Mathematics Colloquia and Seminars

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The fact that wave propagation looks the same whether time is going forward or backward has been known theoretically since the formulation of wave theory. Only recently, however, has array technology and computers been developed to the point that time reversal of waves can actually be performed in real systems. Experiments using ultrasonic and underwater acoustical arrays have shown enhanced focusing, communications, and imaging through complicated media. These results are described mathematically in terms of the time reversal operator (TRO). Application of the singular value decomposition (SVD) to this operator motivates new techniques for enhanced imaging and target characterization. In this talk, we discuss the relationship between the singular values of the TRO and the physical properties of a target for both acoustic and electromagnetic scattering. We show that the number of singular values associated with a single target is governed by the symmetries of the scattering process. We then show how this relationship can be used in a simulation of radar imaging of dielectric spheres over a perfectly conducting surface.