Correction of the contrast transfer function (CTF) of the microscope is a necessary step, in order to achieve high resolution from averaged electron microscopic images. Thereby, the CTF is first estimated and subsequently the electron micrograph is corrected, so that the negative oscillations of the CTF are equalized. Typically, the CTF correction is performed in 2D and the tilt-induced focus gradient is taken into account. Most often, the sample-thickness-induced focus gradient is ignored. Theoretical considerations, as well as implementation suggestions, for a 3D CTF correction that considers both gradients have been proposed before, although an implementation achieving a resolution improvement has been lacking, primarily due to computational reasons. Here, we present a comprehensive solution for a 3D CTF correction based on the Jensen-Kornberg scheme, which performs a slice-by-slice correction of the CTF within the tomographic reconstruction. We show that the computational requirements are comparable to those of 2D CTF correction. Using the examples of mitochondrial ribosomes and tobacco mosaic virus we demonstrate the improvement of the reconstruction quality with the 3D CTF correction, and the resolution gain on sub-tomogram averaging. More interestingly, for tomographic applications, the quality of the individual sub-tomograms before averaging increases significantly. We find that 3D CTF correction always produces equal or better results than 2D CTF correction.
Keywords: CTF correction; Electron tomography; Image processing.
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