Abstract

The importance of multiple scattering for lidar detection of a spherical object obscured by an aerosol is assessed using Monte Carlo radiative transfer calculations. Multiple scattering correction factors are significant and depend on the location and size of the object, and the field of view and time resolution of the detector.

© 1990 Optical Society of America

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References

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  1. G. N. Plass, G. W. Kattawar, “Monte Carlo Calculations of Light Scattering from Clouds,” Appl. Opt. 7, 415–419 (1968).
    [CrossRef] [PubMed]
  2. G. N. Plass, G. W. Kattawar, “Reflection of Light Pulses from Clouds,” Appl. Opt. 10, 2304–2310 (1971).
    [CrossRef] [PubMed]
  3. R. C. Anderson, E. V. Browell, “First- and Second-Order from Clouds Illuminated by Finite Beams,” Appl. Backscattering Opt. 11, 1345–1351 (1972).
    [CrossRef]
  4. K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
    [CrossRef]
  5. I. V. Samokhvalov, “Double-Scattering Approximation of Lidar Equation for Inhomogeneous Atmosphere,” Opt. Lett. 4, 12–14 (1978).
    [CrossRef]
  6. C. M. R. Platt, “Remote Sounding of High Clouds. III: Monte Carlo Calculations of Multiple-Scattered Lidar Returns,” J. Atmos. Sci. 38, 156–167 (1981).
    [CrossRef]
  7. W. G. Tam, “Aerosol Backscattering of a Laser Beam,” Appl. Opt. 22, 2965–2969 (1983).
    [CrossRef] [PubMed]
  8. T. Duracz, N. J. McCormick, “Radiative Transfer Calculations for Characterizing Obscured Surfaces Using Time-Dependent Backscattered Pulses,” Appl. Opt. 28, 544–552 (1989).
    [CrossRef] [PubMed]

1989 (1)

1983 (1)

1981 (1)

C. M. R. Platt, “Remote Sounding of High Clouds. III: Monte Carlo Calculations of Multiple-Scattered Lidar Returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

1978 (1)

1976 (1)

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

1972 (1)

R. C. Anderson, E. V. Browell, “First- and Second-Order from Clouds Illuminated by Finite Beams,” Appl. Backscattering Opt. 11, 1345–1351 (1972).
[CrossRef]

1971 (1)

1968 (1)

Anderson, R. C.

R. C. Anderson, E. V. Browell, “First- and Second-Order from Clouds Illuminated by Finite Beams,” Appl. Backscattering Opt. 11, 1345–1351 (1972).
[CrossRef]

Browell, E. V.

R. C. Anderson, E. V. Browell, “First- and Second-Order from Clouds Illuminated by Finite Beams,” Appl. Backscattering Opt. 11, 1345–1351 (1972).
[CrossRef]

Duracz, T.

Kattawar, G. W.

Kunkel, K. E.

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

McCormick, N. J.

Plass, G. N.

Platt, C. M. R.

C. M. R. Platt, “Remote Sounding of High Clouds. III: Monte Carlo Calculations of Multiple-Scattered Lidar Returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

Samokhvalov, I. V.

Tam, W. G.

Weinman, J. A.

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Appl. Backscattering Opt. (1)

R. C. Anderson, E. V. Browell, “First- and Second-Order from Clouds Illuminated by Finite Beams,” Appl. Backscattering Opt. 11, 1345–1351 (1972).
[CrossRef]

Appl. Opt. (4)

J. Atmos. Sci. (2)

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

C. M. R. Platt, “Remote Sounding of High Clouds. III: Monte Carlo Calculations of Multiple-Scattered Lidar Returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

Opt. Lett. (1)

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Figures (15)

Fig. 1
Fig. 1

Schematic of a spherical object embedded in an aerosol.

Fig. 2
Fig. 2

Returned signal vs time for a sphere of radius 0.01 with its center at distance 4 from a lidar whose FOV half-angle is 5 × 10−3 rad. Time bin duration is 0.05.

Fig. 3
Fig. 3

Returned signal normalized to that in Fig. 2 vs time for a sphere of radius 0.01 with its center at distance 5 from a lidar whose FOV half-angle is 5 × 10−3 rad. Time bin duration is 0.05.

Fig. 4
Fig. 4

Returned signal normalized to that in Fig. 2 vs time for a sphere of radius 0.01 with its center at distance 5 from a lidar whose FOV half-angle is 5 × 10−2 rad. Time bin duration is 0.05.

