Abstract
In this paper closed-form solutions for several configurations of the parametric receiving array are found. 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 using a two-dimensional stationary phase solution of Westervelt's scattering integral. The point source solution is in turn used to generate the solution for parametric receiving arrays with various pump transducers, including a truncated line source transducer, a rectangular piston transducer, and a circular piston transducer. In each case, the observer is assumed to be in the farfield of the pump transducer. However, 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 truncated line receiver is also found. The theoretical solutions also include the effects of misalignment of either the pump or receiving transducer.
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