Cloaking devices based on the coordinate transform approach enable, in principle, a perfect concealment of a region in space provided that the material composing the cloaking shell meets certain criteria. To achieve ideal cloaking it is necessary that the shell material parameters have singular values on the surface bounding the cloaked region which is unphysical. In this paper we assume finite values of cloak parameters and apply the scattering theory formalism to give an estimate of the

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... l performance of an 'imperfect' cloak. We perform full-wave numerical calculations and use our theoretical results to discuss them.