A parabolic equation technique for reducing physical optics shadow boundary errors

A simple procedure is described for reducing the magnitude of the error associated with the physical optics (PO) shadow boundary on a curved surface. The method relies on the fact that the erroneous shadow boundary contribution is not due to the fundamental incorrectness of the PO currents but rather to the abruptness with which they are truncated at the shadow boundary. A heuristic argument is then made for the modification of the currents near the terminator involving a parabolic differential equation. This procedure differs from the Fock theory in that the modified currents obtained do not contain information relevant to higher-order scattering mechanisms such as creeping waves. Thus, the resulting currents are a more continuous but not necessarily a more accurate assumption for the currents around the shadow boundary. However, this does result in a more accurate evaluation of the PO integral, since the erroneous termination effect is diminished.<>