Abstract

A monostatic heterodyne lidar performance model is formulated to study the combined effects of beam truncation and refractive turbulence in the weak scintillation regime. The results show that there is a loss of signal power due to beam truncation and coherence loss, but there is also an enhancement of signal power due to log-amplitude covariance in suitable conditions of long paths with weak turbulence.

© 1984 Optical Society of America

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References

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  1. D. L. Fried, “Monostatic Laser Radar Average Antenna Gain in the Presence of Atmospheric Turbulence,” TR-221 (Optical Science Co., P.O. Box 446, Placentia, Calif. 92670, Sept.1976).
  2. S. S. R. Murty, J. W. Bilbro, “Atmospheric Effects on CO2 Laser Propagation,” NASA Technical Report 1357 (Nov.1978).
  3. S. F. Clifford, S. Wandzura, “Monostatic Heterodyne Lidar Performance: the Effect of the Turbulent Atmosphere,” Appl. Opt. 20, 514 (1981).
    [CrossRef] [PubMed]
  4. D. L. Fried, “Statistics of Wavefront Distortion,” J. Opt. Soc. Am. 55, 1427 (1965).
    [CrossRef]
  5. H. T. Yura, “SNR of Heterodyne Lidar Systems in the Presence of Atmospheric Turbulence,” Opt. Acta 26, 627 (1979).
    [CrossRef]
  6. B. J. Rye, “Refractive-Turbulence Contribution to Incoherent Backscatter Heterodyne Lidar Returns,” J. Opt. Soc. Am. 71, 687 (1981).
    [CrossRef]
  7. S. F. Clifford, L. Lading, “Monostatic Diffraction-Limited Lidars: the Impact of Optical Refractive Turbulence,” Appl. Opt. 22, 1696 (1983).
    [CrossRef] [PubMed]
  8. R. F. Lutomirski, H. T. Yura, “Propagation of a Finite Optical Beam in an Inhomogeneous Medium,” Appl. Opt. 10, 1652 (1971).
    [CrossRef] [PubMed]
  9. M. H. Lee, J. F. Holmes, J. R. Kerr, “Generalized Spherical Wave Mutual Coherence Function,” J. Opt. Soc. Am. 67, 1279 (1977).
    [CrossRef]
  10. R. L. Fante, “EM Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669 (1975).
    [CrossRef]
  11. S. S. R. Murty, J. W. Bilbro, to be published as NASA Technical Report (1984).

1983 (1)

1981 (2)

1979 (1)

H. T. Yura, “SNR of Heterodyne Lidar Systems in the Presence of Atmospheric Turbulence,” Opt. Acta 26, 627 (1979).
[CrossRef]

1977 (1)

1975 (1)

R. L. Fante, “EM Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669 (1975).
[CrossRef]

1971 (1)

1965 (1)

Bilbro, J. W.

S. S. R. Murty, J. W. Bilbro, to be published as NASA Technical Report (1984).

S. S. R. Murty, J. W. Bilbro, “Atmospheric Effects on CO2 Laser Propagation,” NASA Technical Report 1357 (Nov.1978).

Clifford, S. F.

Fante, R. L.

R. L. Fante, “EM Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669 (1975).
[CrossRef]

Fried, D. L.

D. L. Fried, “Statistics of Wavefront Distortion,” J. Opt. Soc. Am. 55, 1427 (1965).
[CrossRef]

D. L. Fried, “Monostatic Laser Radar Average Antenna Gain in the Presence of Atmospheric Turbulence,” TR-221 (Optical Science Co., P.O. Box 446, Placentia, Calif. 92670, Sept.1976).

Holmes, J. F.

Kerr, J. R.

Lading, L.

Lee, M. H.

Lutomirski, R. F.

Murty, S. S. R.

S. S. R. Murty, J. W. Bilbro, to be published as NASA Technical Report (1984).

S. S. R. Murty, J. W. Bilbro, “Atmospheric Effects on CO2 Laser Propagation,” NASA Technical Report 1357 (Nov.1978).

Rye, B. J.

Wandzura, S.

Yura, H. T.

