Ultrasonic 3-D Imaging Using Fourier Domain Reconstruction

为了实现高分辨率和高质量的成像，研究了超声成像方法。该方法将成像系统视为逆散射问题，得到了近似精确解，并通过适当的显示装置将其可视化。一般来说，这种方法需要计算多次数值积分。因此，很难在有效的短时间内获得图像。然而，简单地假设Born近似，就可以证明该解可以通过傅里叶变换及其逆来计算。也就是说，利用快速傅立叶变换(FFT)可以非常快速地计算出该解。通过数值模拟和在水箱中的简单实验，可以证明该理论的可行性。因此，1985年在旧金山召开的超声研讨会和在东京举行的第四届超声电子学研讨会上公布了这一结果。之后，改进了实验装置，并在CRT显示器上成功地显示了铝块上的孔。这些结果在1986年的国际声学、语音和信号处理会议上以及在东京的超声研讨会上发表。作为第二个结果，提出了剪枝FFT算法和扫描系统的测量方法。前者提高了FFT的效率。扫描系统的轻微垂直漂移变得明显。必须开发出测量方法。这两个结果同时发表在1986年IEEE会刊ASSP第8期上。需要研究的问题包括超声波的模式转换和金属与外部介质界面的泄漏表面波。但它们是留给未来的。

The ultrasonic imaging method is investigated to accomplish high resolution and to realize good images. The method regards the imaging system as the inverse scattering problem and obtains the almost exact solution which is visualized by appropriate displaying device. Generally speaking, such a method needs to calculate multiple numerical integral. It is difficult, therefore, to obtain the image in a effectively short time. However, simply assuming Born's approximation, it can be proved that the solution can be calculated by Fourier transform and its inverse. That is, using fast Fourier transform (FFT) the solution can be very speedily calculated.The feasibility of the theory could be shown by a numerical simulation and a simple experiment in a water tank. So, the results were presented at Ultrasonic Symposium held in San Francisco in 1985 and 4th Symposium on Ultrasonic Electronics in Tokyo.After that the experimental setup was improved and holes drilled in an aluminum block were successfully visualized on the CRT display. The results were expressed at International Conference of Acoustics, Speech, and Signal Processing and at Ultrasonic workshop in Tokyo in 1986.As the secondly results the algorithm of pruned FFT and the measuring method of the scanning system were developed. The former increased efficiency of FFT. Slight vertical drift of the scanning system became significant. The measuring method had to be developed. These two results were published simultaneously in IEEE Transactions ASSP No.8 in 1986.The problems including mode-conversion of the ultrasonic waves and the leaky surface waves at the interface between metal and the outer medium has to be investigated. But they are left for the future.