Yang Zaifeng, Tan Xing Haw Marvin, Bui Viet Phuong, Png Ching Eng
Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, Connexis #16-16, Singapore, 138632, Republic of Singapore.
Sci Rep. 2023 Sep 12;13(1):15052. doi: 10.1038/s41598-023-42191-1.
The recent emerging alternative to classic numerical Fast Fourier transform (FFT) computation, based on GHz ultrasonic waves generated from and detected by piezoelectric transducers for wavefront computing (WFC), is more efficient and energy-saving. In this paper, we present comprehensive studies on the modeling and simulation methods for ultrasonic WFC computation. We validate the design of the WFC system using ray-tracing, Fresnel diffraction (FD), and the full-wave finite element method (FEM). To effectively simulate the WFC system for inputs of 1-D signals and 2-D images, we verified the design parameters and focal length of an ideal plano-concave lens using the ray-tracing method. We also compared the analytical FFT solution with our Fourier transform (FT) results from 3-D and 2-D FD and novel 2-D full wave FEM simulations of a multi-level Fresnel lens with 1-D signals and 2-D images as inputs. Unlike the previously reported WFC system which catered only for 2-D images, our proposed method also can solve the 1-D FFT effectively. We validate our proposed 2-D full wave FEM simulation method by comparing our results with the theoretical FFT and Fresnel diffraction method. The FFT results from FD and FEM agree well with the digitally computed FFT, with computational complexity reduced from [Formula: see text] to O(N) for 2-D FFT, and from O(NlogN) to O(N) for 1-D FFT with a large number of signal sampling points N.
最近出现的一种替代传统数值快速傅里叶变换（FFT）计算的方法，基于由压电换能器产生并检测的用于波前计算（WFC）的千兆赫兹超声波，这种方法更高效且节能。在本文中，我们对超声波WFC计算的建模和仿真方法进行了全面研究。我们使用光线追踪、菲涅耳衍射（FD）和全波有限元方法（FEM）对WFC系统的设计进行了验证。为了有效地模拟用于一维信号和二维图像输入的WFC系统，我们使用光线追踪方法验证了理想平凹透镜的设计参数和焦距。我们还将解析FFT解与我们的傅里叶变换（FT）结果进行了比较，这些结果来自以一维信号和二维图像为输入的三维和二维FD以及新型二维全波FEM对多级菲涅耳透镜的模拟。与之前报道的仅适用于二维图像的WFC系统不同，我们提出的方法还可以有效地解决一维FFT问题。我们通过将结果与理论FFT和菲涅耳衍射方法进行比较，验证了我们提出的二维全波FEM模拟方法。FD和FEM的FFT结果与数字计算的FFT结果吻合良好，对于二维FFT，计算复杂度从[公式：见原文]降低到O(N)，对于具有大量信号采样点N的一维FFT，计算复杂度从O(NlogN)降低到O(N)。
