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Generalized (scalar) diffraction tomography is a linear inverse scattering method that can be extended to electromagnetic vector fields with complete polarization information. Its essential equation is a vector form of the Porter–Bojarski integral equation linearized in the material parameters through the Kirchhoff approximation to scattering. This vector equation can be inverted with dyadic algebra and the standard techniques of diffraction tomography using data from multiple frequencies (frequency diversity) or multiple angles of incidence (angle diversity). An algorithm using scattering at multiple frequencies to reconstruct perfectly conducting objects is discussed in detail and checked against synthetic data generated with the MAFIA code for an airplane model. The results are overwhelmingly superior to those obtained by scalar inversion.

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