Abstract

Simulations of beam propagation in three-dimensional random media were used to study the effects of atmospheric refractive turbulence on coherent lidar performance. By use of the two-beam model, the lidar return is expressed in terms of the overlap integral of the transmitter and the virtual (backpropagated) local oscillator beams at the target, reducing the problem to one of computing irradiance along the two propagation paths. This approach provides the tools for analyzing laser radar with general refractive turbulence conditions, beam truncation at the antenna aperture, beam-angle misalignment, and arbitrary transmitter and receiver configurations. Simplifying assumptions used in analytical studies, were tested and treated as benchmarks for determining the accuracy of the simulations. The simulation permitted characterization of the effect on lidar performance of the analytically intractable return variance that results from turbulent fluctuations as well as of the heterodyne optical power and system-antenna efficiency.

© 2000 Optical Society of America

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References

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  1. A. Belmonte, “Coherent lidar returns in turbulent atmosphere: feasibility study for the simulation of beam propagation,” submitted to Appl. Opt.
  2. A. Belmonte, B. J. Rye, W. A. Brewer, R. M. Hardesty, “Coherent lidar returns in turbulent atmosphere from simulation of beam propagation,” presented at the Tenth Biennial Coherent Laser Radar Technology and Applications Conference, Mount Hood, Ore., 28 June–2 July 1999.
  3. J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
    [CrossRef] [PubMed]
  4. 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]
  5. J. Martin, “Simulation of wave propagation in random media: theory and applications,” in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, V. U. Zavorotny, eds., Vol. PMO9 of SPIE Press Monograph (SPIE Press, Bellingham, Wash., 1993).
  6. W. 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]
  7. B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390–1398 (1979).
    [CrossRef] [PubMed]
  8. A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
    [CrossRef]
  9. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
    [CrossRef]
  10. G. N. Pearson, “A high-pulse-repetition-frequency CO2 Doppler lidar for atmospheric monitoring,” Rev. Sci. Instrum. 64, 1155–1157 (1993).
    [CrossRef]
  11. C. J. Grund, “Coherent Doppler lidar for boundary layer wind measurement employing a diode-pumped Tm:Lu:YAG laser,” in Coherent Laser Radar: Technology and Applications, Vol. 19 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 14–16.
  12. B. J. Rye, R. G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. 31, 2891–2899 (1992).
    [CrossRef] [PubMed]
  13. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
    [CrossRef]
  14. V. I. Tatarskii, The Effects of the Turbulence Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971).
  15. J. H. Churnside, “Aperture averaging of optical scintillation in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
    [CrossRef] [PubMed]
  16. D. L. Fried, “Optical heterodyne detection on an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–66 (1967).
    [CrossRef]
  17. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
    [CrossRef]
  18. J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 20, 3292–3312 (1981).
    [CrossRef] [PubMed]
  19. S. F. Clifford, S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. 20, 514–516 (1981); errata 20, 1502(1981).
    [CrossRef] [PubMed]
  20. B. J. Rye, “Refractive-turbulent contribution to incoherent backscatter heterodyne lidar returns,” J. Opt. Soc. Am. 71, 687–691 (1981).
    [CrossRef]
  21. Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1991), Vol. 29, pp. 65–197.
    [CrossRef]
  22. V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).
  23. V. I. Tatarskii, V. U. Zavorotny, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. 18, pp. 205–256.
  24. 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]
  25. R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
    [CrossRef] [PubMed]
  26. R. G. Frehlich, “Effects of refractive turbulence on coherent laser radar,” Appl. Opt. 32, 2122–2139 (1993).
    [CrossRef] [PubMed]

1995 (1)

1993 (2)

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

G. N. Pearson, “A high-pulse-repetition-frequency CO2 Doppler lidar for atmospheric monitoring,” Rev. Sci. Instrum. 64, 1155–1157 (1993).
[CrossRef]

1992 (1)

1991 (2)

1990 (1)

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]

1981 (3)

1979 (2)

B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390–1398 (1979).
[CrossRef] [PubMed]

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)

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

1975 (2)

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

1967 (1)

D. L. Fried, “Optical heterodyne detection on an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–66 (1967).
[CrossRef]

Barabanenkov, Yu. N.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1991), Vol. 29, pp. 65–197.
[CrossRef]

Belmonte, A.

A. Belmonte, “Coherent lidar returns in turbulent atmosphere: feasibility study for the simulation of beam propagation,” submitted to Appl. Opt.

