Precise time-of-flight calculation for 3-D synthetic aperture focusing

Conventional linear arrays can be used for 3-D ultrasound imaging by moving the array in the elevation direction and stacking the planes in a volume. The point-spread function is larger in the elevation plane, because the aperture is smaller and has a fixed elevation focus. Resolution improvements in elevation can be achieved by applying synthetic aperture focusing to the beamformed-in-plane RF data. The proposed method uses a virtual source placed at the elevation focus for postbeamforming. This has previously been done in 2 steps, in-plane focusing followed by synthetic aperture postfocusing in elevation, due to lack of a simple expression for the exact time of flight. This paper presents a new single step method for calculating the time of flight for a 3-D case using a linear array. The new method is more flexible and is able to beamform a fewer number of points much more efficiently. The method is evaluated using both simulated data and phantom measurements using the RASMUS experimental scanner. Computational cost of the method is higher than the 2-step method for a full volume beamforming, but it allows for a reduction of an order-of-magnitude if 3 planes are used for real-time visualization. In addition, the need for a temporary storage of beamformed data is removed.