Uniform and selective excitations of spin ensembles with rf inhomogeneity

Engineering uniform and selective excitations for an ensemble of nuclear spins is an essential step in many applications of nuclear magnetic resonance (NMR), quantum optics, and quantum computation. For example, the application of robust spatially selective radio-frequency (rf) pulses enables precise imaging of a particular region of interest in the human brain. However, inhomogeneity in the applied rf fields, referred as rf inhomogeneity, results in imperfect excitations of spin ensembles, which compromise the fidelity of NMR spectra and the resolution of MR images. In this paper, we develop a control-theoretic method to construct uniform and selective pulses in the presence of rf inhomogeneity based on the technique of small angle approximation and non-harmonic Fourier series. Moreover, projection and constrained optimization techniques are employed to tailor pulses that satisfy practical design criteria.