Series expansion for composite pulses in NMR

Abstract

A new finite-series representation of composite pulses is described for which the expansion parameter is the offset angle θ, cos θ = Δω/√ Δω 2 + ω 1 2, where Δω is the offset resonance and ω 1, is the radiofrequency amplitude in frequency units. Expressed in this way, it is shown that for phase-alternating pulse sequences for spin inversion, those that perform well over a range of offsets have small contributions from higher terms in the series. Optimization is performed by first truncating the series to obtain an initial fit and then successively including higher terms.