Abstract
Analysis of an echo from a solid elastic sphere has been limited to the case of a plane incident wave so far. Plane-wave theory is modified to the case of spherical incident wave first, and then it is modified to the case of an arbitrary ultrasonic transmitter and receiver by considering them as a set of point sources and point receivers, respectively. Using this relation, the general properties of the echo scattered from the sphere are analyzed first, and then the analysis is carried out in full for important practical cases; that is, the sphere is placed on the focal point of a circular concave transducer and in the focal plane of the transducer. It is applied to study the material dependence of the echo from the sphere placed at the focal point of the transducer as well as that of the sidelobe structure of the echo. These results are compared with those experimentally obtained using metal and plastic spheres of 3 mm in diameter, which show very good agreement.
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