International Symposium on Antennas and Propagation
Mathematical Derivation of Scattering Geometrical Optics from a Sphere by Modified Edge Representation Line Integral Around the Stationary Phase Point
Kazuhiro Kumamaru, Luis Rodriguez, Makoto Ando,
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Equivalent Edge Current (EEC) realizes the reduction of PO surface radiation integral to line integral. The authors have been proposing the Modified Edge Representation (MER) for deriving EECs. MER is unique in that it defines EECs not only along the periphery but also everywhere on the scatterer surface. At the Stationary Phase Point (SPP), the MER-EEC has the singularity. Authors have found numerically that the MER line integral around the SPP (MER-SPP) converges to Scattering Geometrical Optics (SGO) for variety of curved surfaces. For a planer surface with one Stationary Phase Point (SPP), it has been proved mathematically. For curved surfaces, SGO can be represented by MER-SPP only if the reflection wave front is spherical. In this article, the authors discuss this "spherical reflection condition" in detail. Firstly, it is confirmed numerically that there is no frequency dependence on SGO extraction errors by MER-SPP. Then the mathematical proof for SGO extraction from a curved surface by MER-SPP is studied. For simplicity, a sphere is considered as the scatterer in this article.