Line integrals and physical optics Part II The conversion of the Kirchhoff surface integral to a line integral

Abstract

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.