NMR imaging and structure measurements using the long-range dipolar field in liquids

We extend the Fourier-based formalism previously developed to analyze structural measurements obtained using the long-range liquid dipolar field in NMR, in the short time regime. It is shown that in the case of a two-spin system, the signal measured in an average structure measurement is related to the spatial cross-correlation function of the spin densities of the two components. It is also demonstrated that in the case of cylindrically symmetrical systems, the measured data are related to the Meijer transform (or K transform) of the radial distribution function of the spin density. Experiments were performed on structured phantoms exhibiting cylindrical symmetry over the length scale probed, and were found to be in excellent agreement with the theory. Finally, it is shown that changes in image contrast with the strength of the modulation gradient can be expressed in terms of the action of a dipolar "filter."