H. T. Yura, “SNR of Heterodyne Lidar Systems in the Presence of Atmospheric Turbulence,” Opt. Acta 26, 627 (1979).
[CrossRef]

R. F. Lutomirski, H. T. Yura, “Propagation of a Finite Optical Beam in an Inhomogeneous Medium,” Appl. Opt. 10, 1652 (1971).
[CrossRef] [PubMed]

Appl. Opt. (3)

J. Opt. Soc. Am. (3)

Opt. Acta (1)

H. T. Yura, “SNR of Heterodyne Lidar Systems in the Presence of Atmospheric Turbulence,” Opt. Acta 26, 627 (1979).
[CrossRef]

Proc. IEEE (1)

R. L. Fante, “EM Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669 (1975).
[CrossRef]

Other (3)

S. S. R. Murty, J. W. Bilbro, to be published as NASA Technical Report (1984).

D. L. Fried, “Monostatic Laser Radar Average Antenna Gain in the Presence of Atmospheric Turbulence,” TR-221 (Optical Science Co., P.O. Box 446, Placentia, Calif. 92670, Sept.1976).

S. S. R. Murty, J. W. Bilbro, “Atmospheric Effects on CO2 Laser Propagation,” NASA Technical Report 1357 (Nov.1978).

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Figures (4)

Fig. 1
Fig. 1

Sketch of the telescope, scatterers, and coordinate system.

Fig. 2
Fig. 2

Area of integration is the area of overlap of circles of diameter D.

Fig. 3
Fig. 3

SNR loss and gain due to beam truncation, coherence loss, and scintillations.

Fig. 4
Fig. 4

SNR loss and gain due to beam truncation, coherence loss, and scintillations.

Equations (28)

