A comparison among localized approximations in one-dimensional profile reconstruction

We use the localized approximation and some modified versions of the localized approximation to study the electromagnetic field interaction of a plane wave with a slab of complex permittivity. The approximation as originally proposed is based on the localization property of the appropriate Green's function and the smooth variation of the internal field. In our one-dimensional case, the Green's function singularity degenerates into a localized peak. We apply two iterative techniques to the localized procedure in order to better simulate the internal fields. The first technique involves iterating the governing equation once before adopting the localized approximation, while the second technique involves iterating the localized approximation once. A study of other approximations based on the Born approximation is also included. In addition we present a generalization of the localized approximation using the Extended-Born approximation. We compare and contrast the performance of the various approximations in simulating the internal and external fields numerically. The localized approximation and the two modified versions are next used in one-dimensional profile reconstruction based on a least-structured version of the least-squares inversion method. We compare and contrast the performance of the approximations in profile reconstruction. A noticeable consequence of these modifications is an aggravation of the nonlinearity in the inverse problem. We investigate the consequences of this aggravation. We conclude with the introduction of a three-dimensional version of the localized approximation, the exploitation of which we leave for future work