Fast and Exact Spin-s Spherical Harmonic Transforms

Understand

We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions.

• In contrast to previous work, where spin transforms are computed independently, our algorithm permits the computation of several distinct spin transforms simultaneously.
• Specifically, only one set of special functions is computed for transforms of quantities with any spin, namely the Wigner d-matrices evaluated at {\pi}/2, which may be computed with efficient recursions.
• For any spin the computation scales as O(L^3) where L is the band-limit of the function.