Abstract

The asymptotic theory has been used to calculate the effect of the inner-scale size of the eddies on the properties of the irradiance variance and covariance of a plane wave propagating in a turbulent medium. It is found that the inclusion of a finite inner scale leads to an increase in the irradiance variance over what is predicted in the limit when the inner scale is zero. In addition, the inclusion of a finite inner scale alters the results for the spatial scales over which the irradiance scintillations are correlated. Finally, the results obtained are compared with recent predictions obtained by using the heuristic theory.

© 1983 Optical Society of America

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  1. C. L. Rino, "On the application of phase screen models to the interpretation of ionospheric scintillation," Radio Sci. 17, 855–867 (1982).
  2. R. K. Crane, "Ionospheric scintillation," Proc. IEEE 65, 180–199 (1977)
  3. K. C. Yeh and C. H. Liu, "Radio wave scintillations in the iono-sphere," Proc. IEEE 70, 324–360 (1982).
  4. I. N. Zhuk, "Scintillation studies of cosmic source angular structure (review)," Radiophys. Quantum Electron. 23, 597–615 (1980).
  5. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).
  6. V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Springfield, Va., 1971).
  7. R. L. Fante, "Electric field spectrum and intensity covariance of a wave in a random medium," Radio Sci. 10, 77–85 (1975).
  8. R. L. Fante, "Covariance of the intensity fluctuations of a wave in a random medium," Air Force Cambridge Research Lab. Rep. AFCRL-TR-74-0478 (September 27, 1974) (available from Defense Documentation Center, Washington, D.C.).
  9. A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in a turbulent media," Proc. IEEE 63, 790–811 (1975).
  10. K. S. Gochelashvili and V. I. Shishov, "Saturated fluctuations in the laser radiation intensity in a turbulent medium," Sov. Phys. JETP 39, 605–609 (1974).
  11. I. G. Yakushkin, "Asymptotic calculation of intensity fluctuations in a turbulent medium for long paths," Radiophys. Quantum Electron. 18, 1224–1229 (1975).
  12. R. Mercier, "Diffraction by a phase screen causing large random phase fluctuations," Proc. Cambridge Philos. Soc. 58, 382–400 (1962).
  13. K. S. Gochelashvily and V. I. Shishov, "Laser beam scintillation beyond a turbulent layer," Opt. Acta 18, 313–320 (1971).
  14. K. S. Gochelashvily and V. I. Shishov, "Focused irradiance fluctuations beyond a layer of turbulent atmosphere," Opt. Acta 19, 327–332(1972).
  15. J. R. Jokippi, "On the thin screen model of interplanetary scintillation," Astrophys. J. 161, 1147–1152 (1970).
  16. V. Rumsey, "Scintillations due to a concentrated layer with a power law turbulence spectrum," Radio Sci. 10, 107–114 (1975).
  17. C. L. Rino, "A power-law phase screen model for ionospheric scintillation (parts 1 and 2)," Radio Sci. 14, 1135–1155 (1979).
  18. B. J. Uscinski, H. G. Booker, and M. Marians, "Intensity fluctuations due to a deep phase screen with a power law spectrum," Proc. R. Soc. London Ser. A 374, 503–530 (1981).
  19. J. Strohbehn, ed., Laser Beam Propagation in the Atmosphere (Springer-Verlag, New York, 1978).
  20. M. Gracheva, "Similarity relations for strong fluctuations of the intensity of light propagating in a turbulent medium," Sov. Phys. JETP 40, 1011–1016 (1975).
  21. V. Banakh, G. Krekov, V. Mironov, S. Khmelevtsov, and S. Tsvik, "Focused laser beam scintillations in the turbulent atmosphere," J. Opt. Soc. Am. 64, 516–518 (1974).
  22. A. S. Gurvich, V. Kan, V. I. Tatarskii, and V. U. Zavorotyni, "Four-point field coherence function in a turbulent medium," Opt. Acta 26, 543–553 (1979).
  23. R. Dashen, "Path integrals for waves in a random medium," J. Math. Phys. 20, 894–920 (1979).
  24. V. V. Zavorotnyi, V. I. Klyatskin, and V. I. Tatarskii, "Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media," Sov. Phys. JETP 46, 252–260 (1977).
  25. M. J. Beran and A. M. Whitman, "Irradiance fluctuations and the assumption of Gaussian statistics for a beam propagating in a random medium," Opt. Acta 23, 287–295 (1976).
  26. H. T. Yura, "Physical model for strong optical-amplitude fluctuations in a turbulent medium," J. Opt. Soc. Am. 64, 59–67 (1974); D. A. DeWolf, "Strong irradiance fluctuations in turbulent air," J. Opt. Soc. Am. 63, 171–179 (1973).
  27. S. F. Clifford, G. R. Ochs, and R. S. Lawrence, "Saturation of optical scintillations by strong turbulence," J. Opt. Soc. Am. 64, 148–154(1974).
  28. R. J. Hill and S. F. Clifford, "Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive index spectra," J. Opt. Soc. Am. 71, 675–686 (1981).
  29. R. J. Hill, "Theory of saturation of optical scintillation by strong turbulence: plane wave variance and covariance and spherical wave covariance," J. Opt. Soc. Am. 72, 212–222 (1982).
  30. R. L. Phillips and L. C. Andrews, "Measured statistics of laser light scattering in atmospheric turbulence," J. Opt. Soc. Am. 71, 1440–1445 (1981).
  31. G. Parry, "Measurements of atmospheric turbulence induced intensity fluctuations in a laser beam," Opt. Acta 28, 715–728 (1981).
  32. W. A. Coles and R. G. Frehlich, "Simultaneous measurements of angular scattering and intensity scintillation in the atmosphere," J. Opt. Soc. Am. 72, 1042–1048 (1982).
  33. P. Hillion and S. Quinnez, "Saturation of scintillations for a light beam in a turbulent medium," Opt. Acta 28, 1485–1500 (1981).
  34. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  35. R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).
  36. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (U.S. Department of Commerce, Washington, D.C., 1964).
  37. R. J. Hill, U.S. Department of Commerce, 325 Broadway, Boulder, Colo. 80303 (personal communication, 1982).

