Abstract

The explanation proposed by Belmonte and Rye [Appl. Opt. 39, 2401 (2000)] for the difference between simulation and the zero-order theory for heterodyne lidar returns in a turbulent atmosphere is incorrect. The theoretical expansion the authors considered is not developed under a square-law structure-function approximation (random-wedge atmosphere). Agreement between the simulations and the zero-order term of the theoretical expansion is produced for the limit of statistically independent paths (bistatic operation with large transmitter–receiver separation) when the simulations correctly include the large-scale gradients of the turbulent atmosphere.

© 2002 Optical Society of America

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  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]
  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. V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, Mass., 1987).
  4. R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
    [CrossRef] [PubMed]
  5. R. G. Frehlich, “Effects of refractive turbulence on coherent laser radar,” Appl. Opt. 32, 2122–2139 (1993).
    [CrossRef] [PubMed]
  6. R. G. Frehlich, “Simulation of laser propagation in a turbulent atmosphere,” Appl. Opt. 39, 393–397 (2000).
    [CrossRef]
  7. A. Belmonte, B. J. Rye, “Heterodyne lidar returns in the turbulent atmosphere: performance evaluation of simulated systems,” Appl. Opt. 39, 2401–2411 (2000).
    [CrossRef]
  8. R. G. Frehlich, “Effects of refractive turbulence on ground-based verification of coherent Doppler lidar performance,” Appl. Opt. 39, 4237–4246 (2000).
    [CrossRef]
  9. V. A. Banakh, I. N. Smalikho, C. Werner, “Numerical simulation of the effect of refractive turbulence on coherent lidar return statistics in the atmosphere,” Appl. Opt. 39, 5403–5414 (2000).
    [CrossRef]
  10. A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39, 5426–5445 (2000).
    [CrossRef]
  11. Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving efficiency of monostatic pulsed coherent lidars. 1. theory,” Appl. Opt. 29, 4111–4119 (1990).
    [CrossRef] [PubMed]
  12. V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).
  13. R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
    [CrossRef]
  14. J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
    [CrossRef]
  15. J. Martin, S. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
    [CrossRef] [PubMed]
  16. J. M. Martin, S. M. Flatté, “Simulation of point-source scintillation through three-dimensional random media,” J. Opt. Soc. Am. A 7, 838–847 (1990).
    [CrossRef]
  17. Wm. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
    [CrossRef] [PubMed]
  18. R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
    [CrossRef]
  19. S. M. Flatté, J. S. Gerber, “Irradiance-variance behavior by numerical simulation for plane-wave and spherical-wave optical propagation through strong turbulence,” J. Opt. Soc. Am. A 17, 1092–1097 (2000).
    [CrossRef]
  20. S. M. Wandzura, “Meaning of quadratic structure functions,” J. Opt. Soc. Am. 70, 745–747 (1980).
    [CrossRef]
  21. V. U. Zavorotnyi, “Strong fluctuations of electromagnetic waves in a random medium with finite longitudinal correlation of the inhomogeneities,” Zh. Eksp. Teor. Fiz. 75, 56–65 (1978).
  22. R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
    [CrossRef]
  23. R. Frehlich, “Laser scintillation measurements of the temperature spectrum in the atmospheric surface layer,” J. Atmos. Sci. 49, 1494–1509 (1992).
    [CrossRef]
  24. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, Jerusalem, 1971).
  25. G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2430–2432 (1985).
    [CrossRef] [PubMed]
  26. R. G. Frehlich, “Variance of focal-plane centroids,” J. Opt. Soc. Am. A 7, 2119–2140 (1990).
    [CrossRef]
  27. B. J. Rye, R. G. Frehlich, “Optimal truncation of Gaussian beams for coherent lidar using incoherent backscatter,” Appl. Opt. 31, 2891–2899 (1992).
    [CrossRef] [PubMed]

2000 (6)

1995 (1)

1993 (1)

1992 (3)

