Singly focused backscattering from small targets in an Airy caustic formed by a curved reflecting surface

When sound scatters off a curved-reflecting surface such as the ocean floor or surface, it can focus forming caustics in the water column. The simplest caustic is an Airy caustic formed by the merging of two rays. In a backscattering experiment with a target residing at or near an Airy caustic, a signal can be focused on the way to the target, upon return from the target, or in both directions. To investigate these processes, an experiment is conducted in which an Airy caustic is formed using a cylindrical half-pipe reflector. The backscattered echo focused only once, either to or from a spherical target, is examined here. These focused echoes can be significantly stronger than the simple direct echo. Approximations are examined where the echo amplitude changes with target position in proportion to an Airy function. The argument of the Airy function is calculated using the relative echo times of transient pulses. This result is extended by applying the uniform approximation method of Chester, Friedman, and Ursell.