Estimation of velocity vector angles using the directional cross-correlation method

A method for determining both velocity magnitude and angle in any direction is suggested. The method uses focusing along the velocity direction and cross-correlation for finding the correct velocity magnitude. The angle is found from beamforming directional signals in a number of directions and then select the angle with the highest normalized correlation between directional signals. The approach is investigated using Field II simulations and data from the experimental ultrasound scanner RASMUS and a circulating flow rig with a parabolic flow having a peak velocity of 0.3 m/s. A 7 MHz linear array transducer is used with a normal transmission of a focused ultrasound field. In the simulations the relative standard deviation of the velocity magnitude is between 0.7% and 7.7% for flow angles between 45 deg and 90 deg. The study showed that angle estimation by directional beamforming can be estimated with a high precision. The angle estimation performance is highly dependent on the choice of the time ktprf Tprf (correlation-time) between signals to correlate. One performance example is given with a fixed value of ktprf for all flow angles. The angle estimation on measured data for flow at 60 to 90 deg, yields a probability of valid estimates between 68% and 98%. The optimal value of ktprf for each flow angle is found from a parameter study and with these values the performance on simulated data yields angle estimates with no outlier estimates and with standard deviations below 2 deg.