Abstract

A diffraction-limited lidar provides for effective rejection of background light. Characteristics of a monostatic system are computed. The range sensitivity is generally different from a square-law dependence. The effect of optical refractive turbulence is analyzed. There is a trade-off between background rejection and insensitivity to refractive turbulence. A monostatic system is much less sensitive to refractive turbulence than a bistatic system is.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Benedetti-Michelangeli, G. Fiocco, “Active and Passive Optical Doppler Techniques for the Determination of Atmospheric Temperature” and “A Highly Coherent Laser Radar,” in Structure and Dynamics of the Upper Atmosphere, F. Verniani, Ed., Developments in Atmospheric Science1 (Elsevier, Amsterdam, 1974).
  2. E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution Lidar,” in Technical Digest, Workshop on Optical and Laser Remote Sensing (Optical Society of America, Washington, D.C., 1982), paper I3.
  3. L. Lading, A. Skov Jensen, Appl. Opt. 19, 2750 (1980).
    [CrossRef] [PubMed]
  4. R. F. Lutomirski, H. T. Yura, Appl. Opt. 10, 1652 (1971).
    [CrossRef] [PubMed]
  5. M. H. Lee, J. F. Holmes, J. R. Kerr, J. Opt. Soc. Am. 67, 1279 (1977).
    [CrossRef]
  6. V. I. Tatarskii, “The Effects of the Turbulent Atmosphere on Wave Propagation,” IPST Catalog 5319 (National Technical Information Service, Springfield, Va., 1971).
  7. S. F. Clifford, S. M. Wandzura, Appl. Opt. 20, 514 (1981).
    [CrossRef] [PubMed]
  8. D. L. Fried, Optical Sciences Co.; private communication (1982).

1981 (1)

1980 (1)

1977 (1)

1971 (1)

Benedetti-Michelangeli, G.

G. Benedetti-Michelangeli, G. Fiocco, “Active and Passive Optical Doppler Techniques for the Determination of Atmospheric Temperature” and “A Highly Coherent Laser Radar,” in Structure and Dynamics of the Upper Atmosphere, F. Verniani, Ed., Developments in Atmospheric Science1 (Elsevier, Amsterdam, 1974).

Clifford, S. F.

Eloranta, E. W.

E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution Lidar,” in Technical Digest, Workshop on Optical and Laser Remote Sensing (Optical Society of America, Washington, D.C., 1982), paper I3.

Fiocco, G.

G. Benedetti-Michelangeli, G. Fiocco, “Active and Passive Optical Doppler Techniques for the Determination of Atmospheric Temperature” and “A Highly Coherent Laser Radar,” in Structure and Dynamics of the Upper Atmosphere, F. Verniani, Ed., Developments in Atmospheric Science1 (Elsevier, Amsterdam, 1974).

Fried, D. L.

D. L. Fried, Optical Sciences Co.; private communication (1982).

Holmes, J. F.

Kerr, J. R.

Lading, L.

Lee, M. H.

Lutomirski, R. F.

Roesler, F. L.

E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution Lidar,” in Technical Digest, Workshop on Optical and Laser Remote Sensing (Optical Society of America, Washington, D.C., 1982), paper I3.

Skov Jensen, A.

Sroga, J. T.

E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution Lidar,” in Technical Digest, Workshop on Optical and Laser Remote Sensing (Optical Society of America, Washington, D.C., 1982), paper I3.

Tatarskii, V. I.

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

Wandzura, S. M.

Yura, H. T.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Other (4)

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

D. L. Fried, Optical Sciences Co.; private communication (1982).

G. Benedetti-Michelangeli, G. Fiocco, “Active and Passive Optical Doppler Techniques for the Determination of Atmospheric Temperature” and “A Highly Coherent Laser Radar,” in Structure and Dynamics of the Upper Atmosphere, F. Verniani, Ed., Developments in Atmospheric Science1 (Elsevier, Amsterdam, 1974).

