A Forward Model for Estimating Phase Aberration in Ultrasound Imaging

In this paper, we first proposed that the phase aberration profile estimated by cross-correlation methods is the sum of the true phase aberration profile and the geometric delay change due to the shifting of the focus point caused by the true phase aberration. Then, we show that the shifting of the focus point can be estimated from the true phase aberration. Lastly, we show that the phase aberration profile estimated by cross-correlation methods from the RF data can be predicted from the true phase aberration. It was shown that both the constant term and linear term of the true phase aberration will be canceled in the estimated phase aberration. However, a quadratic term and a cubic term in the estimated phase aberration will result from the constant term and linear term of the true phase aberration, respectively. Consequently, the quadratic term and a cubic term in the estimated phase aberration can be used to estimate the constant term and linear term of the true phase aberration. The results can be applied to simultaneously estimate the average speed and initial delay of ultrasound probes in both Field II simulation and experimental study. No calibration of probe and phantom is needed to simultaneously estimate the average speed and the initial delay of ultrasound probes.