Double PGSE NMR with Stimulated Echoes: Phase Cycles for the Selection of Desired Encoding

When two pairs of position-encoding pulses are used in a pulsed gradient spin echo (PGSE) NMR experiment, it is possible to examine velocity fluctuations. The one-dimensional version of double PGSE NMR uses identical pulse pairs whose amplitudes are stepped simultaneously. In the two-dimensional version (VEXSY) the pulse pairs are stepped independently, resulting in a velocity exchange spectrum. A key limitation in such experiments is transverse relaxation, so that stimulated echoes are often used as the method of choice. It is shown here that the use of stimulated echoes results in a superposition of signals arising from different magnetization pathways such that the spin phases may reflect both the sum and difference of displacements over the pulse pair encoding times, as well as the displacement over the exchange time between the pulse pairs. A phase cycle scheme that selects desired encodings as required is demonstrated.