Phase Cycling and Gradient Pulses - The James Keeler Group

y
y
180°(±x)
τ
90°(x) – τ
–x
x
–y
180°(±y)
τ
If the phase of the 180° pulse is +x or –x the echo forms along the y-axis,
whereas if the phase is ±y the echo forms on the –y axis. Therefore, as the 180°
pulse is advanced by 90° (e.g. from x to y) the receiver must be advanced by
180° (e.g. from x to –x). Of course, we could just as well cycle the receiver
phases y, –y, y, –y; all that matters is that they advance in steps of 180°. We
will see later on how it is that this phase cycle cancels out the results of
imperfections in the 180° pulse.
–y
I
S
1
2J
y
1
2J
Pulse sequence for INEPT.
Filled rectangles represent 90°
pulses and open rectangles
represent 180° pulses. Unless
otherwise indicated, all pulses
are of phase x.
9.2.8 Difference spectroscopy
Often a simple two step sequence suffices to cancel unwanted magnetization;
essentially this is a form of difference spectroscopy. The idea is well illustrated
by the INEPT sequence, shown opposite. The aim of the sequence is to transfer
magnetization from spin I to a coupled spin S.
With the phases and delays shown equilibrium magnetization of spin I, I z
, is
transferred to spin S, appearing as the operator S x
. Equilibrium magnetization
of S, S z
, appears as S y
. We wish to preserve only the signal that has been
transferred from I.
The procedure to achieve this is very simple. If we change the phase of the
second I spin 90° pulse from y to –y the magnetization arising from transfer of
the I spin magnetization to S becomes –S x
i.e. it changes sign. In contrast, the
signal arising from equilibrium S spin magnetization is unaffected simply
because the S z
operator is unaffected by the I spin pulses. By repeating the
experiment twice, once with the phase of the second I spin 90° pulse set to y
and once with it set to –y, and then subtracting the two resulting signals, the
undesired signal is cancelled and the desired signal adds. It is easily confirmed
that shifting the phase of the S spin 90° pulse does not achieve the desired
separation of the two signals as both are affected in the same way.
In practice the subtraction would be carried out by shifting the receiver by
180°, so the I spin pulse would go y, –y and the receiver phase go x, –x. This is
a two step phase cycle which is probably best viewed as difference
spectroscopy.
This simple two step cycle is the basic element used in constructing the
9–8