E. W. Eloranta, F. L. Roesler, J. T. Sroga, “The High Spectral Resolution Lidar,” in Technical Digest, Workshop on Optical and Laser Remote Sensing (Optical Society of America, Washington, D.C., 1982), paper I3.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Monostatic lidar. The quantities γ, β, and d0 are defined by γ = D0/D, β = dpγ/(d0), and the diameter transmitted in the pinhole plane d0 = 4d/(kD), respectively.

Fig. 2
Fig. 2

Normalized detected power G(z) as a function of range. The focusing distance is zf = 1 km; D0 = 0.3 m and β = γ = 1.

Fig. 3
Fig. 3

Same plots as in Fig. 2 but now with zf = 10 km and β = 1 and 10.

Fig. 4
Fig. 4

G(z) with and without refractive turbulence. zf = 10 km, D0 = 0.3 m, β = γ = 1; and the structure constant at ground level is given for two cases 0 and 7.5 × 10−13 m−2/3.

Fig. 5
Fig. 5

Same plots as in Fig. 4 but assuming independent transmitter and receiver paths.

Fig. 6
Fig. 6

G(z), nondiffraction-limited operation β = 10, γ = 1, zf = 10 km, and D0 = 0.3 m.

Fig. 7
Fig. 7

Effect of integrated refractive turbulence N0 on the return power from the focal region. zf = 10 km, D0 = 0.3 m, γ = 1, and β = 1 and 10.

