Learning the differences from Plane Wave and Synthetic Aperture - 2023.2 English

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Release Date
2023.2 English

In the previous chapter and draws we have briefly introduced the two imaging techniques, but, is it possible to draft a similarity between the two in order to understand that they are actually two faces of the same coin? Indeed we can, and the aim of this chapter is to detail Synthetic Aperture and “re-writes” Plane Wave as it. It is now going to be redrawn the SA step by step:

Let us bind the concept of the SA formulation. Some transducers (or just one, depending on design choices) are excited. The excitement produces a spherical wave, which echoes are collected. Then, a second group of transducers is excited, the spherical wave emitted and then the echoes collected. This process is done by the number of times we want to generate single LRIs. The emissions drawn in the previous scheme are then collected and compounded together. Due to the nature of this process, the delay of emission can be computed and every emission can be focused in both transmission and reception (we will detail later the usage of the virtual sources). Pay attention that the dynamic focusing in the reception is obtained by combining all the LRIs because the origin of the wave is know as well as the transducer(s) which generates it, thus the path Rx-Tx can be calculated. For this reason, due the sequential emission technique of SA, the insonification area created is focussed on the target:

Every line represents the investigation of subgroup of transducer(s), “rectified” in the process of reception thanks to the sequential mode of emissions.

On contrary, PW excites all the elements, as happens in figure 2. The insonification area cannot consequently be focussed, and so must it be computed during the process of Beamforming. To eliminate the differences we need then to perform three operations:

  1. Compute a delay for the reception for the transducers per line
  2. Focus the plane wave emitted on the direction of propagation (in the next pages we are going to introduce the cartesian system of our probe)
  3. Modifying the formulation of the virtual sources to fit a different type of emission

Performing this three operations “rectifies” the insonification by aligning a plane wave emitted (which should covers the overall area of transducers) and obtains the same result as the SA.