Eq. , and using orthonormality of spherical harmonics, as well as the analogous identity for spherical Bessel functions, given by $$\label{eq:BesselOrthog}
\int \! dr \,r^2 j_\ell (k r) j_\ell (k^\prime r) = \frac{\pi}{2 k k^\prime} \delta^D (k - k^\prime),$$ where $\delta^D$ is the Dirac delta function. Note that our convention for the radial transform differs from that of most works in the literature. From Eqs. and , one sees that our convention is symmetric in the following sense. Whether one is switching from $r$-space to $k$-space or vice versa, the prescription is always to multiply by $\sqrt{2 / \pi} j_\ell (kr)$ and the square of the coordinate (i.e., $r^2$ or $k^2$) of the original space before integrating over it. This makes our forward and backward transforms aesthetically and conveniently symmetric. Most previous works (e.g., @leistedt_et_al2012 [@rassat_refregier2012; @yoo_desjacques2013]), in contrast, opt for an asymmetric convention: an extra factor of $k$ is included in the forward transform from $r$ to $k$, and correspondingly there is one fewer factor of $k$ in the backwards transform.

Translationally invariant fields in the spherical Fourier-Bessel formalism {#eq:TransInvarFields}
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In some sense, the decision to expand fluctuation modes along the line of sight in terms of spherical 