Construction of universal rotations from point-to-point transformations

For a desired range of offsets, universal rotations of arbitrary flip angle can be constructed based on point-to-point rotations of I_y with half the flip angle. This approach allows, for example, creation of broadband or bandselective refocussing pulses from broadband or bandselective excitation pulses. Furthermore, universal rotations about any axis can be obtained from point-to-point transformations that can easily be optimized using optimal control algorithms. The construction procedure is demonstrated on the examples of a broadband refocussing pulse, a broadband 120°x rotation and a z-rotation with offset pattern.