Optimal control design of constant amplitude phase-modulated pulses: Application to calibration-free broadband excitation

An optimal control algorithm for generating purely phase-modulated pulses is derived. The methodology is applied to obtain broadband excitation with unprecedented tolerance to RF inhomogeneity. Design criteria were transformation of I_z → I_x over resonance offsets of ±25 kHz for constant RF amplitude anywhere in the range 10-20 kHz, with a pulse length of 1 ms. Simulations transform I_z to greater than 0.99 I_x over the targetted ranges of resonance offset and RF variability. Phase deviations in the final magnetization are less than 2-3° over almost the entire range, with sporadic deviations of 6-9° at a few offsets for the lowest RF (10 kHz) in the optimized range. Experimental performance of the new pulse is in excellent agreement with the simulations, and the robustness of the excitation pulse and a derived refocusing pulse are demonstrated by insertion into conventional HSQC and HMBC-type experiments.