SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition
  The spherical Fourier-Bessel (SFB) decomposition is a natural choice for the
radial/angular separation that allows extraction of cosmological information
from large volume galaxy surveys, taking into account all wide-angle effects.
In this paper we develop a SFB power spectrum estimator that allows the
measurement of the largest angular and radial modes with the next generation of
galaxy surveys. The code measures the pseudo-SFB power spectrum, and takes into
account mask, selection function, pixel window, and shot noise. We show that
the local average effect (or integral constraint) is significant only in the
largest-scale mode, and we provide an analytical covariance matrix. By imposing
boundary conditions at the minimum and maximum radius encompassing the survey
volume, the estimator does not suffer from the numerical instabilities that
have proven challenging for SFB analyses in the past. The estimator is
demonstrated on simplified but realistic Roman-like, SPHEREx-like, and
Euclid-like mask and selection functions. For intuition and validation, we also
explore the SFB power spectrum in the Limber approximation. We release the
associated public code written in Julia.
