The near field of a locally illuminated diffracting edge

It is shown that when both the source and field point are sufficiently close to a diffracting edge to require a closer approximation to the field than is provided by the usual Fresnel integrals, the rigorous solution can be put in terms of the incomplete Hankel function, whose asymptotic properties are known and which is well tabulated. The solution remains valid without change of form in the vicinity of the shadow boundary, and it reduces, respectively, to the known Hankel or Fresnel formulation at the shadow boundary or when either the source or field point is distant from the edge.