ABSTRACT
This chapter considers the diffraction of a diverging cylindrical wave by an edge or a slit aperture. Our starting point is the first Rayleigh-Sommerfeld diffraction integral. The authors show that the asymptotic contribution of the stationary point of the phase function corresponds to a geometrical-optics field. The asymptotic formulae for the geometrical-optics field and the edge-diffracted field become invalid for observation points near a shadow boundary. The authors explore the focusing of a cylindrical wave with first-order aberration. To explain the transition from Huygens' principle to the geometrical theory of diffraction and geometrical optics, they follow Stamnes (1982) and consider the two-dimensional diffraction problem. The problem at the shadow boundary may also be interpreted in terms of rays: the difficulty occurs because an ordinary geometrical ray coincides with a diffracted ray. The accuracy of the asymptotic method of computing the angular spectrum of converging two-dimensional waves has been examined by Stamnes.
