Locality of high frequency electromagnetic scattering phenomena is embodied and imported to the Method of Moments (MoM) to reduce computational load. The proposed method solves currents on small areas only around inner and edge stationary phase points (SPPs) on the scatterer surfaces. The range of MoM area is explicitly specified in terms of Fresnel zone number as a function of frequency, source and observer positions. Based upon this criterion, scatterer of arbitrary size and shape can be solved with almost frequency independent number of unknowns. In some special cases like focusing systems, locality disappears and the method reduces to the standard MoM. The hybrid method called PO-MoM is complementarily introduced to cope with these cases, where Fresnel zone number with analogous but different definition is used. The selective use of Local-MoM and PO-MoM provides frequency insensitive number of unknowns for general combination of source and observation points. Numerical examples of RCS calculation for two dimensional flat and curved surfaces are presented to demonstrate the accuracy and reduction of unknowns of this method. The Fresnel zone, introduced in the scattering analysis for the first time, is a useful indicator of the locality or the boundary for MoM areas.

High frequency (HF) diffraction is known as local phenomena, and only parts of the scatterer contribute to the field such as the edge, corner and specular reflection point etc. Many HF diffraction techniques such as Geometrical Theory of Diffraction (GTD), Uniform Theory of Diffraction (UTD) and Physical Theory of Diffraction (PTD) utilize these assumptions explicitly. Physical Optics (PO), on the other hand, expresses the diffraction in terms of radiation integral or the sum total of contributions from all the illuminated parts of scatterers, while the PO currents are locally defined at the point of integration. This paper presents PO-based visualization of the scattering and diffraction phenomena and tries to provide the intuitive understanding of local property of HF diffraction as well as the relations between PO and the ray techniques such as GTD, UTD etc. A weighting named "eye function" is introduced in PO radiation integrals to take into account of local cancellation between rapidly oscillating contributions from adjacent currents; this extracts important areas of current distribution, whose location moves not only with the source but also with the observation point. PO visualization illustrates both local property of HF scattering and defects associated with ray techniques. Furthermore, careful examination of visualized image reminds us of the error factor in PO as applied for curved surfaces, named fictitious penetrating rays. They have been scarcely recognized if not for visualization, though they disturb the geometrical shadow behind the opaque scatterer and can be the leading error factors of PO in shadow regions. Finally, visualization is extended to slot antennas with finite ground planes by hybrid use of modified edge representation (MER) to assess the significance of edge diffraction.

We have proposed a unique and simple modification to the definition of surface-normal vectors in Physical optics (PO). The modified surface-normal vectors are so defined as that the reflection law is satisfied at every point on the surface. The PO with currents defined by this new surface-normal vector has the enhanced accuracy for the edged scatterers to the level of Geometrical Theory of Diffraction (GTD), though it dispenses with the knowledge of high frequency asymptotic techniques. In this paper, firstly, the remarkable simplicity and the high accuracy of the modified PO as applied to the analysis of Radar Cross Section (RCS) is demonstrated for 2 dimensional problems. Noteworthy is that the scattering not only from edge but also from wedge is accurately predicted. This fringe advantage is confirmed asymptotically by comparing the edge and wedge diffraction coefficients of GTD. Finally, the applicability for three dimensional cube is also demonstrated by comparison with experimental data.

Locality in high frequency diffraction is embodied in the Method of Moments (MoM) in view of the method of stationary phase. Local-domain basis functions accompanied with the phase detour, which are not entire domain but are much larger than the segment length in the usual MoM, are newly introduced to enhance the cancellation of mutual coupling over the local-domain; the off-diagonal elements in resultant reaction matrix evanesce rapidly. The Fresnel zone threshold is proposed for simple and effective truncation of the matrix into the sparse band matrix. Numerical examples for the 2-D strip and the 2-D corner reflector demonstrate the feasibility as well as difficulties of the concept; the way mitigating computational load of the MoM in high frequency problems is suggested.