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A new approach is presented for converting the surface integral, representing the Kirchhoff diffracted field of an aperture on a plane screen, to a line integral. It has the advantages that it is mathematically rigorous and explicit and that it results in a representation that has exactly the same properties as the original Kirchhoff formula, i.e., it admits arbitrary source distributions and it is continuous everywhere in the source-free half-space, including the geometric-optics shadow boundary. Moreover, this new representation involves a unit vector whose direction can be adjusted so as to allow for accurate machine computations.

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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

The purpose of this work is to analyze the physical optics method as applied to electromagnetic scattering theory and to point out its physical and mathematical drawbacks. The main conclusions are (1) that the boundary values assumed by physical optics lead to electromagnetic fields that do not satisfy the finiteness of energy condition and, as a consequence, that integral representations of these fields cannot be obtained via the divergence theorem; (2) that the commonly accepted representations are not solutions of the physical optics problem because they fail to reproduce the assumed discontinuities of the fields on the scatterer. Despite the above conclusions, the present work should not be construed as an attempt to discredit the method but rather as an effort toward a better understanding of it. As it is well known, there have been a number of occasions in which physical optics has yielded quite satisfactory results.