Selective rotation pulses calculated with an inverse scattering algorithm

Selective rotation pulses cause magnetization within a given frequency range (or slice) to undergo a specified rotation, about a specified axis. Magnetization outside this slice remains unaffected if it is initially along the z axis. It has previously been shown that the design of such pulses can be reduced to the design of selective “point-to-point” pulses, which rotate magnetization within the slice from the y axis. By decomposing the point-to-point pulses into two sub-pulses, it is shown that an inverse scattering algorithm for selective pulse design can be used to calculate selective rotation pulses with any desired spinor response, subject to the constraint that the second spinor component have constant phase across the slice. The design of selective refocusing pulses can be treated specially, requiring the calculation, by the same inverse scattering algorithm, of a single sub-pulse.