Geometrical optics terms calculated by a PO-MER line integration methodology

The purpose of this paper is to open the discussion, from the numerical point of view, on the direct equivalence between the physical optics (PO) surface integral and the modified edge representation (MER) line integrals. When the scattered field is composed by the diffracted field and the GO contributions the entity of MER line integration is not clear and the equivalence between the PO surface-to-MER line-integration has not been confirmed. In this paper, it is numerically demonstrated that MER line integration around the stationary phase point (SPP), which is the reflection or the intersection of the ray path between the source and the observer, gives the geometrical optics terms. The GO terms are understood as the reflected wave in the reflection region or the direct incident wave (with negative sign) in the shadow region. The general and important results derived are: the PO surface integral is decomposed into the GO and the diffraction terms via the MER line integrals.