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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5814_Библиотеки_им_академика_М_И_Перельмана
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1.2
Normalized Pulse Echo Signal
Normalized Pulse Echo Amplitude
(b)
1
0.8
0.6
0.4
0.2
0
050 100 150
1.4
1.2
1
Distance
(a)
77Chapter three: Ultrasonic transducers and arrays
Figure 3.33 The spatial resolutions of an ultrasonic transducer in the axial and
lateral directions are determined by the pulse duration and beam width: (a) full
width with main lobe separation, (b) half-main lobe width separation, (c) less than
half-main lobe width separation, and (d) full width half maximum.
For a rectangular array element, beam widths on the x-z plane and y-z
plane are
dx = 2f#xλ and dy = 2f#yλ
where f#x = z0x/b and f#y = z0y/h are the f# values on the x-z plane and y-z
plane, respectively.
0.8
0.6
0.4
0.2
0
40 60 80 100 120 140
Distance
1.4
Normalized Pulse Echo Signal
150
Normalized Pulse Echo Signal
(d)
78 Diagnostic ultrasound: imaging and blood ow measurements
1.2
1
0.8
0.6
0.4
0.2
0
40 60 80 100 120 140
Distance
(c)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
50 100
Distance
Figure 3.33 (Continued) The spatial resolutions of an ultrasonic transducer in the
axial and lateral directions are determined by the pulse duration and beam width:
(a) full width with main lobe separation, (b) half-main lobe width separation, (c)
less than half-main lobe width separation, and (d) full width half maximum.
79Chapter three: Ultrasonic transducers and arrays
=λ
Df
The depth of focus Df, that is, within this region the intensity of the
beam within –3 dB of the maximal intensity at the focus for a circular
aperture and a rectangular aperture, is found to be linearly related to the
wavelength (Kino, 1987; McKeighen, 1998).
=λ
Df
fc fr
2
7.2 and 7.1
#
2
(3.39)
#
The depth of eld can be dened alternatively as the region between axial
distances where the beam widths become 2d.
From these relationships, it is clear that an increase in frequency
that decreases wavelength improves both lateral and axial resolutions by
reducing the beam width and the pulse duration if the number of cycles in
a pulse is xed. Unfortunately, these improvements are achieved at a cost
of a shorter depth of focus.
The axial and lateral resolution of a transducer can be improved from
an increase in the bandwidth with backing or matching and focusing. The
spectrum of an ultrasonic pulse varies as it penetrates into tissue because
the attenuation of the tissues is frequency dependent. It is known that the
center frequency and bandwidth of an ultrasonic pulse decrease as the
ultrasound pulse penetrates deeper. In other words, the axial resolution of
the beam worsens as the beam penetrates deeper into the tissue. In commercial scanners, pulse shape and duration are maintained by time gain
compensation and some form of signal processing.
3.5.5 Focusing
Better lateral resolution at a certain axial distance can be achieved by
acoustic focusing. However, an improvement in the lateral resolution or
focusing at a certain range is always accompanied by a loss of resolution
in the region beyond the focal zone, as illustrated in Figure3.34(a).
The general principles of focusing are identical to those in optics.
The two most often used schemes, a lens and a spherical or bowl-type
transducer, are illustrated in Figure3.34(a), where zf and Df are, respectively, focal distance and depth of focus, and (b). The acoustic lens
shown in Figure3.34(a) is a convex lens, which means that the sound
velocity in the lens material is less than the medium into which the beam
is launched. The convex lens is preferred in biomedical ultrasonic imaging in that it conforms better to the shape of the body curvature. This
is illustrated in Figure3.35. Some of the lens materials frequently used
in medical applications can be found in Table3.4. The most important
requirements are that it should have an acoustic impedance similar to the
last matching layer and be slightly attenuative to absorb reverberations
80 Diagnostic ultrasound: imaging and blood ow measurements
If Sound Velocity in Lens < Sound Velocity in Water
If S
r
Piezoelectric element
Tr
(b)
am
Convex lens
2a
D
ansducer
Spherically focused element
f
z
f
Focused beam
(a)
Nonfocused be
Figure 3.34 Two modes of focusing that have been used to focus ultrasonic
beams: (a) focusing with a lens and (b) self-focusing.