B. J. Rye, R. G. Frehlich, “Optimal truncation of Gaussian beams for coherent lidar using incoherent backscatter,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

R. Frehlich, “Laser scintillation measurements of the temperature spectrum in the atmospheric surface layer,” J. Atmos. Sci. 49, 1494–1509 (1992).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

1991 (1)

1990 (3)

1988 (1)

1986 (1)

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

1985 (1)

1981 (1)

1980 (1)

1979 (2)

R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

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

1978 (2)

V. U. Zavorotnyi, “Strong fluctuations of electromagnetic waves in a random medium with finite longitudinal correlation of the inhomogeneities,” Zh. Eksp. Teor. Fiz. 75, 56–65 (1978).

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
[CrossRef]

1977 (1)

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).

Banakh, V. A.

Belmonte, A.

Clifford, S. F.

Codona, J. L.

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Coles, Wm. A.

Creamer, D. B.

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Dainty, J. C.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Dashen, R.

R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

Filice, J. P.

Flatté, S.

Flatté, S. M.

Frehlich, R.

R. Frehlich, “Laser scintillation measurements of the temperature spectrum in the atmospheric surface layer,” J. Atmos. Sci. 49, 1494–1509 (1992).
[CrossRef]

Frehlich, R. G.

Gerber, J. S.

Glindemann, A.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Hardesty, R. M.

Henyey, F. S.

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Hill, R. J.

G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2430–2432 (1985).
[CrossRef] [PubMed]

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
[CrossRef]

Kavaya, M. J.

Klyatskin, V. I.

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).

Lane, R. G.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Martin, J.

Martin, J. M.

Mironov, V. L.

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

Ochs, G. R.

Post, M. J.

Rye, B. J.

Smalikho, I. N.

Tatarskii, V. I.

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, Jerusalem, 1971).

Wandzura, S.

Wandzura, S. M.

Werner, C.

Yadlowsky, M.

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]

Zavorotnyi, V. U.

V. U. Zavorotnyi, “Strong fluctuations of electromagnetic waves in a random medium with finite longitudinal correlation of the inhomogeneities,” Zh. Eksp. Teor. Fiz. 75, 56–65 (1978).

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).

Zhao, Y.

Appl. Opt. (13)

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

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

R. G. Frehlich, “Simulation of laser propagation in a turbulent atmosphere,” Appl. Opt. 39, 393–397 (2000).
[CrossRef]

A. Belmonte, B. J. Rye, “Heterodyne lidar returns in the turbulent atmosphere: performance evaluation of simulated systems,” Appl. Opt. 39, 2401–2411 (2000).
[CrossRef]

R. G. Frehlich, “Effects of refractive turbulence on ground-based verification of coherent Doppler lidar performance,” Appl. Opt. 39, 4237–4246 (2000).
[CrossRef]

V. A. Banakh, I. N. Smalikho, C. Werner, “Numerical simulation of the effect of refractive turbulence on coherent lidar return statistics in the atmosphere,” Appl. Opt. 39, 5403–5414 (2000).
[CrossRef]

A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39, 5426–5445 (2000).
[CrossRef]

Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving efficiency of monostatic pulsed coherent lidars. 1. theory,” Appl. Opt. 29, 4111–4119 (1990).
[CrossRef] [PubMed]

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

J. Martin, S. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
[CrossRef] [PubMed]

Wm. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
[CrossRef] [PubMed]

G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2430–2432 (1985).
[CrossRef] [PubMed]

B. J. Rye, R. G. Frehlich, “Optimal truncation of Gaussian beams for coherent lidar using incoherent backscatter,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

J. Atmos. Sci. (1)

R. Frehlich, “Laser scintillation measurements of the temperature spectrum in the atmospheric surface layer,” J. Atmos. Sci. 49, 1494–1509 (1992).
[CrossRef]

J. Fluid Mech. (1)

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
[CrossRef]

J. Math. Phys. (1)

R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (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]

Radio Sci. (1)

J. L. Codona, D. B. Creamer, S. M. Flatté, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Waves Random Media (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Zh. Eksp. Teor. Fiz. (2)

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).

