Abstract

Sources of systematic, modeling, and calibration errors that affect the interpretation and calibration of lidar aerosol backscatter data are discussed. The treatment pertains primarily to ground-based pulsed CO2 lidars that probe the troposphere and are calibrated using hard calibration targets. However, a large part of the analysis is relevant to other types of lidar system such as lidars operating at other wavelengths; cw focused lidars; airborne or earth-orbiting lidars; lidars measuring other regions of the atmosphere; lidars measuring nonaerosol elastic or inelastic backscatter; and lidars employing other calibration techniques.

© 1985 Optical Society of America

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References

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  1. M. Halem, R. Dlouhy, “Satellite Meteorology/Remote Sensing Applications,” Proc. AMS 1, 272 (1984).
  2. R. T. Menzies, M. J. Kavaya, P. H. Flamant, D. A. Haner, “Atmospheric Aerosol Backscatter Measurements Using a Tunable Coherent CO2 Lidar,” Appl. Opt. 23, 2510 (1984).
    [CrossRef] [PubMed]
  3. M. J. Kavaya, R. T. Menzies, D. A. Haner, U. P. Oppenheim, P. H. Flamant, “Target Reflectance Measurements for Calibration of Lidar Atmospheric Backscatter Data,” Appl. Opt. 22, 2619 (1983).
    [CrossRef] [PubMed]
  4. W. Staehr, W. Lahmann, C. Weitkamp, “Range-Resolved Differential Absorption Lidar: Optimization of Range and Sensitivity,” Appl. Opt. 24, 1950 (1985).
    [CrossRef] [PubMed]
  5. B. J. Rye, “Refractive-Turbulence Contribution to Incoherent Backscatter Heterodyne Lidar Returns,” J. Opt. Soc. Am. 71, 687 (1981).
    [CrossRef]
  6. J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and Target Detection with a Heterodyne-Reception Optical Radar,” Appl. Opt. 20, 3292 (1981).
    [CrossRef] [PubMed]
  7. J. Y. Wang, “Heterodyne Laser Radar SNR from a Diffuse Target Containing Multiple Glints,” Appl. Opt 21, 464 (1982).
    [CrossRef] [PubMed]
  8. V. S. Rao Gudimetla, J. F. Holmes, “Probability Density Function of the Intensity for a Laser-Generated Speckle Field After Propagation Through the Turbulent Atmosphere,” J. Opt. Soc. Am. 72, 1213 (1982).
    [CrossRef]
  9. M. J. Kavaya, R. T. Menzies, “Aerosol Backscatter Lidar Calibration and Data Interpretation,” Publication 84–6, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif. (1984).
  10. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).
  11. D. S. Zrnic, “Moments of Estimated Input Power for Finite Sample Averages of Radar Receiver Outputs,” IEEE Trans. Aerosp. Electron. Syst. AES-11, 109 (1975).
    [CrossRef]
  12. K. Sassen, G. C. Dodd, “Lidar Crossover Function and Misalignment Effects,” Appl. Opt. 21, 3126 (1982).
    [CrossRef]
  13. W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
    [CrossRef]
  14. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere” AFCRL-72-0497 (AFCRL, Hanscom Air Force Base, Bedford, Mass., Aug.1972).
  15. L. S. Rothman et al., “AFGL Atmospheric Absorption Line Parameters Compilation: 1982 Edition,” Appl. Opt. 22, 2247 (1983).
    [CrossRef] [PubMed]
  16. F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL-TR-80-0067 (AFGL, Hanscom Air Force Base, Bedford, Mass., Feb.1980).

1985

1984

1983

1982

1981

1975

D. S. Zrnic, “Moments of Estimated Input Power for Finite Sample Averages of Radar Receiver Outputs,” IEEE Trans. Aerosp. Electron. Syst. AES-11, 109 (1975).
[CrossRef]

1969

W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).

Capron, B. A.

Dlouhy, R.

M. Halem, R. Dlouhy, “Satellite Meteorology/Remote Sensing Applications,” Proc. AMS 1, 272 (1984).

Dodd, G. C.

