LAUSR

The simultaneous use of linear spatial encoding magnetic fields (L‐SEMs) and nonlinear spatial encoding magnetic fields (N‐SEMs) in B1+ inhomogeneity problems is formulated and demonstrated with both simulations and experiments. Independent excitation k‐space variables for N‐SEMs are formulated for the simultaneous use of L‐SEMs and N‐SEMs by assuming a small tip angle. The formulation shows that, when N‐SEMs are considered as an independent excitation k‐space variable, numerous different k‐space trajectories and frequency weightings differing in dimension, length, and energy can be designed for a given target transverse magnetization distribution. The advantage of simultaneous use of L‐SEMs and N‐SEMs is demonstrated by B1+ inhomogeneity correction with spoke excitation. To fully utilize the independent k‐space formulations, global optimizations are performed for 1D, 2D RF power limited, and 2D RF power unlimited simulations and experiments. Three different cases are compared: L‐SEMs alone, N‐SEMs alone, and both used simultaneously. In all cases, the simultaneous use of L‐SEMs and N‐SEMs leads to a decreased standard deviation in the ROI compared with using only L‐SEMs or N‐SEMs. The simultaneous use of L‐SEMs and N‐SEMs results in better B1+ inhomogeneity correction than using only L‐SEMs or N‐SEMs due to the increased number of degrees of freedom.