Abstract

A phenomenological model is developed for the strength and spatial width of the coherent intensity peak of backscatter produced by reciprocal path scattering through atmospheric turbulence. The model is applied to a ground-based, monostatic laser radar tracking a space target under the condition of optical atmospheric turbulence saturation.

© 1997 Optical Society of America

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References

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  1. L. C. Andrews, W. B. Miller, J. C. Ricklin, “Spatial coherence of a Gaussian-beam wave in weak and strong optical turbulence,” J. Opt. Soc. Am. A 11, 1653–1660 (1994).
    [CrossRef]
  2. M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
    [CrossRef]
  3. M. S. Belen’kii, V. L. Mironov, “Mean diffracted rays of an optical beam in a turbulent medium,” J. Opt. Soc. Am. 70, 159–163 (1980).
    [CrossRef]
  4. J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), pp. 128 and 361–464.
  5. V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere, V. E. Zuev, ed. (Artech, Boston, Mass., 1987), pp. 25–96.
  6. Y. N. Barabanenkov, Y. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics XXIX, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 65–197.
    [CrossRef]
  7. L. C. Andrews, R. L. Phillips, “Optical scintillations and fade statistics for a satellite communication system,” Appl. Opt. 34, 7742–7751 (1995).
    [CrossRef] [PubMed]
  8. W. B. Miller, J. C. Ricklin, L. C. Andrews, “Effects of refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A 11, 2719–2726 (1994).
    [CrossRef]
  9. W. B. Miller, J. C. Ricklin, L. C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A 10, 661–672 (1993).
    [CrossRef]
  10. M. S. Belen’kii, “Effect of atmospheric turbulence on heterodyne lidar performance,” Appl. Opt. 32, 5368–5372 (1993).
    [CrossRef] [PubMed]
  11. J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
    [CrossRef]
  12. J. C. Dainty, T. Mavroidis, C. J. Solomon, “Double passage imaging through turbulence,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. SPIE1487, 2–9, (1991).
  13. T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence: plane-wave illumination,” J. Opt. Soc. Am. A 7, 348–355 (1990).
    [CrossRef]
  14. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw–Hill, New York, 1961).
  15. L. C. Andrews, W. B. Miller, J. C. Ricklin, “Geometrical representation of Gaussian beams propagating through complex paraxial optical systems,” Appl. Opt. 32, 5918–5929 (1993).
    [CrossRef] [PubMed]
  16. R. E. Hufnagel, “Atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Infrared Information and Analysis Center, Environmental Research Institute of Michigan, Ann Arbor, Mich., 1989), pp. 6.1–6.20.
  17. V. A. Banakh, Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk 634055, Russia (personal communication, 1994).
  18. M. S. Belen’kii, “Diffraction of optical radiation by a reflecting disk in a turbulent atmosphere,” Kvantovaya Elektron. (Moscow) N5, 38–45 (1972).
  19. A. S. Gurvich, S. S. Kashkarov, “Amplification of scattering in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 794–796 (1977).
  20. V. I. Tatarskii, “Some new aspects in the problem of waves and turbulence,” Radio Sci. 22, 859–865 (1987).
    [CrossRef]
  21. Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
    [CrossRef]
  22. J. H. Churnside, J. J. Wilson, “Enhanced backscatter of a reflected beam in atmospheric turbulence,” Appl. Opt. 32, 265–2655 (1993).
    [CrossRef]
  23. E. Jakeman, J. P. Frank, G. J. Balmer, “The effect of enhanced backscattering on target detection,” in Proceedings of the Agard Meeting on Atmospheric Propagation Effects Through Natural and Man-Made Obscurants for Visible to Millimeter-Wave Propagation (Mallovea, Italy, 1993).
  24. P. R. Tapster, A. R. Weeks, E. Jakeman, “Observation of backscattering enhancement through an atmospheric phase screen,” J. Opt. Soc. Am. A 6, 517–522 (1989).
    [CrossRef]
  25. B. S. Agrovskii, A. N. Bogaturov, A. S. Gurvich, S. V. Kireev, V. A. Myakinin, “Enhanced backscattering from a plane mirror viewed through a turbulent phase screen,” J. Opt. Soc. Am. A 8, 1142–1147 (1991).
    [CrossRef]
  26. Y. A. Kravtsov, A. I. Saichev, “Properties of coherent waves reflected in a turbulent medium,” J. Opt. Soc. Am. A 2, 2100–2105 (1985).
    [CrossRef]
  27. V. U. Zavorotnyi, V. I. Tatarskii, “Intensification of backscattering of waves by a body located near the irregular boundary of two media,” Sov. Phys. Dokl. 27, 566–567 (1982).
  28. Y. A. Kravtsov, A. I. Saichev, “Effects of partial wave-front reversal during the reflection of waves in randomly inhomogeneous media,” Sov. Phys. JETP 56, 291–294 (1982).
  29. J. F. Holmes, “Enhancement of backscattered intensity for a bistatic lidar operating in atmospheric turbulence,” Appl. Opt. 30, 2643–2646 (1991).
    [CrossRef] [PubMed]
  30. A. G. Vinogradov, Y. A. Kravtsov, V. I. Tatarskii, “Backscatter amplification effect for bodies located in a medium with random inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16, 1064–1090 (1973).
  31. The curve for K including instrument response function in Fig. 2 is reprinted, with permission, from Fig. 2.2 of Ref. 6.
  32. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), pp. 80–115 and 665–667.
  33. A. V. Jelalian, Laser Radar Systems (Artech, Boston, Mass., 1992), pp. 3–10.
  34. L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 380–391 (1992).
  35. J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw–Hill, New York, 1990), pp. 23–44 and 157–159.
  36. C. G. Bachman, Laser Radar Systems and Techniques (Artech, Dedham, Mass., 1979), pp. 9–40.
  37. J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, San Francisco, Calif., 1968), pp. 30–65.
  38. R. A. Murphy, “Scattering from Rough Surfaces and Atmospheric Turbulence in Monostatic Laser Radar Systems,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1995).

