Changes in echo-pulse instantaneous frequency when scanning the transducer

A theoretical model has been proposed that makes it possible to explain peculiarities in the frequency characteristics of echo signals at the output of a receiving transducer depending on the geometrical parameters of a reflecting spherical surface when the transducer axis is displaced with respect to the surface's center of curvature, that is, during scanning. It has been demonstrated that both with and without displacement of the transducer's geometrical axis with respect to the center of curvature of the reflecting surface, the type of changes in the temporal dependences of the instantaneous frequency of signals at the output of the receiving transducer essentially depends on the geometrical parameters of a wavefront reflected from the surface: the smaller the radius of wavefront curvature at the aperture of the receiving transducer, the stronger the changes of the instantaneous frequency in the echo pulse. It has also been shown that the larger the curvature of this surface, the stronger the changes in the frequency characteristics of the echo pulse as the transducer axis is displaced with respect to the center of curvature of the reflecting spherical surface.