Treeby Bradley E, Budisky Jakub, Wise Elliott S, Jaros Jiri, Cox B T
Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom.
IT4Innovations Centre of Excellence, Faculty of Information Technology, Brno University of Technology, Božetěchova 2, Brno, 612 00, Czech Republic.
J Acoust Soc Am. 2018 Jan;143(1):529. doi: 10.1121/1.5021245.
A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.
推导了一种格林函数解，用于计算由任意形状的相控阵换能器在单频连续波激励下产生的声场，该激励具有空间变化的幅度和相位。该解基于空间频域或k空间中齐次波动方程的格林函数。时间卷积积分通过解析求解，其余积分以空间傅里叶变换的形式表示。这使得可以使用两次快速傅里叶变换在一步中计算所有空间位置的声压。通过几个数值示例展示了该模型，包括单元素矩形和球形聚焦碗形换能器，以及多元素线性和半球形阵列。
