Line integrals and physical optics Part I The transformation of the solid-angle surface integral to a line integral

Abstract

The surface integral that measures the solid angle subtended by a planar aperture at a point in space is transformed to a line integral over the boundary of the aperture. The problem is divided into three distinct cases, and in each case a transformation is established. The results have a direct application to the problem of converting the Kirchhoff integral of diffraction by an aperture on a plane screen to a line integral over the rim of the aperture. gan Radiation Laboratory, the Techniis engage

An exact line integral representation of the magnetic physical optics scattered field

“…By extending the work by Asvestas [4]- [6], the traditional surface integral of the electric physical optics (PO) scattered field from a perfectly electrically conducting (PEC) planar plate illuminated by an electric Hertzian dipole was cast into a line integral along the edges of the plate in [7]. The procedure of [7] was recently extended in [8] to derive a line integral representation of the electric PO scattered field from a penetrable planar plate illuminated by a plane wave.…”

Uniform asymptotics of paraxial boundary diffraction waves

“…However, such an indubitable computational advantage is balanced by the presence of singularities in the integrand of the one-dimensional BDW integral, which gives numerical problems, especially whenever the BDW field has to be evaluated close to the geometrical shadow at the observation plane [8]. To overcome such difficulties, important modifications to the BDW theory were provided by several authors [9][10][11][12][13][14][15]. In 2000, Hannay [16] showed that, when the BDW integral (for spherical or plane wave illumination) is written within paraxial approximation, it takes on a mathematical form in which the above singularities are no longer present.…”

An exact line integral representation of the physical optics scattered field: the case of a perfectly conducting polyhedral structure illuminated by electric Hertzian dipoles

“…The present work was inspired by the three papers by Asvestas [13], [15], [16]. Asvestas [13] considered the electromagnetic diffraction by an aperture in a perfectly conducting plane screen and took as his starting point the Kirchhoff diffraction integral for electromagnetic fields as derived by Kottler [17].…”