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29 December 1992 Nonuniqueness in direct and inverse electromagnetic scattering theory
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General statements of impossibility can be important in science and engineering. Ambiguities in inverse problems are cases of non-uniqueness where classes of different objects give the same response. A strong ambiguity is one which no additional data will remove the non- uniqueness, whereas a weak ambiguity is one which can be removed by additional data. In direct scattering theory, different potentials with one or more trapped modes may give the same R(k) or the ei(alpha )R(k) where (alpha) is a real parameter at all wave-numbers k. In three-dimensional direct scattering theory, different material media and sources J, p give the same scattering matrix at all times (or wave numbers) at all scattering angles and all incident angles. Examples of strong ambiguities will be given including one where a temporal relaxation of a homogeneous body is equivalent to a totally different time-independent homogeneous body. Weak ambiguities will be presented including both examples of incident scatters. The conditions on the scatterers at spatial infinity and their trapped mode bound-state structure will be given.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Brian DeFacio and S. H. Kim "Nonuniqueness in direct and inverse electromagnetic scattering theory", Proc. SPIE 1767, Inverse Problems in Scattering and Imaging, (29 December 1992);

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