linearized approximation for the radial distance, we will often (though not always) also make the small angle approximation for converting between the angle $\boldsymbol \theta$ and the transverse comoving position $\mathbf{r}_\perp$ from some reference direction, where $$\label{eq:AngularConversion}
\mathbf{r}_\perp = r \boldsymbol \theta.$$

Given the well-defined prescriptions for converting between instrument-centric parameters (such as frequency $\nu$ and direction on the sky ${\hat{\mathbf{r}}}$) and cosmology-centric ones (such as $r$ and $\mathbf{r}_\perp$), we will often use both sets of parameters to describe the same quantities. For example, we will sometimes write the brightness temperature field as $T({\hat{\mathbf{r}}}, \nu)$, whereas other times we will write the same quantity as $T(\mathbf{r})$, where $\mathbf{r}$ is the comoving position. We will additionally find it useful to exhibit similar flexibility in our notation even for quantities that are not cosmological in nature, such as the primary beam of a radio telescope.

Spherical Fourier-Bessel Formalism {#sec:SphericalPspecFormalism}
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In this section we introduce the mathematical framework for describing the sky in terms of the spherical harmonic power spectrum. Our treatment here is essentially identical to that of @yoo_desjacques2013, albeit with different Fourier-Bessel transform conventions. No claims of originality are made in this section (except perhaps for Section \[sec:RotationalInvarianceOnly\]), and the 