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

P r = P t β s Δ h A r / z 2 ,
P b = Ω A r Δ λ R λ = A p f 2 A r Δ λ R λ ,
A p λ 2 / A t ,
A r A t = A ,
A p λ 2 / A t .
G ( z ) = 1 + γ 2 + 3 β 2 ( z z f ) 2 ( 1 + γ 2 + 3 β 2 ) + μ 2 ( 1 - z z f ) 2 ( 1 + γ 2 + 2 β 2 ) / ( γ 2 + 2 β 2 ) ,
U 1 ( ρ 1 ) = A 0 exp [ i k ρ 1 2 2 ( 1 d - 1 f ) - 2 ρ 1 2 / D * 2 ] ,
U 2 ( ρ 2 ) = - i k 2 π z exp ( i k z ) d 2 ρ 1 U 1 ( ρ 1 ) × exp [ i k ( ρ 2 - ρ 1 ) 2 / ( 2 z ) + Ψ ( ρ 1 , ρ 2 ) ] ,
U 3 ( ρ 3 ) = σ π k - 1 δ ( ρ 2 - ρ 3 ) U 2 ( ρ 2 ) .
U 4 ( ρ 4 ) = - i k 2 π z exp ( i k z ) d 2 ρ 3 U 3 ( ρ 3 ) × exp [ i k ( ρ 4 - ρ 3 ) 2 / ( 2 z ) + Ψ ( ρ 3 , ρ 4 ) ] ,
U 5 ( ρ 5 ) = - i k 2 π d exp ( i k d ) d 2 ρ 4 U 4 ( ρ 4 ) t ( ρ 4 ) × exp [ i k ( ρ 5 - ρ 4 ) 2 / ( 2 d ) ] ,
t ( ρ 4 ) = exp [ - 2 ρ 4 2 / D 0 2 - i k ρ 4 2 / ( 2 f ) ] ,
I ( ρ 2 ) = η d 2 ρ 5 U 5 ( ρ 5 ) U 5 * ( ρ 5 ) W ( ρ 5 ) .
S = n Δ d 2 ρ 2 I ( ρ 2 ) .
S = k 2 η σ n Δ A 0 2 16 π 3 z 2 d 2 d 2 ρ 5 W ( ρ 5 ) d 2 ρ 4 d 2 ρ 4 d 2 ρ 1 d 2 ρ 1 × exp { - 2 ( ρ 4 2 + ρ 4 2 ) / D 0 2 - 2 ( ρ 1 2 + ρ 1 2 ) / D * 2 + i k [ ρ 4 2 - ρ 4 2 + ρ 1 2 - ρ 1 2 ] / ( 2 r ) } × exp [ - i k ρ 5 · ( ρ 4 - ρ 4 ) / d ] δ ( ρ 4 - ρ 4 + ρ 1 - ρ 1 ) × M ( ρ 4 , ρ 4 , ρ 1 , ρ 1 ) ,
M = exp [ Ψ ( ρ 1 , ρ 2 ) + Ψ * ( ρ 1 , ρ 2 ) + Ψ ( ρ 2 , ρ 4 ) + Ψ * ( ρ 2 , ρ 4 ) ] .
M = exp { - ½ [ D ( ρ 1 - ρ 1 ) + D ( ρ 4 - ρ 4 ) + D ( ρ 1 - ρ 4 ) + D ( ρ 4 - ρ 1 ) - D ( ρ 1 - ρ 4 ) - D ( ρ 1 - ρ 4 ) ] + 2 C χ ( ρ 1 - ρ 4 ) + 2 C χ ( ρ 1 - ρ 4 ) } .
D ( ρ i - ρ j ) [ Ψ ( ρ i ) + Ψ * ( ρ j ) ] 2 ,
C χ ( ρ i - ρ j ) = [ χ ( ρ i ) - χ ] [ χ ( ρ j ) - χ ] .
C χ ( r ) = 4 π 2 k 2 0 L d z 0 d K K Φ n ( K ) J 0 ( K r z / L ) × sin 2 [ K 2 z ( L - z ) 2 k L ] ,
D ( r ) = 2 ( r / ρ 0 ) 5 / 3 ,
ρ 0 = [ 1.46 k 2 L 0 1 d t C n 2 ( t ) t 5 / 3 ] - 3 / 5
r = ¼ ( ρ 4 + ρ 4 + ρ 1 + ρ 1 ) , w = ½ ( ρ 4 + ρ 4 - ρ 1 - ρ 1 ) , u = ( ρ 4 - ρ 4 + ρ 1 - ρ 1 ) , v = ½ ( ρ 4 - ρ 4 - ρ 1 + ρ 1 ) ,
ρ 4 = r + ½ w + ¼ u + ½ v , ρ 4 = r + ½ w - ¼ u - ½ v , ρ 1 = r - ½ w + ¼ u - ½ v , ρ 1 = r - ½ w - ¼ u + ½ v .
S = k 2 D 0 2 η σ n Δ A 0 2 64 π 3 z 2 d 2 ( 1 + α 2 ) d 2 ρ 5 W ( ρ 5 ) d 2 w d 2 v × exp ( - i k ρ 5 · v / d + i k w · v / r ) M ( w , v ) × exp [ - 4 w 2 D 0 2 ( α 2 1 + α 2 ) - v 2 D 0 2 ( 1 + α 2 ) ] ,
M ( w , v ) = exp { - ½ [ 2 D ( v ) + 2 D ( w ) - D ( w + v ) - D ( w - v ) ] + 2 C χ ( w + v ) + 2 C χ ( w - v ) } .
w = p t D 0 , v = t D 0 , v · w = v w cos θ ; J = D 0 2 / ( 4 / p ) ,
S S 0 = 4 z f 2 π z 2 [ γ 2 + 2 β 2 + β 2 ( γ 2 + 2 β 2 ) ( 1 + γ 2 + 2 β 2 ) ] 0 π d θ 0 d p 0 d t t M ( p , t , N 0 ) × cos [ Ω p t cos θ ] exp { - t [ 1 + γ 2 + 3 β 2 + 4 p ( γ 2 + 2 β 2 ) / ( 1 + γ 2 + 2 β 2 ) ] } ,
M = exp { - 2 N 0 5 / 3 t 5 / 6 [ 1 + p 5 / 6 - ½ ( 1 + p + 2 p cos θ ) 5 / 6 - ½ ( 1 + p - 2 p cos θ ) 5 / 6 ] } .
G ( z ) = S 0 S 0 = ( 1 + γ 2 + 3 β 2 ) [ ( z 2 z f ( 1 + γ 2 + 3 β 2 ) + μ 2 ( 1 - z / z f ) 2 ( 1 + γ 2 + 2 β 2 ) / ( γ 2 + 2 β 2 ) ) ] ,

Metrics