Biomedical Engineering Reference
In-Depth Information
of the total energy passes through the focal region (Kossoff et
al. 1979). The variation of gain and focal width with transducer
radius at different frequencies, for a transducer of radius of cur-
vature 5 cm, is shown in Figure 5.5.
R
5.2.5.2 Lenses
Converging beams may also be produced by fronting a plane
transducer with a concave lens of velocity of sound greater than
water, such as polystyrene or Perspex (Fry and Dunn 1962).
A plano-concave geometry is the easiest to construct. The focal
length of such a lens is given by
W
h
a
R
FIGURE 5.4
Geometric parameters of a spherical bowl transducer:
h
= bowl depth,
a
= bowl radius,
R
= radius of curvature, and
W
= width
of focal region.
F
=
(5.5)
(
1
−
n
)
where
n
is its refractive index.
A limitation of the use of lenses is that the sound is absorbed
by the lens material, and the acoustic mismatch between
the lens and the medium in which it sits (often water), leads
to reflections at the interfaces. Maximum transmission is
obtained when the transducer and lens are separated by a quar-
ter wavelength plate of a material that provides a good acoustic
match to both.
The width of the focal region,
W
, is given by
R
a
λ
(5.4)
W
= 122
.
where
R
is the radius of curvature, and
a
is the bowl radius. In
a nonattenuating medium, diffraction theory shows that 84%
(a)
1.0E+06
5 MHz
3 MHz
1.0E+05
1 MHz
1.0E+04
1.0E+03
1.0E+02
1.0E+01
1
2
3
4
5
Transducer radius (cm)
1
(b)
0.9
1 MHz
0.8
0.7
0.6
0.5
0.4
3 MHz
3 MHz
03
0.2
5 MHz
0.1
0
1
2
3
4
5
Transducer radius (cm)
FIGURE 5.5
Variation in (a) focal gain and (b) focal width with transducer radius at 1, 3, and 5 MHz.