1982 (3)

1981 (5)

R. J. Hill and S. F. Clifford, "Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive index spectra," J. Opt. Soc. Am. 71, 675–686 (1981).

R. L. Phillips and L. C. Andrews, "Measured statistics of laser light scattering in atmospheric turbulence," J. Opt. Soc. Am. 71, 1440–1445 (1981).

G. Parry, "Measurements of atmospheric turbulence induced intensity fluctuations in a laser beam," Opt. Acta 28, 715–728 (1981).

P. Hillion and S. Quinnez, "Saturation of scintillations for a light beam in a turbulent medium," Opt. Acta 28, 1485–1500 (1981).

B. J. Uscinski, H. G. Booker, and M. Marians, "Intensity fluctuations due to a deep phase screen with a power law spectrum," Proc. R. Soc. London Ser. A 374, 503–530 (1981).

1980 (1)

I. N. Zhuk, "Scintillation studies of cosmic source angular structure (review)," Radiophys. Quantum Electron. 23, 597–615 (1980).

1979 (3)

A. S. Gurvich, V. Kan, V. I. Tatarskii, and V. U. Zavorotyni, "Four-point field coherence function in a turbulent medium," Opt. Acta 26, 543–553 (1979).

R. Dashen, "Path integrals for waves in a random medium," J. Math. Phys. 20, 894–920 (1979).

C. L. Rino, "A power-law phase screen model for ionospheric scintillation (parts 1 and 2)," Radio Sci. 14, 1135–1155 (1979).

1977 (1)

V. V. Zavorotnyi, V. I. Klyatskin, and V. I. Tatarskii, "Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media," Sov. Phys. JETP 46, 252–260 (1977).

1976 (1)

M. J. Beran and A. M. Whitman, "Irradiance fluctuations and the assumption of Gaussian statistics for a beam propagating in a random medium," Opt. Acta 23, 287–295 (1976).

1975 (4)

M. Gracheva, "Similarity relations for strong fluctuations of the intensity of light propagating in a turbulent medium," Sov. Phys. JETP 40, 1011–1016 (1975).

V. Rumsey, "Scintillations due to a concentrated layer with a power law turbulence spectrum," Radio Sci. 10, 107–114 (1975).

