The inverse scattering problem related to the localization of metal bars embedded within a finite-dimensional dielectric was studied in two-dimensional geometry. The dielectric was placed in air and illuminated from the outside using a linear microwave source and a multi-monostatic configuration. The discontinuity at the interface between the air and the dielectric causes reflections that are neglected if a simple linear Born approximation of scattering is assumed. Herein, a new formulation was proposed based on a quadratic approximation of the scattering equation. The formulation maintained the interaction between the metal bars and the dielectric edge, whereas the mutual coupling between the bars was neglected. By exploiting the knowledge of the permittivity of the dielectric and the shape of its section, a relatively simple approximate expression for the scattered field was derived, which allowed for formulation of an inverse linear problem. Numerical examples demonstrated the feasibility of this approach.
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