A condition for multiple source reconstructions with the time-reversal methods

Time reversal (TR) methods have been presented for electromagnetic source reconstructions in inverse problems. Signals or electromagnetic fields emitted by unknown sources are received at preselected output locations, reversed in time and then re-injected into the problem domain at the output locations; the peak values of the fields observed then indicate the source locations. In this paper, we develop a condition that may be used to identify or verify multiple source locations and amplitudes without knowledge of Green's functions and field peaks as required by the existing methods. A numerical example is provided to verify the condition.