CrossRef]
  2. J. D. Klett, “Stable Analytical Inversion Solution for Processing Lidar Returns,” Appl. Opt. 20, 211 (1981).
    [CrossRef] [PubMed]
  3. G. J. Kunz, “Vertical Atmospheric Profiles Measured with Lidar,” Appl. Opt. 22, 1955 (1983).
    [CrossRef] [PubMed]
  4. W. Carnuth, R. Reiter, “Cloud Extinction Profile Measurements by Lidar Using Klett’s Inversion Method,” Appl. Opt. 25, 2899 (1986).
    [CrossRef] [PubMed]
  5. J. D. Lindberg, W. J. Lentz, E. M. Measure, R. Rubio, “Lidar Determinations of Extinction in Stratus Clouds,” Appl. Opt. 23, 2172 (1984).
    [CrossRef] [PubMed]
  6. J. A. Ferguson, D. H. Stephens, “Algorithm for Inverting Lidar Returns,” Appl. Opt. 22, 3673 (1983).
    [CrossRef] [PubMed]
  7. H. G. Hughes, J. A. Ferguson, D. H. Stephens, “Sensitivity of a Lidar Inversion Algorithm to Parameters Relating Atmospheric Backscatter and Extinction,” Appl. Opt. 24, 1609 (1985).
    [CrossRef] [PubMed]
  8. L. R. Bissonnette, “Sensitivity Analysis of Lidar Inversion Algorithms,” Appl. Opt. 25, 2122 (1986).
    [CrossRef] [PubMed]
  9. J. D. Klett, “Lidar Inversion with Variable Backscatter/Extinction Ratios,” Appl. Opt. 11, 1638 (1985).
    [CrossRef]
  10. H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative Lidar at 532 nm for Vertical Extinction Profiles and the Effect of Relative Humidity,” Appl. Phys. B 34, 187 (1984).
    [CrossRef]
  11. G. de Leeuw, G. J. Kunz, C. W. Lamberts, “Humidity Effects on the Backscatter/Extinction Ratio,” Appl. Opt. 25, 3971 (1986).
    [CrossRef] [PubMed]
  12. J. W. Fitzgerald, “Effect of Relative Humidity on the Aerosol Backscattering Coefficient at 0.694- and 10.6-μm Wavelengths,” Appl. Opt. 23, 411 (1984).
    [CrossRef] [PubMed]
  13. M. R. Paulson, “Evaluation of a Dual-Lidar Method for Measuring Aerosol Extinction,” Naval Ocean Systems Center Technical Document 1075 (Apr.1987).
  14. G. J. Kunz, “Bipath Method as a Way to Measure the Spatial Backscatter and Extinction Coefficients with Lidar,” Appl. Opt. 26, 794 (1987).
    [CrossRef] [PubMed]
  15. J. A. Ferguson, M. R. Paulson, “Calibration of the Hand-Held Lidars Used by the Naval Ocean Systems Center,” Naval Ocean Systems Center Technical Document 996 (Dec.1986).
  16. O. D. Barteneva, “Scattering Functions of Light in the Atmospheric Boundary Layer,” Bull. Acad. Sci. USSR Geophys. Ser. 12, 32 (1960).
  17. H. G. Hughes, B. L. Thompson, “Estimates of Optical Pulse Broadening in Maritime Stratus Clouds,” Opt. Eng. 23, 38 (1984).
    [CrossRef]
  18. K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1172 (1976).
    [CrossRef]
  19. J. M. Mulders, “Algorithm for Inverting Lidar Returns: Comment,” Appl. Opt. 23, 2855 (1984).
    [CrossRef] [PubMed]

1987 (2)

M. R. Paulson, “Evaluation of a Dual-Lidar Method for Measuring Aerosol Extinction,” Naval Ocean Systems Center Technical Document 1075 (Apr.1987).

G. J. Kunz, “Bipath Method as a Way to Measure the Spatial Backscatter and Extinction Coefficients with Lidar,” Appl. Opt. 26, 794 (1987).
[CrossRef] [PubMed]

1986 (4)

1985 (2)

1984 (5)

1983 (2)

1981 (1)

1978 (1)

R. H. Kohl, “Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers,” J. Appl. Meteorol. 17, 1034 (1978).
[CrossRef]

1976 (1)

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1172 (1976).
[CrossRef]

1960 (1)

O. D. Barteneva, “Scattering Functions of Light in the Atmospheric Boundary Layer,” Bull. Acad. Sci. USSR Geophys. Ser. 12, 32 (1960).

Barteneva, O. D.

O. D. Barteneva, “Scattering Functions of Light in the Atmospheric Boundary Layer,” Bull. Acad. Sci. USSR Geophys. Ser. 12, 32 (1960).

Bergwerff, J. B.

