Abstract

The reduction in the SNR of a monostatic heterodyne lidar because of the presence of atmospheric refractive turbulence in the medium intervening between the lidar and the target was calculated. We find previous approximations made to perform the calculation, namely, independent refractive turbulence on outward bound and return paths and a quadratic form for the wave structure function, to be erroneous. An exact calculation shows that previous results overestimated signal degradation.

© 1981 Optical Society of America

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Corrections

Steven F. Clifford and Stephen Wandzura, "Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere; correction," Appl. Opt. 20, 1502-1502 (1981)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-20-9-1502

References

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  1. A. Thomson, M. F. Dorian, “Heterodyne Defraction of Monochromatic Light Scattered from a Cloud or Moving Particles,” General Dynamics Convair Report GDC-ERR-AN-1090 (General Dynamics Convair Division, San Diego, Calif., 1967).
  2. S. S. R. Murty, “Laser Doppler Systems in Atmospheric Turbulence,” NASA Technical Memorandum NASA TMX-73354 (National Technical Information Service, Springfield, Va. 22151, 1976).
  3. R. F. Lutomirski, H. T. Yura, Appl. Opt. 10, 1652 (1971).
    [CrossRef] [PubMed]
  4. M. H. Lee, J. F. Holmes, J. R. Kerr, J. Opt. Soc. Am. 67, 1279 (1977).
    [CrossRef]
  5. S. M. Wandzura, J. Opt. Soc. Am. 70, 745 (1980).
    [CrossRef]
  6. V. I. Tatarskii, “The Effects of the Turbulent Atmosphere on Wave Propagation,” IPST Catalog 5319 (National Technical Information Service, Springfield, Va. 22151, 1971).
  7. S. F. Clifford, T. R. Lawrence, G. R. Ochs, T.-i Wang, “Study of a Pulsed Coherent Lidar for Crosswind Sensing,” NOAA Technical Memorandum ERL WPL-48 (U.S. GPO, Washington, D.C., 1980).
  8. S. M. Wandzura, “Systematic Corrections to Quadratic Approximations for Power Law Structure Functions: The δ Expansion,” to be published.

1980 (1)

1977 (1)

1971 (1)

Clifford, S. F.

S. F. Clifford, T. R. Lawrence, G. R. Ochs, T.-i Wang, “Study of a Pulsed Coherent Lidar for Crosswind Sensing,” NOAA Technical Memorandum ERL WPL-48 (U.S. GPO, Washington, D.C., 1980).

Dorian, M. F.

A. Thomson, M. F. Dorian, “Heterodyne Defraction of Monochromatic Light Scattered from a Cloud or Moving Particles,” General Dynamics Convair Report GDC-ERR-AN-1090 (General Dynamics Convair Division, San Diego, Calif., 1967).

Holmes, J. F.

Kerr, J. R.

Lawrence, T. R.

S. F. Clifford, T. R. Lawrence, G. R. Ochs, T.-i Wang, “Study of a Pulsed Coherent Lidar for Crosswind Sensing,” NOAA Technical Memorandum ERL WPL-48 (U.S. GPO, Washington, D.C., 1980).

Lee, M. H.

Lutomirski, R. F.

Murty, S. S. R.

S. S. R. Murty, “Laser Doppler Systems in Atmospheric Turbulence,” NASA Technical Memorandum NASA TMX-73354 (National Technical Information Service, Springfield, Va. 22151, 1976).

Ochs, G. R.

S. F. Clifford, T. R. Lawrence, G. R. Ochs, T.-i Wang, “Study of a Pulsed Coherent Lidar for Crosswind Sensing,” NOAA Technical Memorandum ERL WPL-48 (U.S. GPO, Washington, D.C., 1980).

Tatarskii, V. I.

V. I. Tatarskii, “The Effects of the Turbulent Atmosphere on Wave Propagation,” IPST Catalog 5319 (National Technical Information Service, Springfield, Va. 22151, 1971).

