Theory of the Time-Reversal Operator for a Dielectric Cylinder Using Separate Transmit and Receive Arrays

The DORT method applies to scattering analysis with arrays of transceivers. It consists in the study of the time-reversal invariants. In this paper, a large dielectric cylinder is observed by separate transmit and receive arrays with linear polarizations, E or H, parallel to its axis. The decomposition of the scattered field into normal modes and projected harmonics is used to determine the theoretical time-reversal invariants. It is shown that the number of invariants is about 2k 1 a , where a is the cylinder radius and k 1 the wave number in the surrounding medium. Furthermore, this approach provides approximated expressions of the two first invariants for a sub-resolved cylinder, i.e., when the cylinder diameter is smaller than the resolution width of the arrays. The two first invariants are also expressed in the small object limit for k1a. AMS subject classifications. 35B40, 35P25, 45A05, 74J20,78M35.

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