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere” AFCRL-72-0497 (AFCRL, Hanscom Air Force Base, Bedford, Mass., Aug.1972).

Flamant, P. H.

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere” AFCRL-72-0497 (AFCRL, Hanscom Air Force Base, Bedford, Mass., Aug.1972).

Halem, M.

M. Halem, R. Dlouhy, “Satellite Meteorology/Remote Sensing Applications,” Proc. AMS 1, 272 (1984).

Haner, D. A.

Harney, R. C.

Holmes, J. F.

Kavaya, M. J.

Kneizys, F. X.

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL-TR-80-0067 (AFGL, Hanscom Air Force Base, Bedford, Mass., Feb.1980).

Krupke, W. F.

W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Lahmann, W.

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere” AFCRL-72-0497 (AFCRL, Hanscom Air Force Base, Bedford, Mass., Aug.1972).

Menzies, R. T.

Oppenheim, U. P.

Rao Gudimetla, V. S.

Rothman, L. S.

Rye, B. J.

Sassen, K.

Selby, J. E. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere” AFCRL-72-0497 (AFCRL, Hanscom Air Force Base, Bedford, Mass., Aug.1972).

Shapiro, J. H.

Sooy, W. R.

W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Staehr, W.

Volz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere” AFCRL-72-0497 (AFCRL, Hanscom Air Force Base, Bedford, Mass., Aug.1972).

Wang, J. Y.

J. Y. Wang, “Heterodyne Laser Radar SNR from a Diffuse Target Containing Multiple Glints,” Appl. Opt 21, 464 (1982).
[CrossRef] [PubMed]

Weitkamp, C.

Zrnic, D. S.

D. S. Zrnic, “Moments of Estimated Input Power for Finite Sample Averages of Radar Receiver Outputs,” IEEE Trans. Aerosp. Electron. Syst. AES-11, 109 (1975).
[CrossRef]

Appl. Opt

J. Y. Wang, “Heterodyne Laser Radar SNR from a Diffuse Target Containing Multiple Glints,” Appl. Opt 21, 464 (1982).
[CrossRef] [PubMed]

Appl. Opt.

IEEE J. Quantum Electron.

W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

D. S. Zrnic, “Moments of Estimated Input Power for Finite Sample Averages of Radar Receiver Outputs,” IEEE Trans. Aerosp. Electron. Syst. AES-11, 109 (1975).
[CrossRef]

J. Opt. Soc. Am.

Proc. AMS

M. Halem, R. Dlouhy, “Satellite Meteorology/Remote Sensing Applications,” Proc. AMS 1, 272 (1984).

Other

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere” AFCRL-72-0497 (AFCRL, Hanscom Air Force Base, Bedford, Mass., Aug.1972).

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL-TR-80-0067 (AFGL, Hanscom Air Force Base, Bedford, Mass., Feb.1980).

M. J. Kavaya, R. T. Menzies, “Aerosol Backscatter Lidar Calibration and Data Interpretation,” Publication 84–6, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif. (1984).

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).

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Figures (7)

Fig. 1
Fig. 1

Possible steps in lidar aerosol backscatter data processing.

Fig. 2
Fig. 2

Pulsed lidar temporal profile examples for (a) the transmitted laser pulse power, (b) the backscattered power from the atmospheric aerosol, and (c) the backscattered power from a hard target.

Fig. 3
Fig. 3

Calculated error in the estimated mean value of a random variable x due to averaging the functions √x and lnx vs M where the probability density function of x is the gamma density function of order M.

Fig. 4
Fig. 4

Calculated error vs range due to the assumption of a rectangular transmitted-pulse profile when the actual profile is bilevel with duration τp and parameters a and b.

Fig. 5
Fig. 5

Modeled telescope overlap function of the JPL lidar system vs range at the 10P(20) CO2 laser line as a function of various detector positions (in millimeters) with respect to the optical axis and lying in the receiver focal plane.

Fig. 6
Fig. 6

Flow diagram depicting the main components in the lidar calibration and β profile computation.

