For observation points that are far from the geometrical focus, we derive asymptotic approximations to the field in both the Debye and Kirchhoff approximations. We now assume that the observation point does not lie in the vicinity of the geometrical shadow boundary, and consider the complete asymptotic contribution of the isolated boundary. To illustrate the accuracy of various asymptotic results, we apply them to the diffraction problem, in which a diverging spherical wave is diffracted by an annular aperture. Use of an annular rather than a circular aperture in this case is important, since it makes the numerical integration needed for comparison much less time-consuming. Since the numerical computation was very time-consuming, we checked the accuracy only at a few selected observation points. When the observation point is far from the geometrical focal point, both the Debye integral representation and the impulse-response integral can be evaluated asymptotically by the method of stationary phase.