Sonar cross sections of bodies partially insonified by finite sound beams

An object that is partially insonified by a collimated sound beam may have a scattering cross section sometimes much larger than when the object is totally covered by the incident beam. We quantitatively study this partial insonification problem here, under the classical method of physical optics. The importance of this study stems from the fact that partial coverage of the target by the beam is the situation most likely to occur in many cases of practical importance. We consider several basic target shapes partially insonified by finite beams. These shapes include the spherical, the infinite and finite cylinder, the flat plate, and the capped sphere. High-frequency approximations of the resulting integrals, obtained by means of the saddle-point method, show the relative importance of the scattering centers located at the beam's specular reflection points, or at the edges of the spots that the beam shines on the scatterers. The physical-optics method is extended to obtain formulas for the bistatic cross sections of partially insonified objects. The results are numerically evaluated and graphically displayed in many pertinent instances and compared to the predictions of approaches, such as the Fresnel-zones method and the Geometrical Theory of Diffraction (GTD). The predictions of the physical-optics method have all the advantages and deficiencies of this method and, with very minor modifications, hold equally well for the partial illumination of objects by beams of electromagnetic radiation.