Feature article: Concepts in Magnetic Resonance

R.M. Gregory, A.D. Bain, "The effects of finite rectangular pulses in NMR: Phase and intensity distortions for a spin-1/2," Concepts in Magnetic Resonance Part A 34A (2009) 305-314. http://dx.doi.org/10.1002/cmr.a.20147

Abstract

Pulses in NMR spectrometers have a finite length, but the usual hard-pulse assumption ignores it, and treats the pulse as a rotation of the frame of reference about the direction of the radiofrequency (RF) magnetic field. However, at frequency offsets comparable to the size of the RF field, there are substantial distortions, mainly in the phase of the signal. This effect is well known and can be easily calculated to show that, despite the complex geometry, the phase distortion is almost linear with the offset. This means that it can be corrected by a first-order phase correction or by small corrections to pulse-sequence timing. In this article, we give an analysis of these effects. The deviations from a linear phase correction are analyzed for a general rectangular pulse and illustrated with experimental spectra. The split-operator approximation for the evolution of this system provides a mathematical foundation and a useful method for this analysis. Furthermore, the relationship between the exact behavior of a signal is compared to the Fourier transform of a rectangular pulse. For typical offsets, the match between these approaches is not good, but it improves as the offset increases. Overall, the detailed analysis of the finite pulse effects gives exact results of the response of a spin system, but also some mathematical and physical insights.