For the representation of spin-s band-limited functions on the sphere, we
propose a sampling scheme with optimal number of samples equal to the number of
degrees of freedom of the function in harmonic space. In comparison to the
existing sampling designs, which require ∼2L2 samples for the
representation of spin-s functions band-limited at L, the proposed scheme
requires No=L2−s2 samples for the accurate computation of the spin-s
spherical harmonic transform~(s-SHT). For the proposed sampling scheme, we
also develop a method to compute the s-SHT. We place the samples in our
design scheme such that the matrices involved in the computation of s-SHT are
well-conditioned. We also present a multi-pass s-SHT to improve the accuracy
of the transform. We also show the proposed sampling design exhibits superior
geometrical properties compared to existing equiangular and Gauss-Legendre
sampling schemes, and enables accurate computation of the s-SHT corroborated
through numerical experiments.Comment: 5 pages, 2 figure