Tailoring the optimal control cost function to a desired output: application to minimizing phase errors in short broadband excitation pulses

The de facto standard cost function has been used heretofore to characterize the performance of pulses designed using optimal control theory. The freedom to choose new, creative quality factors designed for specific purposes is demonstrated. While the methodology has more general applicability, its utility is illustrated by comparison to a consistently chosen example-broadband excitation. The resulting pulses are limited to the same maximum RF amplitude used previously and tolerate the same variation in RF homogeneity deemed relevant for standard high-resolution NMR probes. Design criteria are unchanged: transformation of Iz → Ix over resonance offsets of ±20 kHz and RF variability of ±5%, with a peak RF amplitude equal to 17.5 kHz. However, the new cost effectively trades a small increase in residual z magnetization for improved phase in the transverse plane. Compared to previous broadband excitation by optimized pulses (BEBOP), significantly shorter pulses are achievable, with only marginally reduced performance. Simulations transform Iz to greater than 0.98 Ix, with phase deviations of the final magnetization less than 2°, over the targeted ranges of resonance offset and RF variability. Experimental performance is in excellent agreement with the simulations.