The propagation of ultrasonic beams is a phenomenon of widespread interest to a variety of technologies including sonar, medical ultrasound, and nondestructive evaluation. One goal in most applications is the production of a narrow, highly collimated beam of sound. Rigid piston radiators have often been employed and have been thoroughly analyzed. This type of source has the generally undesirable attributes of a complicated near field interference structure as well as far field side lobes. Sources which produce a Gaussian amplitude distribution have been studied since, for this case, the previous disadvantages are eliminated. Unfortunately, Gaussian radiators are more difficult to manufacture [1,2]. Various types of focusing probes have also been analyzed for concentrating the sound in a narrow band over a short depth of field. Conically focussed, or axicon, probes have been examined for the purpose of extending the focal region for resolution over a greater depth of field. One disadvantage common to all of the above sources, and indeed to any physically realizable source, is the phenomenon of beam spread due to diffraction.