to be large enough for the PRTF to converge and the voxels with irreproducible phases to average down. Consider for example the case where the phases are completely random, in which case the sum is a 2D random walk in the complex plane with a fixed step size which has an average distance from the origin of $\sqrt{N}$ after $N$ steps. Thus, the expected lower bound on the PRTF if $N$ reconstructions are averaged is $1/\sqrt{N}$, which is 0.05 for the case of 400 the case here. In keeping with convention, the threshold value to determine the reproducible resolution is considered to be $1/e = 0.37$.

![Reconstruction metrics for the full data set as a function of $q$. Top: Fourier Shell Correlation (FSC) plot with the dashed line showing the half-bit threshold. Middle: Intensity CC$_{1/2}$ plot with the dashed line showing the 0.5 cutoff. Bottom: Phase Retrieval Transfer Function (PRTF) plot with the customary $1/e$ cutoff. Error bars represent the standard deviation across 10 random starts.[]{data-label="fig:full-metrics"}](metrics_full.pdf){width="\columnwidth"}

\[sec:full\_recon\]Metrics applied to full data reconstruction
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We applied the metrics defined above to the reconstructed intensity and electron density calculated using the procedure described in Sec. \[sec:recon\_steps\]. For the FSC and CC$_{1/2}$ calculations, 