Abstract

We propose an algorithm and the results of a numerical study of random realizations and statistics of a pulsed coherent lidar return that allow for refractive turbulence. We show that, under conditions of refractive turbulence, the relative variance of the lidar return power can exceed unity by a factor of as much as 1.5. Clear manifestations of the turbulent effect of backscattering amplification have been revealed from simulations of space-based lidar sensing of the atmosphere with coherent lidar. Under conditions of strong optical turbulence in the atmospheric boundary layer, as a result of the backscattering amplification effect, the mean lidar return power can exceed the return power in the absence of turbulence by a factor of 3.

© 2000 Optical Society of America

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References

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  1. V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, Mass., 1987).
  2. M. Lee, F. Holmes, R. Kerr, “Statistics of speckle propagation through the turbulent atmosphere,” J. Opt. Soc. Am. 66, 1164–1172 (1976).
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  3. F. Holmes, M. Lee, R. Kerr, “Effect of the log-amplitude covariance function on the statistics of speckle propagation through the atmosphere,” J. Opt. Soc. Am. 70, 355–360 (1980).
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  4. R. Gudimetla, F. Holmes, R. Elliott, “Two-point joint-density function of the intensity for a laser-generated speckle field after propagation through the turbulent atmosphere,” J. Opt. Soc. Am. A 7, 672–680 (1990).
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  6. C. McIntyre, R. Kerr, M. Lee, J. Churnside, “Enhanced variance of irradiance from target glint,” Appl. Opt. 18, 3211–3212 (1979).
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  7. C. McIntyre, M. Lee, J. Churnside, “Statistics of irradiance scattered from a diffuse target containing multiple glints,” J. Opt. Soc. Am. 70, 1084–1095 (1980).
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  8. S. F. Clifford, S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. 20, 514–516 (1981).
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  9. B. J. Ray, “Refractive-turbulence contribution to incoherent backscatter heterodyne lidar returns,” J. Opt. Soc. Am. 71, 687–691 (1981).
    [CrossRef]
  10. R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. P. Salamitou, A. Dabas, P. H. Flamant, “Simulation in the time domain for heterodyne coherent laser radar,” Appl. Opt. 34, 499–506 (1995).
    [CrossRef] [PubMed]
  13. R. G. Frehlich, “Effect of wind turbulence on coherent Doppler laser performance,” J. Atmos. Oceanic Technol. 14, 54–75 (1997).
    [CrossRef]
  14. V. A. Banakh, I. N. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).
  15. V. P. Kandidov, “Monte-Carlo method in nonlinear statistical optics,” Usp. Fiz. Nauk 166, 1309–1338 (1996), in Russian.
    [CrossRef]
  16. A. S. Gurvich, A. I. Kon, V. L. Mironov, S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, Moskow, 1976), in Russian.
  17. V. A. Banakh, I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 6, 233–237 (1993).
  18. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1968).
  19. D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
    [CrossRef] [PubMed]
  20. R. G. Frehlich, “Coherent Doppler signal covariance including wind shear and wind turbulence,” Appl. Opt. 33, 6432–6481 (1994).
    [CrossRef]
  21. A. S. Gurvich, M. E. Gracheva, “Simple model for calculation of turbulent noise in optical systems,” Fiz. Atmos. Okeana 16, 1107–1111 (1980), in Russian.

1997

R. G. Frehlich, “Effect of wind turbulence on coherent Doppler laser performance,” J. Atmos. Oceanic Technol. 14, 54–75 (1997).
[CrossRef]

V. A. Banakh, I. N. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

1996

V. P. Kandidov, “Monte-Carlo method in nonlinear statistical optics,” Usp. Fiz. Nauk 166, 1309–1338 (1996), in Russian.
[CrossRef]

1995

1994

R. G. Frehlich, “Coherent Doppler signal covariance including wind shear and wind turbulence,” Appl. Opt. 33, 6432–6481 (1994).
[CrossRef]

1993

R. G. Frehlich, “Effect of refractive turbulence on coherent laser radar,” Appl. Opt. 32, 2122–2139 (1993).
[CrossRef] [PubMed]

V. A. Banakh, I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 6, 233–237 (1993).

1992

1991

1990

1982

1981

1980

1979

1976

Banakh, V. A.

V. A. Banakh, I. N. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

V. A. Banakh, I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 6, 233–237 (1993).

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1968).

Churnside, J.

Clifford, S. F.