1995 (1)

1994 (3)

1993 (4)

1992 (1)

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 380–391 (1992).

1991 (2)

1990 (1)

1989 (1)

1987 (1)

V. I. Tatarskii, “Some new aspects in the problem of waves and turbulence,” Radio Sci. 22, 859–865 (1987).
[CrossRef]

1985 (1)

1983 (1)

M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
[CrossRef]

1982 (3)

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

V. U. Zavorotnyi, V. I. Tatarskii, “Intensification of backscattering of waves by a body located near the irregular boundary of two media,” Sov. Phys. Dokl. 27, 566–567 (1982).

Y. A. Kravtsov, A. I. Saichev, “Effects of partial wave-front reversal during the reflection of waves in randomly inhomogeneous media,” Sov. Phys. JETP 56, 291–294 (1982).

1980 (1)

1977 (1)

A. S. Gurvich, S. S. Kashkarov, “Amplification of scattering in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 794–796 (1977).

1973 (1)

A. G. Vinogradov, Y. A. Kravtsov, V. I. Tatarskii, “Backscatter amplification effect for bodies located in a medium with random inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16, 1064–1090 (1973).

1972 (1)

M. S. Belen’kii, “Diffraction of optical radiation by a reflecting disk in a turbulent atmosphere,” Kvantovaya Elektron. (Moscow) N5, 38–45 (1972).

Agrovskii, B. S.

Andrews, L. C.

Ariel, E. D.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 380–391 (1992).

Bachman, C. G.

C. G. Bachman, Laser Radar Systems and Techniques (Artech, Dedham, Mass., 1979), pp. 9–40.

Balmer, G. J.

E. Jakeman, J. P. Frank, G. J. Balmer, “The effect of enhanced backscattering on target detection,” in Proceedings of the Agard Meeting on Atmospheric Propagation Effects Through Natural and Man-Made Obscurants for Visible to Millimeter-Wave Propagation (Mallovea, Italy, 1993).

Banakh, V. A.

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere, V. E. Zuev, ed. (Artech, Boston, Mass., 1987), pp. 25–96.

V. A. Banakh, Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk 634055, Russia (personal communication, 1994).

Barabanenkov, Y. N.

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

Belen’kii, M. S.

M. S. Belen’kii, “Effect of atmospheric turbulence on heterodyne lidar performance,” Appl. Opt. 32, 5368–5372 (1993).
[CrossRef] [PubMed]

M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Mean diffracted rays of an optical beam in a turbulent medium,” J. Opt. Soc. Am. 70, 159–163 (1980).
[CrossRef]

M. S. Belen’kii, “Diffraction of optical radiation by a reflecting disk in a turbulent atmosphere,” Kvantovaya Elektron. (Moscow) N5, 38–45 (1972).

Bogaturov, A. N.

Churnside, J. H.

J. H. Churnside, J. J. Wilson, “Enhanced backscatter of a reflected beam in atmospheric turbulence,” Appl. Opt. 32, 265–2655 (1993).
[CrossRef]

Dainty, J. C.

