Time domain nearfield acoustical holography without wrap-around error and spectral leakage for forward propagation

Nearfield acoustical holography can be used to visualize time domain evolution of non-stationary sound fields. It requires sampling of the pressure field with a microphone array to calculate the sound field on other parallel surfaces, either toward the source or farther away from it. This paper focuses on forward propagation of fields sampled with a planar array. Several formulations exist to perform such calculation; however, despite being mathematically well-posed, they generate significant errors, especially for larger propagation distances. These errors are mainly due to wrap-around and spectral leakage. It is shown in this paper that generation of leakage can be avoided by sampling the analytical Green's function in the time and space domains. Such formulation allows the application of linear convolution, which completely suppresses wrap-around errors. The results obtained from the proposed formulation are compared to the analytical solution of a baffled piston with transient displacement. The average discrepancy is below 3.5% for propagation distances of 5 to 55 cm. In comparison, the relative error obtained with other propagators varies from 6% to 73%, depending on the propagation distance and method used. Finally, the proposed formulation is applied to experimental data obtained from an impacted plate.