Monostatic and bistatic cross sections of a large (capped) sphere partially insonified at a circular spot

The physical-optics (Kirchhoff) method is used to determine the differential scattering cross section and the sonar cross section of a sphere partially insonified by a beam intersecting the surface of the sphere at a circular spot. The sphere is first assumed bare and then partially covered with a raised, centered cap which is smaller than the beam spot. A procedure to make the Kirchhoff method yield directly the bistatic cross section is extended to account for partial insonification and for the cap’s presence. We show that partial insonifcation alone can enhance the normalized sonar cross section up to four times the geometrical acoustics value, and with the additional introduction of a moderately thin and small cap, the enhancement goes beyond an order of magnitude. Quantitative plots of the cross sections are displayed and the general results are seen to reduce properly to, and in one instance, correct, particular cases available in the literature.