Biomedical Engineering Reference
In-Depth Information
1.5
line aperture
circular aperture
1
0.5
0
0.5
3
2
1
0
1
2
3
Lx/(
λ
, z)or
ρ
a/(
λ
,z)
FIGURE 16.22
(a) Far-field jinc beam shape from a circular aperture normalized to (b) far-field sinc function
from a square aperture with the same aperture area.
EXAMPLE PROBLEM 16.9
To understand the normalization in Figure 16.22, find the FWHM for a circular aperture
having the same area as a square aperture and compare it to the FWHM of the square aperture.
Solution
Set
L(m)/
p
)(
p
/
2
2
, or a(m)
p
a
¼
L
¼
p:
Substitute in Eq. (16.45b), FWHM
¼
0.7047
l
(
m
)
z
(
m
L
(
m
)
¼
1.249
l
(
m
)
z
(
m
)/
L
(
m
). This is close to the value for the square aperture from Eq. (16.45a),
FWHM
¼
1.206
l
z
/
L
(
m
).
To narrow the beams even more and at different depths, geometric focusing is applied.
Like optics, acoustic focusing can be implemented with a type of lens. Unlike optics, both
concave and convex converging lenses can be made because materials exist such that their
sound speeds are either greater or less than that of water (tissue). Under the principles of
ray optics, the rays converge at the geometric focal point,
. From the reciprocal law of
lenses, the overall total focal length is the combined effect of the natural focal length and
the geometrical focal length
F
1
=
F
¼
1
=
F
N
þ
1
=
F
ð
16
:
46
Þ
total