R. L. Fante, "Electric field spectrum and intensity covariance of a wave in a random medium," Radio Sci. 10, 77–85 (1975).

I. G. Yakushkin, "Asymptotic calculation of intensity fluctuations in a turbulent medium for long paths," Radiophys. Quantum Electron. 18, 1224–1229 (1975).

1974 (4)

1972 (1)

K. S. Gochelashvily and V. I. Shishov, "Focused irradiance fluctuations beyond a layer of turbulent atmosphere," Opt. Acta 19, 327–332(1972).

1971 (1)

K. S. Gochelashvily and V. I. Shishov, "Laser beam scintillation beyond a turbulent layer," Opt. Acta 18, 313–320 (1971).

1970 (1)

J. R. Jokippi, "On the thin screen model of interplanetary scintillation," Astrophys. J. 161, 1147–1152 (1970).

1962 (1)

R. Mercier, "Diffraction by a phase screen causing large random phase fluctuations," Proc. Cambridge Philos. Soc. 58, 382–400 (1962).

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (U.S. Department of Commerce, Washington, D.C., 1964).

Andrews, L. C.

Banakh, V.

Beran, M. J.

M. J. Beran and A. M. Whitman, "Irradiance fluctuations and the assumption of Gaussian statistics for a beam propagating in a random medium," Opt. Acta 23, 287–295 (1976).

Booker, H. G.

B. J. Uscinski, H. G. Booker, and M. Marians, "Intensity fluctuations due to a deep phase screen with a power law spectrum," Proc. R. Soc. London Ser. A 374, 503–530 (1981).

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in a turbulent media," Proc. IEEE 63, 790–811 (1975).

Clifford, S. F.

Coles, W. A.

Crane, R. K.

R. K. Crane, "Ionospheric scintillation," Proc. IEEE 65, 180–199 (1977)

Dashen, R.

R. Dashen, "Path integrals for waves in a random medium," J. Math. Phys. 20, 894–920 (1979).

Fante, R. L.

R. L. Fante, "Electric field spectrum and intensity covariance of a wave in a random medium," Radio Sci. 10, 77–85 (1975).

R. L. Fante, "Covariance of the intensity fluctuations of a wave in a random medium," Air Force Cambridge Research Lab. Rep. AFCRL-TR-74-0478 (September 27, 1974) (available from Defense Documentation Center, Washington, D.C.).

R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).

Frehlich, R. G.

Gochelashvili, K. S.

K. S. Gochelashvili and V. I. Shishov, "Saturated fluctuations in the laser radiation intensity in a turbulent medium," Sov. Phys. JETP 39, 605–609 (1974).

Gochelashvily, K. S.

K. S. Gochelashvily and V. I. Shishov, "Focused irradiance fluctuations beyond a layer of turbulent atmosphere," Opt. Acta 19, 327–332(1972).

K. S. Gochelashvily and V. I. Shishov, "Laser beam scintillation beyond a turbulent layer," Opt. Acta 18, 313–320 (1971).

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in a turbulent media," Proc. IEEE 63, 790–811 (1975).

Gracheva, M.

M. Gracheva, "Similarity relations for strong fluctuations of the intensity of light propagating in a turbulent medium," Sov. Phys. JETP 40, 1011–1016 (1975).

Gurvich, A. S.

A. S. Gurvich, V. Kan, V. I. Tatarskii, and V. U. Zavorotyni, "Four-point field coherence function in a turbulent medium," Opt. Acta 26, 543–553 (1979).

Hill, R. J.

Hillion, P.

P. Hillion and S. Quinnez, "Saturation of scintillations for a light beam in a turbulent medium," Opt. Acta 28, 1485–1500 (1981).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Jokippi, J. R.

J. R. Jokippi, "On the thin screen model of interplanetary scintillation," Astrophys. J. 161, 1147–1152 (1970).

Kan, V.

A. S. Gurvich, V. Kan, V. I. Tatarskii, and V. U. Zavorotyni, "Four-point field coherence function in a turbulent medium," Opt. Acta 26, 543–553 (1979).

Khmelevtsov, S.

Klyatskin, V. I.

V. V. Zavorotnyi, V. I. Klyatskin, and V. I. Tatarskii, "Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media," Sov. Phys. JETP 46, 252–260 (1977).

