Abstract

Siegman’s theorem is used to express the heterodyne signal from incoherent backscatter lidar in terms of fields in the target plane. It is then shown directly that, contrary to some previously documented predictions, the mean return from a matched transceiver lidar is, as a consequence of its self-adaptive properties, invariably degraded less by turbulence than is that of a bistatic system; established results for the irradiance statistics of beams propagating in the turbulent atmosphere enable beam centroid and scintillation wander tracking to be distinguished as contributing to this result. A combination of the two systems can give rise to near-field transceiver returns that are greater than returns for free-space propagation of untruncated Gaussian beams. Target-plane expressions for signal variance display the dependence of signal statistics on antenna geometry, and application of these results to return-power estimation is briefly discussed.

© 1981 Optical Society of America

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References

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  1. A. Thomson and M. F. Dorian, “Heterodyne detection of monochromatic light scattered from a cloud of moving particles,” (General Dynamics Convair Division, San Diego, Calif., 1967).
  2. S. S. R. Murty, “Laser Doppler systems in atmospheric turbulence,” (U.S. Government Printing Office, Washington, D.C., 1976).
  3. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1691 (1975).
    [Crossref]
  4. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” in Surveillance of Environmental Pollution and Resources by Electromagnetic Waves, T. Lund, ed. (Reidel, London, 1978), pp. 67–93.
    [Crossref]
  5. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594 (1966); Proc. IEEE 54, 1350–1356 (1966).
    [Crossref] [PubMed]
  6. D. L. Fried and H. T. Yura, “Telescope-performance reciprocity for propagation in a turbulent medium,” J. Opt. Soc. Am. 62, 600–602 (1972).
    [Crossref]
  7. T. S. Chu, “On coherent detection of scattered light,” IEEE Trans. Antennas Propag. AP-15, 703–704 (1967).
    [Crossref]
  8. J. J. Degnan, “Design considerations for optical heterodyne receivers. a review,” presented at NASA Heterodyne Systems Technology Conference, Williamsburg, Virginia, March 1980.
  9. J. H. Shapiro, “Reciprocity of the turbulent atmosphere,” J. Opt. Soc. Am. 61, 492–495 (1971).
    [Crossref]
  10. M. H. Lee, J. F. Holmes, and J. R. Kerr, “Generalized spherical wave mutual coherence function,” J. Opt. Soc. Am. 67, 1279–1281 (1977).
    [Crossref]
  11. S. F. Clifford and et al., “Study of a pulsed lidar for cross-wind sensing,” (U.S. Government Printing Office, Washington, D.C., 1980).
  12. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [Crossref]
  13. S. M. Wandzura, “Meaning of quadratic structure functions,” J. Opt. Soc. Am. 70, 745–747 (1980).
    [Crossref]
  14. Computations of I2(0)〉 using the extended Huygens–Fresnel equations in the phase-only approximation, i.e. (in the present context), of the integrand 〈IT(0)IL(0)〉 using Eqs. (7)–(9) for the matched transceiver geometry, where IT= IL, have been made in the course of calculating the long-term scintillation index [σI2(0)]LT by V. A. Banekh and et al., “Focused laser beam scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. 64, 516–518 (1974) and by M. H. Lee and et al., “Variance of irradiance for saturated scintillations,” J. Opt. Soc. Am. 66, 1389–1392 (1976).
    [Crossref]
  15. S. F. Clifford and S. M. Wandzura, “The effect of the turbulent atmosphere on monostatic heterodyne lidar performance,” Appl. Opt. (submitted for publication).
  16. J. R. Dunphy and J. R. Kerr, “Turbulence effects on target illumination by laser sources: phenomenological analysis and experimental results,” Appl. Opt. 16, 1345–1358 (1977).
    [Crossref] [PubMed]
  17. M. Tur and M. J. Beran, “Propagation of a finite beam through a random medium,” Opt. Lett. 5, 306–308 (1980).
    [Crossref] [PubMed]
  18. B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390–1398 (1979).
    [Crossref] [PubMed]

1980 (2)

1979 (1)

1977 (2)

1975 (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1691 (1975).
[Crossref]

1974 (1)

1972 (1)

1971 (1)

1967 (1)

T. S. Chu, “On coherent detection of scattered light,” IEEE Trans. Antennas Propag. AP-15, 703–704 (1967).
[Crossref]

1966 (1)

1965 (1)

Banekh, V. A.

