Piezoelectric Effect

Sound waves
striking a PZ
material produce
an electrical signal

Can be used to
detect sound (and
echoes)!
Pierre Curie 1880.
Piezoelectric Effect

Sound waves
striking a PZ
material produce
an electrical signal

Can be used to
detect sound (and
echoes)!
Reverse Piezoelectric Effect

Applying an
electrical signal
causes the PZ
element to vibrate

Produces a sound
wave
Transducer
Device that converts signals, or
energy, from one form to another
 Many types of transducers exist

– Pressure transducers
– Air flow transducers, etc.

Ultrasound transducers convert
electrical signals to sound waves, and
vice versa.
Ultrasound Transducer
Materials

Quartz (naturally piezoelectric)
– First used as a stable resonator in time
measurement devices
– Used in some laboratory ultrasound
applications

Most current applications use
piezoelectric ceramics (ie, lead
zirconate titanate; barium titanate)
– Lower “Q” (good for short pulses)
– Good sensitivity
– Many shapes are possible
Miniature quartz
tuning fork; 32,768
Hz.
Polarizing a Piezoelectric
Element

Most ultrasound transducer materials
are not ‘naturally’ piezoelectric
– Lead zirconate titanate
– Microscopic crystals, randomly oriented

Must be polarized
– Heat to ~350oC (Curie Temperature)
– Apply strong voltage across crystal
– Cool while voltage is still applied
Polarization
Single Element Transducers


Uses
– Simple A-mode
machines
– Mechanical scanning
transducers
The design serves as a
useful example of general
construction methods
Single element
transducer construction
Matching layers, lens
Ultrasound
Transducers
Piezoelectric (PZT) ceramic
elements
Backing layer
½ wavelength resonance
d
Resonance frequency corresponds to
the thickness = ½ wavelength
 Speed of sound in Piezoelectric
material ~ 4,620 m/s
 What thickness is required for a 3 MHz
frequency transducer?

c
4,620m / s
 
 0.00154m  1.54m m
f 3,000,000/ s
 / 2  0.77m m
½ wavelength resonance
d
Resonance frequency corresponds to
the thickness = ½ wavelength
 Speed of sound in Piezoelectric
material ~ 4,620 m/s
 What thickness is required for a 3 MHz
frequency transducer?

c
4,620m / s
 
 0.00154m  1.54m m
f 3,000,000/ s
 / 2  0.77m m
½ wavelength resonance
d
Resonance frequency corresponds to
the thickness = ½ wavelength
 Speed of sound in Piezoelectric
material ~ 4,620 m/s
 What thickness is required for a 5 MHz
frequency transducer?

c
4,620m / s
 
 0.000924m  0.924m m
f 5,000,000/ s
 / 2  0.462m m
Resonance Frequency
PZT (c=4620m/s) Thickness vs
5
Frequency
Element Thickness (mm)
4.5
4
3.5
3
2.5
2
Series1
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14
Frequency (MHz)
Backing (Damping) Layer

Need short duration pulses for decent
axial resolution (we will discuss this later)
 Backing
layer helps to reduce vibrations
of the element following excitation
– Like placing your hand on a bell to stop the
ringing!
Pulse Bandwidth
• A pulse of sound contains many
frequencies (analogous to white
light consisting of many colors)
• Range of frequencies quantified
by the frequency “bandwidth” of
the pulse
• Short pulses, very broad
bandwidths
• Longer pulses, narrower
bandwidths
Multi Herz
Matching Layers

Thin layer of material
– ¼ wavelength thick
– Impedance is between that of the element
(quite high) and that of tissue
Provides better sound transmission
from the transducer-patient-transducer
 Improves sensitivity

Center Freq:
- 8 MHz
Bandwidth:
- 6.5 MHz
- 82%
Broadband Transducers
Multiple matching
layers (analogous to
coatings on optical
lenses)
STI-Ultrasound.com
Pulsed Spectra vs
transducer bandwidth
2.5
5
Multi-herz
The transducer design enables operation at various frequencies.
Each pulse is associated with a range of frequencies.
Multi-frequency operation


Modern transducers can
operate over a range of
frequencies (sort of like the
speakers of a stereo sound
system)
By changing the frequency of
the signal applied to the
transducer, and by tuning the
receiver, the center frequency
can be changed
Modern, broad bandwidth
Multi-Hertz
Spatial Detail in
Ultrasound
- depends on beam width, focus (lens);
- depends on pulse duration (axially);
- depends on slice thickness.
Axial Resolution

