 NMR phase cycling

NMR phase cycling systematically changes radio frequency pulse phases and the receiver phase across repeated nuclear magnetic resonance acquisitions so that selected signals reinforce while unwanted contributions cancel. Pulse phase controls the rotation axis in the rotating frame; receiver phase controls how transverse magnetization is represented in the recorded complex signal. A phase change does not mean changing the resonant nucleus or physically rotating the sample.^[ref]

An original two-acquisition example makes the subtraction explicit. Suppose changing an excitation pulse by $\pi$ reverses the desired contribution $S$ while leaving an unwanted background $B$ unchanged. Before correcting the receiver phases, the two measurements areApplying the corresponding receiver sign and averaging gives $(s_1-s_2)/2=S$. With invented values $S=5$ and $B=2$, the recorded values7 and−3 yield5. Adding them without the intended sign would instead retain the background.

The assumptions matter. If the background changes between acquisitions, the residual is $(B_1-B_2)/2$. Nor does a two-step cycle separate contributions that transform in exactly the same way under its phase changes. More elaborate cycles select particular changes in NMR coherence, rather than indiscriminately removing every source of error.^[ref]

Phase patterns can also be built into a train of refocusing pulses. XY8 is an important example for controlling cumulative NMR pulse errors. Within-train pulse compensation and across-acquisition selection are related uses of phase control, but the eight pulses of an XY8 block do not by themselves specify a complete receiver cycle.