Unidirectional magnetic-field gradients and geometric-phase errors during Fourier encoding using orthogonal ac fields

Nuclear magnetic resonance and imaging in very low fields is fundamentally limited by untruncated concomitant gradients, which cause severe distortions in image acquisition and volume selection if the gradient fields are strong compared to the static field. In this paper, it is shown that gradient fields oscillating in quadrature can be used for spatial encoding in low fields and provide substantial improvements over conventional encoding methods using static gradients. In particular, cases where the maximum applied gradient field Bmax is comparable to or higher than the static field B0 over the field of view, i.e., Bmax /B0 1, are examined. With these gradients, undistorted volume selection and image encoding is possible because smaller geometric phase errors are introduced during cyclic motion of the Hamiltonian. In the low field limit, slice selection is achieved with a combination of soft pulse segments and a coherent train of hard pulses to average out concomitant fields over the fast scale of the Hamiltonian.