Krekov, G.

Lawrence, R. S.

Liu, C. H.

K. C. Yeh and C. H. Liu, "Radio wave scintillations in the iono-sphere," Proc. IEEE 70, 324–360 (1982).

Marians, M.

B. J. Uscinski, H. G. Booker, and M. Marians, "Intensity fluctuations due to a deep phase screen with a power law spectrum," Proc. R. Soc. London Ser. A 374, 503–530 (1981).

Mercier, R.

R. Mercier, "Diffraction by a phase screen causing large random phase fluctuations," Proc. Cambridge Philos. Soc. 58, 382–400 (1962).

Mironov, V.

Ochs, G. R.

Parry, G.

G. Parry, "Measurements of atmospheric turbulence induced intensity fluctuations in a laser beam," Opt. Acta 28, 715–728 (1981).

Phillips, R. L.

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in a turbulent media," Proc. IEEE 63, 790–811 (1975).

Quinnez, S.

P. Hillion and S. Quinnez, "Saturation of scintillations for a light beam in a turbulent medium," Opt. Acta 28, 1485–1500 (1981).

Rino, C. L.

C. L. Rino, "On the application of phase screen models to the interpretation of ionospheric scintillation," Radio Sci. 17, 855–867 (1982).

C. L. Rino, "A power-law phase screen model for ionospheric scintillation (parts 1 and 2)," Radio Sci. 14, 1135–1155 (1979).

Rumsey, V.

V. Rumsey, "Scintillations due to a concentrated layer with a power law turbulence spectrum," Radio Sci. 10, 107–114 (1975).

Shishov, V. I.

K. S. Gochelashvili and V. I. Shishov, "Saturated fluctuations in the laser radiation intensity in a turbulent medium," Sov. Phys. JETP 39, 605–609 (1974).

K. S. Gochelashvily and V. I. Shishov, "Focused irradiance fluctuations beyond a layer of turbulent atmosphere," Opt. Acta 19, 327–332(1972).

K. S. Gochelashvily and V. I. Shishov, "Laser beam scintillation beyond a turbulent layer," Opt. Acta 18, 313–320 (1971).

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in a turbulent media," Proc. IEEE 63, 790–811 (1975).

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (U.S. Department of Commerce, Washington, D.C., 1964).

Tatarskii, V. I.

A. S. Gurvich, V. Kan, V. I. Tatarskii, and V. U. Zavorotyni, "Four-point field coherence function in a turbulent medium," Opt. Acta 26, 543–553 (1979).

V. V. Zavorotnyi, V. I. Klyatskin, and 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, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).

V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Springfield, Va., 1971).

Tsvik, S.

Uscinski, B. J.

B. J. Uscinski, H. G. Booker, and M. Marians, "Intensity fluctuations due to a deep phase screen with a power law spectrum," Proc. R. Soc. London Ser. A 374, 503–530 (1981).

Whitman, A. M.

M. J. Beran and A. M. Whitman, "Irradiance fluctuations and the assumption of Gaussian statistics for a beam propagating in a random medium," Opt. Acta 23, 287–295 (1976).

Yakushkin, I. G.

I. G. Yakushkin, "Asymptotic calculation of intensity fluctuations in a turbulent medium for long paths," Radiophys. Quantum Electron. 18, 1224–1229 (1975).

Yeh, K. C.

K. C. Yeh and C. H. Liu, "Radio wave scintillations in the iono-sphere," Proc. IEEE 70, 324–360 (1982).

Yura, H. T.

Zavorotnyi, V. V.

V. V. Zavorotnyi, V. I. Klyatskin, and V. I. Tatarskii, "Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media," Sov. Phys. JETP 46, 252–260 (1977).

Zavorotyni, V. U.

A. S. Gurvich, V. Kan, V. I. Tatarskii, and V. U. Zavorotyni, "Four-point field coherence function in a turbulent medium," Opt. Acta 26, 543–553 (1979).

Zhuk, I. N.

I. N. Zhuk, "Scintillation studies of cosmic source angular structure (review)," Radiophys. Quantum Electron. 23, 597–615 (1980).