Thomson, A.

A. Thomson, M. F. Dorian, “Heterodyne Defraction of Monochromatic Light Scattered from a Cloud or Moving Particles,” General Dynamics Convair Report GDC-ERR-AN-1090 (General Dynamics Convair Division, San Diego, Calif., 1967).

Wandzura, S. M.

S. M. Wandzura, J. Opt. Soc. Am. 70, 745 (1980).
[CrossRef]

S. M. Wandzura, “Systematic Corrections to Quadratic Approximations for Power Law Structure Functions: The δ Expansion,” to be published.

Wang, T.-i

S. F. Clifford, T. R. Lawrence, G. R. Ochs, T.-i Wang, “Study of a Pulsed Coherent Lidar for Crosswind Sensing,” NOAA Technical Memorandum ERL WPL-48 (U.S. GPO, Washington, D.C., 1980).

Yura, H. T.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Other (5)

V. I. Tatarskii, “The Effects of the Turbulent Atmosphere on Wave Propagation,” IPST Catalog 5319 (National Technical Information Service, Springfield, Va. 22151, 1971).

S. F. Clifford, T. R. Lawrence, G. R. Ochs, T.-i Wang, “Study of a Pulsed Coherent Lidar for Crosswind Sensing,” NOAA Technical Memorandum ERL WPL-48 (U.S. GPO, Washington, D.C., 1980).

S. M. Wandzura, “Systematic Corrections to Quadratic Approximations for Power Law Structure Functions: The δ Expansion,” to be published.

A. Thomson, M. F. Dorian, “Heterodyne Defraction of Monochromatic Light Scattered from a Cloud or Moving Particles,” General Dynamics Convair Report GDC-ERR-AN-1090 (General Dynamics Convair Division, San Diego, Calif., 1967).

S. S. R. Murty, “Laser Doppler Systems in Atmospheric Turbulence,” NASA Technical Memorandum NASA TMX-73354 (National Technical Information Service, Springfield, Va. 22151, 1976).

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Figures (1)

Fig. 1
Fig. 1

Curves of the SNR reduction factors F0 (solid curves) and F1 (dashed curves) as a function of integrated refractive-turbulence N0 and Fresnel number Ω.

Equations (15)

