On the placement of latitudes in iso-latitude optimal-dimensionality sampling schemes on the sphere

Abstract

Optimal-dimensionality sampling schemes for band-limited signals (in spherical harmonic degree) on the sphere have been developed such that the number of samples equals the spectral degrees of freedom. These schemes use iso-latitude rings of samples for the computation of the Spherical Harmonic Transform (SHT) to high accuracy. However, the location of the iso-latitude rings had not been fully optimized to attain the highest possible numerical accuracy of the SHT computation. We study the effect of selecting the set of minimal dimensionality set of latitudes from much larger sets distributed according to different measures. In comparison to the other measures on the sphere used in the literature, we show that the placement of iso-latitude rings according to the uniform measure from the larger set allows the most accurate computation of the SHT in the class of (known) optimal-dimensionality sampling schemes. These claims are corroborated with numerical examples.