Abstract

The return signal of coaxial and noncoaxial lidar systems with central obstruction has been calculated by integration of the irradiance in the focal plane. As in the coaxial unobstructed case, a small detector in the focal plane allows a geometrical compression of the detector signal dynamics. In coaxial systems, the shadow cast by the obstruction results in a reduction of the near signal. In noncoaxial arrangements a signal reduction occurs for distances that depend on the transmitter-receiver separation and the inclination angle, whereas the influence of an obstruction is almost negligible. Adequate signals can be obtained from short to long distances with both types of geometry.

© 1979 Optical Society of America

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References

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  1. R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, Berlin, 1976).
  2. J. Riegl, M. Bernhard, Appl. Opt. 13, 931 (1974).
    [CrossRef] [PubMed]
  3. T. Hirschfeld, Appl. Opt. 13, 1435 (1974).
    [CrossRef] [PubMed]
  4. T. Halldórsson, J. Langerholc, Appl. Opt. 17, 240 (1978).
    [CrossRef] [PubMed]
  5. J. Harms, W. Lahmann, C. Weitkamp, Appl. Opt. 17, 1131 (1978).
    [CrossRef] [PubMed]
  6. R. A. McClatchey, J. E. A. Selby, “Atmospheric Attenuation of HF and DF Laser Radiation,” Environmental Research Paper 400, AFCRL-72-0312 (1972).

1978 (2)

1974 (2)

Bernhard, M.

Collis, R. T. H.

R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, Berlin, 1976).

Halldórsson, T.

Harms, J.

Hirschfeld, T.

Lahmann, W.

Langerholc, J.

McClatchey, R. A.

R. A. McClatchey, J. E. A. Selby, “Atmospheric Attenuation of HF and DF Laser Radiation,” Environmental Research Paper 400, AFCRL-72-0312 (1972).

Riegl, J.

Russell, P. B.

R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, Berlin, 1976).

Selby, J. E. A.

R. A. McClatchey, J. E. A. Selby, “Atmospheric Attenuation of HF and DF Laser Radiation,” Environmental Research Paper 400, AFCRL-72-0312 (1972).

Weitkamp, C.

Appl. Opt. (4)

Other (2)

R. A. McClatchey, J. E. A. Selby, “Atmospheric Attenuation of HF and DF Laser Radiation,” Environmental Research Paper 400, AFCRL-72-0312 (1972).

R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, Berlin, 1976).

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Figures (11)

Fig. 1
Fig. 1

Parameters of the receiving optics.

Fig. 2
Fig. 2

Noncoaxial lidar system: (a) transmitter-receiver geometry; (b) circle of confusion in the focal plane.

Fig. 3
Fig. 3

Irradiance in the focal plane of a noncoaxial lidar system; separation of transmitter and receiver 1 m, inclination angle 1 mrad, other parameters as listed in Table I.

Fig. 4
Fig. 4

Regions of overlap between transmitted beam and receiver field of view in a noncoaxial lidar system.

Fig. 5
Fig. 5

Return signal of a noncoaxial lidar system; transmitter-receiver separation 1 m, inclination angle as indicated, other parameters as in Table I.

Fig. 6
Fig. 6

Return signal of a noncoaxial lidar system; transmitter-receiver separation 375 mm (i.e., transmitter touches receiver); inclination angle as indicated, other parameters as in Table I.

Fig. 7
Fig. 7

Lidar system with central obstruction: geometry; shadowed area in the focal plane.

Fig. 8
Fig. 8

Irradiance in the focal plane of a coaxial lidar system with central obstruction: (a) distance 100 m; (b) distances 1 km and 10 km. Radii of the obstruction as indicated, other parameters as in Table I.

Fig. 9
Fig. 9

Return signal of a coaxial lidar system with central obstruction; obstruction radii as indicated, other parameters as in Table I. The waist of the transmitted beam implies an obstruction radius ≥ 75 mm.

