The equivalence between Aperture Field Integration Method (AFIM) and Physical Optical (PO) is discussed for polyhedron surfaces in this paper. The necessary conditions for the equivalence are summarized which demand complete equivalent surface currents and complete apertures. The importance of the exact expressions for both incident and reflected fields in constructing equivalent surface currents is emphasized and demonstrated numerically. The fields from reflected components on additional surface which lies on the Geometrical Optics (GO) reflection boundary are evaluated asymptotically. The analytical expression enhances the computational efficiency of the complete AFIM. The equivalent edge currents (EECs) for AFIM (AFIMEECs) are used to extract the mechanism of this equivalence between AFIM and PO.

Modified Edge Representation (MER) empirically proposed by one of the authors is the line integral representation for computing surface radiation integrals of diffraction. It has remarkable accuracy in surface to line integral reduction even for sources very close to the scatterer. It also overcomes false and true singularities in equivalent edge currents. This paper gives the mathematical derivation of MER by using Stokes' theorem; MER is not only asymptotic but also global approximation. It proves remarkable applicability of MER, that is, to smooth curved surface, closely located sources and arbitrary currents which are irrelevant to Maxwell equations.

Mathematical proof for the equivalent edge currents for physical optics (POEECs) is given for plane wave incidence and the observer in far zone; the perfect accuracy of POEECs for plane wave incidence as well as the degradation for the dipole source closer to the scatterer is clearly explained for the first time. POEECs for perfectly conducting plates are extended to those for impedance plates.