Diffraction by a half-plane: a generalization of the Fresnel diffraction theory

A generalization of the Fresnel approximation in diffraction theory is proposed. The phase term in the diffraction integral is approximated by a parabolic variation, not by a binomial expansion but rather by matching up at the critical points for asymptotic evaluation of the integral. The method provides a correction to the optical coordinates of the Fresnel diffraction theory that extends its region of validity. It is applied to diffraction of an inclined plane wave by a half-plane.