H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative Lidar at 532 nm for Vertical Extinction Profiles and the Effect of Relative Humidity,” Appl. Phys. B 34, 187 (1984).
[CrossRef]

Bissonnette, L. R.

Carnuth, W.

de Leeuw, G.

Ferguson, J. A.

Fitzgerald, J. W.

Hughes, H. G.

Klett, J. D.

J. D. Klett, “Lidar Inversion with Variable Backscatter/Extinction Ratios,” Appl. Opt. 11, 1638 (1985).
[CrossRef]

J. D. Klett, “Stable Analytical Inversion Solution for Processing Lidar Returns,” Appl. Opt. 20, 211 (1981).
[CrossRef] [PubMed]

Kohl, R. H.

R. H. Kohl, “Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers,” J. Appl. Meteorol. 17, 1034 (1978).
[CrossRef]

Kunkel, K. E.

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1172 (1976).
[CrossRef]

Kunz, G. J.

Lamberts, C. W.

Lentz, W. J.

Lindberg, J. D.

Measure, E. M.

Mulders, J. M.

Paulson, M. R.

M. R. Paulson, “Evaluation of a Dual-Lidar Method for Measuring Aerosol Extinction,” Naval Ocean Systems Center Technical Document 1075 (Apr.1987).

J. A. Ferguson, M. R. Paulson, “Calibration of the Hand-Held Lidars Used by the Naval Ocean Systems Center,” Naval Ocean Systems Center Technical Document 996 (Dec.1986).

Reiter, R.

Rubio, R.

Salemink, H. W. M.

H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative Lidar at 532 nm for Vertical Extinction Profiles and the Effect of Relative Humidity,” Appl. Phys. B 34, 187 (1984).
[CrossRef]

Schotanus, P.

H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative Lidar at 532 nm for Vertical Extinction Profiles and the Effect of Relative Humidity,” Appl. Phys. B 34, 187 (1984).
[CrossRef]

Stephens, D. H.

Thompson, B. L.

H. G. Hughes, B. L. Thompson, “Estimates of Optical Pulse Broadening in Maritime Stratus Clouds,” Opt. Eng. 23, 38 (1984).
[CrossRef]

Weinman, J. A.

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1172 (1976).
[CrossRef]

Appl. Opt. (12)

J. D. Klett, “Stable Analytical Inversion Solution for Processing Lidar Returns,” Appl. Opt. 20, 211 (1981).
[CrossRef] [PubMed]

G. J. Kunz, “Vertical Atmospheric Profiles Measured with Lidar,” Appl. Opt. 22, 1955 (1983).
[CrossRef] [PubMed]

W. Carnuth, R. Reiter, “Cloud Extinction Profile Measurements by Lidar Using Klett’s Inversion Method,” Appl. Opt. 25, 2899 (1986).
[CrossRef] [PubMed]

J. D. Lindberg, W. J. Lentz, E. M. Measure, R. Rubio, “Lidar Determinations of Extinction in Stratus Clouds,” Appl. Opt. 23, 2172 (1984).
[CrossRef] [PubMed]

J. A. Ferguson, D. H. Stephens, “Algorithm for Inverting Lidar Returns,” Appl. Opt. 22, 3673 (1983).
[CrossRef] [PubMed]

H. G. Hughes, J. A. Ferguson, D. H. Stephens, “Sensitivity of a Lidar Inversion Algorithm to Parameters Relating Atmospheric Backscatter and Extinction,” Appl. Opt. 24, 1609 (1985).
[CrossRef] [PubMed]

L. R. Bissonnette, “Sensitivity Analysis of Lidar Inversion Algorithms,” Appl. Opt. 25, 2122 (1986).
[CrossRef] [PubMed]

J. D. Klett, “Lidar Inversion with Variable Backscatter/Extinction Ratios,” Appl. Opt. 11, 1638 (1985).
[CrossRef]

G. de Leeuw, G. J. Kunz, C. W. Lamberts, “Humidity Effects on the Backscatter/Extinction Ratio,” Appl. Opt. 25, 3971 (1986).
[CrossRef] [PubMed]

J. W. Fitzgerald, “Effect of Relative Humidity on the Aerosol Backscattering Coefficient at 0.694- and 10.6-μm Wavelengths,” Appl. Opt. 23, 411 (1984).
[CrossRef] [PubMed]

G. J. Kunz, “Bipath Method as a Way to Measure the Spatial Backscatter and Extinction Coefficients with Lidar,” Appl. Opt. 26, 794 (1987).
[CrossRef] [PubMed]

J. M. Mulders, “Algorithm for Inverting Lidar Returns: Comment,” Appl. Opt. 23, 2855 (1984).
[CrossRef] [PubMed]

Appl. Phys. B (1)

H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative Lidar at 532 nm for Vertical Extinction Profiles and the Effect of Relative Humidity,” Appl. Phys. B 34, 187 (1984).
[CrossRef]

Bull. Acad. Sci. USSR Geophys. Ser. (1)

O. D. Barteneva, “Scattering Functions of Light in the Atmospheric Boundary Layer,” Bull. Acad. Sci. USSR Geophys. Ser. 12, 32 (1960).

