Abstract
Closed-form solutions are derived for several configurations of the parametric receiving array. First, the solution for the interaction of a high-frequency spherical wave from a point source and a low-frequency plane wave is obtained theoretically by using a two-dimensional stationary phase solution of Westervelt’s scattering integral. The result is in turn used to generate the solution for parametric receiving arrays with various pump transducers, including a truncated line source, a rectangular piston, and a circular piston. In each case, the observer is assumed to be in the farfield of the pump transducer, but the result includes the effects of interaction in the nearfield of the pump transducer. The solution of the parametric receiving array with a point source pump and a truncated line receiver is also found. The theoretical solutions include the effects of misalignment of either the pump or receiving transducer. Subject Classification; 25.35; 30.85.
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