Abstract

The convolution effect in CO2 lidar return signals caused by the long laser pulse is analyzed by modifying the original lidar equation and introducing a correction function Cr(R). The characteristics of Cr(R) are discussed in detail, leading to a deconvolution technique consisting of a two-step iteration procedure for the extraction of both the backscattering coefficient and the gas species content in differential absorption lidar measurement.

© 1988 Optical Society of America

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References

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  1. P. W. Baker, “Atmospheric Water Vapor Differential Absorption Measurements on Vertical Paths with a CO2 Lidar,” Appl. Opt. 22, 2257 (1983).
    [CrossRef] [PubMed]
  2. M. J. Kavaya, R. T. Menzies, “Data Acquisition, Data Processing, Parameter Modeling, and Hard Target Calibration for Accurate Lidar Aerosol Backscatter Measurements,” in Abstracts of Papers, Twelfth ILRC (Aix en Provence, France, Aug.1984).
  3. W. W. Duley, CO2Lasers: Effects and Applications (Academic, New York, 1976).
  4. K. R. Manes, H. J. Seguin, “Analysis of the CO2 TEA Laser,” J. Appl. Phys. 43, 5073 (1972).
    [CrossRef]
  5. K. J. Andrews, P. E. Dyer, D. J. James, “A Rate Equation Model for the Design of TEA CO2 Oscillators,” J. Phys. E 8, 493 (1975).
    [CrossRef]
  6. M. S. Shumate, R. T. Menzies, J. S. Margolis, L.-G. Rosengren, “Water Vapor Absorption of Carbon Dioxide Laser Radiation,” Appl. Opt. 15, 2480 (1976).
    [CrossRef] [PubMed]

1983

1976

1975

K. J. Andrews, P. E. Dyer, D. J. James, “A Rate Equation Model for the Design of TEA CO2 Oscillators,” J. Phys. E 8, 493 (1975).
[CrossRef]

1972

K. R. Manes, H. J. Seguin, “Analysis of the CO2 TEA Laser,” J. Appl. Phys. 43, 5073 (1972).
[CrossRef]

Andrews, K. J.

K. J. Andrews, P. E. Dyer, D. J. James, “A Rate Equation Model for the Design of TEA CO2 Oscillators,” J. Phys. E 8, 493 (1975).
[CrossRef]

Baker, P. W.

Duley, W. W.

W. W. Duley, CO2Lasers: Effects and Applications (Academic, New York, 1976).

Dyer, P. E.

K. J. Andrews, P. E. Dyer, D. J. James, “A Rate Equation Model for the Design of TEA CO2 Oscillators,” J. Phys. E 8, 493 (1975).
[CrossRef]

James, D. J.

K. J. Andrews, P. E. Dyer, D. J. James, “A Rate Equation Model for the Design of TEA CO2 Oscillators,” J. Phys. E 8, 493 (1975).
[CrossRef]

Kavaya, M. J.

M. J. Kavaya, R. T. Menzies, “Data Acquisition, Data Processing, Parameter Modeling, and Hard Target Calibration for Accurate Lidar Aerosol Backscatter Measurements,” in Abstracts of Papers, Twelfth ILRC (Aix en Provence, France, Aug.1984).

Manes, K. R.

K. R. Manes, H. J. Seguin, “Analysis of the CO2 TEA Laser,” J. Appl. Phys. 43, 5073 (1972).
[CrossRef]

Margolis, J. S.

Menzies, R. T.

M. S. Shumate, R. T. Menzies, J. S. Margolis, L.-G. Rosengren, “Water Vapor Absorption of Carbon Dioxide Laser Radiation,” Appl. Opt. 15, 2480 (1976).
[CrossRef] [PubMed]

M. J. Kavaya, R. T. Menzies, “Data Acquisition, Data Processing, Parameter Modeling, and Hard Target Calibration for Accurate Lidar Aerosol Backscatter Measurements,” in Abstracts of Papers, Twelfth ILRC (Aix en Provence, France, Aug.1984).

Rosengren, L.-G.

Seguin, H. J.

K. R. Manes, H. J. Seguin, “Analysis of the CO2 TEA Laser,” J. Appl. Phys. 43, 5073 (1972).
[CrossRef]

Shumate, M. S.

Appl. Opt.

