Applications of Solid-Angle Functions in Acoustical Scattering

Abstract

It is known that, in the far-field (FF) regime, the pulse-echo (PE) scattering of acoustical waves from a weak, internally uniform inhomogeneity can be simply represented in terms of the planar area function (PArF) of the scatterer. The PArF can be obtained by moving an imaginary cutting-plane, oriented parallel to the incident wavefront, through the scatterer and by recording the areas of the cross-sections as a function of distance. After the PArF is re-expressed as a function of the round-trip time, the impulse response function (IRF) is obtained by taking the second time derivative and multiplying by a known constant. In the case of a strong scatterer a similar procedure is employed, except the shadow zone is regarded as an extension of the object In an earlier paper (Richardson and Wade, 1992), the PArF was discussed at some length, but a generalization, called the solidangle function (SAnF) approach, was discussed only briefly. The purpose of the present paper is to give a full treatment of the latter approach.