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A comparison and study of the Born and Rytov expansions
Since the introduction of the Born and Rytov approximations for use in random wave propagation some forty
years ago, a controversy has boiled over the regions of validity and relative merits of the methods. Although the
methods fail for strong fluctuations and distant path lengths, these two perturbation methods are the only
approaches available for weak fluctuations in a random in homogeneous media. The approximations have also been applied to the inverse problem for optical and acoustical tomography.
The intent of this thesis is to investigate the work of previous authors and attempt to clarify the distinctions of
each method. The conclusion will be reached that neither approximation is necessarily better than the other in
general for all applications. A careful consideration of the problem following the points given should point towards the use of one approximation over the other.