Extending the use of Earth's Field NMR using Bayesian methodology: application to particle sizing

There is currently much interest in extending the use of low-field magnetic resonance measurements and in particular, to obtain spatial information from these data. Here, we demonstrate the application of a Bayesian magnetic resonance approach for the sizing of objects using low magnetic field measurement technology, where there is insufficient signal-to-noise to allow a conventional imaging approach for structural characterisation. The method is illustrated in application to the sizing of spheres, in this case of radius 9.5mm, using an Earth's Field Nuclear Magnetic Resonance (EFNMR) spectrometer with pre-polarisation. Numerical simulations of the measurement at different signal-to-noise ratios and implementation of different k-space sampling schemes are considered to identify the optimal experimental protocol. In this example, the determination of sphere radius is found to be accurate to ±1mm. We confirm that the posterior distribution provides an accurate estimate of the uncertainty in the measurement.