Beran, M. J.

Chu, T. S.

T. S. Chu, “On coherent detection of scattered light,” IEEE Trans. Antennas Propag. AP-15, 703–704 (1967).
[Crossref]

Clifford, S. F.

S. F. Clifford and et al., “Study of a pulsed lidar for cross-wind sensing,” (U.S. Government Printing Office, Washington, D.C., 1980).

S. F. Clifford and S. M. Wandzura, “The effect of the turbulent atmosphere on monostatic heterodyne lidar performance,” Appl. Opt. (submitted for publication).

Degnan, J. J.

J. J. Degnan, “Design considerations for optical heterodyne receivers. a review,” presented at NASA Heterodyne Systems Technology Conference, Williamsburg, Virginia, March 1980.

Dorian, M. F.

A. Thomson and M. F. Dorian, “Heterodyne detection of monochromatic light scattered from a cloud of moving particles,” (General Dynamics Convair Division, San Diego, Calif., 1967).

Dunphy, J. R.

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1691 (1975).
[Crossref]

Fried, D. L.

Holmes, J. F.

Kerr, J. R.

Lee, M. H.

Murty, S. S. R.

S. S. R. Murty, “Laser Doppler systems in atmospheric turbulence,” (U.S. Government Printing Office, Washington, D.C., 1976).

Rye, B. J.

Shapiro, J. H.

Siegman, A. E.

Thomson, A.

A. Thomson and M. F. Dorian, “Heterodyne detection of monochromatic light scattered from a cloud of moving particles,” (General Dynamics Convair Division, San Diego, Calif., 1967).

Tur, M.

Wandzura, S. M.

S. M. Wandzura, “Meaning of quadratic structure functions,” J. Opt. Soc. Am. 70, 745–747 (1980).
[Crossref]

S. F. Clifford and S. M. Wandzura, “The effect of the turbulent atmosphere on monostatic heterodyne lidar performance,” Appl. Opt. (submitted for publication).

Yura, H. T.

D. L. Fried and H. T. Yura, “Telescope-performance reciprocity for propagation in a turbulent medium,” J. Opt. Soc. Am. 62, 600–602 (1972).
[Crossref]

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” in Surveillance of Environmental Pollution and Resources by Electromagnetic Waves, T. Lund, ed. (Reidel, London, 1978), pp. 67–93.
[Crossref]

Appl. Opt. (3)

IEEE Trans. Antennas Propag. (1)

T. S. Chu, “On coherent detection of scattered light,” IEEE Trans. Antennas Propag. AP-15, 703–704 (1967).
[Crossref]

J. Opt. Soc. Am. (6)

Opt. Lett. (1)

Proc. IEEE (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1691 (1975).
[Crossref]

Other (6)

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” in Surveillance of Environmental Pollution and Resources by Electromagnetic Waves, T. Lund, ed. (Reidel, London, 1978), pp. 67–93.
[Crossref]

A. Thomson and M. F. Dorian, “Heterodyne detection of monochromatic light scattered from a cloud of moving particles,” (General Dynamics Convair Division, San Diego, Calif., 1967).

S. S. R. Murty, “Laser Doppler systems in atmospheric turbulence,” (U.S. Government Printing Office, Washington, D.C., 1976).

J. J. Degnan, “Design considerations for optical heterodyne receivers. a review,” presented at NASA Heterodyne Systems Technology Conference, Williamsburg, Virginia, March 1980.

S. F. Clifford and et al., “Study of a pulsed lidar for cross-wind sensing,” (U.S. Government Printing Office, Washington, D.C., 1980).

