Efficient computation of field of 2‐D array with limited diffraction array beams Free

Two‐dimensional (2‐D) arrays are useful for improving quality of three‐dimensional (3‐D) medical imaging in ultrasound. Beams produced with a 2‐D array are usually simulated with the Rayleigh–Sommerfeld diffraction formula (RSDF). In general, the RSDF requires a 2‐D integration for each field point in space and thus is very time consuming. Fresnel approximation may reduce the 2‐D integration to 1‐D but will not yield satisfactory results near the transducer surface or for field at a large angle from the beam axis. In this work, limited diffraction array beams are used to synthesize beams produced with a 2‐D array [J.‐Y. Lu, Int. J. Imaging Syst. Technol. 8, 126–136 (1997)]. In this method, the 2‐D integration is replaced with a 2‐D summation leading to a much faster computation. The method is accurate even if the field to be evaluated is very close to the surface of a transducer. Results of Bessel beams, X waves, and focused Gaussian beams will be shown and compared with those obtained with the RSDF and the experiments. [This work was supported in part by Grant No. HL60301 from the National Institutes of Health of the U.S.A.]