Magnetic resonance measurement and reconstruction of the diffusion propagator

We demonstrate the experimental determination of the diffusion propagator using magnetic resonance (MR) techniques. To this end, a recently introduced method was implemented on a benchtop MR scanner and incorporated into profiling and imaging sequences. Diffusion encoding was obtained by three gradient pulse pairs, each applied around a respective 180$^\circ$ radiofrequency pulse. The data involving two independent wavenumbers were transformed from the measurement domain to the spatial domain, yielding an apparent diffusion propagator. For free diffusion, this apparent propagator converges to the true one when two of the pulse pairs are replaced with pulses of infinitesimal duration.