Phase Cycling and Gradient Pulses - The James Keeler Group

pulse goes x, –x and the receiver goes x, –x.
For non-axial peaks, the two phase shifts cancel one another out, and so have
no effect. However, magnetization which gives rise to axial peaks does not
experience the first phase shift, but does experience the receiver phase shift.
The sign alternation in concert with t 1
incrementation adds a frequency of SW 1
/2
to each peak, thus shifting it to the edge of the spectrum. Note that in States-
TPPI the spectral range in the F 1
dimension is –(SW 1
/2) to +(SW 1
/2) and the
sampling interval is 1/2SW 1
, just as in the SHR method.
The nice feature of States-TPPI is that is moves the axial peaks out of the
way without lengthening the phase cycle. It is therefore convenient to use in
complex three- and four-dimensional spectra were phase cycling is at a
premium.
9.5 Phase cycling
In this section we will start out by considering in detail how to write a phase
cycle to select a particular value of ∆p and then use this discussion to lead on to
the formulation of general principles for constructing phase cycles. These will
then be used to construct appropriate cycles for a number of common
experiments.
9.5.1 Selection of a single pathway
To focus on the issue at hand let us consider the case of transferring from
coherence order +2 to order –1. Such a transfer has ∆p = (–1 – (2) ) = –3. Let
us imagine that the pulse causing this transformation is cycled around the four
cardinal phases (x, y, –x, –y, i.e. 0°, 90°, 180°, 270°) and draw up a table of the
phase shift that will be experienced by the transferred coherence. This is
simply computed as – ∆p φ, in this case = – (–3)φ = 3φ.
step
pulse phase
phase shift experienced by
transfer with ∆p = –3
equivalent phase
1 0 0 0
2 90 270 270
3 180 540 180
4 270 810 90
The fourth column, labelled "equivalent phase", is just the phase shift
experienced by the coherence, column three, reduced to be in the range 0 to
360° by subtracting multiples of 360° (e.g. for step 3 we subtracted 360° and
for step 4 we subtracted 720°).
If we wished to select ∆p = –3 we would simply shift the phase of the
receiver in order to match the phase that the coherence has acquired; these are
the phases shown in the last column. If we did this, then each step of the cycle
would give an observed signal of the same phase and so they four contributions
would all add up. This is precisely the same thing as we did when considering
9–21