Analysis of scattered fields by an impedance discontinuity of a planar surface by using Helmholtz-Kirchhoff integral theorem

In this study, we have derived a reference solution from the Green´s theorem and the Helmholtz-Kirchhoff integral theorem for reflected and scattered fields by a discontinuity of a planar impedance surface. It is assumed that both the transmitting and receiving antennas are placed sufficiently above the planar impedance surface. We have also derived a high-frequency asymptotic solution including higher-order terms from the integral representation obtained from the aperture field method (AFM). By comparing with the reference solution calculated numerically from the Helmholtz-Kirchhoff integral, we have clarified the validity and utility of the asymptotic solution obtained from the AFM.