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U 2 ( ρ 2 ) = - i k exp ( i k z ) 2 π z d 2 ρ 1 U 1 ( ρ 1 ) × exp [ i k ( ρ 2 - ρ 1 ) 2 / ( 2 z ) + ψ ( ρ 1 , ρ 2 , z ) ] .
U 4 ( ρ 3 ) = - i k exp ( i k z ) 2 π z d 2 ρ 2 U 3 ( ρ 2 ) × exp [ i k ( ρ 3 - ρ 2 ) 2 / ( 2 z ) + ψ ( ρ 2 , ρ 3 , z ) ] .
i s 1 = 2 η d 2 ρ 3 W ( ρ 3 ) U 4 ( ρ 3 ) U ref * ( ρ 3 ) exp [ - i k ρ 3 2 / ( 2 f ) ] ,
U 1 ( ρ 1 ) = exp [ - 2 ρ 1 2 / D 0 2 - i k ρ 1 2 / ( 2 f ) ] , W ( ρ 3 ) U ref ( ρ 3 ) = exp ( - 2 ρ 3 2 / D 0 2 ) ,
i s 1 = - ( k π σ η 2 π 2 z 2 ) Re { exp ( i 2 k z ) d 2 ρ 3 × exp [ - 2 ρ 3 2 / D 0 2 + i k ( ρ 3 - ρ 2 ) 2 / ( 2 z ) - i k ρ 3 2 / ( 2 f ) ] d 2 ρ 1 exp [ - 2 ρ 1 2 / D 0 2 - i k ρ 1 2 / ( 2 f ) + i k ( ρ 2 - ρ 1 ) 2 / ( 2 z ) ] exp [ ψ ( ρ 2 , ρ 3 , z ) + ψ ( ρ 1 , ρ 2 , z ) ] } .
i s 1 2 = ( k 2 η 2 σ 8 π 3 z 4 ) { d 2 ρ 3 exp ( - 2 ρ 3 2 / D 1 2 ) d 2 ρ 3 exp ( - 2 ρ 3 2 / D 1 2 * ) d 2 ρ 1 exp ( - 2 ρ 1 2 / D 1 2 ) d 2 ρ 1 exp [ - 2 ρ 1 2 / D 1 2 * - i k ρ 2 · ( ρ 3 - ρ 3 + ρ 1 - ρ 1 ) / 2 ] × exp [ ψ ( ρ 2 , ρ 3 , z ) + ψ ( ρ 1 , ρ 2 , z ) + ψ * ( ρ 2 , ρ 3 , z ) + ψ * ( ρ 1 , ρ 2 , z ) ] } ,
i s 2 = η 2 σ n Δ 2 π z 2 d 2 ρ 3 exp ( - 2 ρ 3 2 / D 1 2 ) d 2 ρ 3 exp ( - 2 ρ 3 2 / D 1 2 * ) × d 2 ρ 1 exp ( - 2 ρ 1 2 / D 1 2 ) × d 2 ρ 1 exp ( - 2 ρ 1 2 / D 1 2 * ) δ ( ρ 3 - ρ 3 + ρ 1 - ρ 1 ) × exp [ ψ ( ρ 3 ) + ψ * ( ρ 3 ) + ψ ( ρ 1 ) + ψ * ( ρ 1 ) ] ,
= exp { - 1 2 [ D ( ρ 3 - ρ 3 ) + D ( ρ 1 - ρ 1 ) + D ( ρ 3 - ρ 1 ) + D ( ρ 3 - ρ 1 ) - D ( ρ 3 - ρ 1 ) - D ( ρ 3 - ρ 1 ) ] } ,
D ( x ) = 2 ( x / ρ 0 ) 5 / 3 ;             ρ 0 = 1.089 k 2 z 0 1 d t C n 2 ( t ) t 5 / 3 .
R = 1 4 ( ρ 3 + ρ 3 + ρ 1 + ρ 1 ) , W ˙ = 1 2 ( ρ 3 + ρ 3 - ρ 1 - ρ 1 ) , U = ( ρ 3 - ρ 3 + ρ 1 - ρ 1 ) , V = 1 2 ( ρ 3 - ρ 3 - ρ 1 + ρ 1 ) ,
ρ 3 = R + 1 2 W + 1 4 U + 1 2 V , ρ 3 = R + 1 2 W - 1 4 U - 1 2 V , ρ 1 = R - 1 2 W + 1 4 U - 1 2 V , ρ 1 = R = 1 2 W - 1 4 U + 1 2 V ,
i s 2 = η 2 σ n Δ 16 z 2 D 0 2 d 2 W d 2 V exp [ - 2 ( V 2 + W 2 ) / D 0 2 ] × exp [ - i k V · W ( 1 f - 1 z ) ] × exp { - 1 2 [ 2 D ( V ) + 2 D ( W ) - D ( W + V ) - D ( W - V ) ] } .
i s 2 = [ π 2 η 2 σ n Δ D 0 6 64 z 2 ( 1 + Ω 2 ) ] F 0 ( Ω , N 0 ) , Ω 2 = [ k D 0 2 ( f - 1 - z - 1 ) / 4 ] 2 ,             N 0 = D 0 / ρ 0 ,
i s 2 = η 2 σ n Δ D 0 2 16 z 2 d 2 W d 2 V exp [ - 2 ( W 2 + V 2 ) / D 0 2 - 2 V 2 / ρ 0 2 + i k V · W ( f - 1 - z - 1 ) ]
i s 2 = [ π 2 η 2 σ n Δ D 0 6 64 z 2 ( 1 + Ω 2 ) ] F 1 ( Ω , N 0 ) ,

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