K and q Dedicated to Paul Callaghan

Abstract

The symbols k and q denote wave numbers in scattering experiments as well as in NMR imaging. Their exploration in NMR is intimately linked to the legacy of Paul Callaghan with his books Magnetic Resonance Microscopy and Translational Dynamics & Magnetic Resonance (Oxford University Press, Oxford 1991 and 2011) placing their focus with their titles on k and q, respectively. Some aspects of k and q have been revisited in the Paul Callaghan lecture of the author at the ISMAR Conference in Shanghai in 2015, which are reviewed here. In particular, there are two definitions of q, one relating to diffusive displacement (q) and the other to coherent flow (qv). Concerning the latter, it turns out, that in the short gradient pulse limit, the common anti-phase pulsed field-gradient scheme can be replaced with schemes employing three and more gradient pulses, which derive from differentiation rules in numerical analysis. Practical gradient modulation schemes with finite gradient pulse widths follow from these to measure velocity with improved accuracy. This approach can be expanded to acceleration and higher order transport coefficients with applications to measurements of flow and potentially also restricted diffusion.