Direct and Analytical Derivation of the Vectorial Geometrical Optics from the Modified Edge Representation Line Integrals for the Physical Optics

The Modified edge representation (MER) is the concept to be used in the line integral approximation for computing the surface radiation integrals of diffraction. The MER as applied to the physical optics (PO-MER), has remarkable accuracy in the surface-to-line integral reduction even for the curved surfaces and for sources very close to the scatterer. In the discussion of the mathematical foundation for this accuracy, the evaluation of the singularities in the integrand of the PO-MER line integration was left for further study.