CTFFIND4: Fast and accurate defocus estimation from electron micrographs

Abstract

CTFFIND is a widely-used program for the estimation of objective lens defocus parameters from transmission electron micrographs. Defocus parameters are estimated by fitting a model of the microscope's contrast transfer function (CTF) to an image's amplitude spectrum. Here we describe modifications to the algorithm which make it significantly faster and more suitable for use with images collected using modern technologies such as dose fractionation and phase plates. We show that this new version preserves the accuracy of the original algorithm while allowing for higher throughput. We also describe a measure of the quality of the fit as a function of spatial frequency and suggest this can be used to define the highest resolution at which CTF oscillations were successfully modeled.

Keywords: Astigmatism; CTF; Defocus; Phase plate.

Figure 1:

Two defocus values, $\mathrm{\Delta }{f}_1$ and $\mathrm{\Delta }{f}_2$, and an angle, α_ast define an astigmatic CTF. The effective defocus at an arbitrary point g (scattering vector) in reciprocal space is defined by Equation 5. Adapted from Figure 3 of Mindell and Grigorieff (2003).

Figure 2:

Diagnostic image from micrograph #1 of set #7 of the CTF challenge, output by CTFFIND4 using runtime parameters detailed in Table 3. The 2-dimensional CTF (CTF_fit) is overlayed onto the preprocessed amplitude spectrum (A_d) up to the radius corresponding to g_max.

Figure 3:

Image E generated from the CTF fit to micrograph #1 of set #7 of the CTF challenge. At every pixel (corresponding to a spatial frequency vector g), this image records n, the number of preceding CTF extrema (Equation 11). Here this value is color-coded, so that pixels at spatial frequencies before the first extremum of the CTF, which have value 0, are displayed in dark blue. Pixels that have 35 or more preceding CTF extrema are shown in dark red.

Figure 4:

Output diagnostic plots describing the experimental amplitudes (${\mathbf{\text{A}}}_{\mathbf{\text{d}}}^{\mathbf{1}\mathbf{\text{D}}}$, green), the fit CTF (${\left|{\mathbf{\text{CTF}}}_{\mathbf{\text{fit}}}\right|}^{\mathbf{1}\mathbf{\text{D}}}$, orange) and goodness of fit (CC_fit, blue) for micrograph #1 of set #7 of the CTF challenge. For this micrograph, the final estimates were $\mathrm{\Delta }{f}_1=29070$ Å, $\mathrm{\Delta }{f}_2=28313$Å and α_ast = 56.5°. The highest resolution at which Thon rings were deemed to be modeled correctly was 6.5 Å. The experimental amplitude profile (green) is normalized such that: the minima of the oscillations are set to 0.0; the second peak of the power spectrum (in this case at around 0.04) is 0.95; the maxima of oscillations are further normalized to 0.1 if their maxima would be <0.1 otherwise. Because of aliasing, one does not observe zeroes in ${\left|{\mathbf{\text{CTF}}}_{\mathbf{\text{fit}}}\right|}^{\mathbf{1}\mathbf{\text{D}}}$. One would normally solve this by increasing N_d, but we restricted ourselves to previously-used parameter values for this experiment (see caption to Table 3 for more details).