Dabas, A.

Elliott, R.

Flamant, P. H.

Frehlich, R. G.

R. G. Frehlich, “Effect of wind turbulence on coherent Doppler laser performance,” J. Atmos. Oceanic Technol. 14, 54–75 (1997).
[CrossRef]

R. G. Frehlich, “Coherent Doppler signal covariance including wind shear and wind turbulence,” Appl. Opt. 33, 6432–6481 (1994).
[CrossRef]

R. G. Frehlich, “Effect of refractive turbulence on coherent laser radar,” Appl. Opt. 32, 2122–2139 (1993).
[CrossRef] [PubMed]

R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
[CrossRef] [PubMed]

Fried, D. L.

Gracheva, M. E.

A. S. Gurvich, M. E. Gracheva, “Simple model for calculation of turbulent noise in optical systems,” Fiz. Atmos. Okeana 16, 1107–1111 (1980), in Russian.

Gudimetla, R.

Gurvich, A. S.

A. S. Gurvich, M. E. Gracheva, “Simple model for calculation of turbulent noise in optical systems,” Fiz. Atmos. Okeana 16, 1107–1111 (1980), in Russian.

A. S. Gurvich, A. I. Kon, V. L. Mironov, S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, Moskow, 1976), in Russian.

Holmes, F.

Kandidov, V. P.

V. P. Kandidov, “Monte-Carlo method in nonlinear statistical optics,” Usp. Fiz. Nauk 166, 1309–1338 (1996), in Russian.
[CrossRef]

Kavaya, M. J.

Kerr, R.

Khmelevtsov, S. S.

A. S. Gurvich, A. I. Kon, V. L. Mironov, S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, Moskow, 1976), in Russian.

Kon, A. I.

A. S. Gurvich, A. I. Kon, V. L. Mironov, S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, Moskow, 1976), in Russian.

Lee, M.

McIntyre, C.

Mironov, V. L.

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

A. S. Gurvich, A. I. Kon, V. L. Mironov, S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, Moskow, 1976), in Russian.

Ray, B. J.

Salamitou, P.

Smalikho, I. N.

V. A. Banakh, I. N. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

V. A. Banakh, I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 6, 233–237 (1993).

Vaughn, J. L.

Wandzura, S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1968).

Appl. Opt.

Atmos. Oceanic Opt.

V. A. Banakh, I. N. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

V. A. Banakh, I. N. Smalikho, “Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere,” Atmos. Oceanic Opt. 6, 233–237 (1993).

Fiz. Atmos. Okeana

A. S. Gurvich, M. E. Gracheva, “Simple model for calculation of turbulent noise in optical systems,” Fiz. Atmos. Okeana 16, 1107–1111 (1980), in Russian.

J. Atmos. Oceanic Technol.

R. G. Frehlich, “Effect of wind turbulence on coherent Doppler laser performance,” J. Atmos. Oceanic Technol. 14, 54–75 (1997).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Usp. Fiz. Nauk

V. P. Kandidov, “Monte-Carlo method in nonlinear statistical optics,” Usp. Fiz. Nauk 166, 1309–1338 (1996), in Russian.
[CrossRef]

Other

A. S. Gurvich, A. I. Kon, V. L. Mironov, S. S. Khmelevtsov, Laser Radiation in the Turbulent Atmosphere (Nauka, Moskow, 1976), in Russian.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1968).

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

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Figures (12)

Fig. 1
Fig. 1

(a) Instantaneous distribution of the sounding beam intensity at R = 0; (b) the scattered beam intensity in the telescope receiving aperture; (c) the scattered beam amplitude in the telescope focal plane; (d) the cosine of phase difference between the reference and scattered beams; (f) the reference beam amplitude in the telescope focal plane. Refractive turbulence is absent [C n 2(0) = 0].

Fig. 2
Fig. 2

Instantaneous intensity distribution of the sounding beam propagated through the vertical path: (a) in the target plane, (b) in the plane of the telescope receiving aperture, (c) in the telescope focal plane. C n 2(0) = 10-13 m-2/3 and z eff = 500 m.

Fig. 3
Fig. 3

Instantaneous intensity distribution of the sounding beam propagated along a horizontal path.

Fig. 4
Fig. 4

Examples of distribution of the parameter η T along the sounding path (independent samples) at C n 2 = 10-14 m-2/3.

