On the Issue of the Born-Rytov Controversy. 1. Comparing Analytical and Approximate Expressions for the One-Dimensional Deterministic Case
LOWELL UNIV MA DEPT OF ELECTRICAL ENGINEERING
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The applicability and domains of validity for the Born and the Rytov methods in scattering theory are established, with mathematical rigor, by comparing successive terms of the Born and the Rytov series calculated for wave propagation in a homogeneous dielectric halfspace and a homogeneous dielectric slab, for which the permittivities are assumed to have a low contrast over that of free-space. While the first order Rytov approximation is superior to the first order Born approximation when it is applied to estimate the scattered field in the homogeneous dielectric half-space, both approximations are inapplicable to estimate to estimate the scattered fields when the dielectric slab is very thick. There is much interest in modelling the propagation and scattering of waves in inhomogeneous media, to solve both direct and inverse scattering problems. The physical properties of these media can be extracted or predicted from the measurable quantities such as the scattered fields and intensities which can be derived from the models. Usually, approximations are sought in order to make the scattered fields which can be expressed as the Fredholm integral equations of the first kind more tractable for numerical computation.
- Theoretical Mathematics