Abstract
A model is formulated for the ultrasonic response of a scatterer in a fluid that lies on the axis of a transducer, where the transducer acts as both a sender and receiver of ultrasonic waves (pulse-echo setup). The transducer is modelled as a uniform velocity (piston) source and the scatterer can have arbitrary shape and material properties. Using a superposition of plane waves to form the bounded beam generated by the transducer, the T-matrix formalism to handle the scattering process exactly, and a combination of coordinate transformations and high frequency asymptotics, explicit analytical expressions are derived for the measured ultrasonic response. Experiments made for the response of an on-axis sphere show excellent agreement with the theory even in the near-field of the transducer.
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