Defined as the
minimum distance
between 2
reflectors along the
beam direction,
such that the
reflectors can be
distinguished on
the display.
Beam Direction
Axial Resolution
Beam Direction
Axial Resolution
Axial resolution depends
on the “pulse duration”
Pulse duration is the amount of time
the transducer oscillates during each
transmit pulse
 The shorter the pulse duration, the
better the axial resolution

Axial Resolution 2
Axial vs Freq
GE Logiq 700
Horizontal spacing: 2 mm, 1 mm, 0.5 mm, 0.25 mm
Vertical Spacing: 2 mm, 1 mm, 0.5 mm, 0.25 mm
4 MHz
12 MHz
27. Axial resolution is determined by:
A. pulse duration
B. beam width
C. beam diameter
D. pulse repetition period
28. Axial resolution is most affected by
changes in:
A. beam frequency and beam diameter
B. beam intensity and beam focusing
C. beam frequency and pulse damping
D. beam focusing and beam diameter
29. A decrease in pulse duration results in
________ frequency bandwidth.
A. a wider
B. a narrower
C. an equivalent
D. elimination of
Lateral Resolution and Beam
Width
Linear Array
Poor
Lateral Resolution and Beam
Width
Linear Array
Excellent
Lateral resolution depends on
the “beam width”



Lateral resolution is how closely spaced 2
reflectors can be, along a line perpendicular
to the ultrasound beam, and still be
distinguished on the display
It depends of the beam width at depth
considered
The narrower the beam, the better the
lateral resolution
Beam Physics

Huygen’s Principle
– “All points on a propagating
sound wave serve as the
source of spherical
wavelets; the total wave at
any location (and time) is
the sum of these wavelets.”
“Point sources”
Christian Huygens (1629-1695)
Dutch Physicist
Interference

2 sources:
– Final signal can be large
or small, depending on
the relative phase of the
waves.

Many sources
– Final signal can be large
or small, depending on
relative phases of all
waves.
Huygens's Principle: all points on a propagating
wavefront serve as the source of spherical secondary
wavelets, such that the total wave at any location
(and time) is the sum of these wavelets.
1 point source; spherical wave
“Point sources”
Huygens's Principle: all points on a propagating
wavefront serve as the source of spherical secondary
wavelets, such that the total wave at any location
(and time) is the sum of these wavelets.
2 point sources; wave interference
Interference creates minima and
maxima
Unfocused Transducer Beam
10 mm
Beam properties depend on width of
aperture and the wavelength (frequency);
2.5 MHz
10 mm
NFL
NFL
5.0 MHz
Unfocused Transducer Beam
a2
d2
NFL 

 4
a= transducer radius
d=2a=transducer diameter
Unfocused Transducer Beam
NFL=D_squared over 4
lambda
NFL for 2 MHz
(=0.77 mm)
Diameter NFL
1 cm
3.2 cm
2 cm
13 cm
4 cm
52 cm
Assume D = 1 cm=10mm
D 2 (10m m) 2
NFL 

4  4 x 0 .7 m m
100m m2

3.08m m
 32.4m m
 3.2cm
If the diameter doubles, NFL increases by 4.
NFL for 2 MHz
(=0.77 mm)
NFL for 4 MHz
(=0.385 mm)
Diameter NFL
Diameter NFL
1 cm
3.2 cm
1 cm
6.4 cm
2 cm
13 cm
2 cm
26 cm
4 cm
52 cm
4 cm
104 cm
If the diameter doubles, NFL increases by 4.
If the frequency doubles, NFL doubles.
Divergence in far field



(The ‘sin’ is a function of the angle)
Larger diameter diverges less
Higher frequency (smaller wavelength)
diverges less
What is the divergence angle for a 2 cm diameter, 3
MHz transducer?
1.2
sin  
d
c
1540m / s
1,540,000m m/ s
 

0.51m m
f 3,000,000/ s
3,000,000/ s
1.2  0.51m m
sin  
 0.036
20m m
  sin 1 0.036  1.75o
What is the divergence angle for a 2 cm diameter, 6
MHz transducer?
1.2
sin  
d
c
1540m / s
1,540,000m m/ s
 

0.256m m
f 6,000,000/ s
6,000,000/ s
1.2  0.256m m
sin  
 0.01536
20m m
  sin 1 0.01536 0.88o
Dependence on frequency
Dependence on diameter
Focusing, Methods


