Transient, planar, nonlinear acoustical holography for reconstructing acoustic pressure and particle velocity fields

Abstract

A steady-state, nonlinear nearfield acoustical holography procedure, based on the Westervelt Wave Equation (WWE), was developed by the authors of this article to accurately reconstruct nonlinear acoustic “pressure” fields. Here, a “transient,” nonlinear acoustic holography algorithm is introduced that can be used to reconstruct three-dimensional, nonlinear acoustic pressure as well as particle velocity fields from two-dimensional acoustic pressure data measured on a measurement plane. This procedure is based on the Kuznetsov Wave Equation (KWE) that is directly solved by applying temporal and spatial Fourier Transforms to the KWE. When compared to the WWE-based procedure, the proposed procedure can be used to reconstruct acoustic particle velocity fields in addition to acoustic pressure fields. It can also be applied to multi-frequency source cases where each frequency component can contain both linear and nonlinear components. The KWE-based procedure is validated by conducting four numerical simulations with: (1) an infinite-size panel vibrating at a single frequency, (2) a pulsating sphere with a bifrequency excitation, (3) a finite-size, vibrating panel generating bended wave rays, and (4) an ultrasound transducer with a transient excitation. The numerical results show that holographically projected acoustic fields match well with directly calculated ones.