Reconstruction of Multiscale Electromagnetic Sources from Multifrequency Electric Far Field Patterns at Sparse Observation Directions

We introduce a multistep scheme for reconstructing multiscale sources from multifrequency sparse electric far field patterns. The unknown source is a combination of electric dipoles, magnetic dipoles and extended sources. The dipoles are shown to be uniquely identified by the multifrequency electric far field patterns at properly chosen sparse observation directions. Motivated by the constructive uniqueness, two indicator functions are then designed for locating the magnetic dipoles and the electric dipoles. After locating all the dipoles, the formulas for computing the corresponding polarization strengths are proposed. The stability of the formulas with respect to the frequency band is also derived. Finally, an indicator for the support of the extended sources is introduced once the dipoles are identified. Some numerical examples are presented to show the validity and robustness of the proposed algorithm.