Abstract

The performance of single-ended multiangle lidar for measurements of atmospheric extinction and backscattering is analyzed in the presence of shot noise. An algorithm for determining the transmission coefficient in the presence of horizontal inhomogeneities is described. The analysis indicates that real-time measurements of atmospheric properties with the multiangle lidar may be feasible even in inhomogeneous regions.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984), Chap. 9, p. 320.
  2. S. T. Shipley, D. H. Tracey, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
    [CrossRef] [PubMed]
  3. J. T. Sroga, E. W. Eloranta, S. T. Shipley, F. L. Roesler, P. J. Tryon, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 2: Calibration and data analysis,” Appl. Opt. 22, 3725–3732 (1983).
    [CrossRef] [PubMed]
  4. A. Ansmann, M. Riebesell, C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with a Raman lidar,” Opt. Lett. 15, 746–748 (1990).
    [CrossRef] [PubMed]
  5. G. J. Kunz, “Bipath method as a way to measure the spatial backscatter and extinction coefficients with lidar,” Appl. Opt. 26, 794–795 (1987).
    [CrossRef] [PubMed]
  6. H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
    [CrossRef] [PubMed]
  7. J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
    [CrossRef]
  8. M. R. Paulson, “Atmospheric horizontal-inhomogeneity effects on the optical depths determined by the double-evaluation-angle lidar technique,” Rep. TD 1600, DTIC AD-A212 836 (Naval Ocean Systems Center, San Diego, Calif., 1989).
  9. M. C. W. Sandford, “Laser scatter measurements in the mesosphere and above,” J. Atmos. Terr. Phys. 29, 1657–1662 (1967).
    [CrossRef]
  10. P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
    [CrossRef]
  11. H. Shimizu, Y. Sasano, H. Nakane, N. Sugimoto, I. Matsui, N. Takeuchi, “Large scale laser radar for measuring aerosol distribution over a wide area,” Appl. Opt. 24, 617–626 (1985).
    [CrossRef] [PubMed]
  12. J. Rothermel, W. Jones, “Ground-based measurements of atmospheric backscatter and absorption using coherent CO2 lidar,” Appl. Opt. 24, 3487–3496 (1985).
    [CrossRef] [PubMed]
  13. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
    [CrossRef] [PubMed]
  14. J. D. Klett, “Lider inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
    [CrossRef] [PubMed]
  15. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1970), p. 245.

1990

1988

1987

1985

1983

1981

1980

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

1969

P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
[CrossRef]

1967

M. C. W. Sandford, “Laser scatter measurements in the mesosphere and above,” J. Atmos. Terr. Phys. 29, 1657–1662 (1967).
[CrossRef]

Ansmann, A.

Eloranta, E. W.

Feller, W.

W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1970), p. 245.

Hamilton, P. M.

P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
[CrossRef]

Herman, B. M.

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

Hughes, H. G.

Jones, W.

Klett, J. D.

Kunz, G. J.

Matsui, I.

Measures, R. M.

R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984), Chap. 9, p. 320.

Nakane, H.

Paulson, M. R.

H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
[CrossRef] [PubMed]

M. R. Paulson, “Atmospheric horizontal-inhomogeneity effects on the optical depths determined by the double-evaluation-angle lidar technique,” Rep. TD 1600, DTIC AD-A212 836 (Naval Ocean Systems Center, San Diego, Calif., 1989).

Reagan, J. A.

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

Riebesell, M.

Roesler, F. L.

Rothermel, J.

Sandford, M. C. W.

M. C. W. Sandford, “Laser scatter measurements in the mesosphere and above,” J. Atmos. Terr. Phys. 29, 1657–1662 (1967).
[CrossRef]

Sasano, Y.

Shimizu, H.

Shipley, S. T.

Spinhirne, J. D.

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

Sroga, J. T.

Sugimoto, N.

Takeuchi, N.

Tracey, D. H.

Trauger, J. T.

Tryon, P. J.

Weinman, J. A.

Weitkamp, C.

Appl. Opt.

