Broadband 180 degree universal rotation pulses for NMR spectroscopy designed by optimal control

Broadband inversion pulses that rotate all magnetization components 180 degrees about a given fixed axis are necessary for refocusing and mixing in high-resolution NMR spectroscopy. The relative merits of various methodologies for generating pulses suitable for broadband refocusing are considered. The de novo design of 180 degree universal rotation pulses using optimal control can provide improved performance compared to schemes which construct refocusing pulses as composites of existing pulses. The advantages of broadband universal rotation by optimized pulses (BURBOP) are most evident for pulse design that includes tolerance to RF inhomogeneity or miscalibration. We present new modifications of the optimal control algorithm that incorporate symmetry principles and relax conservative limits on peak RF pulse amplitude for short time periods that pose no threat to the probe. We apply them to generate a set of pulses suitable for widespread use in Carbon-13 spectroscopy on the majority of available probes.

Design and application of robust rf pulses for toroid cavity NMR spectroscopy

We present robust radio frequency (rf) pulses that tolerate a factor of six inhomogeneity in the B1 field, significantly enhancing the potential of toroid cavity resonators for NMR spectroscopic applications. Both point-to-point (PP) and unitary rotation (UR) pulses were optimized for excitation, inversion, and refocusing using the gradient ascent pulse engineering (GRAPE) algorithm based on optimal control theory. In addition, the optimized parameterization (OP) algorithm applied to the adiabatic BIR-4 UR pulse scheme enabled ultra-short (50 microsec) pulses with acceptable performance compared to standard implementations. OP also discovered a new class of non-adiabatic pulse shapes with improved performance within the BIR-4 framework. However, none of the OP-BIR4 pulses are competitive with the more generally optimized UR pulses. The advantages of the new pulses are demonstrated in simulations and experiments. In particular, the DQF COSY result presented here represents the first implementation of 2D NMR spectroscopy using a toroid probe.