Multipole theory of composite pulses. II. Time-reversal and offset-alternating sequences with experimental confirmation

Abstract

In the multipole basis, a pure δ pulse has the effect of a rotation of the multipole polarizations with the rotations described by Wigner rotation matrices. By retaining the form of these Wigner rotation matrices, an exact analytical expression for a composite pulse, described by a product of rotations, is given with its explicit dependence to offset Δω RF amplitude ω 1 and phase φ. By the analysis of the symmetries of the tilt angle β and azimuthal angle α to these parameters, composite sequences in which off-resonance and phase-distortion effects are minimized can be developed. Experimental confirmation for up to six composite pulses is given.