Excitation trajectories shaped pulses

The major difference between soft shaped pulses and DANTE methods is the occurrence of strong sideband excitation windows either side of the principal window with DANTE. These occur at offsets from the transmitter at multiples of the hard-pulse frequency, 1/x. They arise from magnetisation vectors that are far from resonance and which process full circle during the x period. Since this behaviour is precisely equivalent to no precession, they are excited as if on-resonance. Further sidebands at 2/x, 3/x and so on also occur by virtue of trajectories completing multiple full circles during x. Such multisite excitation can at times be desirable [50,51] but if only a single excitation window is required, the hard pulse repetition frequency must be adjusted by varying x to ensure the sideband excitations do not coincide with other resonances. 

Fig. 1. Computer simulations of four selective excitation pulses. (Top) Pulse shapes. From left to right 90° rectangular pulse, 270° Gaussian truncated at 2.5%, Quaternion cascade Q, and E-BURP-1. The vertical axis shows the relative rf amplitudes, whereas the horizontal axis shows the time. (Middle) Trajectories of Cartesian operators in the rotating frame...

More elaborate pulse shapes have been developed over the years which aim to produce a near top-hat profile yet retain uniform phase for all excited resonances within a predefined frequency window. These operate without the need for purging pulses or further modifications, allowing them to be used directly in place of hard pulses. They are typically generated by computerised procedures which result in more exotic pulse envelopes (and acronyms Fig. 9.11) that drive magnetisation vectors along rather more tortuous trajectories than the simpler Gaussian-shap>ed cousins. Trajectories are shown in Fig. 9.15... 

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