RF Shimming Pulses For Ex-Situ NMR Spectroscopy and Imaging Using B1 Inhomogeneities

I describe a method for generating "shim pulses" for NMR spectroscopy and imaging (MRI) by taking advantage of the inherent inhomogeneity in the static and radiofrequency (RF) fields of a one-sided NMR system. The RF inhomogeneity here is assumed, without loss of generality, to be a linear gradient. General polynomials in the spatial variables can be generated using x, y and z RF gradients using trains of hard pulses which result in linear combinations of monomials xy, y^2, xz etc., and any desired scalings of these monomials. The basic shim pulse is constructed using small tip angle approximations.