Abstract

The extended Huygens-Fresnel formulation is used to calculate the enhanced backscattered intensity as a function of the off-axis receiver distance for a bistatic lidar operating in atmospheric turbulence. The result is simple and compact and allows the regime where there is significant enhancement to be readily identified. In addition, the result depends only on the logamplitude covariance, which implies that the enhancement is due to incoherent turbulence perturbation effects.

© 1991 Optical Society of America

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References

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  1. V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, 1987).
  2. E. Jakeman, “Enhanced Backscattering Through a Deep Random Phase Screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988).
    [CrossRef]
  3. P. R. Tapster, A. R. Weeks, E. Jakeman, “Observation of Backscattering Enhancement through Atmospheric Phase Screens,” J. Opt. Soc. Am. A 6, 517–522 (1989).
    [CrossRef]
  4. G. Welch, R. Phillips, “Simulation of Enhanced Backscatter by a Phase Screen,” J. Opt. Soc. Am. A 7, 578–584 (1990).
    [CrossRef]
  5. R. F. Lutomirski, H. T. Yura, “Propagation of a Finite Optical Beam in an Inhomogeneous Medium,” Appl. Opt. 10, 1652–1658 (1971).
    [CrossRef] [PubMed]
  6. H. T. Yura, “Mutual Coherence Function of a Finite Cross Section Optical Beam Propagating in a Turbulent Medium,” Appl. Opt. 11, 1399–1406 (1972).
    [CrossRef] [PubMed]
  7. M. H. Lee, J. F. Holmes, J. R. Kerr, “Generalized Spherical Wave Mutual Coherence Function,” J. Opt. Soc. Am. 67, 1279–1281 (1977).
    [CrossRef]
  8. V. S. Rao Gudimetla, J. F. Holmes, R. A. Elliott, “Two-Point Joint-Density Function of the Intensity for a Laser-Generated Speckle Field after Propagation Through the Turbulent Atmosphere,” J. Opt. Soc. Am. A 7, 1008–1014 (1990).
    [CrossRef]

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1988

1977

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1971

Banakh, V. A.

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, 1987).

Elliott, R. A.

Holmes, J. F.

Jakeman, E.

Kerr, J. R.

Lee, M. H.

Lutomirski, R. F.

Mironov, V. L.

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, 1987).

Phillips, R.

Rao Gudimetla, V. S.

Tapster, P. R.

Weeks, A. R.

Welch, G.

Yura, H. T.

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Figures (2)

Fig. 1
Fig. 1

Bistatic backscattered intensity enhancement factor as a function of transmitter and receiver spacing.

Fig. 2
Fig. 2

Finite aperture backscattered intensity enhancement factor for the monostatic case as a function of the normalized aperture radius.

Equations (22)

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U ( ρ ) = k exp ( i k L ) 2 π i L d r U ( r ) exp [ i k 2 L ρ - r 2 + ψ 1 ( ρ , r ) ] ,
U ( r ) = U 0 exp ( - r 2 / 2 α 0 2 - i k r 2 / 2 F ) ,
U ( p ) = k exp ( i k L ) 2 π i L d ρ T ( ρ ) U ( ρ ) exp [ i k 2 L p - ρ 2 + ψ 2 ( p , ρ ) ] ,
T ( ρ 1 ) T * ( ρ 2 ) = 4 π k 2 T 0 2 δ ( ρ 1 - ρ 2 ) ,
I ( p ) = U ( p ) U * ( p ) = ( k 2 π L ) 2 d ρ 1 d ρ 2 T ( ρ 1 ) T * ( ρ 2 ) U ( ρ 1 ) U * ( ρ 2 ) × exp [ i k 2 L ( p - ρ 1 2 - p - ρ 2 2 ) + ψ 2 ( p , ρ 1 + ψ 2 * ( p , ρ 2 ) ] .
I ( p ) = T 0 2 U 0 2 π L 2 ( k 2 π L ) 2 d ρ d r 1 d r 2 × exp [ - r 1 2 + r 2 2 2 α 0 2 + i k 2 L ( 1 - L / F ) ( r 1 2 - r 2 2 ) - i k L ρ e ¯ · ( r ¯ 1 - r ¯ 2 ) ( r 1 - r 2 ) ] × exp [ ψ 1 ( ρ , r 1 ) + ψ 1 * ( ρ , r 2 ) + ψ 2 ( p , ρ ) + ψ 2 * ( p , ρ ) ] ,
= exp { - ½ [ D ψ ( r 1 - r 2 ) + D ψ ( 0 ) + D ψ ( r 1 - p ) + D ψ ( r 2 - p ) - D ψ ( r 1 - p ) - D ψ ( r 2 - p ) + 2 C χ ( o , p - r 1 ) + 2 C χ ( o , p - r 2 } = exp { - ½ [ D ψ ( r 1 - r 2 ) + 2 C χ ( o , p - r 1 ) + 2 C χ ( o , p - r 2 ) ] } ,
r = r 1 - r 2 ,             2 R = r 1 + r 2 ,
I ( p ) = T 0 2 U 0 2 π L 2 ( k 2 π L ) 2 d ρ d r d R × exp [ - ( R 2 + r 2 / 4 ) α 0 2 + i k L ( 1 - L F ) R · r - i k L ρ · r - 1 2 D ψ ( r ) + 2 C χ ( o , p - R - r 2 ) + 2 C χ ( o , p - R + r 2 ) ] .
d ρ exp ( - i k L ρ · r ) = ( 2 π L k ) 2 δ ( r ) .
I ( p ) = T 0 2 U 0 2 π L 2 d R exp [ - R 2 α 0 2 + 4 C χ ( o , p - R ) ] .
I ( p ) = T 0 2 U 0 2 α 0 2 π L 2 d R exp [ - R 2 + 4 C χ ( o , p - R α 0 ) ] ,
C χ ( o , p - R α 0 ) = 0.132 π 2 k 2 L 0 1 d t C n 2 ( t ) 0 d u u - 8 / 3 × sin 2 [ u 2 L t ( 1 - t ) 2 k ] J 0 [ u p - R α 0 ( 1 - t ) ] .
u = u α 0 ,             p = p / α 0 ,             Ω = α 0 2 k / L ,
C χ ( o , p - R α 0 ) = 2.386 ( α 0 ρ 0 ) 5 / 3 0 1 d t 0 d u u - 8.3 × sin 2 [ u t ( 1 - t ) 2 Ω ] J 0 [ u p - R ( 1 - t ) ] ,
BIEF ( p ) = I ( p ) I ( ) .
I ( ) = T 0 2 U 0 2 α 0 2 L 2 ,
BIEF ( p ) = 1 π d R exp [ - R 2 + 4 C χ ( o , p - R α 0 ) ] .
exp ( - R 2 / α 0 2 ) exp [ 4 C χ ( o , p - R ) ] .
σ χ 2 = 0.124 k 7 / 6 L 11 / 6 C n 2
BIEF A ( ρ ¯ 0 ) = aperture I ( p ¯ 0 + r ¯ ) d r ¯ aperture I ( ) d r ¯ = 1 A aperature BIEF ( p ¯ 0 + r ¯ ) d r ¯ ,
BIEF A ( 0 ) = 2 π A 0 r 0 BIEF ( r ) r d r ,

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