A. Belmonte, B. J. Rye, W. A. Brewer, R. M. Hardesty, “Coherent lidar returns in turbulent atmosphere from simulation of beam propagation,” presented at the Tenth Biennial Coherent Laser Radar Technology and Applications Conference, Mount Hood, Ore., 28 June–2 July 1999.

Brewer, W. A.

A. Belmonte, B. J. Rye, W. A. Brewer, R. M. Hardesty, “Coherent lidar returns in turbulent atmosphere from simulation of beam propagation,” presented at the Tenth Biennial Coherent Laser Radar Technology and Applications Conference, Mount Hood, Ore., 28 June–2 July 1999.

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Capron, B. A.

Churnside, J. H.

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, W. 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]

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Filice, J. P.

Flatté, S. M.

Frehlich, R. G.

Fried, D. L.

D. L. Fried, “Optical heterodyne detection on an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–66 (1967).
[CrossRef]

Gochelashvily, K. S.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Grund, C. J.

C. J. Grund, “Coherent Doppler lidar for boundary layer wind measurement employing a diode-pumped Tm:Lu:YAG laser,” in Coherent Laser Radar: Technology and Applications, Vol. 19 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 14–16.

Hardesty, R. M.

A. Belmonte, B. J. Rye, W. A. Brewer, R. M. Hardesty, “Coherent lidar returns in turbulent atmosphere from simulation of beam propagation,” presented at the Tenth Biennial Coherent Laser Radar Technology and Applications Conference, Mount Hood, Ore., 28 June–2 July 1999.

Harney, R. C.

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]

Kavaya, M. J.

Klyatskin, V. I.

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

Kravtsov, Yu. A.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1991), Vol. 29, pp. 65–197.
[CrossRef]

Martin, J.

J. Martin, “Simulation of wave propagation in random media: theory and applications,” in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, V. U. Zavorotny, eds., Vol. PMO9 of SPIE Press Monograph (SPIE Press, Bellingham, Wash., 1993).

Martin, J. M.

Ozrin, V. D.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1991), Vol. 29, pp. 65–197.
[CrossRef]

Pearson, G. N.

G. N. Pearson, “A high-pulse-repetition-frequency CO2 Doppler lidar for atmospheric monitoring,” Rev. Sci. Instrum. 64, 1155–1157 (1993).
[CrossRef]

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Rye, B. J.

Saichev, A. I.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1991), Vol. 29, pp. 65–197.
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Shapiro, J. H.

Shishov, V. I.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Tatarskii, V. I.

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

V. I. Tatarskii, The Effects of the Turbulence Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971).

V. I. Tatarskii, V. U. Zavorotny, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. 18, pp. 205–256.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Wandzura, S.

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]

Zavorotny, V. U.

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

V. I. Tatarskii, V. U. Zavorotny, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. 18, pp. 205–256.

Appl. Opt. (9)

B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390–1398 (1979).
[CrossRef] [PubMed]

S. F. Clifford, S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. 20, 514–516 (1981); errata 20, 1502(1981).
[CrossRef] [PubMed]

J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 20, 3292–3312 (1981).
[CrossRef] [PubMed]

J. H. Churnside, “Aperture averaging of optical scintillation in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
[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]

B. J. Rye, R. G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

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

W. 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]

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

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]

Proc. IEEE (3)

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

D. L. Fried, “Optical heterodyne detection on an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–66 (1967).
[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]

Rev. Sci. Instrum. (1)

G. N. Pearson, “A high-pulse-repetition-frequency CO2 Doppler lidar for atmospheric monitoring,” Rev. Sci. Instrum. 64, 1155–1157 (1993).
[CrossRef]

Sov. Phys. JETP (1)

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

Other (8)

V. I. Tatarskii, V. U. Zavorotny, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. 18, pp. 205–256.

C. J. Grund, “Coherent Doppler lidar for boundary layer wind measurement employing a diode-pumped Tm:Lu:YAG laser,” in Coherent Laser Radar: Technology and Applications, Vol. 19 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 14–16.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

V. I. Tatarskii, The Effects of the Turbulence Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971).

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1991), Vol. 29, pp. 65–197.
[CrossRef]

A. Belmonte, “Coherent lidar returns in turbulent atmosphere: feasibility study for the simulation of beam propagation,” submitted to Appl. Opt.

