Chapter 9 : Ultrasound fields Flashcards
Near field
The near field region begins at the transducer surface and extends outwards in the shape of a cylinder approximately the same diameter as the source.
Far field
The far field region is characterised by the smooth decay of the pressure amplitude in both the axial and radial directions. In this region, the path length difference between the plane waves and edge waves is small and the waves are almost in phase, particularly close to the beam axis. The field diverges gradually, and the pressure amplitude falls off smoothly due to geometrical spreading with increasing z without any rapid fluctuations.
The structure of the beam emitted by a circular piston can be explained using _______’s principle
Huygens
The acoustic pressure at any point in front of a transducer (on-axis) can be calculated from knowledge of the normal particle velocity on the transducer surface using the _______
Rayleigh integral
Where are the maxima and minima of this on-axis pressure signal? They will occur when the sin term is a minima or maxima, i.e., when
Using r = sqrt(a^2+z^2)
and lambda=co/f
and the equations shown in the image
write an equation for the positions that the minima and maxima and last axial maximum occur,
and what the last axial maximum would be if the transducer surface is large
At what distance does the near field end and the far field begin?
the same as the position of the last axial maximum!
What equation is this?
The far field directivity function - which is the approximate variation of the pressure amplitude as a function of the angle.
What is the angle that the pressure first falls to zero in the far field?
three ways to produce a curved wavefront?
Curved elements
Lenses
Electronically
What is the ratio of the pressure at the focus to the pressure at the surface of the transducer called and the equation of it?
The focusing gain
g=kh where h is the height of the bowl
What is the width of the focal zone given by?
The length of the focal zone (also called the depth of focus or depth of field ) is given by
What is the positive and negative sides of a highly focused transducer?
It will have good lateral resolution but poor depth of field.
what is a major advantage of using an array transducer with multiple elements?
the acoustic waves emitted from the transducer can be controlled by changing the electronic signal used to drive each individual element.
For a linear (plane wave) array transducer if the individual elements are used in groups the time delays for the ith element relative to the central element can be calculated how?
For an element pitch of d, the angle of the grating lobes will be given by ?
what is dynamic receive focusing
When the ultrasound waves are transmitted, a single value for the time delay for each element is used to focus or steer the beam to a particular location. However in recieve the entire waveform for each element is digitised and thus the signals can be summed in different ways. In dynamic receive focusing, the time delays for each element are updated dynamically so the focus depth matches the depth where the echoes originated from. The time delays where the focal distance is set dynamically to F = 0.5 * c* t.
aperture expansion
the beam width for a given aperture is proportional to the focal depth, thus when using dynamic receive focusing, the image resolution will degrade at larger depths. To counteract this, the receive aperture can be expanded as the focus depth is increased to maintain a constant beamwidth.
Multi-zone transmit
While dynamic receive focusing and aperture expansion can improve focusing on receive, the focusing on transmit is still fixed (the waves can only physically focus in one position). To improve image resolution, multiple transmit pulses can be used, each focused at a different imaging depth, and the resulting scan lines (or images) later combined. However, this also has the effect of reducing the imaging frame rate, as a larger number of transmit-receive events are needed to form the image.
co-processed transmit focusing
One way to improve the frame rate is by using different sub-sets of the transducer array to acquire scan lines at the same time. While this can improve the frame rate, it requires more advanced electronics to process multiple A-mode scan lines at the same time.
Apodisation
To reduce side lobes, the signals from the individual elements can be weighted such that the elements in the middle contribute more to the summation. This makes the summation less sensitive to waves arriving from outside the main lobe of the receive beam, at the expense of slightly increasing the main lobe width.
What is frequency filtering?
The scan lines are filtered using a band-pass filter centered around the transmit frequency or the second harmonic. This reduces the effects of noise outside the transmit frequency range, or in the latter case, obtains the harmonic signal for tissue harmonic imaging.
Envelope detection
Before display, the high frequency variations in the scan lines (which depend on both of the reflected waves and the transmitted ultrasound pulse) are removed in a demodulation process known as envelope detection. This removes the oscillations at the transmit frequency, leaving only information about the amplitude of reflections.
