Construction of high frame rate images with Fourier transform

Traditionally, images are constructed with a delay‐and‐sum method that adjusts the phases of received signals (echoes) scattered from the same point in space so that they are summed in phase. Recently, the relationship between the delay‐and‐sum method and the Fourier transform is investigated [Jian‐yu Lu, Anjun Liu, and Hu Peng, ‘‘High frame rate and delay‐and‐sum imaging methods,’’ IEEE Trans. Ultrason. Ferroelectr. Freq. Control (submitted)]. In this study, a generic Fourier transform method is developed. Two‐dimensional (2‐D) or three‐dimensional (3‐D) high frame rate images can be constructed using the Fourier transform with a single transmission of an ultrasound pulse from an array as long as the transmission field of the array is known. To verify our theory, computer simulations have been performed with a linear array, a 2‐D array, a convex curved array, and a spherical 2‐D array. The simulation results are consistent with our theory. [Work supported in part by Grant 5RO1 HL60301 from NIH.]