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Chapter 7:
Second-Order Statistics: Strong Fluctuation Theory
Overview: In Chap. 6 we introduced the mutual coherence function (MCF) based on weak fluctuation theory, whereas in this chapter we will examine the MCF based on methods applicable to strong fluctuation theory. Although several techniques have been used over the years to deal with the MCF under strong fluctuations, it has been shown that all of them are essentially equivalent to one another under certain assumptions. For that reason we limit our treatment of strong fluctuation theories to the parabolic equation method and the extended Huygens-Fresnel principle. Of the above two methods, the one most similar to the Rytov approximation is the extended Huygens-Fresnel principle. Because it is somewhat easier to use than other methods, we will develop this technique in more detail than the parabolic equation method. In addition to these methods, we also introduce a more “heuristic approach” that uses the notion of “effective beam parameters” to redefine the free-space Gaussian beam in terms of an effective Gaussian-beam wave that takes into account the refractive and diffractive characteristics imposed on the beam by the random medium. The method of effective beam parameters is used to develop an expression for the spatial coherence radius of a Gaussian-beam wave and to extend the beam wander variance developed in Chap. 6 to conditions of moderate-to-strong irradiance fluctuations.
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