V. U. Zavorotnyi, “Strong fluctuations of electromagnetic waves in a random medium with finite longitudinal correlation of the inhomogeneities,” Zh. Eksp. Teor. Fiz. 75, 56–65 (1978).

Other (2)

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, Jerusalem, 1971).

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

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Figures (2)

Fig. 1
Fig. 1

System efficiency η S (R) versus range R for a coherent Doppler lidar with the Hill spectrum [Eq. (15)] and with statistically independent paths for the transmit and BPLO beams (bistatic limit). The exact theoretical prediction (solid curve) [Eq. (9)] and the square-law structure-function approximation (dashed curve) [see Eqs. (9), (10), (21)] are compared with the results from the robust simulation algorithm (FFT–SH) and the traditional simulation algorithm (FFT). The case of no turbulence is shown as a dashed curve.

Fig. 2
Fig. 2

System efficiency η S (R) versus range R for a monostatic coherent Doppler lidar with the Hill spectrum [Eq. (15)]. The zero-order term of the theoretical expansion for weak scattering (solid curve) [Eq. (9)] and strong scattering (dashed curve) [Eq. (22)] are compared with the results from the robust simulation algorithm (FFT–SH) and the traditional simulation algorithm (FFT). The results for the exponential spectrum [Eq. (16)] and the traditional simulation algorithm (FFT–exp) are also shown for comparison.

Equations (26)

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SNRR  CR =ARηSRR2
ηSR=R2λ2AR- jTp, RjBPLOp, Rdp,
eTp, R=- eLu, 0WTuGp; u, Rdu,
eBPLOp, R=- eLO*u, 0WRuGp; u, Rdu,
ηSR=R2λ2AR----- eTu1, 0eT*u2, 0×eBPLOu3, 0eBPLO*u4, 0×Γ4p, u1, u2, u3, u4, Rdu1du2du3du4dp,
Γ4p, u1, u2, u3, u4, R=Gp; u1, RG*p; u2, R×Gp; u3, RG*p; u4, R
Γ4p, u1, u2, u3, u4, R =G4fp, ui, R  Dr1  Dr2  Dr3  Dr4×exp-120Rdr1-r2, z+dr3-r4, z+dr1-r4, z+dr2-r3, z-dr1-r3, z-dr2-r4, zdz,
ds, R=4πk2-1-coss · q×Φnqx, qy, qz=0, Rdq,
ηS0lfR=1AR- OTs, RBPLO*s, R×exp-DSs, Rds,
DSs, R=0Rds1-z/R, zdz
OTs, R=- eTr+s/2, 0eT*r-s/2, 0×expikr · s/Rdr,
OBPLOs, R=- eBPLOr+s/2, 0eBPLO*r-s/2, 0×expikr · s/Rdr.
ηS0lfR=λ2R2AR- jTp, RjBPLOp, Rdp,
Φnq, z=ACn2zq-11/3fql0z,
fx=1.0+0.70937x+2.8235x2-0.28086x3+0.08277x4exp-1.109x.
fx=exp-x2/34.91815
DSs=8π2ACn2k2l05/3RHs/l0,
Hz=01 gxzdx,
gx=0 q-8/3fq1-J0qxdq.
DSρ0=1,
DSs=s2/ρ02,
ηSSR=ηS0lfR+ηS0hfR=2ηS0lfR,
Φnq, z=BL0-2+q22,
ds  L021-sL0 K1s/L0,
ds  0.307966-0.5 ln s+0.5 ln L0)s2,
Γ4p, u1, u2, u3, u4, R=k22πR2 ×expikRα · δ+β · γ-2p · δ×exp-2δ20R1-z/R2Tzdz× Dβ1  Dγ1 exp-ik 0Rβ1 · γ¨1dz,

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