Comparison of asymptotic solution obtained from aperture field method with Helmholtz-Kirchhoff integral for scattered fields by an impedance discontinuity of a planar surface

We have investigated the scattered field by an impedance discontinuity of a planar surface. A reference solution has been derived by using the Helmholtz-Krichhoff (H-K) integral theorem, while an asymptotic solution has been derived by using the aperture field method (AFM) and the saddle point technique. The validity and utility of the asymptotic solution have been confirmed by comparing with the reference solution. It is found that when both transmitting and receiving antennas are placed at sufficiently higher positions, the asymptotic solution agrees very well with the reference solution.