Evolution from a Fraunhofer to a Pearcey diffraction pattern

A cylindrical lens of small aperture produces in its focal plane a row of wave dislocations (phase singularities or optical vortices) as part of the Fraunhofer diffraction pattern for a slit. On the other hand, when the aperture is large, aberration produces a cusp caustic at the focus and its associated diffraction, namely, the Pearcey pattern. Passing smoothly from one extreme to the other shows that the Fraunhofer dislocations move to become the dislocations outside the caustic while the dislocations inside the caustic are created successively in pairs. The pairs are accompanied by phase saddles, as expected from previous work. Similar sequences would be expected for all the higher diffraction catastrophes. In this way the movement of the structurally stable dislocations forms a link between the structurally unstable line or point focus of engineering optics and the stable caustics of catastrophe optics.