Plane Wave and Synthetic Aperture formulation - 2023.2 English

Vitis Libraries

Release Date
2023.2 English


To ease the comprehension of the Advanced Ultrasound Imaging Toolbox, it is essential for the reader to understand the theory behind the libraries and the possible range of applications.

This Beamformer works with 3D data input axial, lateral and elevation, captured from ultrasound transducers to produce a visible image of the region impinged by ultrasonic waves. There are two modalites specific of this library: Synthetic Aperture Imaging (SA from now on), and Plane Wave Imaging (PW form now on). The Beamformer however can be used with other imaging technique such as flow imaging.

In ultrasound medical imaging, beamforming captures the spatial distribution of the acustic waves pressure field amplitude in the volume of interest elaborating the signals generated by an ultrasonic transducer, reflected by an anatomic part as scattered waves, and received by the same ultrasonic transducer, for the purpose of generating images.

There are several parameters that affects the final image quality:

Spatial resolution: the smallest spatial distance for which two scatterers can be distinguished in the final image. Spatial resolution can be either axial (along the direction of propagation of the ultrasound wave), lateral, or elevation resolution (along the plane to which the direction of propagation is perpendicular). This feature is normally expressed in mm.

Temporal resolution: the time interval between two consecutive images. This feature is normally expressed in Hz.

Contrast: the capability to visually delineate different objects, e.g., different tissue types, in the generated images. This feature is generally expressed in dB, and it is a relative measure between image intensities.

Penetration depth: the larger depths for which a sufficiently high signal-to-noise ratio (SNR) level can be maintained. This feature is normally expressed in cm.

Array aperture: the physical sizes of the surface representing the combined distribution of active and passive ultrasound sensors: in other words, the array footprint. The array aperture is defined by the number of ultrasound sensors (elements), their sizes, and their distribution. This feature is generally expressed in cm2.

Field of view (FOV): the sizes of the area represented by the obtained images. This feature is generally expressed in cm2 or cm3

All such features are correlated and interdependent.

## Synthetic Aperture Formulation

Synthetic aperture techniques were originally conceived for radar systems. There are many similarities between Radar and ultrasound systems, but there are also very significant differences.

SA Radar systems usually employ one transmitter and receiver, and the aperture in synthesized by moving the antenna over the region of interest in an airplane or satellite.

In medical ultrasound, the array has a fixed number of elements and is usually stationary.

For Radar, the object is most often in the far-field of the array.

For a medical ultrasound system the object is always in the near-field of the array, which complicates the reconstruction.

Since the medical array is stationary, it is possible to repeat measurements rapidly, which is not the case for a SA Radar systems. The position between the different elements is also fixed in ultrasound, whereas the deviations from a straight flight path for airplane often have to be compensated for in Radar systems.

A vital difference is also that the dynamic range in a Radar image is significantly less than the 40–80 dB dynamic range in ultrasound images.

SA technique consists in exciting a one (or more) transducers to emit an unfocused spherical wave covering the full image region. The received signals for all or part of the elements in the aperture are sampled for each transmission. This data is used for making a Low Resolution Image (LRI from now on), from the received radio-frequency data (RF-data) are then obtained by the value registered by all the transducers available in the ultrasound probe. LRI is a noisy image and to improve the image quality SA performs multiple emissions, to obtain a corresponding set of LRIs. For example if the SA performs 7 emissions then the Beamformer must create 7 LRIs. The LRIs received must be compounded in a single image, creating a High Resolution Image (HRI from now on). Higher the number of emissions higher the quality of the image, until an SNR limit is reached beyond that there is no percived quality improvement. The HRI image is then displayed on a healthcare monitor. Every HRI created is counted as a frame in this imaging technique. To be clearer, if we need 30 FPS, then we must create 30 HRIs every second. To bind this concept with the LRIs, if we perform 7 emissions per HRI, with a fixed frame rate of 30 FPS, we will need to perform 7 emissions per frame and so we will need to create 7*30=210 LRIs. The LRIs are going then to be compounded by groups of 7, every 1/30 seconds, to achieve the fixed frame rate of 30fps. Following an image which summarise what explained until now.