Focusing Theory - 2023.2 English

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2023.2 English


Before starting with the formulation of focusing and virtual sources for SA and PW it is essential to introduce the coordinate system for our ultrasound probe, detailed in the following picture:

It is essential to underline the fact that the direction of propagation of the waves is on the Z axis, which will lead later to a significant optimization in terms of computational resources. Moreover, this system implies that the transducers are represented symmetrically, and they will be split in two different and equivalent groups, on with X coordinate negative and one with X coordinate positive depending on the values of Kerf and dimension of the single element.

Design of virtual transmit sources

Whether we use SA or PW, which we have seen could be re-written one as the other, there is the necessity to use virtual transmit sources. What are them and why are so useful? Virtual transmit sources are a construct which overcome the problem of increasing the SNR parameter in SA while increasing the investigation depth. The calculation of the transmitted field is ambiguous if multiple transducers are involved. The emit focal point is then considered as a source of spherical emission itself, and then the computation of the propagation in transmission became uniquely computable by the formula:

rf is the position of the virtual source, tf is the time taken, including delays, to propagate to the virtual source. The reception is time has a simpler formula (assuming c 1540 m/s, speed of sound while propagating in the tissues):

Where ri is the position of the emitter (on the probe) and rp is the position of the point which the focusing has been calculated into.

Knowing the formulation of virtual sources, the SA and PW formulation follows easily.