S. F. Clifford and S. M. Wandzura, “The effect of the turbulent atmosphere on monostatic heterodyne lidar performance,” Appl. Opt. (submitted for publication).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagrams of (a) beam propagation in turbulence; (b) transmitter and BPLO beams for bistatic lidar; (c) same for matched transceiver system.

Fig. 2
Fig. 2

Gain G = GBCGSC against No = D/ρo from approximate model (dashed lines) compared with curves from Clifford and Wandzura15 (solid lines). Also plotted is GBC for Ω = 4.

Fig. 3
Fig. 3

Predicted return against range R of incoherent-backscatter lidar-transmitting collimated untruncated Gaussian beam of 1/e2 radius 5.6 cm (D = 8 cm) at wavelength 0.488 μm. Graph labels are (1) Cn2 = 0; (2) Cn2 = 10−14 m−2/3, matched bistatic geometry; (3) Cn2 = 10−14 m−2/3, matched transceiver; (4) Cn2 = 10−13 m−2/3, matched bistatic; and (5) Cn2 = 10−13 m−2/3, matched transceiver. The return is expressed as A/R2, where A is the effective antenna area (AR/n1 in Ref. 18), atmospheric absorption and range variation of backscattering coefficient and Cn2 being neglected.

Equations (29)

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i = 2 ( η e / h ν ) A D V S ( a ) V L * ( a ) d 2 a ,
u ( b ) = V ( a ) h ( b , a ) d 2 a ,
V * ( a ) = u * ( b ) h ( a , b ) d 2 b ,
i = 2 ( η e / h ν ) A R u S ( b ) u L * ( b ) d 2 b ,
i 2 = 2 ( η e / h ν ) 2 A D A D V S ( a 1 ) V S * ( a 2 ) V L * ( a 1 ) × V L ( a 2 ) d 2 a 1 d 2 a 2 = 2 ( η e / h ν ) 2 A R A R u S ( b 1 ) u S * ( b 2 ) u L * ( b 1 ) u L ( b 2 ) × d 2 b 1 d 2 b 2 .
i 2 ~ U S ( s 1 ) U L * ( s 1 ) U S * ( s 2 ) U L ( s 2 ) d 2 s 1 d 2 s 2 ~ U T ( s 1 ) U T ( s 2 ) U L * ( s 1 ) U L ( s 2 ) × e j ( ϕ 1 - ϕ 2 ) d 2 s 2 d 2 s 2 = I T ( s ) I L ( s ) d 2 s ,
e j ( ϕ 1 - ϕ 2 ) ~ δ ( s 1 - s 2 ) .
I T ( s ) I L ( s ) = u T ( b 1 ) u T * ( b 2 ) u L * ( b 1 ) u L ( b 2 ) × h ( s , b 1 ) h * ( s , b 2 ) h * ( s , b 1 ) h ( s , b 2 ) d 2 b 1 d 2 b 2 d 2 b 1 d 2 b 2 ,
h ( s , b 1 ) h * ( s , b 2 ) h * ( s , b 1 ) h ( s , b 2 ) = exp [ j k ( β - β ) · s / r ] exp { j k [ ( b 1 ) 2 - ( b 2 ) 2 - b 1 2 + b 2 2 ] / 2 r } H ( s ; b 1 , b 2 , b 1 , b 2 ) .