Astrophys. J. (1)

J. R. Jokippi, "On the thin screen model of interplanetary scintillation," Astrophys. J. 161, 1147–1152 (1970).

J. Math. Phys. (1)

R. Dashen, "Path integrals for waves in a random medium," J. Math. Phys. 20, 894–920 (1979).

J. Opt. Soc. Am. (7)

Opt. Acta (6)

A. S. Gurvich, V. Kan, V. I. Tatarskii, and V. U. Zavorotyni, "Four-point field coherence function in a turbulent medium," Opt. Acta 26, 543–553 (1979).

G. Parry, "Measurements of atmospheric turbulence induced intensity fluctuations in a laser beam," Opt. Acta 28, 715–728 (1981).

M. J. Beran and A. M. Whitman, "Irradiance fluctuations and the assumption of Gaussian statistics for a beam propagating in a random medium," Opt. Acta 23, 287–295 (1976).

P. Hillion and S. Quinnez, "Saturation of scintillations for a light beam in a turbulent medium," Opt. Acta 28, 1485–1500 (1981).

K. S. Gochelashvily and V. I. Shishov, "Laser beam scintillation beyond a turbulent layer," Opt. Acta 18, 313–320 (1971).

K. S. Gochelashvily and V. I. Shishov, "Focused irradiance fluctuations beyond a layer of turbulent atmosphere," Opt. Acta 19, 327–332(1972).

Proc. Cambridge Philos. Soc. (1)

R. Mercier, "Diffraction by a phase screen causing large random phase fluctuations," Proc. Cambridge Philos. Soc. 58, 382–400 (1962).

Proc. R. Soc. London Ser. (1)

B. J. Uscinski, H. G. Booker, and M. Marians, "Intensity fluctuations due to a deep phase screen with a power law spectrum," Proc. R. Soc. London Ser. A 374, 503–530 (1981).

Radio Sci. (4)

V. Rumsey, "Scintillations due to a concentrated layer with a power law turbulence spectrum," Radio Sci. 10, 107–114 (1975).

C. L. Rino, "A power-law phase screen model for ionospheric scintillation (parts 1 and 2)," Radio Sci. 14, 1135–1155 (1979).

C. L. Rino, "On the application of phase screen models to the interpretation of ionospheric scintillation," Radio Sci. 17, 855–867 (1982).

R. L. Fante, "Electric field spectrum and intensity covariance of a wave in a random medium," Radio Sci. 10, 77–85 (1975).

Radiophys. Quantum Electron. (2)

I. G. Yakushkin, "Asymptotic calculation of intensity fluctuations in a turbulent medium for long paths," Radiophys. Quantum Electron. 18, 1224–1229 (1975).

I. N. Zhuk, "Scintillation studies of cosmic source angular structure (review)," Radiophys. Quantum Electron. 23, 597–615 (1980).

Sov. Phys. JETP (3)

K. S. Gochelashvili and V. I. Shishov, "Saturated fluctuations in the laser radiation intensity in a turbulent medium," Sov. Phys. JETP 39, 605–609 (1974).

M. Gracheva, "Similarity relations for strong fluctuations of the intensity of light propagating in a turbulent medium," Sov. Phys. JETP 40, 1011–1016 (1975).

V. V. Zavorotnyi, V. I. Klyatskin, and V. I. Tatarskii, "Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media," Sov. Phys. JETP 46, 252–260 (1977).

Other (11)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (U.S. Department of Commerce, Washington, D.C., 1964).

R. J. Hill, U.S. Department of Commerce, 325 Broadway, Boulder, Colo. 80303 (personal communication, 1982).

J. Strohbehn, ed., Laser Beam Propagation in the Atmosphere (Springer-Verlag, New York, 1978).

R. L. Fante, "Covariance of the intensity fluctuations of a wave in a random medium," Air Force Cambridge Research Lab. Rep. AFCRL-TR-74-0478 (September 27, 1974) (available from Defense Documentation Center, Washington, D.C.).

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, "Laser irradiance propagation in a turbulent media," Proc. IEEE 63, 790–811 (1975).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, New York, 1967).

V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Springfield, Va., 1971).

R. K. Crane, "Ionospheric scintillation," Proc. IEEE 65, 180–199 (1977)

K. C. Yeh and C. H. Liu, "Radio wave scintillations in the iono-sphere," Proc. IEEE 70, 324–360 (1982).

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