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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 4 — Apr. 1, 1978
  • pp: 475–479

Waves in random media: Weak scattering reconsidered

D. A. de Wolf  »View Author Affiliations

JOSA, Vol. 68, Issue 4, pp. 475-479 (1978)

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Wave propagation in a weak random medium has generally been understood to give rise to lognormal field statistics, and first Born approximation of log amplitude and phase. Yet no derivation of the field probability distribution seems to exist; only an inference. The moments of the field (not just the amplitude) are derived from moment equations, and from these it is shown that extra terms must be identified with phase and amplitude in the customary representation of the field.

© 1978 Optical Society of America

D. A. de Wolf, "Waves in random media: Weak scattering reconsidered," J. Opt. Soc. Am. 68, 475-479 (1978)

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  1. A. Prokhorov, F. Bunkin, K. Gochelashvily, and V. Shishov, "Laser irradiance propagation in turbulent media," Proc. IEEE 63, 790–811 (1975).
  2. R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).
  3. Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, and V. I. Tatarski, "Status of the theory of propagation of waves in a randomly inhomogeneous medium," Sov. Phys. Uspekhi, 13, 551–680 (1971).
  4. P. G. Bergmann, "Propagation of radiation in a medium with random inhomogeneities," Phys. Rev. 70, 486–492 (1946).
  5. C. L. Pekeris, "Note on the scattering of radiation in an inhomogeneous medium," Phys. Rev. 71, 268–269 (1947).
  6. J. B. Keller, "Wave propagation in random media," in Proc. Symp. in Applied Mathematics, edited by G. Birkhoff, R. Bellman, and C. C. Lin, (American Mathematical Society, 1962, Providence, R.I.), Vol. 13, pp. 227–246.
  7. H. G. Booker and W. E. Gordon, "A theory of radio scattering in the troposphere," Proc. IRE 38, 401–412 (1950).
  8. L. Chernov, Wave Propagation in a Random Medium (McGraw- Hill, New York, 1960) (also Dover, 1967).
  9. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961) (also Dover, 1967).
  10. H. Bremmer, "Random volume scattering," J. Res. Nat. Bur. Stand. Sect. D: 68, 967–981 (1964).
  11. D. L. Fried, "Optical resolution through a randomly inhomogeneous medium for very long and very short exposures," J. Opt. Soc. Am. 56, 1372–1379 (1966).
  12. V. I. Tatarski, "Strong amplitude fluctuations of a wave propagating in a medium with weak random inhomogeneities," Izv. Vyssh. Ucheb. Zaved. Radiofiz., 10, 48–58 (1967).
  13. This calculation is given in D. A. de Wolf, "Strong irradiance fluctuations in turbulent air: plane waves", J. Opt. Soc. Am. 63, 171–179 (1973), in Secs. I and II. Sections III and IV of this work were based on a saturation-regime approximation that was later shown to be incorrect, hence are not correct. However, Secs. I and II for weak scattering, and Sec. V for very strong scattering (not realizable in optical turbulence) do not depend on the invalidated saturation-regime approximation.
  14. V. I. Tatarski, The Effect of the Turbulent Atmosphere on Wave Propagation (U.S. Dept. of Commerce, Springfield, Va., 1971), (see Chap. 5 for historic review of Russian contributions).
  15. W. P. Brown, Jr., "Moment equations for waves propagated in random media," J. Opt. Soc. Am., 62, 45–54 (1972).
  16. K. Furutsu, "Statistical theory of wave propagation in a random medium and the irradiance distribution function," J. Opt. Soc. Am. 62, 240–254 (1972).
  17. H. Bremmer, "General remarks concerning theories dealing with scattering and diffraction in random media," Radio Sci. 8, 511–534 (1973).
  18. W. P. Brown, Jr., "Propagation in random media-cumulative effect of weak inhomogeneities," IEEE Trans. Antennas Propag. AP-15, 81–89 (1967).
  19. D. A. de Wolf, "Multiple scattering in a random continuum," Radio Sci. 2, 1379–1392 (1967) [and erratum, Radio Sci. 3, 308 (1968)].
  20. A. S. Gurvich and V. I. Tatarski, "Coherence and intensity fluctuations of light in the turbulent atmosphere," Radio Sci. 10, 3–14 (1975).
  21. R. L. Fante, "Electric field spectrum and intensity covariance of a wave in a random medium," Radio Sci. 10, 77–85 (1975).
  22. K. Gochelashvili and V. Shishov, "Saturated intensity fluctuations of laser radiation in a turbulent medium," (in Russian), Zh. Eksp. Teor. Fiz. 66, 1237–1247 (1974).
  23. W. C. Hoffmann, "Wave propagation in a general random continuous medium," in Proc. Symp. in Applied Mathematics, edited by R. Bellman, (American Mathematical Society, Providence, R.I., 1964), Vol. 16, pp. 117–144.
  24. Reference 3, sections 3b (and 3c) can direct the reader to the pertinent literature.
  25. H. Bremmer, "A mathematical connecting scattering and diffraction phenomena, including Bragg-type interferences", TH-Rep. 71-E-26 (Technische Hogeschool Eindhoven), 64 pp., Dec. 1971.
  26. R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970) (tabular summaries of some of these equations).
  27. Reference 14, sections 40–49, contains plane-wave and sphericalwave derivations by Tatarski and co-workers of these formulas.
  28. R. Barakat, "Sums of independent lognormally distributed random variables," J. Opt. Soc. Am. 66, 211–216 (1976).
  29. J. W. Strohbehn, T-I. Wang, and J. P. Speck, "On the probability distribution of line-of-sight fluctuations of optical signals," Radio Sci. 10, 59–70 (1975).

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