## Waves in random media: Weak scattering reconsidered

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

http://dx.doi.org/10.1364/JOSA.68.000475

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### Abstract

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

**Citation**

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

http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-68-4-475

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### References

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- 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.
- 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).
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- Reference 3, sections 3b (and 3c) can direct the reader to the pertinent literature.
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- 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).
- Reference 14, sections 40–49, contains plane-wave and sphericalwave derivations by Tatarski and co-workers of these formulas.
- R. Barakat, "Sums of independent lognormally distributed random variables," J. Opt. Soc. Am. 66, 211–216 (1976).
- 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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