7.12 : NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered inhomogenous by the presence of the sample and the probe, resulting in broadened peaks with extraneous side-bands and poor resolution.

These inhomogeneities are corrected before the spectra are recorded by a process called shimming. A set of shim coils surrounds the probe and generates small magnetic fields depending on the current passed through them. These fields can enhance or oppose B₀ in the vicinity of the sample. Shimming involves manipulating the coil fields to obtain the most uniform magnetic field across the sample, correcting the inhomogeneities. Shimming, optimized pulse sequence parameters, and proper sample preparation ensure good peak shape, low signal-to-noise ratio, and maximum resolution.