Spatial coherence phenomena arising from translational spin motion in gradient spin echo experiments

The use of pulsed magnetic field gradients to encode spin magnetization for position or positional displacement leads to a variety of spatial coherences in the spin phases, each coherence being manifest in a characteristic diffraction pattern, whether in k-space or q-space. These phenomena, which are sensitive to different temporal moments of the gradient waveform, range from the original Mansfield–Grannell position diffraction, through diffusive and flow diffraction, to diffraction patterns which arise owing to Taylor dispersion in a heterogeneous velocity field. We describe each of these and suggest an appropriate terminology. Of particular recent interest is the double pulsed gradient spin echo nuclear magnetic resonance experiment, which may be used to study stochastic processes in dispersive flow. We give a detailed analysis of this type of experiment, illustrated with the example of Poiseuille flow in a pipe.