Scalar diffraction of spherical waves by a plane aperture: a general analysis based on the critical points.

We present a formulation of the scalar diffraction of spherical waves through plane apertures that takes advantage of the importance of the critical points and the semiperiodic zones that are defined in the plane of the aperture. Our approach overcomes the intrinsic limitations of stationary-phase methods (when the critical points coalesce) and allows a direct implementation in terms of numerical algorithms for computations of any predefined accuracy. The method is illustrated with examples corresponding to a rectangular aperture.