Target characterization using decomposition of the time-reversal operator: electromagnetic scattering from small ellipsoids

Abstract

Decomposition of the time-reversal operator for an array, or equivalently the singular value decomposition of the multistatic response matrix, has been used to improve imaging and localization of targets in complicated media. Typically, each singular value is associated with one scatterer even though it has been shown in several cases that a single scatterer can generate several singular values. In earlier papers Chambers and Berryman (2004 Phys. Rev. Lett. 92 0239021–4; 2004 IEEE Trans. Ant. Prop. 52 1729–38) showed that a small spherical scatterer can generate up to six singular values depending on the array geometry and sphere composition. It was shown that the existence and characteristics of multiple singular values for each scatterer can, in principle, be used to determine certain properties of the scatterers, e.g. conducting or non-conducting material. In this paper, we extend this analysis to non-spherical targets and show how orientation information about the target may be obtained from the spectrum of singular values. The general properties of the decomposition for small non-spherical dielectric (and possibly conductive) targets in an electromagnetic field are derived and detailed results are obtained for the specific cases of non-magnetic and perfectly conducting needles and discs. It is shown that scatterer orientation can be estimated by tracking the singular values of a linear array as it is rotated around its midpoint.