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

S. T. Shipley, D. H. Tracey, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
[CrossRef] [PubMed]

J. T. Sroga, E. W. Eloranta, S. T. Shipley, F. L. Roesler, P. J. Tryon, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 2: Calibration and data analysis,” Appl. Opt. 22, 3725–3732 (1983).
[CrossRef] [PubMed]

H. Shimizu, Y. Sasano, H. Nakane, N. Sugimoto, I. Matsui, N. Takeuchi, “Large scale laser radar for measuring aerosol distribution over a wide area,” Appl. Opt. 24, 617–626 (1985).
[CrossRef] [PubMed]

J. D. Klett, “Lider inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
[CrossRef] [PubMed]

J. Rothermel, W. Jones, “Ground-based measurements of atmospheric backscatter and absorption using coherent CO2 lidar,” Appl. Opt. 24, 3487–3496 (1985).
[CrossRef] [PubMed]

G. J. Kunz, “Bipath method as a way to measure the spatial backscatter and extinction coefficients with lidar,” Appl. Opt. 26, 794–795 (1987).
[CrossRef] [PubMed]

H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
[CrossRef] [PubMed]

Atmos. Environ.

P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
[CrossRef]

J. Appl. Meteorol.

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

J. Atmos. Terr. Phys.

M. C. W. Sandford, “Laser scatter measurements in the mesosphere and above,” J. Atmos. Terr. Phys. 29, 1657–1662 (1967).
[CrossRef]

Opt. Lett.

Other

W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1970), p. 245.

R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984), Chap. 9, p. 320.

M. R. Paulson, “Atmospheric horizontal-inhomogeneity effects on the optical depths determined by the double-evaluation-angle lidar technique,” Rep. TD 1600, DTIC AD-A212 836 (Naval Ocean Systems Center, San Diego, Calif., 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Expected lidar return for a model A of horizontal inhomogeneity [Eq. (40)1: 1, below inhomogeneity (T0 = 0.6, T1 = 1.0, Aβ = 0); 2, at the lower edge of inhomogeneity (T0 = 0.5, T1 = 1.0, Aβ = 1); 3, inside inhomogeneity (T0 = 0.4, T1 = 0.5, Aβ = 1); 4, inside inhomogeneity (T0 = 0.3, T1 = 0.6, Aβ = 1); 5, above inhomogeneity (T0 = 0.2, T1 = 0.6, Aβ = 0).

Fig. 2
Fig. 2

Expected idar return for a model B of horizontal inhomogeneity [Eq. (41)]; the different cases are defined in Fig. 1.

Fig. 3
Fig. 3

Algorithm performance for a model A of horizontal inhomogeneity with Δθ = 5°; the different cases are defined in Fig. 1.

Fig. 4
Fig. 4

Algorithm performance for a model A of horizontal inhomogeneity with Δθ = 1°; the different cases are defined in Fig. 1.

Fig. 5
Fig. 5

Algorithm performance for a model B of horizontal inhomogeneity with Δθ = 5°; the different cases are defined in Fig. 1.

Fig. 6
Fig. 6

Algorithm performance for a model B of horizontal inhomogeneity with Δθ = 1°; the different cases are defined in Fig. 1.

Equations (45)

Equations on this page are rendered with MathJax. Learn more.

