Excitation of a circular-aperture transducer with an echo pulse reflected from a spherical surface

A theoretical model is suggested that allows one to explain peculiarities of the frequency response of echo signals at the output of a receiving transducer versus geometrical parameters of reflecting surfaces. It is shown that the way the instantaneous frequency of signals at the output of the receiving transducer changes depends on the curvature radius of reflected wavefront at the receivingtransducer aperture. It has been established that the frequency modulation of the pulsed echo signal is due to nonuniformity of the distribution of the phase of acoustic signal at the receiving-transducer aperture; this can be characterized by the radii of Fresnel zones that correspond to the reflected wavefront in relationship to the aperture radius of the circular transducer. Data on the frequency modulation of pulsed echo signals expressed in terms of dimensionless parameters (normalized frequency deviations) that were obtained experimentally and calculated by the suggested theoretical model demonstrate fair qualitative and quantitative agreement.