Abstract

The effect of atmospheric turbulence on heterodyne lidar performance is studied by use of scattering theory. A theoretical analysis is carried out for both bistatic and monostatic lidar systems with independently variable transmitter and receiver parameters in regimes of weak and strong intensity fluctuations. The conditions of validity of a diffuse target model for description of the optical wave scattering by aerosols in a turbulent atmosphere are presented. The equations for signal power degradation and the conditions under which the time-averaged output of a heterodyne lidar does not depend on either turbulent conditions of propagation along the path or the transmitter parameters, including transmitter coherence length, are obtained. A physical interpretation of these results is given, and a comparison with the data of previous theories is made.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. L. Freed, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
    [CrossRef]
  2. S. F. Clifford, S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. 20, 514–516 (1981).
    [CrossRef] [PubMed]
  3. K. P. Chan, D. K. Killinger, N. Sugimoto, “Heterodyne Doppler 1-μm lidar measurement of reduced effective telescope aperture due to atmospheric turbulence,” Appl. Opt. 30, 2617–2627 (1991).
    [CrossRef] [PubMed]
  4. K. P. Chan, D. K. Killinger, “Enhanced detection of atmospheric-turbulence-distorted 1-μm coherent lidar returns using a two-dimensional heterodyne detector array,” Opt. Lett. 16, 1219–1221 (1991).
    [CrossRef] [PubMed]
  5. R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
    [CrossRef] [PubMed]
  6. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vols. 1 and 2.
  7. V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech, Dedham, Mass., 1987).
  8. M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortion of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
    [CrossRef]
  9. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
    [CrossRef]
  10. M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
    [CrossRef]
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  12. M. S. Belen’kii, V. L. Mironov, “A laser method for determination of a turbulence Cn2 parameter based on the light scattering by an atmospheric aerosol,” Radiophys. Quantum Electron. 24, 298–302 (1981).
  13. A. B. Krupnik, A. I. Saichev, “Coherent properties and focusing of wave beams reflected in a turbulent medium,” Radiophys. Quantum. Electron. 24, 840–843 (1981).
    [CrossRef]
  14. Yu. A. Kravtsov, A. I. Saichev, “The effects of the wave double passage in the randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1983).
    [CrossRef]

1991 (3)

1983 (1)

Yu. A. Kravtsov, A. I. Saichev, “The effects of the wave double passage in the randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1983).
[CrossRef]

1981 (3)

M. S. Belen’kii, V. L. Mironov, “A laser method for determination of a turbulence Cn2 parameter based on the light scattering by an atmospheric aerosol,” Radiophys. Quantum Electron. 24, 298–302 (1981).

A. B. Krupnik, A. I. Saichev, “Coherent properties and focusing of wave beams reflected in a turbulent medium,” Radiophys. Quantum. Electron. 24, 840–843 (1981).
[CrossRef]

S. F. Clifford, S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. 20, 514–516 (1981).
[CrossRef] [PubMed]

1980 (1)

M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
[CrossRef]

1979 (1)

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

1977 (1)

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortion of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

1967 (1)

D. L. Freed, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

Banakh, V. A.

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

Belen’kii, M. S.

M. S. Belen’kii, V. L. Mironov, “A laser method for determination of a turbulence Cn2 parameter based on the light scattering by an atmospheric aerosol,” Radiophys. Quantum Electron. 24, 298–302 (1981).

M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
[CrossRef]

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortion of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Chan, K. P.

Clifford, S. F.

Freed, D. L.

D. L. Freed, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

Frehlich, R. G.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vols. 1 and 2.

Kavaya, M. J.

Killinger, D. K.

Kon, A. I.

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortion of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

Kravtsov, Yu. A.

Yu. A. Kravtsov, A. I. Saichev, “The effects of the wave double passage in the randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1983).
[CrossRef]

Krupnik, A. B.

A. B. Krupnik, A. I. Saichev, “Coherent properties and focusing of wave beams reflected in a turbulent medium,” Radiophys. Quantum. Electron. 24, 840–843 (1981).
[CrossRef]

Mironov, V. L.

M. S. Belen’kii, V. L. Mironov, “A laser method for determination of a turbulence Cn2 parameter based on the light scattering by an atmospheric aerosol,” Radiophys. Quantum Electron. 24, 298–302 (1981).

M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
[CrossRef]

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortion of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

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

Saichev, A. I.

Yu. A. Kravtsov, A. I. Saichev, “The effects of the wave double passage in the randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1983).
[CrossRef]

A. B. Krupnik, A. I. Saichev, “Coherent properties and focusing of wave beams reflected in a turbulent medium,” Radiophys. Quantum. Electron. 24, 840–843 (1981).
[CrossRef]

Sugimoto, N.

Wandzura, S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Yura, H. T.

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

Appl. Opt. (3)

Opt. Acta (1)

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

D. L. Freed, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

Radiophys. Quantum Electron. (1)

M. S. Belen’kii, V. L. Mironov, “A laser method for determination of a turbulence Cn2 parameter based on the light scattering by an atmospheric aerosol,” Radiophys. Quantum Electron. 24, 298–302 (1981).

