Tilt estimation and correction in CTFFIND5. (a) Power spectra are calculated in 128×128 pixel patches as indicated on a representative micrograph. The dots represent the locations of the patches and the box indicates patch size. (b) A model of the expected power spectrum in each patch given an average defocus Δf, tilt angle θ, and tilt axis ϕ is compared to the actual power spectra of tiles. After an optimal set of θ and ϕ has been found a corrected power spectrum is calculated by summing the tile power spectra, scaled to correct for the defocus difference. Power spectra shown are an exaggerated example. The convention of ϕ as a counterclockwise rotation from the x-axis is indicated. (c) Comparison of the original power spectrum (EPA, solid line, blue) to the tilt-corrected power spectrum (solid line, black). The tilt-corrected power spectrum exhibits clear peaks at higher spatial resolution than the uncorrected power spectrum, as evident by the “goodness-of-fit” scores (dashed lines). The estimated CTF parameters are Δf1 = 10603 A, Δf2 = 10193 A, α = 85.9° for the uncorrected power spectrum and Δf1 = 10492 A, Δf2 = 10342 A, α = 81.2°, θ = 12.3°, ϕ = 261.6° for the tilt-corrected power spectrum. The fit resolution is 5.9 Å for the uncorrected power spectrum (dashed line, blue) and 4.6 Å for the tilt-corrected spectrum (dashed line, black).

Validation of tilt estimation using tilt series data and comparison of defocus estimation using CTFFIND4 and CTFFIND5. (a) Estimated tilt angle and axis of 40 micrographs of a tilt series taken on a FIB-milled biological specimen. For each image the tilt angle (dots, top plot) and tilt axis direction (crosses, second plot) are plotted as a function of the nominal stage angle. The data were fitted to a model of the specimen tilt and constant stage tilt axis before tilting the stage (red dashed line in first and second plot). The estimated stage tilt axis has an angle of 178.2° and the estimated specimen pre-tilt is 20.6° with a tilt axis of 171.8°, which is consistent with the FIB-milling angle of 20° and manual alignment of the milling direction to the goniometer tilt axis. The third plot shows the fit residuals for tilt angle and axis are plotted. The fourth and fifth plot show a plot of the estimated defocus value and fit resolution for each tilt image, as derived from CTFFIND4 (red) or CTFFIND5 (black. (b) Data for another tilt series plotted as described for (a). The estimated stage tilt axis is 179.8°, the estimated specimen pre-tilt is -21.9° with a tilt axis of 183.8°. This is consistent with this grid being inserted in the opposite orientation as the grid shown in (a), but still with a rough alignment of milling direction and tilt axis.

Sample thickness estimation by fitting Thon ring patterns. (a) Comparison of the CTF model used in CTFFIND4, and after applying the modulation function (right) described by (McMullan et al., 2015). A star symbol (*) denotes the position of the first zero in the CTF and a pound symbol (#) denotes the position of the first node. (b-d) Representative examples of Thon ring fitting in micrographs without (top-left graph) and with (bottom-leftgraph) thickness estimation. The micrograph is shown to the right. Each graph shows that EPA of the power spectrum in solid black lines, the fitted CTF model in dashed red lines, and the goodness of fit indicator as a dotted blue lines. (b) Thon ring fitting of a micrograph taken from a FIB-milling derived lamella. The tilt of the specimen was estimated to be 12.3°. When fitting without thickness estimation the estimated parameters were Δf1 = 10492 A, Δf2 = 10342 A, α = 81.2°. When taking sample thickness into account the estimated parameters were Δf1 = 10481 A, Δf2 = 10286 A, α = 69.6°, t = 969 A. The estimated fit resolution was 4.6 A and 3.4 A without and with sample thickness estimation, respectively. (c) Thon ring fitting of a micrograph taken from a FIB-milling derived lamella. The tilt of the specimen was estimated to be 6.7°. When fitting without thickness estimation the estimated parameters were Δf1 = 8002 A, Δf2 = 7717 A, α = 73.4°. When taking sample thickness into account the estimated parameters were Δf1 = 8549 A, Δf2 = 8343 A, α = 63.3°, t = 2017 A. The estimated fit resolution was 4.3 A and 4.2 A without and with sample thickness estimation, respectively. (d) Thon ring fitting of a micrograph taken from plunge frozen rotavirus double-layered particles (Grant and Grigorieff, 2015). When fitting without thickness estimation the estimated parameters were Δf1 = 7027 A, Δf2 = 6808 A, α = −20.3°. When taking sample thickness into account the estimated parameters were Δf1 = 7027 A, Δf2 = 6808 A, α = −22.9°, t = 850 A. The estimated fit resolution was 4.2 A and 3.2 A without and with sample thickness estimation, respectively.

Validation of sample thickness estimation in CTFFIND5 by comparing the estimates to the intensity attenuation by the zero-loss energy filter. An estimation of the linear relationship using the RANSAC algorithm results in a slope of 1/316.6 nm and an x-axis intercept at -14 nm (red dashed line). Data points that were labeled as outliers by the RANSAC algorithm were manually inspected and color-coded according to visual inspection of the micrographs.

Validation of sample thickness estimation in CTFFIND5 by tomography. The distribution of thickness measurements in seven tomograms are shown as box plots with the median indicated by a red line. The position on the x-axis corresponds to the thickness estimate by CTFFIND5. The black dashed line indicates identity. The red dashed line indicates the result of a linear fit.

CTF correction of medium magnification overviews. (a) Representative area of a micrograph of a cellular sample at a pixel size of 40 Å without CTF correction. (b) Fit of the power spectrum of the micrograph shown in panel a CTF model. (c-d) The same micrograph as shown in panel (a) after CTF correction by phase flipping (c) or with a Wiener-like filter (d). The custom fall-off parameter was set to 1.3 and the custom strength parameter was set to 0.7.

Comparison of CTFFIND5 estimation of sample tilt with crystallographic analysis

Runtime of CTFFIND5 on representative micrographs