Pressure Intensity
• The pressure intensity at a point can be
calculated using the solution of wave
equation:
– 1D case
– Circular aperture
• The pressure distribution is proportional with
the fourier transform of the aperture.
Side Lobes
Side lobes are small beams of greatly reduced intensity that are emitted at angles to
the primary beam and they often cause image artifacts.
• the origin of these lobes are due from radial vibrations from the edges of the
transducer
Focused Transducers
High frequency beams have two advantages over low-frequency beams:
(1) axial resolution is superior; and
(2) the Fresnel zone is longer
It would seem logical to use high frequencies for all imaging. High frequencies
however, have a major drawback related to penetration. Tissue absorption increases
with increasing frequency, so a relatively low frequency beam is required to
penetrate thick parts.
It would then seem logical to use low frequency transducers and to increase the size
of the transducer to keep the beam coherent for sufficient depth to reach the point of
interest (longer Fresnel zone). Although larger transducers improve coherence they
deteriorate lateral resolution. The dilemma is at least partially resolved with the use
focused transducers.
NOTE
• focused transducers reduce beam width which improves lateral resolution
• they also concentrate beam intensity thereby increasing penetration and echo
intensity thus improving image quality
• the focal zone is the region over which the beam is focused
• the focal length is the distance from the transducer to the centre of the focal zone
• the depth of focus is the distance over which the beam is in a reasonable focus
• a small diameter transducer has a shorter focal zone and spreads more rapidly in
the far zone
• most diagnostic transducers are focused, which is achieved using a either a curved
piezoelectric crystal, an acoustic lens or electronics (phased arrays)
Ultrasound Pulse Production and Reception
A transducer is a device that can convert one form of energy into another. Ultrasound
transducers are used to convert an electrical signal into ultrasonic energy that can be
transmitted into tissue, and to convert ultrasonic energy reflected back from the tissue
into an electrical signal.
The general composition of an ultrasound transducer is shown below:
• the most important component is a thin
piezoelectric (crystal) element located near the
face of the transducer
• the front and back face of the element is coated
with a thin conducting film to ensure good
contact with the two electrodes
• the outside electrode is grounded to protect the
patient from electrical shock
• an insulated cover is used to make the device
watertight
• an acoustic insulator made of cork or rubber is
used to prevent the passing of sound into the
housing (i.e.: reduces transducer vibrations)
• the inside electrode is against a thick backing block that absorbs sound waves
transmitted back into the transducer
Transducers, (apertures)
• Bulk Acoustic wave transducers
• Surface acoustic wave transducers
quartz crystal
microbalance
• In the bulk of an ideally infinite unbounded solid, two
types of bulk acoustic waves (BAW) can propagate.
They are the longitudinal waves, also called
compressional/extensional waves, and the transverse
waves, also called shear waves, which respectively
identify vibrations where particle motion is parallel and
perpendicular to the direction of wave propagation.
• When a single plane boundary interface is present
forming a semi- infinite solid, surface acoustic waves
(SAW) can propagate along the boundary.
• Probably the most common type of SAWs are the Rayleigh
waves, which are actually two-dimensional waves given by
the combina- tion of longitudinal and transverse waves and
are confined at the surface down to a penetration depth of
the order of the wavelength.
• Shear horizontal (SH) particle displacement has only a very
low pene- tration depth into a liquid, hence a device with
pure or pre- dominant SH modes can operate in liquids
without significant radiation losses in the device.
• Love waves (LW), where the acoustic wave is guided in a
foreign layer
• Plate waves, also called Lamb waves, require two parallel
boundary planes.
• flexural plate wave (FPW)
• Bulk Wave:
– Conventional piezo
– CMUT
– Thin film
• SAW
– Microfabrication
– CMUT
Frequency- Material width Relation
• df/dl=?
Why should the transducer thickness be equal to 1/2 of the desired wavelength?
Back surface
A
Backing
Block

