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Contrast transfer function
About: Contrast transfer function is a(n) research topic. Over the lifetime, 934 publication(s) have been published within this topic receiving 26533 citation(s).
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TL;DR: Modifications to the CTFFIND algorithm are described which make it significantly faster and more suitable for use with images collected using modern technologies such as dose fractionation and phase plates.
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.
2,228 citations
TL;DR: Two computer programs are presented, CTFFIND3 and CTFTILT, which determine defocus parameters from images of untilted specimens, as well as defocus and tilt parameters from image of tilted specimens, respectively, using a simple algorithm.
Abstract: Accurate knowledge of defocus and tilt parameters is essential for the determination of three-dimensional protein structures at high resolution using electron microscopy. We present two computer programs, CTFFIND3 and CTFTILT, which determine defocus parameters from images of untilted specimens, as well as defocus and tilt parameters from images of tilted specimens, respectively. Both programs use a simple algorithm that fits the amplitude modulations visible in a power spectrum with a calculated contrast transfer function (CTF). The background present in the power spectrum is calculated using a low-pass filter. The background is then subtracted from the original power spectrum, allowing the fitting of only the oscillatory component of the CTF. CTFTILT determines specimen tilt parameters by measuring the defocus at a series of locations on the image while constraining them to a single plane. We tested the algorithm on images of two-dimensional crystals by comparing the results with those obtained using crystallographic methods. The images also contained contrast from carbon support film that added to the visibility of the CTF oscillations. The tests suggest that the fitting procedure is able to determine the image defocus with an error of about 10nm, whereas tilt axis and tilt angle are determined with an error of about 2 degrees and 1 degrees, respectively. Further tests were performed on images of single protein particles embedded in ice that were recorded from untilted or slightly tilted specimens. The visibility of the CTF oscillations from these images was reduced due to the lack of a carbon support film. Nevertheless, the test results suggest that the fitting procedure is able to determine image defocus and tilt angle with errors of about 100 nm and 6 degrees, respectively.
1,412 citations
TL;DR: The resolving power of the electron microscope and the contrast in the image are calculated for different conditions of focusing, illumination and aperture as mentioned in this paper, which can change the limit of resolution by a factor of about 3.
Abstract: The resolving power of the electron microscope and the contrast in the image are calculated for different conditions of focusing, illumination and aperture. These conditions can change the limit of resolution by a factor of about 3. The contrast in the image of an atom is appreciably increased by defocusing and spherical aberration. Nevertheless, the contrast improves when the numerical value of the aberration constant is diminished. The effect of different methods of spherical correction is discussed briefly.
823 citations
IBM1
TL;DR: The implementation of a computer-controlled aberration correction system in a scanning transmission electron microscope, which is less sensitive to chromatic aberration, is reported here and allows dynamic imaging of single atoms, clusters of a few atoms, and single atomic layer ‘rafts' of atoms coexisting with Au islands on a carbon substrate.
Abstract: Following the invention of electron optics during the 1930s, lens aberrations have limited the achievable spatial resolution to about 50 times the wavelength of the imaging electrons. This situation is similar to that faced by Leeuwenhoek in the seventeenth century, whose work to improve the quality of glass lenses led directly to his discovery of the ubiquitous "animalcules" in canal water, the first hints of the cellular basis of life. The electron optical aberration problem was well understood from the start, but more than 60 years elapsed before a practical correction scheme for electron microscopy was demonstrated, and even then the remaining chromatic aberrations still limited the resolution. We report here the implementation of a computer-controlled aberration correction system in a scanning transmission electron microscope, which is less sensitive to chromatic aberration. Using this approach, we achieve an electron probe smaller than 1 A. This performance, about 20 times the electron wavelength at 120 keV energy, allows dynamic imaging of single atoms, clusters of a few atoms, and single atomic layer 'rafts' of atoms coexisting with Au islands on a carbon substrate. This technique should also allow atomic column imaging of semiconductors, for detection of single dopant atoms, using an electron beam with energy below the damage threshold for silicon.
786 citations
TL;DR: In this article, the strength of the very weak high-resolution Fourier components of the image of a two-dimensional crystal was determined using real space correlation analysis, and the amplitude and phase information was extracted from the distortion-corrected image of the crystal.
Abstract: Electron micrographs of the purple membrane have been recorded using liquid nitrogen and liquid helium cooling on three cryoelectron microscopes. The best micrographs show optical diffraction spots, arising from the two-dimensional crystal, out to resolutions of around 6 A. Large areas of several of these micrographs have been analysed using a procedure which determines the strength of the very weak high resolution Fourier components of the image of the crystal. The procedure consists of reciprocal space filtering followed by real space correlation analysis to characterise image distortions, removal of the distortions by interpolation, and finally extraction of the amplitudes and phases of the Fourier components from the distortion-corrected image of the crystal. These raw image amplitudes and phases are then used, together with previously measured amplitude and phase information, to refine the beam tilt and crystal tilt, phase origin and amount of defocus and astigmatism of the image. The phases can then be corrected for the effects of the contrast transfer function, beam tilt and phase origin. The amplitudes of all the spots which are expected to be strong from their known electron diffraction intensity are observed to be significantly above the background noise level, and the independent phases from different images, and from symmetry-related directions in the same image, show excellent agreement out to a resolution of 3.5 A. Although only images from untilted or slightly tilted (
687 citations