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence: plane-wave illumination,” J. Opt. Soc. Am. A 7, 348–355 (1990).
[CrossRef]

J. C. Dainty, T. Mavroidis, C. J. Solomon, “Double passage imaging through turbulence,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. SPIE1487, 2–9, (1991).

Frank, J. P.

E. Jakeman, J. P. Frank, G. J. Balmer, “The effect of enhanced backscattering on target detection,” in Proceedings of the Agard Meeting on Atmospheric Propagation Effects Through Natural and Man-Made Obscurants for Visible to Millimeter-Wave Propagation (Mallovea, Italy, 1993).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), pp. 128 and 361–464.

J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, San Francisco, Calif., 1968), pp. 30–65.

Gurvich, A. S.

B. S. Agrovskii, A. N. Bogaturov, A. S. Gurvich, S. V. Kireev, V. A. Myakinin, “Enhanced backscattering from a plane mirror viewed through a turbulent phase screen,” J. Opt. Soc. Am. A 8, 1142–1147 (1991).
[CrossRef]

A. S. Gurvich, S. S. Kashkarov, “Amplification of scattering in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 794–796 (1977).

Hallerman, G. R.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 380–391 (1992).

Harvey, J. E.

J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
[CrossRef]

Holmes, J. F.

Hufnagel, R. E.

R. E. Hufnagel, “Atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Infrared Information and Analysis Center, Environmental Research Institute of Michigan, Ann Arbor, Mich., 1989), pp. 6.1–6.20.

Jakeman, E.

P. R. Tapster, A. R. Weeks, E. Jakeman, “Observation of backscattering enhancement through an atmospheric phase screen,” J. Opt. Soc. Am. A 6, 517–522 (1989).
[CrossRef]

E. Jakeman, J. P. Frank, G. J. Balmer, “The effect of enhanced backscattering on target detection,” in Proceedings of the Agard Meeting on Atmospheric Propagation Effects Through Natural and Man-Made Obscurants for Visible to Millimeter-Wave Propagation (Mallovea, Italy, 1993).

Jelalian, A. V.

A. V. Jelalian, Laser Radar Systems (Artech, Boston, Mass., 1992), pp. 3–10.

Kashkarov, S. S.

A. S. Gurvich, S. S. Kashkarov, “Amplification of scattering in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 794–796 (1977).

Kireev, S. V.

Kotha, A.

J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
[CrossRef]

Kravtsov, Y. A.

Y. A. Kravtsov, A. I. Saichev, “Properties of coherent waves reflected in a turbulent medium,” J. Opt. Soc. Am. A 2, 2100–2105 (1985).
[CrossRef]

Y. A. Kravtsov, A. I. Saichev, “Effects of partial wave-front reversal during the reflection of waves in randomly inhomogeneous media,” Sov. Phys. JETP 56, 291–294 (1982).

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

A. G. Vinogradov, Y. A. Kravtsov, V. I. Tatarskii, “Backscatter amplification effect for bodies located in a medium with random inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16, 1064–1090 (1973).

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

Mavroidis, T.

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence: plane-wave illumination,” J. Opt. Soc. Am. A 7, 348–355 (1990).
[CrossRef]

J. C. Dainty, T. Mavroidis, C. J. Solomon, “Double passage imaging through turbulence,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. SPIE1487, 2–9, (1991).

Miller, W. B.

Mironov, V. L.

M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Mean diffracted rays of an optical beam in a turbulent medium,” J. Opt. Soc. Am. 70, 159–163 (1980).
[CrossRef]

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere, V. E. Zuev, ed. (Artech, Boston, Mass., 1987), pp. 25–96.

Murphy, R. A.

R. A. Murphy, “Scattering from Rough Surfaces and Atmospheric Turbulence in Monostatic Laser Radar Systems,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1995).

Myakinin, V. A.

Northcott, M. J.

Ozrin, V. D.

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

Payson, H. C.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 380–391 (1992).

Phillips, R. L.

Ricklin, J. C.

Saichev, A. I.

Y. A. Kravtsov, A. I. Saichev, “Properties of coherent waves reflected in a turbulent medium,” J. Opt. Soc. Am. A 2, 2100–2105 (1985).
[CrossRef]

Y. A. Kravtsov, A. I. Saichev, “Effects of partial wave-front reversal during the reflection of waves in randomly inhomogeneous media,” Sov. Phys. JETP 56, 291–294 (1982).

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

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

Shirley, L. G.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 380–391 (1992).

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), pp. 80–115 and 665–667.

Solomon, C. J.

J. C. Dainty, T. Mavroidis, C. J. Solomon, “Double passage imaging through turbulence,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. SPIE1487, 2–9, (1991).