Fig. 5
Fig. 5

Returned signal vs time for a sphere of radius 0.01 with its center at distance 4 from a lidar whose FOV half-angle is 5 × 10−3 rad. Time bin duration is 0.25.

Fig. 6
Fig. 6

Returned signal normalized to that in Fig. 5 vs time for a sphere of radius 0.01 with its center at distance 5 from a lidar whose FOV half-angle is 5 × 10−3 rad. Time bin duration is 0.25.

Fig. 7
Fig. 7

Returned signal normalized to that in Fig. 5 vs time for a sphere of radius 0.01 with its center at distance 5 from a lidar whose FOV half-angle is 5 × 10−2 rad. Time bin duration is 0.25.

Fig. 8
Fig. 8

Multiple scattering correction factor for the symmetric peak time bin for a sphere of radius 0.01 vs the lidar-to-sphere center distance and detector FOV half-angle. Symmetric time bin duration is 0.05.

Fig. 9
Fig. 9

Multiple scattering correction factor for the symmetric peak time bin for a sphere of radius 0.01 vs the lidar-to-sphere center distance and detector FOV half-angle. Symmetric time bin duration is 0.15.

Fig. 10
Fig. 10

Multiple scattering correction factor for the symmetric peak time bin for a sphere of radius 0.01 vs the lidar-to-sphere center distance and detector FOV half-angle. Symmetric time bin duration is 0.25.

Fig. 11
Fig. 11

Multiple scattering correction factor for the symmetric peak time bin for a sphere of radius 0.1 vs the lidar-to-sphere center distance and detector FOV half-angle. Symmetric time bin duration is 0.05.

Fig. 12
Fig. 12

Multiple scattering correction factor for the symmetric peak time bin for a sphere of radius 0.1 vs the lidar-to-sphere center distance and detector FOV half-angle. Symmetric time bin duration is 0.25.

Fig. 13
Fig. 13

Normalized returned signal for a sphere of radius 0.01 vs the lidar-to-sphere center distance and detector FOV half-angle. Symmetric time bin duration is 0.25.

Fig. 14
Fig. 14

Multiple scattering correction factor for a fixed time bin grid for a sphere of radius 0.01 vs the lidar-to-sphere center distance and detector FOV half-angle. Time bin duration is 0.25.

Fig. 15
Fig. 15

Multiple scattering correction factor for a fixed time bin grid for a sphere of radius 0.01 vs the lidar-to-sphere center distance. The detector FOV half-angle is 10−1 and the time bin duration is 0.25 rad.

Equations (17)

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x a + r o < x o < x b - r o , y o 0 , z o = 0.
d 2 θ x o ,
θ x o > r o .
2 π - 1 1 p ( μ ) d μ = 1 .
S i j ( t ) = K w ( t j ) r - 2 exp ( - d ) p ( μ ) δ ( t - t j - r / v ) ,
S ( t ) = K ( a o / 2 π ) r - 2 δ ( t - 2 r / v ) , y o < r o , = 0 , otherwise .
r = t d v / 2 ,
a o = S o π ( t d v ) 2 / 2 K .
( x o - r ) 2 + y o 2 = r o 2 .
S ( 1 ) ( t ) = K exp [ - 2 d ( t / 2 ) ] { 2 ( v t ) - 2 ω p ( - 1 ) × [ Θ ( t - 2 x a / v ) - Θ ( t - 2 r / v ) ] + r - 2 ( a o / 2 π ) δ ( t - 2 r / v ) } , y o < r o , = K exp [ - 2 d ( t / 2 ) ] 2 ( v t ) - 2 ω p ( - 1 ) Θ ( t - 2 x a / v ) , y o > r o ,
Θ ( t ) = 1 , t 0 , = 0 , t < 0.
S ( t ) = i , j S i j ( t ) = B ( t ) + R ( t ) ,
S k = i , j Δ t k S i j ( t ) d t ,
Δ t k = [ ( k - 1 ) Δ t , k Δ t ] , k 1.
C k = S k [ N Δ t k S ( 1 ) ( t ) d t ] - 1 ,
e k = S k - 1 { i , j [ Δ t k S i j ( t ) d t ] 2 } 1 / 2 .
Δ t s p = [ 2 ( x o - r o ) - Δ t / 2 , 2 ( x o - r o ) + Δ t / 2 ] .

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