Defocus Accuracy for High-Resolution CryoEM

The accuracy of defocus determination is very important for high-resolution cryoEM reconstructions. Assuming the difference between the true defocus of a micrograph and the estimated defocus is $\mathrm{\Delta }z$ , the phase error $\mathrm{\Delta }\gamma (s)$ is calculated by Eq. (4): $\mathrm{\Delta }\gamma (s)=\pi \lambda \mathrm{\Delta }{\mathit{zs}}^2$
Derived from Eq. (4), the defocus-inaccuracy dependent phase error is proportional to frequency squared for a certain micrograph Eq. (5). $\frac{\mathrm{\Delta }\gamma (s_1)}{\mathrm{\Delta }\gamma (s_2)}=\frac{s_1^2}{s_2^2}$
Obviously from Eqs. (4), (5), an error in CTF determination, which can be ignored for a lower resolution reconstruction, might cause a critical error at high resolution. If the CTF is not properly determined, there are increasing phase errors against the frequency. The contrast of CTF is inverted for a 180 degree phase error. When this error is smaller than 90 degree, the probability to have the correct contrast of CTF is more than 50%. Gctf uses such a 90 degree criterion in order to guarantee at least half of information from the EM images after CTF correction. Based on this criterion, CTF phase error versus frequency for different defocus errors between 10 nm and 200 nm were plotted (Fig. 1a). The maximum allowed CTF defocus errors were plotted against frequency for three typical voltages used in cryoEM reconstruction s (Fig. 1b).
In practice, defocus inaccuracy is only one of the factors that cause CTF phase error. Magnification distortion, chromatic or comatic aberration (Glaeser et al., 2011 (link)), astigmatism inaccuracy, mechanical and beam induced movement of the samples, curvature or deformation of the carbon substrate (Shatsky et al., 2014 (link)), sample thickness (DeRosier, 2000 (link)) can all contribute to the phase error during an experiment. Data processing can also lead to large phase errors, especially at high frequency. Although Gctf uses this 90 degree criterion, it should be noted that the highest quality micrographs might need a stricter criterion in practice.