Abstract

The impact of refractive turbulence on monostatic and bistatic lidars is investigated; a phase screen model is used. Experimental verifications are given. For monostatic lidars perturbing lens effects dominate, for bistatic lidars tilt effects dominate. Monostatic systems are the least sensitive to refractive turbulence.

© 1984 Optical Society of America

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References

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  1. S. F. Clifford, L. Lading, “Monostatic Diffraction-Limited Lidars: the Impact of Optical Refractive Turbulence,” Appl. Opt. 22, 1696 (1983).
    [CrossRef] [PubMed]
  2. S. F. Clifford, S. M. Wandzura, “Monostatic Heterodyne Lidar Performance: the Effect of the Turbulent Atmosphere,” Appl. Opt. 20, 514 (1981).
    [CrossRef] [PubMed]
  3. B. J. Rye, “Refractive-Index Turbulence Contribution to Incoherent Backscatter Heterodyne Lidar Returns,” J. Opt. Soc. Am. 71, 687 (1981).
    [CrossRef]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  5. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 10.
  6. D. L. Fried, “Statistics of Wavefront Distortion,” J. Opt. Soc. Am. 55, 1427 (1965).
    [CrossRef]
  7. S. M. Wandzura, “Meaning of Quadratic Structure Functions,” J. Opt. Soc. Am. 70, 745 (1980).
    [CrossRef]
  8. S. F. Clifford, “The Classical Theory of Wave Propagation in a Turbulent Medium,” in Laser Beam Propagation in the Atmosphere, J. W. Srohbehn, Ed. (Springer, Berlin, 1978), pp. 9–41.
    [CrossRef]
  9. L. Lading, “A Fourier Optical Model for the Laser Doppler Velocimeter,” Opto-electronics 4, 385 (1972).
    [CrossRef]
  10. V. I. Tatarski, “The Effect of the Turbulent Atmosphere on Wave Propagation,” IPST Catalog 5319 (National Technical Information Service, Springfield, Va., 1971).

1983

1981

1980

1972

L. Lading, “A Fourier Optical Model for the Laser Doppler Velocimeter,” Opto-electronics 4, 385 (1972).
[CrossRef]

1965

Clifford, S. F.

Fried, D. L.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Lading, L.

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 10.

Rye, B. J.

Tatarski, V. I.

V. I. Tatarski, “The Effect of the Turbulent Atmosphere on Wave Propagation,” IPST Catalog 5319 (National Technical Information Service, Springfield, Va., 1971).

Wandzura, S. M.

Appl. Opt.

J. Opt. Soc. Am.

Opto-electronics

L. Lading, “A Fourier Optical Model for the Laser Doppler Velocimeter,” Opto-electronics 4, 385 (1972).
[CrossRef]

Other

V. I. Tatarski, “The Effect of the Turbulent Atmosphere on Wave Propagation,” IPST Catalog 5319 (National Technical Information Service, Springfield, Va., 1971).

S. F. Clifford, “The Classical Theory of Wave Propagation in a Turbulent Medium,” in Laser Beam Propagation in the Atmosphere, J. W. Srohbehn, Ed. (Springer, Berlin, 1978), pp. 9–41.
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 10.

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Figures (4)

Fig. 1
Fig. 1

Layout of a system for experimentally investigating both monostatic and bistatic lidars. The transmitter and receiver beams are parallel between the first two lenses. The two axes intersect in the pinhole. The angle between the beams is controlled by the lateral position of the mirror. The pinhole plane is imaged by the large lens at range zf. Monostatic operation is achieved if the two beam axes are coincident in the beam splitter. Bistatic operation occurs if the spacing is larger than the sum of the beam radii.

Fig. 2
Fig. 2

Turbulence susceptibility for a diffraction-limited monostatic system χ as a function of range. The focusing range was 1 m; the spacing between transmitter lens and turbulence generator was a, 50 mm; b, 250 mm, and c, 450 mm. The dashed curve is the nonperturbed normalized range weight curve.

Fig. 3
Fig. 3

Turbulence susceptibility for a nondiffraction-limited monostatic system (β2 = 25). Otherwise as in Fig. 1.

Fig. 4
Fig. 4

Turbulence susceptibility from the focal range as a function of the spacing between transmitter and receiver as measured in the beam splitter plane (see Fig. 1): a, weak turbulence; b, strong turbulence.

