Lu Jian-Yu, Cheng Jiqi
Ultrasound Laboratory, Department of Bioengineering, The University of Toledo, Toledo, OH 43606, USA.
Ultrason Imaging. 2005 Oct;27(4):237-55. doi: 10.1177/016173460502700403.
A method is developed for calculating fields produced with a two-dimensional (2D) array transducer. This method decomposes an arbitrary 2D aperture weighting function into a set of limited diffraction array beams. Using the analytical expressions of limited diffraction beams, arbitrary continuous wave (cw) or pulse wave (pw) fields of 2D arrays can be obtained with a simple superposition of these beams. In addition, this method can be simplified and applied to a 1D array transducer of a finite or infinite elevation height. For beams produced with axially symmetric aperture weighting functions, this method can be reduced to the Fourier-Bessel method studied previously where an annular array transducer can be used. The advantage of the method is that it is accurate and computationally efficient, especially in regions that are not far from the surface of the transducer (near field), where it is important for medical imaging. Both computer simulations and a synthetic array experiment are carried out to verify the method. Results (Bessel beam, focused Gaussian beam, X wave and asymmetric array beams) show that the method is accurate as compared to that using the Rayleigh-Sommerfeld diffraction formula and agrees well with the experiment.
开发了一种用于计算二维（2D）阵列换能器产生的场的方法。该方法将任意二维孔径加权函数分解为一组有限衍射阵列波束。利用有限衍射波束的解析表达式，通过这些波束的简单叠加即可获得二维阵列的任意连续波（cw）或脉冲波（pw）场。此外，该方法可以简化并应用于有限或无限仰角高度的一维阵列换能器。对于由轴对称孔径加权函数产生的波束，该方法可以简化为先前研究的傅里叶 - 贝塞尔方法，此时可使用环形阵列换能器。该方法的优点是准确且计算效率高，特别是在离换能器表面不远的区域（近场），这对医学成像很重要。进行了计算机模拟和合成阵列实验以验证该方法。结果（贝塞尔波束、聚焦高斯波束、X波和非对称阵列波束）表明，与使用瑞利 - 索末菲衍射公式的方法相比，该方法是准确的，并且与实验结果吻合良好。
