Comparison of various image induction (II) methods with physical optics (PO) for the far-field computation of flat-sectioned segmented reflectors

Kottler's (1923) extension of Kirchhoff's diffraction integral to electromagnetic fields yields the copolarized and cross-polarized fields of segmented reflectors. For flat sections, the Maggi-Rubinowicz (1888, 1917) potential can be used to transform Kottler's surface integral into a line integral resulting in an expression composed entirely of line integrals. Computation is simplified by the use of the Asvestas (1985) potential which eliminates the need to compute a geometrical optics term required by the original Maggi-Rubinowicz potential. In computing the far fields, a further simplification is realized by considering the antenna in reception rather than in transmission as an involved dyadic potential is then replaced by a simple vector potential. This is an exact-analysis method in the context of the image-induction model which, in theory, provides results which are very close to the physical optics (PO) model for the transmitting antenna. An approximate closed-form method is obtained by applying the Gordon (1975) transform to Silver's (1949) vector far field equations.