<title>Performance of velocity vector estimation using an improved dynamic beamforming setup</title>

Estimation of velocity vectors using transverse spatial modulation has previously been presented. Initially, the velocity estimation was improved using an approximated dynamic beamformer setup instead of a static combined with a new velocity estimation scheme. A new beamformer setup for dynamic control of the acoustic field, based on the Pulsed Plane Wave Decomposition (PPWD), is presented. The PPWD gives an unambiguous relation between a given acoustic field and the time functions needed on an array transducer for transmission. Applying this method for the receive beamformation results in a setup of the beamformer with different filters for each channel for each estimation depth. The method of the PPWD is illustrated by analytical expressions of the decomposed acoustic field and these results are used for simulation. Results of velocity estimates using the new setup are given on the basis of simulated and experimental data. The simulation setup is an attempt to approximate the situation present when performing a scanning of the carotid artery with a linear array. Measurement of the flow perpendicular to the emission direction is possible using the approach of transverse spatial modulation. This is most often the case in a scanning of the carotid artery, where the situation is handled by an angled Doppler setup in the present ultrasound scanners. The modulation period of 2 mm is controlled for a range of 20-40 mm which covers the typical range of the carotid artery. A 6 MHz array on a 128-channel system is simulated. The flow setup in the simulation is based on a vessel with a parabolic flow profile for a 60 and 90-degree flow angle. The experimental results are based on the backscattered signal from a sponge mounted in a stepping device. The bias and std. Dev. Of the velocity estimate are calculated for four different flow angles (50,60,75 and 90 degrees). The velocity vector is calculated using the improved 2D estimation approach at a range of depths.