The determination of the acoustic far field of a radiating body in an acoustic fluid from boundary measurements

Abstract

The far field (FF) of a radiating or scattering object immersed in an acoustic fluid can be represented in the frequency domain as a finite dimension linear combination of basis functions, which are determined by the shape and the size of the object in acoustic wavelengths. The coefficients of the linear combination are obtained as the outputs of a bank of spatial filters whose inputs are either the boundary normal velocity—for the radiation problem—or the boundary pressure and the normal velocity—for the scattering problem—measured by a dense set of sensors. The filter outputs provide the information sufficient to reconstruct the radiated or scattered far field, amplitude and phase. The structure of the filters is identified from the singular valve decomposition of the appropriate radiation or scattering operator, mapping the boundary normal velocity, or the combination of normal velocity and pressure, into the FF. Also, from the filter outputs, the efficiently radiating component of the boundary field can be extracted. For example the boundary total normal velocity may have a localized high peak, which however may be completely or almost completely absent in the radiating component. Selected results of an extensive simulation are presented illustrating the accuracy of the reconstruction of the FF from the spatial filtering of the boundary field.