Element size effect on phase aberration correction

The distortion effect of tissue on ultrasonic beamforming is simplified as a 2-D time-shifting screen placed against the array surface. The ideal correction of such distortion requires a 2-D array with infinitesimally small elements. However, elements of finite sizes must be utilized in practice, causing the so-called residual phase error (RPE). As element size is reduced, the magnitude of the RPE is reduced, and its spatial feature becomes finer. Analyses have been performed to reveal that the magnitude of the RPE is proportional to the imaging frequency, the rms magnitude of the original time-delay error, and the diagonal size of individual rectangular elements, and is inversely proportional to the correlation length of the original time-delay error. Simulations have been performed to study the peak sidelobe level caused by the RPE as the element sizes are reduced. The sidelobe is defined here as the difference between the ideal beam (with no phase error) and the beam obtained in the presence of the RPE. For a multi-row array in which a conventional 1-D array is divided into N rows of independent elements in the elevation direction, the peak sidelobe level is found to vary approximately as N/sup -1/ instead of the anticipated N/sup -2/. The reduction is caused by the reduced magnitude of the RPE, and the finer spatial feature of the RPE, although apparent in the reduced spatial correlation length, does not result in additional reduction of the sidelobe level. The reason for this has been analyzed. The results of this study provide guidance for designing multi-row arrays suitable for phase aberration correction.