Stokes surfaces of diffraction catastrophes with codimension three

The Stokes set, where exponentially small complex (i.e. evanescent) rays appear and disappear, is the locus of wavefield positions where stationary points of a diffraction integral have equal phase. In three dimensions, it is a surface. Stokes surfaces are calculated and displayed for the diffraction patterns decorating the swallowtail, elliptic and hyperbolic umbilic singularities. The surfaces are smooth apart from cusped edges where they meet the cusp lines of the real bifurcations set (caustic), and finite-angled creases at the complex whiskers of the singularity.