This spectrum is inverse Fourier transformed to produce an FID of the distorted singlet, FID r exp(t). In the reference deconvolution technique, one selects a high signal-to-noise ratio singlet peak as a reference in the experimental spectrum and sets all other points in the spectrum to zero. If we could find the error function and divide the experimental FID, by it, we could produce a perfect (or at least improved) FID, the Fourier transform of which would be a spectrum corrected from the effects of field inhomogeneity. The imperfect FID giving rise to the offensive spectrum, FID exp(t), is essentially a perfect FID, FID(t) multiplied by an error function, E(t), resulting from the inhomogeneous field. The distortions in a spectrum from an inhomogeneous magnetic field affect all peaks in the spectrum in the same way. Have you ever looked at such a spectrum and longed to recover the hidden beauty, resolution and information you know is present in the depths of its repulsive form? In many such cases reference deconvolution is a processing technique able to help. These repugnant, distasteful spectra are often obtained when automatic shimming routines are used on under-filled samples, samples with solids present (precipitates, floaters of suspended solids), samples with thermal gradients, poorly mixed samples etc…. Inhomogeneous fields yield low resolution NMR spectra with broad asymmetric peaks pleasing no one. Their majesty depends on the homogeneity of the NMR magnet around the sample. The pleasingly symmetric and narrow Lorentzian resonances in a high resolution NMR spectrum are truly things of stunning beauty, appreciated by all NMR spectroscopists.

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