Fig. 5
Fig. 5

Instantaneous values of the normalized lidar return power (1/2)|j C |2 as a function of R. The values of η T are represented by solid curves.

Fig. 6
Fig. 6

Normalized mean lidar return power 〈η T 〉 as a function of range R at (1) C n 2 = 10-15 m-2/3, (2) C n 2 = 10-14 m-2/3, (3) C n 2 = 10-13 m-2/3. The result calculated at C n 2 = 0 is depicted by the dashed curve.

Fig. 7
Fig. 7

Dependences of the relative fluctuations, σ ST , of power that is due to the refractive turbulence, and the relative variance of the instantaneous lidar return power σ S 2 on range R at (1) C n 2 = 10-15 m-2/3, (2) C n 2 = 10-14 m-2/3, (3) C n 2 = 10-13 m-2/3.

Fig. 8
Fig. 8

Coefficients of spatial correlation C T (R 0, R) of (a) the lidar return power fluctuations and (b) the dependence of correlation scales L c + and L c - on range R at C n 2 = 10-14 m-2/3.

Fig. 9
Fig. 9

Time correlation coefficients C T (τ) of the lidar return power fluctuations at C n 2 = 10-14 m-2/3 and R = 5 km.

Fig. 10
Fig. 10

Models of height profiles of C n 2(h) under (1) the poorest, (2) moderate, and (3) the finest turbulent conditions for light beam propagation.

Fig. 11
Fig. 11

Ratio of the mean lidar return power 〈η T 〉 to the return power in the absence of turbulence η T0 as a function of height h under (1) the poorest and (2) moderate turbulent conditions for the beam propagation.

Fig. 12
Fig. 12

Dependence of the lidar return power fluctuations σ ST , caused by the refractive turbulence, on height h under the poorest turbulent conditions.

Equations (28)

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jDt=eηhνD d2ρILρ, t+IBρ, t+ICρ, t+jnt,
ICρ=2|ULf, ρ||UBf, ρ|cosΔΨf, ρ
UB,Lf, ρ=k2πjf  d2ρFtρUB,L0, ρ×exp-j k2f ρ2+j k2fρ-ρ2,
US,L0, ρ=US,L0 exp-ρ2/2a02,
jCR, t=2 eηhνλKRPL1/2πa02l=1ns αlPS1/2t-2zl/c×AS2zl, ρl; texp2jkzl+2πjfLS-2/λVrzlt,
KR=exp-0Rdzαaz,
2jk ASz+ΔρAS+2k2nz, ρ; tAS=0,
AS0, ρ=exp-ρ2/2a02Ftρ,
PSt=EPπσPexp-t2/σP2,
Ftρ=1, |ρ|at0, |ρ|>at,
|jCR, t|2¯=12π3eηhνλKRa022×βπRcEPPL-+ d2ρIS2R, ρ, t,
S0=18π2eηhν λ2βπ0cEPPL1-exp-2at2/a02a02.
SR=S0K2RβπR/βπ01+R/ka022.
ηTR, t=1/2|jCR, t|2¯ βπ0/S0K2RβπR.
ηTR, t=2πa02-+ d2ρIS2R, ρ, t.
σST2R=ηT2/ηTR2,
CTR1, R2=ηTR1, tηTR2, t/×ηT2R1, tηT2R2, t1/2,
CTR, τ=ηTR, t+τηTR, t/ηT2R,
σS2R=1+2σST2R.
jCR, t=2βπRS0ηTR, tΔRβπ0EPc1/2×KRl=1NS PS1/22ΔR1-Ns/2/cξl+m×exp2πjfLS-2λ VrΔRlt,
ASzi+1, ρ=F-1exp-jπλΔRκ2×FASzi, ρexpjΨ,
FXm, l=m=0N-1l=0N-1 xm, l×exp-2πjmm+ll/N,
ΦΨκ=σΨ20.265 8.42Ln21+8.42Ln2κ211/6,
σΨ2=1.273Cn2zLn5/3k2ΔR
DΨz, ρ=2.92Cn2zk2ΔR|ρ|5/3
ASR, ρ=Δh2λRexpj πλR ρ2×FAS0, ρexpj πλR ρ2+jΨρ.
AB0, ρ=λ4ΔhNxyβπRσPcπ1/2×expj πλR ρ2+jΨρ×FξρASR, ρexpj πλR ρ2,
AB,Lf, ρt=Δh2λfexpj πλf ρt2FFtρAB,L0, ρ

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