a double-walled shell with a slight reduction in density just inside the outer shell, consistent with other treatments of the data [@Kurta:2017; @Rose:2018].

\[sec:metrics\]Quantifying reconstruction quality
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A set of quantitative metrics are required in order to compare reconstructions and assess overall reconstruction quality, for reconstructions of both the full and diluted data sets. We used two metrics established in the literature, which we define in this section for clarity, and applied them to the reconstruction performed with the full data set described above.

\[sec:fsc\]“Gold-standard” cross correlations
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The first of these metrics, inspired by cryo-electron microscopy, involves a slight change in the analysis pipeline itself. The ‘gold-standard‘ Fourier shell correlation from CryoEM [@Henderson:2012] calls for the separation of the dataset into two equal halves. Each half is analyzed independently, the final volumes rotationally aligned, and the relative agreement is calculated as a function of resolution using the Fourier Shell Correlation (FSC) metric: $$\mathrm{FSC}(q) = \operatorname{Re}\left[\frac{\sum\limits_{|\mathbf{q}_i| = q} F_1(\mathbf{q}_i) F_2^*(\mathbf{q}_i)}
{\sqrt{\sum\limits_{|\mathbf{q}_i| = q} |F_1(\mathbf{q_i})|^2}\sqrt{\sum\limits_{|\mathbf{q}_i| = q} |F_2(\mathbf{q_i})|^2}}\right]$$ where $F(\mathbf{q}) = \mathcal{F}[\rho](\mathbf{q})$. In practice, the FSC is calculated in $q$ bins which are shells of a certain thickness.

A similar correlation can also be calculated between the two half-dataset intensities. In 