A. Belmonte, B. J. Rye, W. A. Brewer, R. M. Hardesty, “Coherent lidar returns in turbulent atmosphere from simulation of beam propagation,” presented at the Tenth Biennial Coherent Laser Radar Technology and Applications Conference, Mount Hood, Ore., 28 June–2 July 1999.

J. Martin, “Simulation of wave propagation in random media: theory and applications,” in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, V. U. Zavorotny, eds., Vol. PMO9 of SPIE Press Monograph (SPIE Press, Bellingham, Wash., 1993).

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Figures (21)

Fig. 1
Fig. 1

System-antenna efficiency η S and the average coherent power gain (in decibels) as a function of range z and different levels of refractive turbulence Cn2 for the 2-µm monostatic system by use of the simulation of truncated Gaussian beam propagation in three-dimensional random media. The level of refractive turbulence has the typical daytime values of strong- and moderate-turbulence conditions: Cn2 = 10-12 m-2/3 and Cn2 = 10-13 m-2/3. The dotted line and curve correspond to the absence of refractive turbulence (free-space propagation).

Fig. 2
Fig. 2

System-antenna efficiency η S and the average coherent power gain (in decibels) as a function of range z and different levels of refractive turbulence Cn2 for the 2-µm truncated bistatic system. The lidar system parameters and levels of refractive turbulence are similar to those of Fig. 1.

Fig. 3
Fig. 3

System-antenna efficiency η S and the average coherent power gain (in decibels) as a function of range z and different levels of refractive turbulence Cn2 for the 2-µm truncated monostatic system. The level of refractive turbulence has the typical nighttime values of moderate- and weak-turbulence conditions: Cn2 = 10-14 m-2/3 and Cn2 = 10-15 m-2/3. The dotted line and curve correspond to the absence of refractive turbulence.

Fig. 4
Fig. 4

System-antenna efficiency η S and the average coherent power gain (in decibels) as a function of range z and different levels of refractive turbulence Cn2 for the 2-µm bistatic system. The lidar system parameters and levels of refractive turbulence are similar to those of Fig. 3.

Fig. 5
Fig. 5

Average coherent power gain (in decibels) as a function of the level of refractive turbulence Cn2 and at different ranges z. Both monostatic and bistatic configurations are considered for the 2-µm truncated system. The range has values of z = 1, km z = 2 km, and z = 3 km. The importance of the refractive turbulence on the coherent lidar performance is pronounced for any range z under typical daytime conditions of strong and moderate turbulence (Cn2 higher than 10-14 m-2/3).

Fig. 6
Fig. 6

System-antenna efficiency η S and the average coherent power gain (in decibels) as a function of range z and different levels of refractive turbulence Cn2 the 10-µm truncated monostatic system. The level of refractive turbulence has the daytime values of strong- and moderate-turbulence conditions: Cn2 = 10-12 m-2/3, Cn2 = 5 × 10-13 m-2/3, and Cn2 = 10-13 m-2/3. The dotted line and curve correspond to free-space propagation.

Fig. 7
Fig. 7

System-antenna efficiency η S and the average coherent power gain (in decibels) as a function of range z and different levels of refractive turbulence Cn2 for the 10-µm truncated bistatic system. The levels of refractive turbulence are similar to those of Fig. 6.

Fig. 8
Fig. 8

System-antenna efficiency η S and the average coherent power gain (in decibels) as a function of range z and different levels of refractive turbulence Cn2 for the truncated 10-µm monostatic system. The level of refractive turbulence has values of moderate-turbulence conditions: Cn2 = 5 × 10-14 m-2/3 and Cn2 = 10-14 m-2/3. The dotted line and curve correspond to the absence of refractive turbulence.

Fig. 9
Fig. 9

System-antenna efficiency η S and the average coherent power gain (in decibels) as a function of range z and different levels of refractive turbulence Cn2 for the 10-µm truncated bistatic system. The levels of refractive turbulence are similar to those of Fig. 8.

Fig. 10
Fig. 10

Average coherent power gain (in decibels) as a function of the level of refractive turbulence Cn2 and different ranges. Both monostatic and bistatic geometries are considered for the 10-µm truncated system. The range has values of z = 1 km, z = 2 km, and z = 3 km. The effect of the refractive turbulence on the coherent lidar performance is less important than for the 2-µm lidar (see Fig. 5). However, under conditions of strong turbulence (Cn2 higher than 10-13 m-2/3) the turbulence disturbances have to be considered for any range z.

