NMR diffraction and spatial statistics of stationary systems

Nuclear magnetic resonance (NMR) spatial imaging data may be acquired, processed, and interpreted in ways that provide information directly analogous to diffraction experiments, with length scales determined by gradient strengths rather than radiation wavelengths. This approach, originally considered by Mansfield nearly two decades ago, provides access to autocorrelations of sample density that statistically characterize small-scale density variations. These NMR "Patterson functions" can be acquired orders of magnitude more rapidly than comparably resolved NMR images and are suitable for spatial characterization of small features in bulk samples, such as morphology in structural materials. Unlike hindered diffusion approaches, neither mobility, penetrants, nor transport time are required for examining granularity and porosity.