Abstract
The present contribution provides a method for the derivation of analytical near- and far-field expressions for the pressure step-function response of nonuniformly excited ultrasonic transducers modeled as pistons of arbitrary shape in an infinite rigid baffle. Explicit inversion of the Laplace transformed ultrasonic field using Cagniard's idea results in elementary functions or definite integrals of elementary functions, depending on the assumed nonuniform aperture distribution. The basic signal distortion is illustrated in terms of three-dimensional space-time plots of the pressure unit step-function response of a rectangular uniform aperture. The corresponding results for a phased-array transducer are also given. In addition, we investigate the pressure profile on the axis perpendicular to a uniform rectangular piston and its horizontal radiation pattern for different bandwidths of the exciting impulse.
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