Abstract
The decomposition of the time-reversal operator is a signal analysis method applicable to ultrasonic methods of target detection and characterization. In this paper, the eigenmodes of the time-reversal operator are studied for a single rigid cylinder with elliptical cross-section leading to an asymmetric response matrix formed by the interelement response of an active transducer array. The elliptical cylinder is of considerable interest in scattering problems since it encompasses within the limit both the circular cross-section case (very low eccentricity) and the strip (eccentricity approaching infinity). Variable cylinder properties will include parameters such as cross-sectional area, eccentricity, and angle of inclination of the semimajor axis with respect to the axis of a probing transducer array. Exact solutions for determination of the far-field response matrix using the familiar modal expansion with scattering coefficients computed via Mathieu functions will be discussed. The basis functions spanning the range of the time-reversal operator under conditions for which reciprocity no longer holds will also be discussed. Theoretical analysis will indicate that for scatterers near the Rayleigh limit, it is possible to characterize the aspect ratio of the target using a subarray method.
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