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw–Hill, New York, 1990), pp. 23–44 and 157–159.

Tapster, P. R.

Tatarskii, V. I.

V. I. Tatarskii, “Some new aspects in the problem of waves and turbulence,” Radio Sci. 22, 859–865 (1987).
[CrossRef]

V. U. Zavorotnyi, V. I. Tatarskii, “Intensification of backscattering of waves by a body located near the irregular boundary of two media,” Sov. Phys. Dokl. 27, 566–567 (1982).

A. G. Vinogradov, Y. A. Kravtsov, V. I. Tatarskii, “Backscatter amplification effect for bodies located in a medium with random inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16, 1064–1090 (1973).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw–Hill, New York, 1961).

Vinogradov, A. G.

A. G. Vinogradov, Y. A. Kravtsov, V. I. Tatarskii, “Backscatter amplification effect for bodies located in a medium with random inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16, 1064–1090 (1973).

Vivilecchia, J. R.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 380–391 (1992).

Weeks, A. R.

Wilson, J. J.

J. H. Churnside, J. J. Wilson, “Enhanced backscatter of a reflected beam in atmospheric turbulence,” Appl. Opt. 32, 265–2655 (1993).
[CrossRef]

Zavorotnyi, V. U.

V. U. Zavorotnyi, V. I. Tatarskii, “Intensification of backscattering of waves by a body located near the irregular boundary of two media,” Sov. Phys. Dokl. 27, 566–567 (1982).

Appl. Opt. (5)

Izv. Vyssh. Uchebn. Zaved. Radiofiz. (2)

A. S. Gurvich, S. S. Kashkarov, “Amplification of scattering in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 794–796 (1977).

A. G. Vinogradov, Y. A. Kravtsov, V. I. Tatarskii, “Backscatter amplification effect for bodies located in a medium with random inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16, 1064–1090 (1973).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Kvantovaya Elektron. (Moscow) (1)

M. S. Belen’kii, “Diffraction of optical radiation by a reflecting disk in a turbulent atmosphere,” Kvantovaya Elektron. (Moscow) N5, 38–45 (1972).

Lincoln Lab. J. (1)

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 380–391 (1992).

Opt. Commun. (1)

J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
[CrossRef]

Radio Sci. (1)

V. I. Tatarskii, “Some new aspects in the problem of waves and turbulence,” Radio Sci. 22, 859–865 (1987).
[CrossRef]

Radiophys. Quantum Electron. (1)

M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
[CrossRef]

Sov. Phys. Dokl. (1)

V. U. Zavorotnyi, V. I. Tatarskii, “Intensification of backscattering of waves by a body located near the irregular boundary of two media,” Sov. Phys. Dokl. 27, 566–567 (1982).

Sov. Phys. JETP (1)

Y. A. Kravtsov, A. I. Saichev, “Effects of partial wave-front reversal during the reflection of waves in randomly inhomogeneous media,” Sov. Phys. JETP 56, 291–294 (1982).

Sov. Phys. Usp. (1)

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

Other (15)

E. Jakeman, J. P. Frank, G. J. Balmer, “The effect of enhanced backscattering on target detection,” in Proceedings of the Agard Meeting on Atmospheric Propagation Effects Through Natural and Man-Made Obscurants for Visible to Millimeter-Wave Propagation (Mallovea, Italy, 1993).

R. E. Hufnagel, “Atmospheric turbulence,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Infrared Information and Analysis Center, Environmental Research Institute of Michigan, Ann Arbor, Mich., 1989), pp. 6.1–6.20.

V. A. Banakh, Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk 634055, Russia (personal communication, 1994).

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), pp. 128 and 361–464.

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere, V. E. Zuev, ed. (Artech, Boston, Mass., 1987), pp. 25–96.

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

J. C. Dainty, T. Mavroidis, C. J. Solomon, “Double passage imaging through turbulence,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. SPIE1487, 2–9, (1991).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw–Hill, New York, 1961).

The curve for K including instrument response function in Fig. 2 is reprinted, with permission, from Fig. 2.2 of Ref. 6.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), pp. 80–115 and 665–667.

A. V. Jelalian, Laser Radar Systems (Artech, Boston, Mass., 1992), pp. 3–10.

J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw–Hill, New York, 1990), pp. 23–44 and 157–159.

C. G. Bachman, Laser Radar Systems and Techniques (Artech, Dedham, Mass., 1979), pp. 9–40.

J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, San Francisco, Calif., 1968), pp. 30–65.

