Many single-sided permanent magnet NMR systems have been proposed over the years allowing for 1D proton-density profiling, diffusion measurements and relaxometry. In this manuscript we make use of a recently published unilateral magnet for low-field NMR exhibiting an extremely uniform magnetic field gradient with moderate strength and cylindrical symmetry, allowing for a well-defined sweet spot. Combined with a goniometer, our system is used to characterize precisely the uniformity of its gradient and to achieve micrometric precision 1D profiling, as well as spatially localized relaxometry and diffu-sometry on thick ($150 lm) membrane samples. Profiling with this magnet did not require repositioning of the samples with respect to the 1D tomograph.