Analysis of diffraction in acoustic nonlinear parametric convolvers

Abstract

Acoustic parametric convolvers operate by spatially integrating a term produced by the nonlinear interaction of two propagating strain waves. The integrand will have an additional spatially dependent weighting factor and inaccuracies in the convolution output will result if the product term is not uniformly produced and summed. Under appropriate assumptions, the expansion of the acoustic field into an angular spectrum of plane waves is used to show that no erroneous weighting is introduced by diffraction, although diffraction does contribute a uniform loss to the convolver output. Under additional assumptions, the diffraction loss for the convolved output is shown to equal that which occurs in transmitting from one transducer to the other. Subject Classification: [43]25.30, [43]25.35; [43]35.54; [43]60.30.