Rapid B1 mapping using orthogonal, equal-amplitude radio-frequency pulses.

We present a new phase-based method for mapping the amplitude of the radio-frequency field (B(1) ) of a transmitter coil in three-dimension. This method exploits the noncommutation relation between rotations about orthogonal axes. Our implementation of this principle in the current work results in a simple relation between the phase of the final magnetization and the flip angle (FA). In this study, we focus on FAs less than 90°. Our method is rapid and easy to implement compared with the existing B(1) mapping schemes. The mapping sequence can be simply obtained by adding to a regular three-dimensional gradient-echo sequence a magnetization preparation radio-frequency pulse of the same FA but orthogonal in phase to the excitation radio-frequency pulse. This method is demonstrated capable of generating reliable maps of the B(1) field within 1 min using FAs no larger than 60°. We show that it is robust against T(1), small chemical shift, and mild background inhomogeneity. This method may especially be suitable for B(1) mapping in situations (e.g., long-T(1) and hyperpolarized-gas imaging) where magnitude-based methods are not readily applicable. A noise calculation of the FA map using this method is also presented.