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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 72, Iss. 8 — Aug. 1, 1982
  • pp: 1034–1041

Fresnel scattering by a corrugated random surface with fractal slope

E. Jakeman  »View Author Affiliations


JOSA, Vol. 72, Issue 8, pp. 1034-1041 (1982)
http://dx.doi.org/10.1364/JOSA.72.001034


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Abstract

Consideration of the density of rays emanating from an infinite, corrugated Gaussian surface with fractal slope reveals a hitherto unexplored shortwave scattering regime that is uncomplicated by the presence of caustics in the scattered wave field. The statistical and coherence properties of the ray-density fluctuations in this regime are calculated as a function of fractal dimension D, and it is shown that in the Brownian case (D = 1.5) the problem can be solved exactly. The properties of the intensity pattern in a coherent scattering configuration are also investigated. The contrast of the pattern is computed as a function of propagation distance, and the asymptotic behavior in the strong scattering limit is again found to be exactly solvable when D = 1.5. It is shown that the intensity fluctuations are K distributed in this case. The effects of a finite outer-scale size are evaluated and discussed.

© 1982 Optical Society of America

Citation
E. Jakeman, "Fresnel scattering by a corrugated random surface with fractal slope," J. Opt. Soc. Am. 72, 1034-1041 (1982)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-72-8-1034


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References

  1. J. C. Dainty, ed., Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975).
  2. E. Jakeman, "Speckle statistics with a small number of scatterers," Proc. Soc. Photo-Opt. Instrum. Eng. 243, 9–19 (1980).
  3. M. Nakagami, "The m-distribution—a general formula of intensity distribution of rapid fading," in Statistical Methods in Radio Wave Propagation (Pergamon, New York, 1960), pp. 3–36.
  4. M. M. Siddiqui and G. H. Weiss, "Families of distributions for hourly median power and instantaneous power of received radio signals," J. Res. Nat. Bur. Stand. 67D, 753–762(1963).
  5. P. Beckmann, Probability in Communication Engineering (Harcourt Brace and World, New York, 1967), p. 167.
  6. E. Jakeman and P. N. Pusey, "A model for non-Rayleigh microwave sea echo," IEEE Trans. Antennas Propag. AP-24, 806–814 (1976).
  7. G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, "The statistical and correlation properties of light scattered by a random phase screen," in Coherence and Quantum Optics IV, L. Mandel and E. Wolf, eds. (Plenum, New York, 1978), pp. 351–361.
  8. G. Parry and P. N. Pusey, "K-distributions in atmospheric propagation of laser light," J. Opt. Soc. Am. 69, 796–798 (1979).
  9. E. Jakeman and P. N. Pusey, "Photon counting statistics of optical scintillation," Inverse Scattering Problems in Optics, Vol. 20 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 73-116.
  10. G. Parry, "Measurements of atmospheric turbulence induced intensity fluctuations in a laser beam," Opt. Acta 28, 715–728 (1981).
  11. S. F. Clifford and R. J. Hill, "Relation between irradiance and log-amplitude variance for optical scintillation described by the K distribution," J. Opt. Soc. Am. 71, 112–114 (1981).
  12. R. L. Phillips and L. C. Andrews, University of Central Florida Research Rep. No. N61339-79-D-0105 (University of Central Florida, Orlando, Fla., 1980).
  13. K. D. Ward, "Compound representation of high resolution sea clutter," Electron. Lett. 17, 561–653 (1981).
  14. B. J. Hoenders, E. Jakeman, H. P. Baltes, and B. Steinle, "K correlations and facet models in diffuse scattering," Opt. Acta 26, 1307–1319 (1979).
  15. A. Zardecki, "Statistical features of phase screens from scattering data," Inverse Source Problems in Optics, Vol. 9 of Topics in Current Physics (Springer-Verlag, Berlin, 1978), pp. 155–189.
  16. M. V. Berry, "Diffractals," J. Phys. A 12, 781–797 (1979).
  17. B. B. Mandelbrot, Fractals (Freeman, San Francisco, 1977).
  18. M. V. Berry, "Focussing and twinkling: critical exponents from catastrophes in non-Gaussian random shortwaves," J. Phys. A 10, 2061–2081 (1977).
  19. M. V. Berry and C. Upstill, "Catastrophe optics: morphologies of caustics and their diffraction patterns," in Progress in Optics XIII (North-Holland, Amsterdam, 1980), pp. 258–346.
  20. V. H. Rumsey, "Scintillations due to a concentrated layer with a power law turbulence spectrum," Radio Sci. 10, 107–114 (1975).
  21. C. L. Rino, "A power law phase screen model for ionospheric scintillation," Radio Sci. 14, 1135–1155 (1979).
  22. B. J. Uscinski, H. G. Booker, and M. Marians, "Intensity fluctuations due to a deep phase screen with power-law spectrum," Proc. Roy. Soc. Lond. A 374, 503–530 (1981).
  23. E. Jakeman, "On the statistics of K-distributed noise," J. Phys. A 13, 31–48 (1980).
  24. W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).
  25. E. Jakeman, "Scattering by a corrugated random surface with fractal slope," J. Phys. A Math. Nucl. Gen. 15, L55–L59 (1982).
  26. R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766–2788 (1963).
  27. E. Jakeman and J. G. McWhirter, "Correlation function dependence of scintillation behind a random phase screen," J. Phys. A 10, 1599–1643 (1977).
  28. L. S. Taylor and C. I. Infosino, "Diffraction theory of optical scintillation due to turbulent layers," J. Opt. Soc. Am. 65,78–84 (1975).
  29. E. Jakeman and P. N. Pusey, "Significance of K distributions in scattering experiments," Phys. Rev. Lett. 40, 546–550 (1978).
  30. Lord Rayleigh, "On the problem of random vibrations and of random flights in one, two or three dimensions," Philos. Mag. 37, 321–347 (1919).
  31. N. A. J. Hastings and J. B. Peacock, Statistical Distributions (Butterworths, London, 1974).
  32. A. Hewish, "The diffraction of radio waves in passing through a phase changing ionosphere," Proc. Roy. Soc. Lond. A 209, 81 (1951).
  33. V. I. Shishov, "Dependence of the form of the scintillation spectrum on the form of the spectrum of refractive-index inhomogeneities," Radiophys. Quantum Electron. 17, 1287–1292 (1974).
  34. V. I. Shishov, "Scintillation spectrum as a function of the spectrum of refractive index inhomogeneities," Radiosphys. Quantum Electron. 19, 62–68 (1976).

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