Feedback Pulses

Abstract: We have a new paradigm to design NMR pulses. Pulses, we call feedback pulses. We want broadband inversion and excitation. We have many offsets, start evolving them all starting from the north pole. Monitor them on the Bloch sphere, see which offset is worst (most away from south pole). Change the rf-phase to the offset ($\pi/2$ ahead of offset transverse magnetization phase) and irradiate at that offset frequency and evolve for some time and monitor and repeat, looking for worst offset. When we are on resonance to a offset, we are doing well, inverting it and when we are off resonant, we don't hurt much (even if hurt little, we will come back to the offset in good time). By the process of monitoring, and setting phase we eventually push everything to the south pole and bingo, we have an inversion pulse. Feedback is done in simulation, but what results in end is a broadband inversion pulse. For broadband excitation, start with all offsets (symmetric around origin) on y axis. By feedback push them to the south pole. When we run the resulting sequence backward with phases, $\pi$ incremented, we will get an excitation pulse. For band-selective excitation pulse put offsets in pass band on the $y$ axis and in the stop band on the south pole. Use feedback to push everything to the south pole. Again, run backwards with $\pi$ incremented phases, to get band selective excitation. Suddenly, we have it all, simple and easy. The paper, introduces the feedback pulse algorithm, simulations and experiments.