Imaging through a homogeneous circular cylinder: the role of virtual caustics, rainbow glare points, and image fragmentation.

Abstract

Small air bubbles on the rear inside surface of a water-filled cylinder, near its edges, appear horizontally elongated, joined in pairs, and take on color. Similarly, if an extended object is sufficiently close to the water-filled cylinder, three images of the object are seen when looking through the cylinder. The center image joins onto the left or right image as the observer moves his or her head back and forth in front of the cylinder. The first observation is explained in terms of glare points of light, and the real and virtual parts of the external caustic of the light transmitted through the water-filled cylinder. The second observation is explained as an example of Berry's caustic touching theorem which describes the topological method of fragmentation of an object's image into multiple images. For the situation studied here, an imaginary cylindrical aberration caustic of the water-filled cylinder decomposes object space into a three-ray region sandwiched between two one-ray regions. As an extended object crosses the caustic boundary from one of the one-ray regions into the three-ray region, an image-pair creation event occurs, which is followed by an image-pair disconnection event producing the three images. Similarly, when the extended object crosses the caustic boundary from the three-ray region into one of the one-ray regions, an image-pair merging event occurs, which is followed by an image-pair annihilation event producing the one remaining image.