The concept of resolution in the domain of rotations

The metric of the SO(3) group of rotations can be used to define the angular resolution of a function of rotations. The resolution is related to the degree of the highest representation present in the expansion of the function in terms of Wigner functions. The peculiar non-Euclidean metric of the rotation domain, however, implies that the terms which effectively contribute to the expansion vary through two-dimensional sections of the rotation domain and are within limiting resolution circles in two-dimensional reciprocal sections. This reconciles an economic sampling of the expansion with the acceleration provided by fast Fourier transform (FFT) techniques.