A method of obtaining an arbitrary, admissible transverse magnetization
profile as the summed response of two, self refocused selective "half
pulse" excitations for use in, e.g., magnetic resonance imaging pulse
generation. The problem of finding the pair of half pulses is rephrased
in the inverse scattering formalism and a simple closed form algorithm
for the solution is given, provided the target transverse profile has
constant phase (modulo 180.degree.). The problem has a unique low energy
solution for sufficiently small, complex valued data, and an algorithm
for finding the solution is provided. This solution is used to generate
pairs of half pulses for given target transverse profiles.
