  A general reformulation of classical sharp-edge diffraction theory is
proposed within paraxial approximation. The, not so much known, Poincar\'e
vector potential construction is employed directly inside Fresnel's 2D integral
in order for it to be converted into a single 1D contour integral over the
aperture boundary. Differently from the recently developed paraxial
revisitation of BDW's theory, such approach can be applied to arbitrary
wavefield distributions impinging onto arbitrarily shaped sharp-edge planar
apertures. A couple of interesting examples of application of the proposed
method is presented.

Optics