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The article investigates the properties of scatterers with an impedance surface when the direction of linear polarization of the incident electromagnetic wave changes. It has been established that between the solutions of inverse problems of the synthesis of impedance coatings with diffe­rent polarizations, there is a functional relationship that allows us to get to the integrooperator equation to determine the coating dual to the original one. It differs in the fact that if you simultaneously change the coating and the polarization of the incident wave, the scattering diagram (SD) will not change. This allows you to synthesize a cross-polarization masking coating, in which the SD does not change when polarization changes to a transverse polarization. An approach to the construction of scatterers with the property of cross-polarization equivalence is proposed. The advantage of the proposed algorithms for the synthesis of surface impedance distributions is that they do not require the use of regularization procedures. The formulation of an optimization problem that provides coatings in classes of functions with a minimum norm is studied.

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