of signals inside the lens. As illustrated in Figure3.36, the focal length zf
of a lens is given by
R
c
=
z
f
(3.40)
−11/
n
where Rc is the radius of curvature and n = c1/c2, c1 is the velocity in the
lens and c2 is being that in the medium. A popular material for convex
Piezoelectric element
Figure 3.35 Convex and concave lenses.
ound Velocity in Lens > Sound Velocity in Wate
Convex lens
Concave lens
81Chapter three: Ultrasonic transducers and arrays
R
c
2a
Figure 3.36 Focusing geometry.
z
f
z
lens is RTV silicon rubber, which has a velocity of 1010 m/s, acoustic
impedance of 1.5 MRayl, and attenuation of 7 dB/cm-MHz. For a silicon rubber lens in water and a focal distance of 4 cm, Rc can be readily
calculated to be 2.12 cm from Equation (3.40). Concave lenses made of
polyurethane or polystyrene have also been used. For concave transducers a suitable ller material is needed to make the transducer face at.
Polyurethane has been shown to t this need. The focal region formed
by an acoustic lens is usually ellipsoidal. Its dimension depends on the
relationship between wavelength and the diameter of the lens. In general, the bigger the diameter, the smaller the focal point. Ultrasonic imaging is diffraction limited because the beam cannot be properly focused in
the region close to the transducer and beyond the near-eld and far-eld
transition point. For a circular piston transducer of radius a, z0 = a2/λ. The
f# is a/(2λ), which is determined by the ratio of radius to wavelength. For
a ratio of radius to wavelength = 10, f# = 5. This means that the beam cannot be focused beyond an f# of 5. The only way to obtain focusing at a distance greater than this is to either increase the aperture size or decrease
the wavelength.
3.5.6 Protection circuits for transducers
Large signals in the order of 100 peak-to-peak volts are needed to drive a
transducer. The receiving electronics must be protected from these high
voltages (Lockwood et al., 1991; Cobbold, 2007). Figure 3.37(a) shows a
protection scheme that is commonly used. Rs, Cs, and Lc represent source
output resistance, capacitance, and inductance for a matching network.
The load resistance Rl should be much larger than the input resistance of
the receiving electronics, Ri, which is in general 50 Ω. When the source
is on, both diodes D1 and D2 appear to be shorted. During transmission
and reception the circuit behaves like the circuit shown in Figure3.37(b)
82 Diagnostic ultrasound: imaging and blood ow measurements
D1
V
(c)
R
s
s
C
s
L
c
R
l
Preamplifier
R
i
D2
Transducer
(a)
V
R
s
s
C
s
R
L
l
c
Transducer
(b)
C
s
L
c
R
l
R
i
Transducer
Figure 3.37 (a) A commonly used transducer protection circuit. (b) and (c) Circuit
during transmission and reception.
83Chapter three: Ultrasonic transducers and arrays
+γ
+γ
+β
+β
Zx
Zx
Z
x
Z
in
0
Z
l
Figure 3.38 An electrical cable terminated by load impedance Zl.
and (c). At high frequencies (>20 MHz), the cable length may be changed
or tuned to match to Ri. The input electrical impedance to a cable shown
in Figure3.38 is given by
ZZ x
=
ZZ
0
in
ZZ x
tanh
0
l
tanh
0
l
(3.41)
where γ is a complex number = α + jβ, α = attenuation coefcient of the cable,
β = propagation constant for an electromagnetic wave, and Z0 = characteristic
electrical impedance of the cable. Assuming a lossless cable, Equation (3.41)
becomes
Zj
=
ZZ
0
in
Zj
tan
0
l
tan
0
l
At 50 MHz the electromagnetic wavelength is 600 cm, and the cable
needs to be considered. If Zl is zero, when x is λ/4 = 150 cm in this case,
βx = π/2, tanβx = ∞, and Z
= ∞. It means that the electrical impedance
in
from the transducer looking into the receiving electronics is ∞ or an open
circuit. Another observation is that if Zl = Z0, Z
= Z0 for all x. If the trans-
in
ducer output impedance is Z0, the load is matched to the transducer independent of the cable length.