Focusing reduces the beam width in the
focal zone
Methods
– Lens
– Curved element
– Electronic
Focal Definitions
2.5 MHz
20 mm
20 mm
In Most Applications, Beams Are Focused
- curved element
- lens
- electronic (arrays)
Improves lateral resolution near the focal distance
Higher frequencies produce narrower beams
5.0 MHz
Short pulse (50% bw)
2.5 MHz
5.0 MHz
CW
5.0 MHz
20 mm
10 mm
- Previous diagrams exhibit sidelobes
- Must be eliminated for good image quality
- Pulsing reduces (or even eliminates) side lobes
2.5 MHz
d
F
1.2 F
Beam width 
d
24. In order to focus a sound beam relatively
far away from the transducer, it is
advantageous to ______ of the element.
A. increase the thickness
B. increase the diameter
C. increase the temperature
D. decrease the diameter
25. Lateral resolution is determined by:
A. beam length
B. pulse duration
C. pulse length
D. beam width
Array Transducer



“Scanhead” containing
many small PZT
elements
Element, along with a
transmit-receive circuit
in the machine is a
channel.
128 channels are
common.
Beam Forming (Transmit)
Group also permits electronic beam steering
and electronic focusing.
Curvilinear
Phased Array
Linear-Phased
(“Virtual Convex”)

Linear array
– Rectangular FOV,
defined by transducer
footprint

VC adds beam
steering to expand
imaged region at
edges
Annular
Multiple Tx Focus
Multiple Tx Focus
4 Tx focal zones
12 Hz frame rate
Focus During Reception
Dynamic Receive
Focusing
Focusing delays change in real time.
(Not adjusted by the sonographer.)
Dynamic Aperture
Side Lobes, Grating Lobes
- Both are forms of off axis sound transmission
- Both lead to undesirable effects

Side Lobes: part of the beam pattern
from any transducer (single element,
array)
– Reduce using short duration, broad band
pulses
– Reduce using apodization

Grating Lobes: result from having the
transducer surface cut into small
elements (think of grating cheese)
– Reduce using very closely spaced
elements
Spatial Resolution
Typical values
 Axial: 0.1 to 1
mm
 Lateral: 0.2mm to
10mm
Spatial Pulse Length
Transducer “Q”
Q stands for “quality factor”
 A high Q system is one that rings
at a pure tone
 A low Q system is well damped
 Low Q is needed for short
duration pulses

Miniature quartz
tuning fork; 32,768
Hz.
Slice Thickness
(Conventional)
Spherical Lesion Phantom
2 and 4 mm diameter
spherical targets;
 Low scatter level;
 Target centers are co
planar.
Conventional
Transducer
Conventional Phased and linear
Electronic focusing applies to
lateral only.
Annular
Image-plane beam width = slice thickness
Electronic focusing applies to both dimensions.
1 ½ D Probe
(matrix probe)
100 – 200 elements
in lateral direction
5 – 7 rows
Matrix
Transducer
1 ½ D (Matrix) Transducer
Matrix
Conventional
Use of “Matrix” or “1 ½ D” Arrays

Advantages:
– Better control of slice thickness

Disadvantages
– Size (older models)
– Cost
– Complexity
2-D Array
One of the transducer types
used in 3-D imaging
Volumetrics - Image
Formats
“Traditional”
“C-scans”
(constant depth)
Use in 2-D arrays
(Phillips)
2400 element 2-D array
Possible Scan Planes
Use in 2-D arrays
(Phillips)
2400 element 2-D array
Applications of 3-D

Visualization of coronal planes

Volume calculations

OB Imaging
– facial and other anatomical anomalies
– detailed information on orientation

Improved visualization of vasculature
with 3-D color flow
Important features of
arrays

Enable electronic scanning
– Time delays between elements (phased
arrays)
– Electronic switching groups of elements
(linear and curvilinear)

Enable electronic focusing
Type of
transducer
Linear array
Method used for Method used
beam focusing for scanning
Electronic
Electronic
Curvilinear array Electronic
Electronic
Phased array
Electronic
Electronic
Annular array
Electronic
Mechanical
Single element
Mechanical lens Mechanical
Homework
Calculate the NFL for a 3 cm diameter
transducer operating at 5 MHz.
Assume c=1540 m/s.
 Calculate the resonance frequency of
a piezoelectric ceramic material whose
thickness is 0.25mm.