H ( s ; b 1 , b 2 , b 1 , b 2 ) = exp { - ½ [ D ( β ) + D ( β ) + D ( b 1 - b 1 + β ) + D ( b 2 - b 2 ) - D ( b 1 - b 2 ) - D ( b 2 - b 1 ) ] }
exp [ j k ( β - β ) · s / r ] d 2 s = δ ( β - β )
I T ( s ) I L ( s ) d 2 s = u T ( b 1 ) u T * ( b 2 ) u L * ( b 1 ) u L ( b 2 ) exp { j k ( b 1 ) 2 - ( b 2 ) 2 - b 1 2 + b 2 2 ] / 2 r } H ( s ; b 1 , b 2 , b 1 , b 2 ) d 2 b 1 d 2 b 2 d 2 b 1 d 2 b 2 ,
H ( s ; b 1 , b 2 , b 1 , b 2 ) = H ( s ; b 1 , b 1 - β , b 1 , b 1 - β ) = exp { - [ ( D / β ) + D ( b 1 - b 1 ) - ½ D ( b 1 - b 1 + β ) - ½ D ( b 1 - b 1 - β ) ] } .
i 2 ~ I T ( s ) I L ( s ) LT d 2 s = I T ( s ) I L ( s ) WT d 2 s ,
i 4 ~ u S ( b 1 ) u S * ( b 2 ) u S ( b 3 ) u S * ( b 4 ) u L * ( b 1 ) u L ( b 2 ) u L * × ( b 3 ) u L ( b 4 ) d 2 b 1 d 2 b 2 d 2 b 3 d 2 b 4 = u s ( s 1 ) u S * ( s 2 ) u S ( s 3 ) u S * ( s 4 ) u L * ( s 1 ) u L ( s 2 ) u L * × ( s 3 ) u L ( s 4 ) d 2 s 1 d 2 s 2 d 2 s 3 d 2 s 4 = u T ( s 1 ) u T ( s 2 ) u T ( s 3 ) u T ( s 4 ) u L * ( s 1 ) u L × ( s 2 ) u L * ( s 3 ) u L ( s 4 ) × exp [ - j ( ϕ 1 - ϕ 2 + ϕ 3 - ϕ 4 ) ] d 2 s 1 d 2 s 2 d 2 s 3 d 2 s 4 = 2 I T ( s 1 ) I T ( s 2 ) I L ( s 1 ) I L ( s 2 ) d 2 s 1 d 2 s 2 ,
exp [ j ( ϕ 1 - ϕ 2 + ϕ 3 - ϕ 4 ) ] ~ δ ( ϕ 1 - ϕ 2 ) δ ( ϕ 3 - ϕ 4 ) + δ ( ϕ 1 - ϕ 4 ) δ ( ϕ 2 - ϕ 3 ) .
i 4 ~ 2 I T ( s 1 ) I T ( s 2 ) I L ( s 1 ) I L ( s 2 ) d 2 s 1 d 2 s 2 = 2 [ I T ( s ) I L ( s ) d 2 s ] 2 = 2 i 2 2
σ P 2 = ( i 4 - i 2 2 ) / i 2 2 = 1 ,
σ ex 2 = σ P 2 - 1 = 2 I T ( s 1 ) I T ( s 2 ) I L ( s 1 ) I L ( s 2 ) d 2 s 1 d 2 s 2 [ I T ( s 1 ) I L ( s 1 ) d 2 s 1 ] 2 - 1 ,
i 2 B ~ I T ( s ) I L ( s ) d 2 s = I T ( s ) I L ( s ) d 2 s .
i 2 MB ~ I T ( s ) 2 d 2 s .
i 2 MT ~ I T 2 ( s ) d 2 s = [ 1 + σ I 2 ( s ) ] I T ( s ) 2 d 2 s .
G = ( 1 + σ I 2 ) WT I T WT 2 d 2 s I T LT 2 d 2 s .
[ σ I 2 ( s ) ] WT [ σ I 2 ( 0 ) ] WT = ( σ I 2 ) WT .
[ σ I 2 ( 0 ) ] WT = - exp [ - σ 1 2 ]
I T ( s ) 2 d 2 s = P T 2 π ρ s 2 = 1 2 P T I T ( 0 ) ,
G BC = I T ( 0 ) WT I T ( 0 ) LT = ρ s 2 LT ρ s 2 WT = 1 + Ω 2 + N o 2 1 + Ω 2 + N o 2 ( 1 - 0.62 N o - 1 / 3 ) 6 / 5 ,
i 4 MB ~ 2 I T ( s 1 ) I T ( s 2 ) 2 d 2 s 1 d 2 s 2 ,
i 4 MT ~ 2 I T 2 ( s 1 ) I T 2 ( s 2 ) d 2 s 1 d 2 s 2 .