J. Appl. Meteorol. (1)

R. H. Kohl, “Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers,” J. Appl. Meteorol. 17, 1034 (1978).
[CrossRef]

J. Atmos. Sci. (1)

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1172 (1976).
[CrossRef]

Naval Ocean Systems Center Technical Document 1075 (1)

M. R. Paulson, “Evaluation of a Dual-Lidar Method for Measuring Aerosol Extinction,” Naval Ocean Systems Center Technical Document 1075 (Apr.1987).

Naval Ocean Systems Center Technical Document 996 (1)

J. A. Ferguson, M. R. Paulson, “Calibration of the Hand-Held Lidars Used by the Naval Ocean Systems Center,” Naval Ocean Systems Center Technical Document 996 (Dec.1986).

Opt. Eng. (1)

H. G. Hughes, B. L. Thompson, “Estimates of Optical Pulse Broadening in Maritime Stratus Clouds,” Opt. Eng. 23, 38 (1984).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Measured values for data set 1 of the range compensated power return S(r) for lidars 1 and 2 vs the range from lidar 1. (b) Differences in the S(r) values for lidars 1 and 2 vs the range from lidar 1

Fig. 2
Fig. 2

(a) Measured values for data set 2 of the range compensated power return S(r) for lidars 1 and 2 vs the range from lidar 1. (b) Differences in the S(r) values for lidars 1 and 2 vs the range from lidar 1.

Fig. 3
Fig. 3

(a) Extinction coefficient σ(r), (b) backscatter coefficient β(r), and (c) backscatter/extinction ratio C(r) vs the range from lidar 1 for data set 1

Fig. 4
Fig. 4

(a) Extinction coefficient σ(r), (b) backscatter coefficient β(r), and (c) backscatter/extinction ratio C(r) vs the range from lidar 1 for data set 2.

Fig. 5
Fig. 5

Comparison of extinction coefficients σ(r) vs range from lidar 1 calculated from lidar 1 and 2 individual returns using forward integration and those measured using the double-ended technique for (a) data set 1 and (b) data set 1 and when C(r) is assumed to be constant.

Fig. 6
Fig. 6

Comparison of extinction coefficients σ(r) vs range from lidar 1 calculated from lidar 1 and 2 individual returns using reverse integration and those measured using the double-ended technique for (a) data set 1 and (b) data set 2 and when C(r) is assumed to be constant.

Fig. 7
Fig. 7

Comparison of extinction coefficients σ(r) calculated from lidar 1 and 2 individual returns using forward integration vs range from lidar 1 for (a) data set 1 and (b) data set 2 and when C(r) is allowed to vary as measured.

Fig. 8
Fig. 8

Comparison of extinction coefficients σ(r) calculated from lidar 1 and 2 individual returns using reverse integration vs range from lidar 1 for (a) data set 1 and (b) data set 2 and when C(r) is allowed to vary as measured.

Equations (11)

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σ ( r ) = exp [ S ( r ) ] exp [ S ( r 0 ) ] σ ( r 0 ) - 2 r 0 r exp [ S ( r ) ] d r ,
σ ( r ) = exp [ S ( r ) ] exp [ S ( r f ) ] σ ( r f ) + 2 r r f exp [ S ( r ) ] d r ,
β ( r ) = C ( r ) σ ( r ) k ,
σ ( r ) = 1 C ( r ) exp [ S ( r ) ] exp [ S ( r 0 ) ] C ( r 0 ) σ ( r 0 ) - 2 r 0 r 1 C ( r ) exp [ S ( r ) ] d r
σ ( r ) = 1 C ( r ) exp [ S ( r ) ] exp [ S ( r f ) ] C ( r f ) σ ( r f ) + 2 r r f 1 C ( r ) exp [ S ( r ) ] d r ,
S ( r ) 1 = ln K 1 + ln [ β ( r ) ] - 2 0 r σ ( r ) d r ,
S ( r ) 2 = ln K 2 + ln [ β ( r ) ] - 2 r d σ ( r ) d r ,
S ( r ) 1 - S ( r ) 2 = ln ( K 1 / K 2 ) - 2 0 r σ ( r ) d r + 2 r d σ ( r ) d r .
r d σ ( r ) d r = 0 d σ ( r ) d r - 0 r σ ( r ) d r .
S ( r ) 1 - S ( r ) 2 = ln ( K 1 / K 2 ) - 4 0 r σ ( r ) d r + 2 0 d σ ( r ) d r .
σ ( r ) = - 1 4 d d r [ S ( r ) 1 - S ( r ) 2 ] .

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