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.