Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada M5S 3G9.
Ultrasonics. 2013 Mar;53(3):745-53. doi: 10.1016/j.ultras.2012.11.001. Epub 2012 Nov 12.
A plane piston transducer can be focused by a continuous variation of the excitation signal phase (or time delay) over the transducer surface. Prior analyses of this scheme used the Fresnel approximation, thereby limiting the validity. Using the angular spectrum method, an accurate radiation model of such a transducer has been developed that includes amplitude and phase apodization. The derivation includes the effects of diffraction and evanescent waves without using the Fresnel approximation. Moreover, this model develops insights into radiated field characteristics, including: (a) the spatial frequency bandwidth is constant over axial depth, suggesting that spatial resolution can be improved away from the focus; (b) the phase of the angular spectrum determines the spatial resolution for a given transducer configuration-a constant phase is optimal on any observation plane; (c) focusing can significantly increase the spatial frequency bandwidth; (d) the velocity potential on a plane parallel to the transducer is the Hankel convolution of the transducer surface velocity with the Green's function; and (e) evanescent waves decay both with increasing spatial frequency and axial depth. The analytical model and associated insights enhance understanding of the radiated field characteristics, which can be of value in the development of signal processing techniques for image enhancement.
平面活塞换能器可以通过在换能器表面上连续改变激励信号的相位（或时间延迟）来聚焦。该方案的先前分析使用了菲涅耳近似，从而限制了其有效性。本文使用角谱方法，开发了一种精确的辐射模型，该模型包括幅度和相位的变迹。该推导包括衍射和消逝波的影响，而不使用菲涅耳近似。此外，该模型深入了解了辐射场特性，包括：（a）在轴向深度上，空间频率带宽是恒定的，这表明可以在离焦点更远的地方提高空间分辨率；（b）角谱的相位决定了给定换能器配置的空间分辨率-在任何观察平面上，恒定相位是最佳的；（c）聚焦可以显著增加空间频率带宽；（d）与换能器平行的平面上的速度势是换能器表面速度与格林函数的汉克尔卷积；（e）消逝波随着空间频率和轴向深度的增加而衰减。分析模型和相关见解增强了对辐射场特性的理解，这对于开发用于图像增强的信号处理技术具有重要价值。
