A review of resolution measures and related aspects in 3D Electron Microscopy.

Fourier Shell Correlation, Spectral Signal-to-Noise Ratio, Fourier Neighbour Correlation, and Differential Phase Residual are different measures that have been proposed over time to determine the spatial resolution achieved by a certain 3D reconstruction. Estimates of B-factors to describe the reduction in signal-to-noise ratio with increasing resolution is also a useful parameter. All these concepts are interrelated and different thresholds have been given for each one of them. However, the problem of resolution assessment in 3DEM is still far from settled and preferences are normally adopted in order to choose the "correct" threshold. In this paper we review the different concepts, their theoretical foundations and the derivation of their statistical distributions (the basis for establishing sensible thresholds). We provide theoretical justifications for some common practices in the field for which a formal justification was missing. We also analyze the relationship between SSNR and B-factors, the electron dose needed for achieving a given contrast and resolution, the number of images required, etc. Finally, we review the consequences for the number of particles needed to achieve a certain resolution and how to analyze the Signal-to-Noise Ratio for a sequence of imaging operations.