Phase Cycling and Gradient Pulses - The James Keeler Group

dimensional spectra. This is considered in more detail in section 9.5.6.
9.5.5.2 Grouping pulses together
The sequence shown opposite can be used to generate multiple quantum
coherence from equilibrium magnetization; during the spin echo anti-phase
magnetization develops and the final pulse transfers this into multiple quantum
coherence. Let us suppose that we wish to generate double quantum, with p =
±2, as show by the CTP opposite.
As has already been noted, the first pulse can only generate p = ±1 and the
180° pulse only causes a change in the sign of the coherence order. The only
pulse we need to be concerned with is the final one which we want to generate
only double quantum. We could try to devise a phase cycle for the last pulse
alone or we could simply group all three pulses together and imagine that, as a
group, they achieve the transformation p = 0 to p = ±2 i.e. ∆p = ±2. The phase
cycle would simply be for the three pulses together to go 0°, 90°, 180°, 270°,
with the receiver going 0°, 180°, 0°, 180°.
It has to be recognised that by cycling a group of pulses together we are only
selecting an overall transformation; the coherence orders present within the
group of pulses are not being selected. It is up to the designer of the experiment
to decide whether or not this degree of selection is sufficient.
The four step cycle mentioned above also selects ∆p = ±6; again, we would
have to decide whether or not such high orders of coherence were likely to be
present in the spin system. Finally, we note that the ∆p values for the final
pulse are ±1, ±3; it would not be possible to devise a four step cycle which
selects all of these pathways.
2
1
0
–1
–2
Pulse sequence for generating
double-quantum coherence.
Note that the 180° pulse simply
causes a change in the sign of
the coherence order.
9.5.5.3 The last pulse
We noted above that only coherence order –1 is observable. So, although the
final pulse of a sequence may cause transfer to many different orders of
coherence, only transfers to p = –1 will result in observable signals. Thus, if
we have already selected, in an unambiguous way, a particular set of coherence
orders present just before the last pulse, no further cycling of this pulse is
needed.
9.5.5.4 Example – DQF COSY
A good example of the applications of these ideas is in devising a phase cycle
for DQF COSY, whose pulse sequence and CTP is shown below.
t 1 t 2
p
2
1
0
–1
–2
∆p=±1 ±1,±3
+1,–3
Note that we have retained symmetrical pathways in t 1
so that absorption mode
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