J. Appl. Phys.

K. R. Manes, H. J. Seguin, “Analysis of the CO2 TEA Laser,” J. Appl. Phys. 43, 5073 (1972).
[CrossRef]

J. Phys. E

K. J. Andrews, P. E. Dyer, D. J. James, “A Rate Equation Model for the Design of TEA CO2 Oscillators,” J. Phys. E 8, 493 (1975).
[CrossRef]

Other

M. J. Kavaya, R. T. Menzies, “Data Acquisition, Data Processing, Parameter Modeling, and Hard Target Calibration for Accurate Lidar Aerosol Backscatter Measurements,” in Abstracts of Papers, Twelfth ILRC (Aix en Provence, France, Aug.1984).

W. W. Duley, CO2Lasers: Effects and Applications (Academic, New York, 1976).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the energy level related to CO2 laser.

Fig. 2
Fig. 2

Normalized laser pulse shape P(t)/E: (a) long pulse: He:CO2:N2 = 9:1:0.7 (log scale); (b) short pulse: He:CO2:N2 = 6.2:1:0 (log scale); (c) long pulse as (a) (linear scale); (d) short pulse as (b) (linear scale).

Fig. 3
Fig. 3

Integrated laser energy as a function of t: 1, long pulse; 2, short pulse.

Fig. 4
Fig. 4

Receiving efficiency functions: 1, coaxial system; 2, biaxial system.

Fig. 5
Fig. 5

Correction function in the horizontal case for a long pulse: 1a, extinction coefficient = 0.2/km, coaxial system; 1b, extinction coefficient = 1.5/km, coaxial system; 2a, extinction coefficient = 0.2/km, biaxial system, axes separation = 40 cm; 2b, extinction coefficient = 1.5/km, biaxial system, axes separation = 40 cm.

Fig. 6
Fig. 6

Correction function in the horizontal case for a short pulse: 1a, extinction coefficient = 0.2/km, coaxial system; 1b, extinction coefficient = 1.5/km, coaxial system; 2a, extinction coefficient = 0.2/km, biaxial system, axes separation = 40 cm; 2b, extinction coefficient = 1.5/km, biaxial system, axes separation = 40 cm.

Fig. 7
Fig. 7

Parametrized laser pulse, corresponding correction function: (a) normalized pulse power P(t)/Pm (Pm is the peak power); (b) Fig. correction functions. The parameters for each curve are as follows:

Fig. 8
Fig. 8

Correction functions in vertical direction for different atmospheric models: (a) Five models of backscattering coefficient and water vapor distribution: 1, βπ(z) = β0 exp(−z/500), w/w0 = exp(−z/2000); 2, βπ(z) = β0{exp[−0.004(z + 40)] − exp[−0.0044(z + 40)]}, w/w0 = exp(−z/2000); 3, βπ(z) = 1.25β0 [1 − 2.46 × 10−7 (z − 900)2], w/w0 = exp(−z/2000), z ≤ 900 m; βπ(z) = 1.25β0 exp(−z/1000), w/w0 = 0.2 exp(−z/2000), z > 900 m; 4, βπ(z) = 1.25β0 [1 − 2.46 × 10−7 (z − 900)2], w/w0 = exp(−z/2000), z ≤ 900 m; βπ(z) = 0.25β0 exp(−z/1000), w/w0 = 0.2 exp(−z/2000), z > 900 m; 5, βπ(z) = 1.25β0 [1 − 2.46 × 10−7 (z − 900)2], w/w0 = exp(−z/2000), z ≤ 900 m; βπ(z) = 0.25β0 exp(−z/1000), w/w0 = 0.5 exp(−z/2000), z > 900 m. (b) Correction functions for long laser pulse under the above models. Surface extinction coefficient σ0 = 0.262/km [equivalent to the total absorption coefficient at R(18) when water vapor pressure = 20 mbar].

Fig. 9
Fig. 9

Relative errors in the DIAL measurement in the horizontal case. Atmospheric extinction coefficient at off-line and on-line wavelengths are σ1 = 0.2/km, σ2 = 1.5 km: (a) for long pulse: 1, coaxial system; 2, biaxial system, axes separation = 40 cm; 3, biaxial system, axes separation = 60 cm; (b) for short pulse: 1, coaxial system; 2, biaxial system, axes separation = 40 cm; 3, biaxial system, axes separation = 60 cm.

