New strategies for designing robust universal rotation pulses: application to broadband refocusing at low power

Optimizing pulse performance often requires a compromise between maximizing signal amplitude and minimizing spectral phase errors. We consider methods for the de novo design of universal rotation pulses, applied specifically but not limited to refocusing pulses. Broadband inversion pulses that rotate all magnetization components 180° 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° universal rotation pulses (180(UR)(°)) 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. Nearly ideal refocusing is possible over a resonance offset range of ± 170% relative to the nominal pulse B(1) field, concurrent with tolerance to B(1) inhomogeneity/miscalibration of ± 33%. We present new modifications of the optimal control algorithm that incorporate symmetry principles (S-BURBOP) 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 low-power 180(BURBOP)(°) pulses suitable for widespread use in (13)C spectroscopy on the majority of available probes. A quantitative measure for the reduced spectral phase error provided by these symmetry principles is also derived. For pulses designed according to this symmetry, refocusing phase errors are virtually eliminated upon application of EXORCYCLE or an equivalent G-180(S-BURBOP)(°)-G gradient sandwich, independent of resonance offset and RF inhomogeneity. The magnitude of the refocused component is not significantly compromised in achieving such ideal phase performance.