Radiophys. Quantum. Electron. (1)

A. B. Krupnik, A. I. Saichev, “Coherent properties and focusing of wave beams reflected in a turbulent medium,” Radiophys. Quantum. Electron. 24, 840–843 (1981).
[CrossRef]

Sov. J. Quantum Electron. (2)

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortion of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
[CrossRef]

Sov. Phys. Usp. (1)

Yu. A. Kravtsov, A. I. Saichev, “The effects of the wave double passage in the randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1983).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vols. 1 and 2.

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

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.


Equations (28)

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

U S ( R ) = m = 1 N A m G ( R , R m ) P ( R m ) U i ( R m ) ,
Γ 2 S ( R 1 , R 2 ) = 4 π 2 β a l k 2 d 2 R 0 d 2 R 0 d 2 R m U 0 ( R 0 ) U 0 * ( R 0 ) × Γ 40 ( R m , R 1 , R 2 ) × Γ 4 t ( R 1 , R 2 ; R 0 , R 0 ) ,
Γ 40 ( R m 1 ; R 1 , R 2 ) = ( k 2 π L ) 4 exp { i k 2 L [ ( R 0 2 - R 0 2 ) + ( R 1 2 - R 2 2 ) + 2 R m ( R 0 - R 0 + R 2 - R 1 ) ] } Γ 4 t = G ˜ ( R 0 , R m ) G ˜ ( R m , R 1 ) × G ˜ * ( R 0 , R m ) G ˜ * ( R m , R 2 ) ;
Γ 2 S = U S ( R 1 ) U S * ( R 2 ) ~ m = k N m = k N + m k N m k N R m
τ < 1 ,             L a ¯ 2 / λ ,             L c τ i / 2 λ .
p 0 = [ 1.45 k 2 0 L c n 2 ( ξ ) ( 1 - ξ / L ) 5 / 3 d ξ ] - 3 / 5 ,
Γ 4 t = exp { - ½ F ( R 0 , R 0 ; R 1 , R 2 ) } ,
F = D ( R 0 - R 0 ) + D ( R 1 - R 2 ) + D ( R 2 - R 0 ) + D ( R 1 - R 0 ) - D ( R 1 - R 0 ) - D ( R 2 - R 0 ) .
F ( R 0 , R 0 ; R 1 , R 2 ) = D ( R 0 - R 0 ) + D ( R 1 - R 2 ) .
U 0 ( R 0 ) = U 0 exp ( - R 0 2 / 2 a 0 2 - i k R 0 2 / 2 F i ) ,
Γ 2 S ( R , p ) = B a l I 0 Σ L 2 exp [ - ( 1 / p c a 2 + 1 / p 0 2 ) p 2 + i k L Rp ] ,
γ ( p ) = Γ 2 s ( R , p ) I ( R + p / 2 ) I ( R - p / 2 ) = exp [ - ( 1 / p c a 2 + 1 / p 0 2 ) p 2 ] ,
p c = { k 4 L [ Ω ( 1 - L F i ) 2 + Ω - 1 + 8 q ] } - 1 / 2 ,
γ ( p ) = exp [ - ( 1 / p c a 2 - 1 / p 0 2 ) p 2 ] .
Γ 2 S ( R , p ) = Γ 2 ( 1 ) ( R , p ) + Γ 2 ( 2 ) ( Rp ) ,
Γ 2 ( 1 ) ( R , p ) = I exp [ - ( 1 / p c a 2 + 1 / p 0 2 ) p 2 - ( i k / L ) Rp ]
Γ 2 ( 2 ) ( R , p ) = I p 0 2 2 a 0 2 exp [ - R 2 a 0 2 - p 2 4 a 0 2 - i k L R , p ] ,
I = B a l I 0 Σ / L 2 .
i 2 = ζ 2 d 2 p d 2 R Γ 2 S ( R , p ) Γ 20 ( R , p ) W ¯ ( R , p ) ,
W ¯ ( R , p ) = exp ( - 4 R 2 a L 2 - p 2 a L 2 - i k F L Rp ) ,
Γ 20 ( R , p ) = exp ( i k F L Rp ) ,
W ( p ) = exp ( - 2 p 2 / a L 2 - i k p 2 / 2 F L ) ,
i 2 B = ζ 2 π a L 4 I F 1 ( a L / p 0 , Ω F ) ,
F 1 ( a L / p 0 , Ω F ) = [ 1 + a L 2 / p 0 2 ( 1 + Ω F 2 ) ] - 1 , Ω F 2 = 1 + q - 1 Ω - 1 / 4 + q - 1 Ω ( 1 - L / F i ) 2 / 4.
Ω F 2 = 1 + q - 1 Ω - 1 / 4 + q - 1 Ω ( 1 - L F i ) 2 / 4 + q - 1 q k / 4 ,
F 1 = F 10 = { 1 + a L 2 4 a 0 2 [ 1 + Ω 2 ( 1 - L F i ) 2 ] } - 1
i 2 = ζ 2 π a L 4 I F 10 .
i 2 = 2 i 2 B .

Metrics