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W ( r 2 ) = 1 if r 2 = D / 2 = 0 if r 2 > D / 2.
U ( p ) = - i k exp ( i k L ) 2 π L U 1 ( r 1 ) exp [ i k ( p - r 1 ) 2 2 L + ψ ( r 1 , p ) ] d 2 r 1 .
U 1 ( r 1 ) = u 0 exp ( - r 1 2 2 a 2 - i k r 1 2 2 f ) ,             r 1 D / 2 = 0             otherwise .
U 2 ( r 2 ) = ( σ 4 π L 2 ) 1 / 2 U ( p ) exp [ - i k r 2 2 2 f + i k ( p - r 2 ) 2 2 L + i ( k L + Δ ω t ) + ψ ( p , r 2 ) ] ,
U l ( r 2 ) = U l exp ( - r 2 2 / 2 a 2 ) ,
i s = 2 η U 2 ( r 2 ) U l * ( r 2 ) W ( r 2 ) d 2 r 2 ,
i s = - i k η π L ( σ 4 π L 2 ) 1 / 2 exp ( i 2 k L + i Δ ω t ) U 1 ( r 1 ) × exp [ i k 2 L ( p - r 1 ) 2 + ψ 1 ( p , r 1 ) ] d 2 r 1 · U 1 ( r 2 ) exp [ i k 2 L ( p - r 2 ) 2 + ψ ( p , r 2 ) ] W ( r 2 ) d 2 r 2 .
I s 2 = i s 2 n ( r ) d r d V = c τ 2 i s 2 n ( r ) d r d 2 p .
i s 2 = k 2 η 2 σ 8 π 3 L 4 U 1 ( r 1 ) U 1 * ( r 3 ) × exp [ i k 2 L ( p - r 1 ) 2 - ( p - r 3 ) 2 ] d 2 r 1 d 2 r 3 × U 1 ( r 2 ) U 1 * ( r 4 ) exp { i k 2 L [ ( p - r 2 ) 2 - ( p - r 4 ) 2 ] } × M ( r 1 , r 2 , r 3 , r 6 ) W ( r 2 ) W ( r 4 ) d 2 r 2 d 2 r 4 ,
M ( r 1 , r 2 , r 3 , r 4 ) = exp [ ψ ( p , r 1 ) + ψ ( r 2 , p ) + ψ * ( p , r 3 ) + ψ * ( r 4 , p ) ]
M ( r 1 , r 2 , r 3 , r 4 ) = exp [ 2 C x ( r 1 - r 3 ) + 2 C x ( r 3 - r 4 ) ] × exp - ( 1 / 2 ) [ D 13 + D 14 + D 24 + D 23 - D 12 - D 34 - i ( D 1 l Φ - D 3 l Φ ) ] ,
D ( ρ ) = 2 ( ρ / ρ 0 ) 5 / 3 , ρ 0 = 1.089 k 2 L 0 1 d z c n 2 ( z ) z 5 / 3 .
C x ( ρ ) = 4 π 2 k 2 0 L d z 0 d K K ϕ n ( K ) J 0 ( K ρ z / L ) × sin 2 [ K 2 z ( L - z ) 2 K L ] ,
C x ( ρ ) = C x ( o ) [ 1 - 10.9 ( ρ 2 λ L ) 5 / 6 + 10.7 ρ 2 λ L ] .
R A = ½ ( r 1 + r 3 ) , ρ A = r 1 - r 3 , R B = ½ ( r 2 + r 4 ) , ρ B = r 2 - r 4 .
i s 2 = k 2 η 2 σ 8 π 3 L 4 u 0 2 u l 2 { exp { - ρ A 2 4 a 2 - i k L ρ A · p } d 2 ρ A × exp { - R A 2 a 2 + i k L ( 1 - L f ) · R A · ρ A } d 2 R A × exp { - ρ B 2 4 a 2 - i k L ρ B · p } d 2 ρ B × exp [ - R B 2 a 2 + i k L ρ B · R B ( 1 - L f ) ] W ( R B + ρ B 2 ) · W ( R B - ρ B 2 ) · M ( ρ A , ρ B , R A , R B ) d 2 R B } .
S = i s 2 d 2 p = k 2 η 2 σ 8 π 3 L 4 u 0 2 u i 2 d 2 ρ × exp [ - i k L p · ( ρ A + ρ B ) ] d 2 ρ A exp ( - ρ A 2 4 a 2 ) × d 2 ρ B exp ( - ρ B 2 4 a 2 )     d 2 R A × exp ( - R A 2 a 2 + i α R A · ρ A ) d 2 R B exp ( - R B 2 a 2 + i α R B · ρ B ) × W ( R B + ρ B 2 ) W ( R B - ρ B 2 ) · M ( ρ A , ρ B , R A , R B ) ,
δ ( x ) = 1 ( 2 π ) 2 exp ( - i k · x ) d 2 k ,
S = k 2 η 2 σ u 0 2 u l 2 8 π 3 L 4 · ( 2 π L k ) 2 d 2 ρ A δ ( ρ A + ρ B ) d 2 R A d 2 ρ B × d 2 R B exp [ - ρ A 2 + ρ B 2 4 a 2 - R A 2 + R B 2 a 2 + i α ( R A · ρ A + R B · ρ B ) ] × W ( R B + ρ B 2 ) W ( R B - ρ B 2 ) M ( ρ A , ρ B , R A , R B ) .
S = ( 2 π L k u 0 u 1 ) 2 k 2 η 2 σ 8 π 3 L 4 d 2 ρ B d 2 R A d 2 R B × exp [ - ρ B 2 2 a 2 - R A 2 + R B 2 a 2 + i α ( R B - R A ) · ρ B ] × M 1 ( ρ B , R A , R B ) · W ( R B + ρ B 2 ) W ( R B - ρ B 2 ) ,
M 1 ( ρ B , R A , R B ) = exp [ 2 C x ( R A - R B - ρ B ) + 2 C x ( R A - R B + ρ B ) ] × exp - [ D ( ρ B ) + D ( R A - R B ) - ½ D ( R A - R B - ρ B ) - ½ D ( R A - R B + ρ B ) ] .
δ = D / 2 a , δ 0 for plane wave , δ for infinite Gaussian wave , x = ρ B / D , u = 2 R A / D , v = 2 R B / D , η = ϕ - ψ , ξ = θ - ψ .
S = ( 2 π L k u 0 u 1 ) 2 k 2 η 2 σ D 6 · 2 π 8 π 3 L 4 0 1 d x 0 π / 2 d ξ 0 π / 2 d η × 0 ν ( η ) d v 0 1 d u · P ( x , u , η , ξ ) ,
exp { 0.184 ( N 0 A ) 5 / 3 [ 1 - 5.45 A 5 / 3 ( W 1 5 / 6 + W 2 5 / 6 ) + 5.35 A 2 ( W 1 + W 2 ) ] } × exp [ - 2 N 0 5 / 3 ( x 5 / 3 + 0.315 W 3 5 / 3 - 0.5 W 1 5 / 3 - 0.5 W 2 5 / 3 ) ] ,
W 1 2 = 0.25 W 3 2 + x 2 - u x cos ξ - v x cos η , W 2 2 = 0.25 W 3 2 + x 2 + u x cos ξ + v x cos η , W 3 2 = u 2 + v 2 - 2 u v cos ( η - ξ ) , ν ( η ) = ( 1 - x 2 sin η ) 1 / 2 - x cos η , N 0 = D / ρ 0 ,             A = D / ( λ L ) 1 / 2 ,             α = π 2 A 2 ( 1 - L f ) . }
σ x 2 = 0.12 K 7 / 16 L 11 / 16 C n 2 ,
σ 0 = ( 0.545 k 2 L C n 2 ) - 3 / 5 .
σ x 2 = 0.0492 ( N 0 / A ) 5 / 3 .

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