Basic Physics of MR Signal and Image Generation - Advance Image Processing in Magnetic Resonance Imaging - page 25

Shaped 90-degree pulse

∆ t

Frequency
spectrum
of pulse

ω

ω 0

∆ω

z

Gz

0

∆ z

Slice

FIGURE 1.12 Selective excitation of a thin slice of the sample.

is related to the shape and the duration of the pulse; if we consider a
Gaussian-shaped pulse,

∆ω

is the full width at half maximum
(FWHM) of the pulse's frequency spectrum, and

∆ω = 2 π / ∆ t , where ∆ω

t is the relevant FWHM of the
pulse envelope in seconds. From Equation 1.33, the slice can be made thinner by
decreasing the spectral bandwidth of the pulse (i.e., by making the pulse longer
in time) or by increasing the strength of the slice selection gradient G z .
The slice profile is determined by the spectral contents of the selective pulse,
and it is approximately given by the Fourier transform of the RF pulse envelope.
Thus, a Gaussian-shaped 90

∆

pulse gives a roughly Gaussian slice profile.
The slice selection pulse sequence can be represented by a pulse timing

°

diagram , as shown in Figure 1.13 , showing the RF pulse and selection gradient

as a function of time. The selection gradient is followed by a negative gradient
pulse in order to bring the spins back into phase across the slice.
After a signal has been activated by a selective or nonselective pulse, spatial
information can be encoded into the signal during the free precession period. We
have essentially two ways to encode spatial information: frequency encoding and
phase encoding.

1.9.2 F REQUENCY E NCODING

Frequency encoding makes the oscillation frequency of an MR signal linearly
dependent on its spatial origin. Let us consider an idealized one-dimensional
object with spin distribution

ρ (x). If the magnetic field that the object experiences