Wave scattering theory is the basis for many key technologies that have important military and commercial applications. The familiar examples are radar, sonar, and various ultrasound instruments commonly used in remote sensing, target identification, non-destructive evaluation, medical diagnosis, and many other areas. Their mathematical model involves the solution of the so-called inverse scattering problem where an incident wave is used to probe a remote or inaccessible object. From the scattered field measurement, the shape and/or the material composition of the object can be determined.; A new wave scattering theory, termed limiting circle theory (LCT), has been developed in this dissertation based on a novel approach of decomposing the wave scattering matrix. LCT has rigorously proved that the scattered wave field from any penetrable object (of cylinder and sphere geometries) is composed of three contributions: a rigid background, a soft background, and a pure resonance. This is a significant modification to the existing resonance scattering theory (RST) which states that the scattered field is made up of only two components: a proper background (either rigid or soft), and a pure resonance. LCT formalism led to the discovery of the limiting circle patterns associated with all normal modes or partial waves. These patterns provide a clear understanding of the resonance behavior such as the resonance period and the resonance intensity. The analytical LCT approach could also be the key to solving the background problems for shell structures that have remained unsolved for many years in acoustics.
展开▼