Equations (43)

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1 2 π j ( z 1 / k ) exp [ - 1 2 x 2 + y 2 j ( z 1 / k ) + j k z 1 ] ,
t = exp { - 1 2 ( x 2 + y 2 ) [ 1 j ( f / k ) ] } .
G m ( z ) = C 1 z 2 · β 2 β 2 + 1 + ( r a 2 k ) 2 ( 1 z f - 1 z ) 2 ,
G b ( z ) = G m ( z ) exp [ - 2 ( α z r b ) 2 ] ,
t = exp [ j ϕ ( x , y ) ] ,
ϕ a = g 0 + r · g 0 + 1 2 r · g 0 · r + ,
( g 0 ) 2 + ( g 0 y ) 2 .
( g 0 x ) 2 = - 2 x 2 { R ϕ * R w } r = 0 = - 2 R ϕ x 2 * R w r = 0 ,
D ϕ ( r ) = 2 R ϕ ( o ) - 2 R ϕ ( r ) .
( g 0 x ) 2 = ( g 0 y ) 2 ,
2 R ( 0 ) x 2 = 2 R ( 0 ) r 2 R ( 0 ) .
( g 0 x ) 2 + ( g 0 y ) 2 = 2 x 2 { D ( r ) * R g ( r ) } r = 0 .
{ 2 g 0 x 2 2 g 0 x y 2 g 0 y x 2 g 0 y 2 } .
ξ 1 = - 1 k { 1 2 ( 2 g 0 x 2 + 2 g 0 y 2 ) + [ 1 4 ( 2 g 0 x 2 + 2 g 0 y 2 ) 2 + ( 2 g 0 x y ) 2 ] 1 / 2 } ,
ξ 2 = - 1 k { 1 2 ( 2 g 0 x 2 + 2 g 0 y 2 ) - [ 1 4 ( 2 g 0 x 2 + 2 g 0 y 2 ) 2 + ( 2 g 0 x y ) 2 ] 1 / 2 } .
- k ξ 1 + ξ 2 = 2 g x 2 + 2 g y 2 ,
ξ 1 + ξ 2 = 0.
( ξ 1 + ξ 2 ) 2 = 1 k 2 4 r 4 ( D ϕ * R w ) r = 0 .
G m ( z ) = C z 2 β [ β 2 + 1 + ( r a 2 k ) 2 ( ξ f - ξ + δ ξ 1 ) 2 ] 1 / 2 × β [ β 2 + 1 + ( r a 2 k ) 2 ( ξ f - ξ + δ ξ 2 ) 2 ] 1 / 2 ,
F F o + F o 1 δ ξ 1 + F o 2 δ ξ 2 + 1 2 F o 1 ( δ ξ 1 ) 2 + 1 2 F o 2 ( δ ξ 2 ) 2 + F o 12 δ ξ 1 δ ξ 2 ,
F = - F d P ( δ ξ 1 , δ ξ 2 ) .
F = F o - 2 F o 1 k 2 ( 2 g x 2 ) 2 .
χ = P t / P 0 - 1 ,
χ m = - 2 F o F o 1 k 2 ( 2 g x 2 ) 2 .
G b t ( z f ) = G b ( z f ) r 2 r t 2 + r 2 ,
δ r = z t k r · g 0 ,
r t 2 = 2 ( δ r ) 2 ,
r t 2 = 2 ( z t k ) 2 2 x 2 ( D * R w ) .
Φ ( q ) = C q - 11 / 3 ,
Φ x y ( κ ) = C 0 ( κ 2 + q z 2 ) - 11 / 6 d q z = C κ - 8 / 3 0 ( 1 + v 2 ) - 11 / 6 d v ,
S w ( κ ) = { 1 0 r < r w 0 otherwise .
r t = z t k [ ( g 0 x ) 2 + ( g 0 y ) 2 ] 1 / 2 ,
n D x n r = 0 = - j n 2 π 2 - κ x n S d κ 2 ,
r t 2 = ( z t k ) 2 0 Φ x y ( κ ) κ x 2 d κ 2 .
r t 2 = C 1 2 π 2 0 π 0 1 / r w κ - 8 / 3 κ 2 cos 2 θ κ d κ d θ ,
C 1 = C 0 ( 1 + v 2 ) - 11 / 6 d v .
r 2 = 3 C 1 16 π ( z t κ ) 2 r w - 4 / 3 .
χ b = r r 2 r r 2 + r z 2 - 1 .
χ b - r t 2 r z 2 .
χ b 3 C 1 16 π r w 2 / 3 .
χ m = 9 C 1 160 π r a 4 r w - 10 / 3 .
χ b / χ m = 10 3 r w 4 / r a 4 = 10 3 z t 4 / z f 4 ,
χ b χ m = 160 π 9 C 1 r w 10 / 3 r a 4 .

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