Log compression
The strenght of reflections from different tissue interfaces typically cover a wide dynamic range, on the order of 60dB for soft tissue imaging. This exceeds the gray scale range that can be displayed by a computer monitor which is generally only 20 dB. To improve the differentiation of weaker signals, a nonlinear amplifier is used, where the output is proportional to the log of the input signal. One way to perform the log compression is via
where senv is the A-mode scan line after envelope detection, reject sets the zero value, and dynamic range sets the maximum value displayed in dB.
Scan conversion
After the individual A-mode scan lines have been acquired, they are combined together and converted to the correct resolution for display on screen. For steered beams, this includes converting from polar coordinates to cartesian coordinates using interpolation.
Speckle Reduction
Modern commercial ultrasound machines also include a range of other image acquisition and signal processing techniques, including parallel and adaptive receive beamforming, synthetic aperture imaging, denoising, and edge detection. These are often done using proprietary algorithms (ie. they are not made public), and often don’t change the ultrasound image drastically, so they are not discussed here. However, one common processing technique that is worth briefly discussing is image compounding. This is used to reduce the effect of speckle and noise on the image by averaging several ultrasound images taken under different conditions.
Three methods of speckle reduction?
There are three main flavors:
- Temporal compounding or persistence where several subsequent image frames are averaged. Something must change between the images - perhaps a slight movement of the imaging probe or tissue - or the speckle, which is deterministic, will be the same.
- Spatial compounding where images from different scan directions are averaged.
- Frequency compounding where images at different frequencies are averaged, either by using several band-pass filters on receive or using several images with different transmit frequencies.
Frame rate
(a B-mode ultrasound image is composed of a series of A-mode scan lines taken at different positions in the tissue)
FR = PRF/N = C0/2NLmax
If an image consists of N vertical (or radial) scan lines, the rate at which an ultrasound image can be formed, called the frame rate (FR), is given by the PRF divided by N.
What is the far field beam divergence angle?
The angle at which the pressure first falls to zero in the far field.
as the frequency or the aperture size are increased what happens to the main lobe and the side lobes?
The beam becomes increasingly directional with a smaller main lobe and a larger number of side lobes. The length and width of the near field region also increases.
What is the PRF?
The rate at which scan lines can be acquired is called the pulse repetition frequency. (It is limited by the time required for the ultrasound pulse to travel to the desired maximum imaging depth Lmax and return to the transducer.)
PRF = 1/round-trip time = C0 / 2Lmax
Types of spatial resolution
Axial resolution
Lateral resolution
Axial resolution
corresponds to the ability to distinguish between two objects at di↵erent depths in the image. Reflected pulses can be distinguished provided their separation in time is greater than the full-width at half maximum (FWHM) of the pulse envelope tp. Accounting for two way propagation, this means the axial resolution is given by
• Lateral resolution ?
corresponds to the ability to distinguish between two objects at the same depth but different lateral positions within the imaging plane. it is = the beam width.
Types of Image artefacts?
Reverberation
Acoustic shadowing and enhancement
Target misregistration
Mirror image artefacts
Why are the elements of an imaging transducer array normally used in groups and not one at a time?
As the elements are very narrow in the in-plane direction, they are typically pulsed in groups to increase the size of the near field zone and allow electronic steering and focusing.
what element pitch should be used to avoid grating lobes?
d < half a wavelength
can you remember off by heart (need to remember for the exam perhaps) the equation for calculating the time delay between the central and outside elements?
Explain the main differences between a linear phased array and a sector transducer
A sector transducer is curved physically so that the elements are placed offset to eachother wilst the linear phased array does this offset by triggering them at different times so they provide a curved wave.
demodulation?
The process of removing the transmit frequency, f, from the measured signal so that the doppler frequency can be estimated.
In general, lateral resolution for focused beams is highly spatially variant, and can be improved by ____ _____ _____ .
In general, lateral resolution for focused beams is highly spatially variant, and can be improved by multi-zone focusing.