Fig. 10
Fig. 10

Ratios of the correction function at R(18) to that at R(20) for the atmospheric models in Fig. 8(a). Surface water vapor pressure = 20 mbar.

Fig. 11
Fig. 11

Relative errors in DIAL measurement for water vapor in the vertical direction under the atmospheric models in Fig. 8(a): (a) for long pulse; (b) for short pulse.

Fig. 12
Fig. 12

Sensitivity of Δ lnRcz to the backscattering coefficient distribution and the water vapor content: (a) Δ lnRcz for models 1, 2, and 3 in Fig. 8(a); surface water vapor pressure = 20 mbar; (b) Δ lnRcz for model 1 under two surface water vapor pressures.

Tables (1)

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Table I Main Parameters of the Lidar System used In the Computation

Equations (52)

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V ( R ) = C A E β π ( R ) T 2 ( R ) / R 2 ,
exp [ - 2 0 R σ ( r ) d r ] ,
ln [ V ( R ) R 2 ] = ln ( C A β π 0 ) - 2 σ 0 R .
r = c ( t - t ) / 2.
V i ( t ) = κ 0 c t / 2 P ( t - 2 r c ) · T 2 ( r ) · β π ( r ) · η ( r ) r 2 d r ,
V ( t ) = V i ( t ) E = κ E 0 c t / 2 P ( t - 2 r c ) · T 2 ( r ) · β π ( r ) · η ( r ) r 2 d r .
t = t - 2 R c , R = c t / 2 ,
r = R - c t 2 , d r = - c d t 2 ,
V ( R ) = C A 0 2 R / C × [ P ( t ) / E ] · T 2 ( R - c t 2 ) · β π ( R - c t 2 ) · η ( R - c t 2 ) ( R - c t 2 ) 2 d t
V ( R ) = C A β π ( r ) T 2 ( r ) C r ( R ) / R 2 .
C r ( R ) = 1 E 0 2 R / C P ( t ) ( 1 - c t 2 R ) - 2 × [ β π ( R - c t 2 ) β π ( R ) ] [ T 2 ( R - c t 2 ) T 2 ( R ) ] · η ( R - c t 2 ) d t = 1 E 0 2 R / C P ( t ) S ( R - c t 2 ) B ( R - c t 2 ) × T r ( R - c t 2 ) η ( R - c t 2 ) d t ,
S ( R - c t 2 ) = ( 1 - c t ' 2 R ) - 2 , B ( R - c t 2 ) = [ β π ( R - c t 2 ) β π ( R ) ] , T r ( R - c t 2 ) = [ T 2 ( R - c t 2 ) T 2 ( R ) ] .
R c τ / 2 , ( 1 - c t 2 ) ,
C r ( R ) = 1 E 0 2 R / C P ( t ) d t 1 .
S ( R - c t 2 )
T r ( R - c t 2 )
B ( R - d t 2 )
η ( R - c t 2 )
S ( R - c t 2 ) ,             T r ( R - c t 2 ) .
d n 1 / d t = α 1 ( n 0 - f n 1 ) - κ 13 n 1 + κ ( N n 0 - n 1 N 0 ) - s q ( n 1 - n 2 ) , d n 2 / d t = α 2 ( n 0 - f n 2 ) - κ 2 n 2 + s q ( n 1 - n 2 ) , d n 3 / d t = α 3 ( n 0 - f n 3 ) + κ 2 n 2 - κ 3 n 3 , d N / d t = β ( N 0 - f N ) - κ ( N n 0 - n 1 N 0 ) , d q / d t = s q ( n 1 - n 2 ) - w q + D n 1 ,
I ( r ) = I 0 exp [ - ( r - 0.6 r 0 ) 2 / 0.1 r 0 2 ] ,
T r ( R - c t 2 ) = exp [ - 2 σ 0 ( R - c t 2 ) ] exp ( - 2 σ 0 R ) = exp ( c σ 0 t ) . B ( R - c t 2 ) = 1.
