  We apply optimal control theory (OCT) to the design of refocusing pulses
suitable for the CPMG sequence that are robust over a wide range of B0 and B1
offsets. We also introduce a model, based on recent progress in the analysis of
unitary dynamics in the field of quantum information processing (QIP), that
describes the multiple refocusing dynamics of the CPMG sequence as a dephasing
Pauli channel. This model provides a compact characterization of the
consequences and severity of residual pulse errors. We illustrate the methods
by considering a specific example of designing and analyzing broadband OCT
refocusing pulses of length 10 t180 that are constrained by the maximum
instantaneous pulse power. We show that with this refocusing pulse, the CPMG
sequence can refocus over 98% of magnetization for resonance offsets up to 3.2
times the maximum RF amplitude, even in the presence of +/- 10% RF
inhomogeneity.
