A strategy for sampling on a sphere applied to 3D selective RF pulse design

Conventional constant angular velocity sampling of the surface of a sphere results in a higher sampling density near the two poles relative to the equatorial region. More samples, and hence longer sampling time, are required to achieve a given sampling density in the equatorial region when compared with uniform sampling. This paper presents a simple expression for a continuous sample path through a nearly uniform distribution of points on the surface of a sphere. Sampling of concentric spherical shells in k-space with the new strategy is used to design 3D selective inversion and spin-echo pulses. These new 3D selective pulses have been implemented and verified experimentally.