On a consideration of correction factors in the dipole theory of Rayleigh-Mandel'shtam-bethe diffraction

The classical variant in the dipole theory of diffraction by small apertures is based on the model of an isolated hole in an infinite flat screen. The prescence of closely spaced parallel or perpendicular additional metal screens or other holes leads to corrections since the polarizability coefficients are no longer calculated from the problem of an isolated hole but from static problems having a more complicated geometry. This was pointed out in the literature where a numerical method based on a direct solution of integral equations of the first kind for the fields in the aperture is given for a parallel additional screen. In the case of a circular aperture the method of paired integral equations, associated with the Hankel transformation is extremely effective. In this case the problem reduces to integral Fredholm equations of the second kind for the auxiliary functions. In most cases they can be be solved by an iteration method, leading to approximate analytical expressions for the stated correction factors. The goal is to derive these analytical expressions.