Fig. 11
Fig. 11

Coherent power fluctuation variance as a function of range z and daytime condition for the 2-µm monostatic lidar. The system parameters are those of Fig. 1. The existence of a maximum is a consequence of the partial focusing of the beam by the turbulence, which reduces the beam-averaging effect (see the text for further details). Error bars are shown for only some of the studied ranges.

Fig. 12
Fig. 12

Similar to Fig. 11 but for moderate and weak Cn2 turbulence levels. In the last situation (Cn2 = 10-15 m-2/3), for which the beam irradiance fluctuations are less important, a smaller variance, which rises slightly with range z, results.

Fig. 13
Fig. 13

Variance of the coherent power turbulent fluctuations as a function of range z and daytime conditions for the 10-µm monostatic lidar. The system parameters are those of Fig. 6, and the comments for Figs. 11 and 12 apply.

Fig. 14
Fig. 14

Similar to Fig. 13 but for weaker-turbulence conditions. For ranges in the far field of the transmitter aperture, where the bright spots’ radii and beam widths are again similar, the averaging of the fluctuations should increase.

Fig. 15
Fig. 15

When the turbulent distorted beam width is presented along with the average size of the bright intensity spots as a function of range z, the results show that the maximum of the variance occurs when the beam size is similar to the bright spots’ size. In this figure the level of turbulence Cn2 = 10-12 m-2/3 considered corresponds to the variances described in Figs. 11 and 13 (for the 2- and 10-µm lidars, respectively).

Fig. 16
Fig. 16

Average coherent power gain (in decibels) as a function of range z and daytime conditions of the strong-turbulence level (Cn2 = 10-12 m-2/3) for both monostatic and bistatic configurations. The lidar system parameters are a 2-µm wavelength, a 14-cm transmitter-and-receiver aperture, and truncation by the telescope. Simulation results (solid curves) are compared with those obtained by use of the analytical zero-order approximation (dotted curves).24 The simulation results obtained by use of the same simplifying assumptions (untruncated Gaussian aperture and random-wedge atmosphere) that were needed to implement the analytical results are also presented (dashed curves).

Fig. 17
Fig. 17

Similar to Fig. 16 but for a larger wavelength (λ = 10 µm).

Fig. 18
Fig. 18

Similar to Fig. 16. Typical nighttime conditions of weak turbulence (Cn2 = 10-15 m-2/3).

Fig. 19
Fig. 19

Average coherent power gain (in decibels) as a function of range z and the moderate-turbulence level (Cn2 = 10-14 m-2/3) for both monostatic and bistatic configurations. The lidar system parameters are a 2-µm wavelength, a 14-cm transmitter-and-receiver aperture, and truncation by the telescope. Simulation results (solid curves) are compared with those obtained by use of the analytical zero-order approximation (dotted curves). To distinguish the effects of beam truncation we repeated the same simulation, ignoring the receiver-and-transmitter aperture (dashed curves).

Fig. 20
Fig. 20

Parameters are similar to those in Fig. 19. Again, simulation results (solid curves) are compared with those obtained by use of the analytical zero-order approximation (dotted curves). The simulation model represented by the dashed curves includes the simplified quadratic phase structure used in analytical work by assumption of a simple random-wedge atmosphere; it also includes beam truncation.

Fig. 21
Fig. 21

Parameters are similar to those of Fig. 19. Again, simulation results (solid curves) are compared with those obtained by use of the analytical zero-order approximation (dotted curves). In this case we modified the simulation by considering untruncated Gaussian beams and by describing the atmosphere through simple random wedges (dashed curves).

Equations (8)

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

Pt=Kz2βzλ2- ITp, z, tIBPLOp, zdp,
jTp, z, t=ITp, z, tPLt,jBPLOp, z=IBPLOp, zPLO.
Pt=PLtPLOKz2βzλ2×- jTp, z, tjBPLOp, zdp.
Pt=PLtPLOKz2βzARz2 ηSz, t,
ηSz, t=z2λ2AR- jTp, z, tjBPLOp, zdp
Pz, tPfz=- jTp, z, tjBPLOp, zdp- jTfp, zjBPLOfp, zdp,
σP2=- jTp, z, tjBPLOp, zdp2- jTp, z, tjBPLOp, zdp2-1.
P=Plf+q21+q2 Phf,

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