C r ( R ) = 1 E 0 2 R / C P ( t ) S ( R - c t 2 ) η ( R - c t 2 ) exp ( c σ 0 t ) d t .
P ( t ) = exp [ A ( 0.25 t 2 / t 1 2 ) exp ( - t t 1 + 2 ) + B - C t 3 ] , t 15 t 1 ; P ( t ) = exp [ B - G ( t - 15 t 1 ) - H ( t - 15 t 1 ) 2 - C t 3 ] , t > 15 t 1 .
β π ( r ) = β π 0 exp ( - r H sec θ ) ,
B ( R - c t 2 ) = exp ( c t 2 H sec θ ) ,
C r ( R ) = 1 E 0 2 R / C P ( t ) S ( R - c t 2 ) η ( R - c t 2 ) × exp [ c ( σ + Δ σ ) t ] d t ,
Δ σ = 1 2 H sec θ and σ = 2 R - ( c t / 2 ) R σ ( r ) d r / c t .
D f ( R ) = V 1 ( R ) / V 2 ( R ) = [ T 1 2 ( R ) / T 2 2 ( R ) ] [ C r 1 ( R ) / C r 2 ( R ) ] = [ T 1 2 ( R ) / T 2 2 ( R ) ] R c ( R ) ,
N ( R ) = Δ ln D f Δ R - Δ ln R c Δ R 2 ( α 2 - α 1 ) = Δ ln D f Δ R - δ 2 ( α 2 - α 1 ) ,
g ( t , z ) = P ( t ) S ( t , z ) B ( t , z ) η ( t , z ) ,
R c = C r 1 ( z ) C r 2 ( z ) = 0 2 R / C g ( t , z ) T r 1 2 ( t , z ) d t 0 2 R / C g ( t , z ) T r 2 2 ( t , z ) d t = T 1 a 2 ( z ) T 2 a 2 ( z ) ,
δ = Δ ln [ T 1 a 2 ( z ) T 2 a 2 ( a ) ] Δ z .
0 z N ( z ) d z ,
δ = f ( z ) N ( z ) .
δ a / δ b ~ w a / w b .
β π ( z ) = V ( z ) C A T 2 ( z ) C r ( z ) ;
b ( z ) = C A β π ( z ) ,
b ( z ) = V ( z ) / T 2 ( z ) C r ( z ) .
b ( 0 ) ( z ) = b 0 ,
C r ( 0 ) ( z ) = 0 2 R / C P ( t ) S ( z - c t 2 ) × T r ( z - c t 2 ) η ( z - c t 2 ) d t ,
b ( 1 ) ( z ) = V ( z ) / [ T 2 ( z ) C r ( 1 ) ( z ) ] , C r ( 1 ) ( z ) = 0 2 R / C P ( t ) B ( 1 ) ( z - c t 2 ) S ( z - c t 2 ) × T r ( z - c t 2 ) η ( z - c t 2 ) d t b ( n ) ( z ) = V ( z ) / [ T 2 ( z ) C r ( n - 1 ) ( z ) ] , C r ( n ) ( z ) = 0 2 R / C P ( t ) B ( n - 1 ) ( z - c t 2 ) S ( z - c t 2 ) × T r ( z - c t 2 ) η ( z - c t 2 ) d t
b ( n ) ( z ) - b ( n - 1 ) ( z ) 2 d z < .
T 1 2 ( z ) = T w ( z ) T c ( z ) ;
T 2 2 ( z ) = [ T w ( z ) ] S 1 T c ( z ) ,
T w ( z ) = [ D f ( z ) R c ( z ) ] S 2 ,
T 1 2 ( z ) ( 0 ) = T w ( z ) ( 0 ) T c ( z ) , T 2 2 ( z ) ( 0 ) = [ T w ( z ) ( 0 ) ] S 1 T c ( z ) ,
R c ( z ) ( 0 ) = C r 1 ( z ) ( 0 ) / C r 2 ( z ) ( 0 ) .
T w ( z ) ( 1 ) = [ D f ( z ) / R c ( z ) ( 0 ) ] S 2 .
T 1 2 ( z ) ( n - 1 ) = T w ( z ) ( n - 1 ) T c ( z ) ; T 2 2 ( z ) ( n - 1 ) = [ T w ( z ) ( n - 1 ) ] S 1 T c ( z ) ; R c ( z ) ( n - 1 ) = C r 1 ( z ) ( n - 1 ) / C r 2 ( z ) ( n - 1 ) ; T w ( z ) ( n ) = [ D f ( z ) / R c ( z ) ( n - 1 ) ] S 2 .
T w ( z ) ( n ) - T w ( z ) ( n - 1 ) T w ( z ) ( n ) d z < .
W ( z ) = [ Δ ln T w ( z ) / Δ z ] / ( 2 α 1 ) .

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