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The spherical Fourier-Bessel (SFB) decomposition is a natural choice for theradial/angular separation that allows extraction of cosmological informationfrom large volume galaxy surveys, taking into account all wide-angle effects.In this paper we develop a SFB power spectrum estimator that allows themeasurement of the largest angular and radial modes with the next generation ofgalaxy surveys. The code measures the pseudo-SFB power spectrum, and takes intoaccount mask, selection function, pixel window, and shot noise. We show thatthe local average effect (or integral constraint) is significant only in thelargest-scale mode, and we provide an analytical covariance matrix. By imposingboundary conditions at the minimum and maximum radius encompassing the surveyvolume, the estimator does not suffer from the numerical instabilities thathave proven challenging for SFB analyses in the past. The estimator isdemonstrated on simplified but realistic Roman-like, SPHEREx-like, andEuclid-like mask and selection functions. For intuition and validation, we alsoexplore the SFB power spectrum in the Limber approximation. We release theassociated public code written in Julia.

SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition