Exact half pulse synthesis via the inverse scattering transform

J Magn Reson. 2004 Dec;171(2):305-13. doi: 10.1016/j.jmr.2004.09.004.

Abstract

In a paper of Nielson et al. it is shown, using the linear approximation, that it might be possible to create a pair of RF-pulses, which, after summation of the unrephased signals achieve a specified transverse magnetization. Such pulses, designed using the linear approximation, show rather poor slice selectivity. Using the inverse scattering transform formalism we give an algorithm to exactly achieve a specified "summed" transverse magnetization profile. Indeed for a constant phase transverse profile, our algorithm produces infinitely many solutions.