Biomedical Engineering Reference
In-Depth Information
p
/2
p
RF
G
z
tp
G
y
G
x
spin echo
S(t)
T
E
T
R
FIGURE 16.47
Essential rf excitation, and gradient pulse sequences,
G
z
,
G
y
,
G
x
, for spin-echo detection,
s
(
t
).
intervals so the positions of the spins are translated into different frequencies that vary with
position along the
x
-axis. Finally, a
y
gradient pulse excites the coils along the
y
-axis with an
amplitude appropriate to phase encode the position
y
. Spin echoes are sensed at
t
¼
T
E
. The
sequence is repeated at intervals of
.
To form an image, the set of acquired signals and the object to be imaged (a distribution
of net magnetization vectors) are assumed to be related by Fourier transforms. If a particu-
lar slice plane has been selected at
T
R
), which
implies that a double Fourier transform (for two dimensions) is involved. It will be easier
to consider each dimension separately (
z
, then the object is a function of position (
x
,
y
) and then combine them into a 2D transform.
Signals detected from a net magnetization distribution at a position (
x
or
y
x
n
,
y
m
) will be
considered.
Before starting with the
-axis, it will be helpful to review the role of the impulse in
Fourier transform theory described in Section 16.2. The impulse and its transform play
an essential role in the understanding of MRI. The impulse function is a generalized func-
tion that has the unusual property of sampling the integrand, as introduced in
Section 16.1.1:
y
1
dð
f
f
Þ
R
ð
f
Þ
df
¼
R
ð
f
Þ
ð
16
:
77a
Þ
0
0
1
