This paper is the last in a series [1–4] of five papers on the diffraction and imaging properties of generalized curvilinear diffraction gratings. Here we show how the bifurcation properties of two-dimensional potential functions may be studiedviaa diffraction grating representation. In particular, we derive the grating functions appropriate to Thom's seven elementary catastrophes. We then present a detailed study of the cusp grating and discuss the behaviour of its point source image diffraction pattern (IDP) in the context of catastrophe theory. In this way, we show how catastrophe theory allows for a simple geometric interpretation of discontinuous type image diffraction patterns.