constants of proportionality) will be defined in Section \[sec:SphericalPspecFormalism\]. Instead of the $k_\perp$-$k_\parallel$ plane, power spectrum measurements are now expressed on an $\ell$-$k$ plane. Now, we will show in Section \[sec:SphericalPspecFormalism\] that in the limit of a translationally invariant cosmological field, $S_\ell (k)$ reduces to $P(k)$. Therefore, just as $P(k_\perp, k_\parallel)$ can be averaged along contours of constant $k$ to form $P(k)$ once systematic effects are under control, the same can be done for $S_\ell (k)$ to form $P(k)$ by averaging over all values of $\ell$ for a particular $k$.

Spherical Fourier-Bessel methods have been explored in the past within the galaxy survey literature [@binney_quinn1991; @lahav_et_al1994; @fisher_et_al1994; @fisher_et_al1995; @heavens_taylor1995; @zaroubi_et_al1995; @castro_et_al2005; @leistedt_et_al2012; @rassat_refregier2012; @shapiro_et_al2012; @pratten_munshi2013; @yoo_desjacques2013]. In this paper, we build upon these methods and present a framework for implementing them in an analysis of intensity mapping data. We emphasize the way in which intensity mapping surveys have unique geometric properties, and how these properties affect spherical Fourier-Bessel methods. For instance, we pay special attention to the fact that particularly for the highest redshift observations, intensity mapping experiments probe survey volumes that are radially compressed but angularly expansive (as illustrated in Figure \[fig:surveyGeom\]). In harmonic space, this expectation is reversed, 