Gaussian Pulses
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JOURNAL OF MAGNETIC RESONAN CE s&442-457 (1984) Gaussian Pulses CHRISTOPHER BAUER, RAY FREEMAN, TOM FRENIUEL,* JAMES REELER, AND A. J. SHAKA Physical Chem istry Laboratory, Oxford University, Oxford, England Received Decem ber 15. 1983 An analysis is made of frequency-selective radiofrequency pulses used for high-resolution NM R studies of li quids. If the pulse envelope is rectangular, there are extensive sidelobes in the frequency-domain excitation pattern, whereas a Gaussian envelope gives a frequency- domain pattern (for the absolute-value mode) that is a slightly distorted Gaussian with no sidelobes. This affords much better selectivity. Furthermore the Gaussian pulse excites a signal with a phase angle which is almost a linear function of offset. The calculations are based on magnetization trajectories predicted by the Bloch equations, neglecting re- laxation. It is shown that at appreciable olfsets from resonance the Gaussian pulse produces a characteristic “teardrop” trajectory which always terminates near the +Z axis, irrespective of offset AB. Examples of applications of Gaussian-shaped pulses include the investigation of the fine structure on carbon-13 resonances, selective coherence transfer experiments between protons, and nuclear Overhauser effect measurem ents in crowded proton spectra. INTRODUCTION Sever al NMR experiments require the application of radiofrequency pulses that are selective in the frequency domain. Such “soft” pulses may be generat ed as a single burst of weak irradiation of rela tivel y long du ration (I) or as a train of repeate d hard pulses with intervening periods of free precession (2). Select ivity is measured by the abil ity to excite a chosen resonance (or group of resonances) without appreciabl y affecting near neighbors. For a given net flip angle, sele ctiv ity is determined by the duration of the soft pulse or the total duration of the pulse train; it can be made very high, a s demonstrated by experiments which burn a hole in an inhomogeneously broade ned line (3). Normally the envelope of the pulse (or pulses ) is rectangular since this is the simpl est scheme to implement. Unfortunately this entails the existence of side lobes in the frequency-domain excitati on function, approximating the form of a sin x/x function, since to a firs t approximation the time- and frequency-domain profiles form a Fourier transform pair. In some applicati ons excitation by a side lobe could lead to ambiguous results . This arti cle examines methods for suppressing these unwanted side lobes by shaping the pulse envelope to eliminate the step-function discont inuities as the pulse is switched on and off. Sim ilar ideas have been used in NMR imaging experiments (4, 5) but not, apparently, in high-resolution spectrosco py. For sim pli city the case of the sing le soft pulse is considered here; the extension to * Present address: National Institute for Medical Research, Mill Hill, London, England OO22-2364184 3.00 Copyright 0 1984 by Academic Press, Inc. Al l rights of reproduction in any form rescrxd. 442
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