Front surface
C
B
 
D

Patient
Thickness (t)
When the piezoelectric element is driven by a alternating voltage the crystal
vibrates (i.e.: the width of the crystal moves back and forth). The front face of the
crystal emits sound both in the forward and backward directions as does the back
surface.
• wave front (A) will get absorbed by the transducer’s backing material
• wave front (D) will enter into the patient
• the wave front (C) is reflected at the back face of the disk, and by the time it joins
wave front (D), it has traveled an extra distance 2t. If this distance equals a
wavelength the wave fronts (D) and (C) reinforce for they are in phase, and
constructive interference or resonance occurs.
• if wave fronts (D) and (C) are not in phase, then there will be some destructive
interference
• same reasoning applies to wave front (B)
Creating a sound wave from an electrical pulse
When a positive voltage (A) is applied across the surface of the crystal, it creates an
electric field across the crystal surface which cause the molecules (dipoles) in the crystal
to realign and thus changing the shape (width) of the crystal.
A
B
C
Voltage Pulse
Positive
Time
Negative
When the voltage polarity is changed from positive to negative, there is a point in time
when the electric field across the crystal is zero (at voltage equal to zero) and the crystal
relaxes (B). When the voltage polarity is reversed (i.e.: negative) the crystal realigns
once again and changes its width once again (C).
The net effect the alternating voltage pulse has on the crystal is to make it oscillate back
and forth about its width. This change in shape of the crystal increases and decreases
the pressure in front of the transducer, thus producing ultrasound waves.
Ultrasound wave direction
Rarefaction region created when crystal
surface is contracting (less pressure on surface)
wavefront diagram
Ultrasound wave direction
Compression region created when crystal
surface is expanding (more pressure on surface)
Creating sound wave using CMUT
CMUT vs Piezoelectric
• The frequency of operation depends on the cell
size (cavity of membrane), and on the stiffness of
the material used as a membrane.
• As it is built on silicon, the integration of
electronics would be easier for the CMUTs
compared to other transducer technologies.
• Large Bandwith/High frequency
• Smaller dimensions
Resonant Frequency
The frequency at which the transducer is the most efficient as a transmitter of sound
is also the frequency at which it is most sensitive as a receiver of sound. This
frequency is called the natural or resonant frequency of the transducer.
• the thickness and the material (i.e.: speed of sound in the crystal) of the piezoelectric
crystal determines the resonant frequency of the transducer
• transducers crystals are normally manufactured so that their thickness (t) is equal to
one-half of the wavelength () of the ultrasound produced by the transducer
Bandwidth
The range of frequencies in the
emitted ultrasound wave is called the
bandwidth and is defined to be the full
width of the frequency distribution at
half maximum (FWHM).
bandwidth  SPL 
Spatial Pulse Length (SPL)
Resonant Frequency
Continuous voltage waveform
Pulsed voltage waveform
Frequency distribution of emitted ultrasound wave
Continuous waveform
can be represented by
a single sine wave (one
frequency), thus frequency
distribution is very
narrow
Pulsed waveform
can be represented by
the sum of many sine
waves each of different
frequency, thus frequency
distribution is wide
Q-factor
The Q-factor of a transducer system describes the shape of the frequency distribution
(response curve) and is defined as
Q-factor
=
f0
(f2 - f1)
Bandwidth = (f2 - f1)
where f0 is the resonance frequency, f1 is the frequency below resonance at which
intensity is reduced by half and f2 is the frequency above resonance at which
intensity is reduced by half
• high Q transducers produce relatively
pure frequency spectrums and low Q
transducers produce a wider range of
frequencies
• short pulses correspond to reduce Q
values and vice versa
bandwidth  Q-factor 
Pulse Ultrasound Mode
Because a transducer can be a transmitter and a receiver of ultrasonic energy, it
clearly stands to reason that a continuous voltage waveform can not be used. If such
a waveform was used, the transducer would always function as a transmitter. Since
the internally generated sound waves are stronger than the returning echoes, the
returning signal is lost in the noise of the system. To over come this problem, most
transducers are used in a pulse mode where the voltage waveform consists of many
pulses each separated by a fixed distance and time. The transducer functions as a
transmitter during pulse excitation and as a receiver during the time interval between
pulses.
Voltage waveform
Ultrasound pulses produced by transducer
NOTE
• most transducers are designed to have short pulses (improved resolution) with low
Q values (broad bandwidth - desirable in order to receive echoes of many different
frequencies)
Pulse Repetition Frequency (PRF)
• PRF is the number of pulses occurring in 1 second
Pulse Repetition Period (PRP)
• PRP is the time from the beginning of one pulse to the beginning of the next pulse
Spatial Pulse Length (SPL)
SPL is the length of space over which a single pulse occurs, and is defined as
SPL = n • 
where n is the number of cycles in the pulse and  is the wavelength.
NOTE
An important parameter when considering axial resolution