A single-element transducer can be translated or steered mechanically to form an image. Linear translators do not allow movements
permitting generation of images at a rate higher than a few frames per
second, although there are sector scanning devices that allow steering the
transducer within a limited angle at a rate of 30 frames per second. Early
real-time ultrasonic imaging devices almost exclusively used this type of
transducer, which is called mechanical sector probe. A typical mechanical
84 Diagnostic ultrasound: imaging and blood ow measurements
Single elemen
transducer
l
Mechanical sector
Mechanical
drive
Oil
t
Figure 3.39 Detailed construction of a mechanical sector probe.
Cable
Probe housing
Coupling ge
Skin
Tissues
sector probe is shown in Figure3.39. The transducer is housed in a dome
bathed in some form of oil to facilitate the transmission of the ultrasonic
energy from the transducer to the housing. Mechanical sector probes
that suffer from poor near-eld image quality because of reverberations
between the transducer and the housing and xed focusing capability
have now been largely replaced by linear arrays.
3.6 Arrays
Arrays are transducer assemblies with more than one element. These
elements may be rectangular in shape and arranged in a line, called linear array or 1D array, shown in Figure 3.40(a), or square in shape and
arranged in rows and columns, called two-dimensional (2D) array, shown
in Figure3.40(b), or ring shaped and arranged concentrically, called annular array, shown in Figure3.40(c).
A linear switched array (sometimes called a linear sequence or simply
a linear array) is operated by applying voltage pulses to groups of elements in succession, as shown in Figure3.41, where the solid line and the
dashed line indicate, respectively, the rst and second beams. In this way,
the sound beam is moved across the face of the transducer electronically
producing a picture similar to that obtained by scanning a single-element
transducer manually. The amplitude of the voltage pulses can be uniform
or varied across the aperture as shown in the gure by arrows of varying length. As mentioned previously, amplitude apodization or varying
the input pulse amplitude across the aperture is sometimes used to suppress side lobes at the expense of worsening the lateral resolution. If the
electronic sequencing or scanning is repeated fast enough (30 frames per
second), a real-time image can be generated. Linear arrays are usually
Pitch
X (Azimuth)
(a)
ts
(b)
Annuli
(c)
Kerf
Kerf width
Array element
Y (Elevation)
Array elemen
85Chapter three: Ultrasonic transducers and arrays
Z
Figure 3.40 (a) A linear array. (b) A 2D array. (c) An annular array.
1 cm wide and 10 to 15 cm long with 128 to 256 elements. Typically 32 or
more elements are red in a group. For the sake of achieving as good a
lateral resolution as possible, the irradiating aperture size must be made
as large as possible. The aperture size is in turn limited by the requirement of maintaining a large number of scan lines. This point will become
86 Diagnostic ultrasound: imaging and blood ow measurements
ts
Array elemen
Direction of electronic
scanning
Figure 3.41 An image is formed by a linear array by electronically sweeping the
beam. A group of elements are red simultaneously to form one beam.
clearer in Chapter 4. Figure3.42 shows the detailed construction of a linear array consisting of a backing material, a layer of piezoelectric material sandwiched between two electrodes, and two matching layers. Here
a concave lens is used to focus the imaging plane in the elevational direction or the slice thickness of the imaging plane. This is a problem of crucial importance in 2D imaging with 1D arrays because the slice thickness
cannot be controlled throughout the depth of view. The slice thickness is
the thinnest only at the focal point of the lens and becomes worse closer
to the array or beyond the focal point. Figure3.43 illustrates how a large
slice thickness can cause serious image artifacts, including reduction in
contrast. The top panel shows that scatterers outside of the cyst region
can cause the echogenicity within the cyst to increase in the eld of view
where the slice thickness is large. The lower panel shows that although the
location of the cyst farther from the transducer is not on the same imaging
plane as the cyst closer to the transducer, an ultrasonic image will not be
able to tell the difference.
In Figures 3.40(a) and 3.44, the space between two elements is
called a kerf and the distance between the centers of two elements is
called a pitch. The kerfs may be lled with acoustic isolating material or simply air to minimize acoustic cross talk. The kerfs are often
cut into the lens and backing to minimize acoustic cross talk between
adjacent elements through the backing, the lens, and matching layers.
The size of a pitch in a linear array ranges from λ/2 to 3λ/2, where λ
is the wavelength in the medium into which ultrasound is launched
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