“…But in the context of catastrophe theory, 1 they are merely different manifestations of the same general caustic morphology if the assumptions of normal incidence and plane waves are relaxed. For example, if a plane wave illuminates the cylinder at a progressively steeper angle of incidence or, equivalently, if the refractive index of the cylinder progressively increases, 2 the two branches of the far-zone (p Ϫ 1)-order rainbow caustic approach each other, join together at infinity [3][4][5][6][7] in what has been called the caustic merging transition, and evolve into a near-zone focusing caustic. If the angle of incidence is further increased, the focal line of the near-zone caustic approaches the cylinder and touches its surface, and the caustic evolves into a cusp lying entirely within the cylinder.…”