Solving the background mystery in acoustical resonance scattering theory (RST)

Abstract

The acoustical resonance scattering theory (RST) aims to solving inverse scattering problems by decomposing the backscattering echoes into a background part and a resonance part. The former contains scatterers shape information, and the latter contains the material composition information. RST assumes the existence of an intermediate background for general scatterer and surrounding combinations. However, despite the efforts taken in the 1970s through 80s, such a background still remains elusive. This long-standing difficult problem is re-investigated in this study. It is concluded here that an intermediate background or alike is not needed for the purpose of solving inverse scattering problems. The simplest rigid or soft background is sufficient for the extraction of resonance information for any type of scatterer and surrounding combinations. In other words, the missing background problem is not a problem at all. Another new finding of this study is that a rational expression for the backscattering echoes is better suited to convey the resonance information than the additive decomposition expression as in RST. Explicit and concise relations exist between the rational expression and the acoustical properties of any scatterer, which is important for applications such as underwater target identification. This presentation will be illustrated by animation movies.