Fourier Diffraction Theorem for 3d Ultrasound Imaging with a Row-Column Array

Row-column arrays (RCAs) have been shown to produce high-resolution, three-dimensional ultrasound volumes while reducing the number of electronic connections. Typically, standard reconstruction methods in the time domain such as delay-and-sum (DAS) beamforming have been applied. Here, we derive the Fourier diffraction theorem for reconstructing 3D volumes from backscattered data obtained using an RCA with broadband plane wave excitation under a range of angles. Based on this theory, we propose a novel spatial frequency domain method that offers additional theoretical insight for the optimization of RCA beamforming. In comparison to time domain methods, it also promises higher computational efficiency by using the fast Fourier transform and it enables alternative signal processing and filtering schemes in the frequency domain. We validate our reconstruction algorithm with simulation data. The results demonstrate improved image quality and resolution compared to DAS beamforming.