formalism is included only for completeness. We will, however, occasionally provide previews of how various parts of the framework are particularly helpful for intensity mapping and interferometry. In the spherical Fourier-Bessel basis, angular fluctuations are expressed by expanding the temperature field $T({\hat{\mathbf{r}}}, \nu)$ in spherical harmonics, such that $$\label{eq:SHTdef}
a_{\ell m} (\nu) \equiv \int d\Omega Y_{\ell m}^* ({\hat{\mathbf{r}}}) T({\hat{\mathbf{r}}}, \nu).$$ To capture modes along the line-of-sight, we perform a Fourier-Bessel transform along the frequency direction, yielding $$\label{eq:FBdef}
\overline{T}_{\ell m} (k) \equiv \sqrt{\frac{2}{\pi}} \int_0^\infty \! dr\, r^2 j_\ell (kr) a_{\ell m} (\nu_r),$$ with these last two expressions of course combining to give Eq. . The temperature field of the sky may therefore be thought of as being a linear combination of a set of basis functions $\psi_{\ell m } (k; {\hat{\mathbf{r}}}, \nu)$ that are indexed by $(k,\ell,m)$, so that $$\label{eq:InverseTrans}
T({\hat{\mathbf{r}}}, \nu) = \sum_{\ell m} \int dk\, \psi_{\ell m } (k; {\hat{\mathbf{r}}}, \nu) \overline{T}_{\ell m} (k),$$ where $$\label{eq:BasisFcts}
\psi_{\ell m } (k; {\hat{\mathbf{r}}}, \nu) \equiv k^2 \sqrt{\frac{2}{\pi}} j_\ell (kr_\nu) Y_{\ell m} ({\hat{\mathbf{r}}}).$$ Eqs. and are the forward transforms into the harmonic basis, while Eqs. and define the inverse transforms back into configuration space. This can be verified by substituting Eq. into 