E ( z , θ ) = C z 2 cos 2 θ β ( z , θ ) exp [ - 2 cos θ 0 z d z k ext ( z , θ ) ] ,
T ( R = z / cos θ ) exp [ - 2 cos θ 0 z d z k ext ( z , θ ) ] = [ Q ( z ) ] γ ,
γ = cos ( θ + Δ θ ) cos ( θ + Δ θ ) - cos θ ,
Q ( z ) E ( z / cos θ ) E [ z / cos ( θ + Δ θ ) ] cos 2 ( θ + Δ θ ) cos 2 θ .
k ext ( z ) = - 1 2 γ cos ( θ ) z ln Q ( z ) .
p ( N k ) = ( N s + N b ) N k N k ! exp [ - ( N s + N b ) ] ,
N k = N s + N b ,
σ N 2 = N k 2 - N k 2 = N s + N b .
n = 1 K k = 1 K N k ,
n = N s + N b ,
σ n 2 = ( N s + N b ) / K .
T ( z , θ ) = A γ ( n 1 - N b 1 n 2 - N b 2 ) γ ,
A = cos 2 ( θ ) cos 2 ( θ + Δ θ ) ,
γ = cos ( θ + Δ θ ) cos ( θ ) - cos ( θ + Δ θ ) .
T = A γ I γ ( N s 1 , N b 1 , K 1 ) I - γ ( N s 2 , N b 2 , K 2 ) ,
σ T 2 = A 2 γ [ I 2 γ ( N s 1 , N b 1 , K 1 ) I - 2 γ ( N s 2 , N b 2 , K 2 ) - I γ 2 ( N s 1 , N b 1 , K 1 ) I - γ 2 ( N s 2 , N b 2 , K 2 ) ] ,
I α ( N s , N b , K ) = ( n - N b ) α .
p ( n ) = [ K 2 π ( N s + N b ) ] 1 / 2 exp [ - K ( n - N s - N b ) 2 2 ( N s + N b ) ] .
I α ( N s , N b , K ) = [ K 2 π ( N s + N b ) ] 1 / 2 N b + N s d n ( n - N b ) α × exp [ - K ( n - N s - N b ) 2 2 ( N s + N b ) ] .
I α ( N s , N b , K ) = N s α π - ( 1 - ) δ d z ( 1 + z δ ) α exp ( - z 2 ) ,
δ 2 = K N s 2 2 ( N s + N b ) .
I α ( N s , N b , K ) = N s α n = 0 α 2 n ( 2 n - 1 ) ! ! 2 n δ 2 n + O [ exp ( - δ 2 ) ] ,
a 0 = 1 ,             a n = α ( α - 1 ) ( α - n + 1 ) / n ! ,             n 1.
σ T 2 T 2 = γ 2 [ N s 1 + N b 1 K 1 N s 1 2 + N s 2 + N b 2 K 2 N s 2 2 ] + γ 2 ( γ - 1 ) ( 3 γ - 5 ) ( N s 1 + N b 1 ) 2 2 K 1 2 N s 1 4 + γ 2 ( γ + 1 ) ( 3 γ + 5 ) ( N s 2 + N b 2 ) 2 2 K 2 2 N s 2 4 + 3 γ 4 ( N s 1 + N b 1 ) ( N s 2 + N b 2 ) 2 K 1 K 2 N s 1 2 N s 2 2 + O ( δ - 6 ) .
F ( z , θ ) = C β ( z , θ ) exp [ - 2 cos θ 0 z d z k ext ( z , θ ) ] = C β ( z , θ ) T ( z , θ ) .
β ( z , θ ) = β 0 ( z ) [ 1 + f β ( z , θ ) ] ,
k ext ( z , θ ) = k 0 ( z ) [ 1 + f k ( z , θ ) ] ,
f β ( z , θ m ) = f β ( z , θ n ) ,
f k ( z , θ m ) = f k ( z , θ n ) .
T ( z , θ n ) = [ F ( z , θ n ) F ( z , θ m ) ] γ m n ,
γ m n = cos ( θ m ) cos ( θ m ) - cos ( θ n ) .
θ ln F ( z , θ ) = - 2 tan θ cos θ 0 z d z k ext ( z ) .
G ( θ n ) = cos θ n [ F ( θ n + Δ θ ) - F ( θ n - Δ θ ) ] tan θ n F ( θ n ) const .
G ( θ i ) - G ( θ j ) = min ,             γ i j γ 0 .
G ( θ i ) - G ( θ i - 1 ) + G ( θ i ) - G ( θ i + 1 ) = min
F h ( z , θ ) = C β h ( z ) [ T h ( z ) ] 1 / cos θ C β 0 ( z ) [ T 0 ( z ) ] 1 / cos θ ,
T h ( z ) = [ F ( z , θ i ) / F ( z , θ j ) ] γ i j cos θ i , C β h ( z ) = F ( z , θ i ) [ T h ( z ) ] - 1 / cos θ i .
Δ F ( z , θ n ) = ln [ F ( z , θ n ) / F h ( z , θ n ) ] ln [ 1 + f β ( z , θ n ) ] - 2 cos θ n 0 z d z k 0 ( z ) f k ( z , θ n ) .
Δ F ( z , θ m ) = Δ F ( z , θ n ) .
cos θ m Δ F ( z , θ m ) = cos θ n Δ F ( z , θ n ) .
T ( z , θ n ) = [ F ( z , θ n + i ) F ( z , θ n - j ) ] γ ex ,
γ ex = cos ( θ n + i ) cos ( θ n - j ) cos ( θ n ) [ cos ( θ n - j ) - cos ( θ n + i ) ] γ 0 .
f ( θ ) = { exp [ - ( θ - θ c ) 2 / 2 θ w 2 ] , z 0 z z 1 0 , otherwise .
f ( θ ) = { exp [ - ( θ - θ c ) 2 / 2 θ w 2 ] , + 0.5 exp [ - ( θ - θ c + 4 θ w ) 2 / 2 θ w 2 ] ,             z 0 z z 1 0 , otherwise .
F ( z , θ ) = β ( z ) [ 1 + A β f ( θ ) ] T 0 ( z ) 1 / cos θ T 1 ( z ) A k f ( θ ) / cos θ .

Metrics