Natural focusing and catastrophes

Contrived focusing is achieved by the disturbance of waves by man-made devices such as lenses or antenna dishes, and the theory of the process is well established. Natural focusing or caustics, on the other hand, are produced in waves subjected to natural, or nonspecial, disturbance such as propagation through an irregular medium or reflection from an irregular surface. The appropriate theory of such focusing had to await the mathematics of catastrophe theory developed only in the last decade, the different natural focusings being the different catstrophes. With it the caustic geometry of the focusings are described, as is the characteristic associated wave diffraction pattern. These can then be used, for example, to calculate intensity fluctuations in a randomly disturbed wave of short wavelength.