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References

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  1. J. D. Klett, “Lidar Calibration and Extinction Coefficients,” Appl. Opt. 22, 514 (1983).
    [CrossRef] [PubMed]
  2. J. A. Ferguson, D. H. Stephens, “Algorithm for Inverting Lidar Returns,” Appl. Opt. 22, 3673 (1983).
    [CrossRef] [PubMed]
  3. J. A. Mulders, “Algorithm for Inverting Lidar Returns: Comment,” Appl. Opt. 23, 2855 (1984).
    [CrossRef] [PubMed]
  4. J. D. Klett, “Stable Analytical Inversion Solution for Processing Lidar Returns,” Appl. Opt. 20, 211 (1981).
    [CrossRef] [PubMed]
  5. J. D. Klett, “Estimation of Extinction Boundary Values for Lidar Inversion,” ERADCOM Report ASL-CR-85-0093-1, U.S. Army Atmospheric Sciences Laboratory, White Sands Missile Range, White Sands, NM 88002 (1985), 45 pp.

1984

1983

1981

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Figures (2)

Fig. 1
Fig. 1

Plot of y1 = Gm and y2, given by the right-hand side of Eq. (11), showing the location of the boundary values at the intersections of the curves.

Fig. 2
Fig. 2

Constant input distribution and the inversion solution having an unrealistic drop-off with range. Both profiles can be used to generate the same calibrated signal.

Equations (18)

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β = B σ k ,
S ( r ) ln [ r 2 P ( r ) ] = C + k ln σ - 2 0 τ σ d r .
C = ln ( 0.5 P 0 B c τ A ) ,
σ ( r ) = exp [ ( S - S m ) / k ] { σ m - 1 + 2 k r r m exp [ ( S - S m ) / k ] d r } ,
S m = C + k ln σ m - 2 0 r m d r .
r 0 r m σ d r = k 2 ln { 1 + 2 σ m k r 0 r m exp [ ( S - S m ) / k ] d r } , = k 2 ln ( 1 + I Ω m ) .
I ( r m - r 0 ) - 1 r 0 r m exp [ ( S - S m ) / k ] d r ,
Ω m 2 σ m ( r m - r 0 ) / k .
0 r m σ d r = [ r m / ( r m - r 0 ) ] r 0 r m σ d r ,
G m = ln Ω m - r m ( r m - r 0 ) ln ( 1 + I Ω m ) ,
G m ( S m - C ) / k + ln [ 2 ( r m - r 0 ) / k ] .
y 2 = ln Ω - r m ( r m - r 0 ) ln ( 1 + I Ω ) .
Ω c = ( r m - r 0 ) / r 0 I .
Ω m = ln ( 1 + I Ω m ) .
G m = G m + 2 r 0 σ 0 / k = ln Ω m - ln ( 1 + I Ω m ) .
Ω m = [ exp ( - G m ) - I ] - 1 .
Ω m = Ω c
S 0 = C + k ln σ 0 - 2 σ 0 r 0 .

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