Fig. 7
Fig. 7

Plot of error vs altitude in calculated β values resulting from the assumption of incorrect atmospheric models or boundary layer altitude. The nominal backscatter profile used actual 21 July 1983 backscatter data at the 10P(20) CO2 laser line; a mid-latitude–summer temperature, pressure, and humidity profile; and a boundary layer altitude of 1.5 km.

Equations (23)

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P b ( t ) = c ( t τ p ) / 2 c t / 2 P t b ( t 2 R c ) β ( R ) A R 2 η O ( R ) × exp [ 2 0 R α b ( R ) d R ] d R ,
P b ( t ) = β ( R b ) A η O ( R b ) c ( t τ p ) / 2 c t / 2 P t b ( t 2 R c ) R 2 × exp [ 2 0 R α b ( R ) d R ] d R .
P b ( R b ) = β ( R b ) A R b 2 η O ( R b ) exp [ 2 0 R b α b ( R ) d R ] c 2 0 τ p P t b ( t ) d t .
P s ( t ) = P t s ( t 2 R s c ) ρ * A R s 2 η O ( R s ) × exp [ 2 0 R s α s ( R ) d R ] ,
I s = 2 R s c 2 R s c + τ p P s ( t ) d t = ρ * A R s 2 η O ( R s ) exp [ 2 0 R s α s ( R ) d R ] E t s .
β ( R b ) = P b ( t ) E t b × E t s I s × ρ * × O ( R s ) O ( R b ) × 2 c × R b 2 R s 2 × exp [ 2 0 R s α s ( R ) d R ] exp [ 2 0 R s α s ( R ) d R ] ,
V t ( t ) = G t × F t [ P t ( t ) ] * [ 1 τ t exp ( t / τ t ) × H ( t ) ] ,
V b ( t ) = G b × F b [ P b ( t ) ] * [ 1 τ b exp ( t / τ b ) × H ( t ) ] ,
V s ( t ) = G s × F s [ P s ( t ) ] * [ 1 τ s exp ( t / τ s ) × H ( t ) ] ,
V t b ( t ) = G t P t b ( t ) ,
V t s ( t ) = G t P t s ( t ) .
V b ( t ) = G b × F r { P b ( t ) } ,
V s ( t ) = G s × F r { P s ( t ) } .
β ( R b ) = F r 1 { V b ( t ) / G b } 0 r p V t b ( t ) d t × 0 r p V t s ( t ) d t 2 R s c 2 R s c + τ p F r 1 { V s ( t ) / G s } d t × ρ * × O ( R s ) O ( R b ) × 2 c × R b 2 R s 2 × exp [ 2 0 R s α s ( R ) d R ] exp [ 2 0 R b α b ( R ) d R ] ,
< β ( R b ) > = 1 N b i = 1 N b F r 1 [ V b i ( t ) / G b ] 0 τ p i V t b i ( t ) d t 1 N s j = 1 N s 2 R s c 2 R ¯ s c + τ p j F r 1 [ V s j ( t ) / G s ] d t 0 τ p j V t s j ( t ) d t × ρ * × O ( R s ) O ( R b ) × 2 c × R b 2 R s 2 × exp [ 2 0 R s α s ( R ) d R ] exp [ 2 0 R b α b ( R ) d R ] ,
< y > = < x > = x p ( x ) d x
F r 1 { < F r ( x ) > } = F r 1 { F r ( x ) p ( x ) d x } .
< x > 2 < x > = π M [ 1 × 3 × 5 × × ( 2 M 1 ) ( M 1 ) ! × 2 M ] 2 ,
exp [ < ln x > ] < x > = ( 0 . 561 ) M 1 [ exp n = 1 M 1 1 n ] ,
S = 1 N i = 1 N K i E i ,
S = 1 N i = 1 N K i 1 N i = 1 N E i .
S S S = i = 1 N K i ε i E 0 i = 1 N K i + 0 ( ε i E 0 ) 2 .
P 1 = ( a b a + b 1 ) P 0 .

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