R. A. Murphy, “Scattering from Rough Surfaces and Atmospheric Turbulence in Monostatic Laser Radar Systems,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1995).

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Figures (6)

Fig. 1
Fig. 1

Comparison of the uplink and downlink field spatial-coherence widths versus altitude for a 1.064-µm laser radar with a transceiver aperture diameter of D x = 1 cm at an altitude of h o = 2 m for a path zenith angle of ξsp = 86°, a ground-level structure constant of C n,o 2 = 1.9 × 10-14 m-2/3, a high-altitude wind speed of ws = 21 m/s, and a target altitude of H = 300 km.

Fig. 2
Fig. 2

Comparison of the traditional backscatter-amplification factor K with the coherent RPS enhancement factor f c,AT when incoherent random focusing is neglected (solid curve) and included (dashed curve).6,34 K and f c,AT are equivalent when incoherent random focusing is neglected.

Fig. 3
Fig. 3

Area of the uplink beam A * defines the cross-sectional area at the equal-coherence plane through which strictly reciprocal propagation paths can occur. The location of the equal-coherence plane within the atmosphere was obtained by determining the altitude H * for the round-trip propagation path at which the uplink and downlink field spatial-coherence widths are equal.

Fig. 4
Fig. 4

Uplink and downlink round-trip propagation paths to and from the target through the turbulence occur either through the same coherence cell or through different coherence cells in the equal-coherence plane.

Fig. 5
Fig. 5

Normalized average coherent RPS intensity component versus radial position in the transceiver aperture plane.

Fig. 6
Fig. 6

Normalized average total intensity versus radial position in the transceiver aperture plane.

Tables (1)

Tables Icon

Table 1 Atmospheric Turbulence RPS Model Performance for Various Propagation Environments

Equations (30)

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σR2=1.23Cn2k7/6L11/6.
Ωo=1-L/Ro, Ω=2L/kωo2,
L=H-ho/cosξsp.
W=ωoΩo2+Ω21/2, Λ=ΩΩo2+Ω2=2LkW2, Θ=ΩoΩo2+Ω2,
Cn2h=0.00594ws27210-5h10 exp-h1000+2.7×10-16 exp-h1500+Cn,o2 exp-h100,
Wl=W1+6.72k7/6Λm06/5H-hosξsp11/51/2,
m0=hoHCn2hdh.
Ws=Wl-1.96W21/2ωo1/3kLΛm01/2.
lup=1.46k2m2+0.622Λt5/6m0-3/5cos3/5ξsp,
m2=1/H-ho5/3hoHh-ho5/3Cn2hdh.
Λt=Λ1+1.624σR26/5Λ,
σR2=2.25k7/6s11/6ξspH5/61H-ho5/3×hoH1-h-hoH-ho5/6Cn2hdh.
ldown=1.46k2m0-3/5cos3/5ξsp.
I11=I22=I12=I21=I12,21=I21,12=κtIt,
Ic=I12,21+I21,12=2κtIt, Iic=I11+I22+I12+I21=4κtIt.
fc,n=2=Ic+IicIic=6κtIt4κtIt=32.
Ic=nn-1κtIt,Iic=nκtIt+nn-1κtIt,
fc,n=Ic+IicIic=n+2nn-1n+nn-1=2-1n, limfc,nn2.
fc,AT=2-1/ncells,
lRPS=2.44(λL*/DAT,eff=1.22λL*/W*,
Iic,SCθs=ncellsAtrgtL2It cosθs,
Iic,DCθs=ncellsncells-1AtrgtL2It cosθs.
Iicθs=Iic,SCθs+Iic,DCθs=ncells2AtrgtL2It cosθs.
ncellsA*/Acell32378.
fc,AT=Itotθs=0Iicθs=0=Ic,ATθs=0+Iicθs=0Iicθs=0=2-1ncells=1.99997.
Ieffρo=kW*2/2L*22J1kW*/L*ρokW*/L*ρo2,
Ieffθs2J1kW*/L*L tanθskW*/L*L tanθs2.
Ic,ATθs=ncellsncells-1AtrgtL2It cosθs×2J1kW*L*L tanθskW*/L*L tanθs2
Itotθs=Iicθs+Ic,ATθs=ncells2AtrgtL2It cosθs+ncellsncells-1AtrgtL2It cosθs×2J1kW*/L*L tanθskW*/L*L tanθs2=ncells2AtrgtL2It cosθs1+ncells-1ncells×2J1kW*/L*L tanθskW*/L*L tanθs2.
fc,AT=Itotθs=0Iicθs=0=1+ncells-1ncells=2-1ncells.

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