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The inverse problem of scattering is solved for 3D inhomogeneities of the complex permittivity in multilayer media. The proposed solution involves an analysis of the 2D lateral distributions of the scattered field with the imposed condition of the probing field invariability relative to the receiver. A generalization of the solution beyond the Born approximation is given. Necessary k-space representations of Green functions for a multilayer medium with an arbitrary located source are obtaineddoi:10.1088/0266-5611/26/12/125013 fatcat:rtxxbvlju5csvbbb5klvsexm5q