Fig. 10
Fig. 10

Irradiance in the focal plane of a noncoaxial lidar system with central obstruction; obstruction radius 100 mm, transmitter-receiver separation 375 mm, inclination angle 0.1 mrad, other parameters as in Table I. The position and size of the detector (radius 0.4 mm) are indicated.

Fig. 11
Fig. 11

Return signal of a noncoaxial lidar system with central obstruction; obstruction radii 0 mm and 100 mm; transmitter-receiver separation 375 mm, inclination angle 0.1 mrad, other parameters as in Table I.

Tables (1)

Tables Icon

Table I Specifications of a Commercial DF Laser, Geometric Parameters, and Atmospheric Constants Used in the Calculations

Equations (23)

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P ( z ) = P ¯ c τ 2 β ( z ) A z 2 exp [ - 2 0 z α ( z * ) d z * ] ,
S f ( r f , z ) = P ¯ c τ 2 β ( z ) 1 f 2 exp [ - 2 0 z α ( z * ) d z * ] × 2 π w 2 ( z ) A ( r o , R ) exp [ - 2 r o * 2 w 2 ( z ) ] d A * ,
w ( z ) = w o { 1 + [ ( ϕ t z ) / 2 w o ] 2 } 1 / 2 .
a ( z ) = d - δ z .
S f ( x f , y f , z ) = P ¯ c τ 2 β ( z ) 1 f 2 exp [ - 2 0 z α ( z * ) d z * ] × 2 π w 2 ( z ) A ( x o , y o ; R ) exp { - 2 x o * 2 + [ y o * - a ( z ) ] 2 w 2 ( z ) } d A * .
a f ( z ) = a ( z ) ( f / z ) = f [ ( d / z ) - δ ] .
r r ( z ) = R + [ ( ϕ r ) / 2 ] z
r b l = [ z / ( z - s b ) ] r b
x d l = - [ s b / ( z - s b ) ] x o ,             y d l = - [ s b / ( z - s b ) ] y o .
r b f = [ f / ( z - s b ) ] r b
x d f = - [ f / ( z - s b ) ] x o ,             y d f = - [ f / ( z - s b ) ] y o .
[ ( x d f * - x f ) 2 + ( y d f * - y f ) 2 ] 1 / 2 < r b f ,
[ ( x o * - z - s b z x o ) 2 + ( y o * - z - s b z y o ) 2 ] 1 / 2 < r b f · z - s b f = r b ,
x d o = [ ( z - s b ) / z ] x o ,             y d o = [ ( z - s b ) / z ] y o .
S f ( x f , y f , z ) = P ¯ c τ 2 β ( z ) 1 f 2 exp [ - 2 0 z α ( z * ) d z * ] × 2 π w 2 ( z ) exp { - 2 x o * + [ y o * - a ( z ) ] 2 w 2 ( z ) } d A * A ( x o , y o ; R ) \ A ( x d o , y d o ; r b ) ,
r r ( z ) = R + [ ( ϕ r ) / 2 ] z ,
w ( z ) = w o { 1 + [ ( ϕ t z ) / ( 2 w o ) ] 2 } 1 / 2 ,
a ( z ) = d - δ z
d - δ z 1 - w ( z 1 ) = R + [ ( ϕ r ) / 2 ] z 1 .
d - δ z 2 + w ( z 2 ) = R + [ ( ϕ r ) / 2 ] z 2 .
d - δ z 3 - w ( z 3 ) = - R - [ ( ϕ r ) / 2 ] z 3 .
d - δ z 4 + w ( z 4 ) = - R - [ ( ϕ r ) / 2 ] z 4 .
z = 1 { ( δ + [ ( ϕ r ) / 2 ] } 2 - ( ϕ t ) / 2 ] 2 ( ( d - R ) ( δ + ϕ r 2 ) + ( - 1 ) k × { ( ϕ t 2 ) 2 ( d - R ) 2 + ( w o 2 ) 2 [ ( δ + ϕ r 2 ) 2 - ( ϕ t 2 ) 2 ] } ) 1 / 2 .

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