ACE: Automated CTF Estimation

BackgroundThe transmission electron microscope is used to acquire structural information of macromolecular complexes. However, as any other imaging device, it introduces optical aberrations that must be corrected if high-resolution structural information is to be obtained. The set of all aberrations are usually modeled in Fourier space by the so-called Contrast Transfer Function (CTF). Before correcting for the CTF, we must first estimate it from the electron micrographs. This is usually done by estimating a number of parameters specifying a theoretical model of the CTF. This estimation is performed by minimizing some error measure between the theoretical Power Spectrum Density (PSD) and the experimentally observed PSD. The high noise present in the micrographs, the possible local minima of the error function for estimating the CTF parameters, and the cross-talking between CTF parameters may cause errors in the estimated CTF parameters.ResultsIn this paper, we explore the effect of these estimation errors on the theoretical CTF. For the CTF model proposed in [1] we show which are the most sensitive CTF parameters as well as the most sensitive background parameters. Moreover, we provide a methodology to reveal the internal structure of the CTF model (which parameters influence in which parameters) and to estimate the accuracy of each model parameter. Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.ConclusionWe show that the estimation errors for the CTF detection methodology proposed in [1] does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms. All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.

Automatic CTF correction for single particles based upon multivariate statistical analysis of individual power spectra

The Electron Microscopy eXchange (EMX) initiative.

Contrast transfer function (CTF) estimation is essential to the data processing workflow of cryo-electron tomography (cryoET). Here, we present a protocol for CTF estimation of the cryoET tilt series with CTFMeasure. CTFMeasure can estimate the CTF parameters together with the absolute tilt angle offset of the sample. We describe steps for configuring the input files and estimating the CTF parameters and the absolute tilt angle offset of the input tilt series. We then detail procedures for visualizing the power spectra and analyzing the output files. For complete details on the use and execution of this protocol, please refer to Zhang etal.1.

Recently, neuro-transfer function (neuro-TF) has become a recognized method for electromagnetic (EM) parametric modeling. The existing neuro-TF methods use the vector fitting technique to perform transfer function (TF) parameter extraction, commonly encountering nonsmoothness and discontinuity issues for the extracted TF parameters with respect to geometrical parameters. This letter proposes an advanced autoencoder TF parameter extraction technique for neuro-TF parametric modeling of microwave components. In the proposed technique, the autoencoder is introduced to extract a set of TF parameters as TF parameters from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$</tex-math> </inline-formula> -parameters with the encoder part and generate a decoder function as the TF in the original neuro-TF model. The TF parameters extracted using the proposed technique behave much smoother than the TF parameters extracted using traditional vector fitting. Meanwhile, the proposed technique avoids the discontinuity problem caused by vector fitting in the standard neuro-TF method. Parametric modeling using the smooth TF parameters can thus have higher accuracy than modeling with nonsmooth TF parameters. The proposed technique is demonstrated by two examples of EM parametric modeling of microwave components.

This paper demonstrates a convenient experimental tech- nique for measuring the resolution of a digital imaging system. The spa- tial frequency response of the system is obtained by deriving the modu- lation transfer function (MTF) from the measured contrast transfer function (CTF). Basic signal-processing techniques are used to establish a relationship between the MTF and the CTF. Experimental methodology is discussed with respect to avoidance of shift variation in the CTF. Dis- crete Fourier transformation is applied for a power-spectrum analysis of the MTF. Using the CTF as a measure of performance, a series of ex- periments were carried out to characterize an imaging system based on an integrated CMOS camera. The experimental results showed that this approach can be applied in general, for the assessment of spatial reso- lution for digital imaging systems. © 1998 Society of Photo-Optical Instrumenta- tion Engineers. (S0091-3286(98)00609-6)

Application of template matching technique to particle detection in electron micrographs

The cryo-EM structure of ETB-Gi complex, obtained using the Fusion-G system, provides insights into the distinct activation mechanism and G-protein promiscuity of ETB, aiding in the design of ETB agonists for therapeutic applications.

Image formation in phase-contrast electron microscopy is governed by the contrast transfer function (CTF). The key parameter to tune the CTF is the defocus. A precise and unbiased estimate of the defocus is essential to determine the forward model and interpret high resolution images in cryo-TEM. We present an algorithm based on the weak-phase approximation for determination of the defocus and astigmatism of the objective lens from recorded images of an amorphous sample. The algorithm identifies Thon rings in the power spectrum density (PSD) and uses them to estimate astigmatism and defocus together with their uncertainties. For the astigmatism estimation we use a transformation to polar coordinates to fit ellipses to the Thon rings. Averaging the PSD over these ellipses reduces CTF estimation to a 1D problem and enhances the signal-to-noise ratio.

Quantifying resolution limiting factors in subtomogram averaged cryo-electron tomography using simulations.

TomoAlign: A novel approach to correcting sample motion and 3D CTF in CryoET

Correction of axial chromatic aberration improves the contrast transfer in bright-field phase contrast imaging

Images taken by transmission electron microscopes are usually affected by lens aberrations and image defocus, among other factors. These distortions can be modeled in reciprocal space using the contrast transfer function (CTF). Accurate estimation and correction of the CTF is essential for restoring the high-resolution signal in cryogenic electron microscopy (cryoEM). Previously, we described the implementation of algorithms for this task in the cisTEM software package (Grant et al., 2018). Here we show that taking sample characteristics, such as thickness and tilt, into account can improve CTF estimation. This is particularly important when imaging cellular samples, where measurement of sample thickness and geometry derived from accurate modeling of the Thon ring pattern helps judging the quality of the sample. This improved CTF estimation has been implemented in CTFFIND5, a new version of the cisTEM program CTFFIND. We evaluated the accuracy of these estimates using images of tilted aquaporin crystals and eukaryotic cells thinned by focused ion beam milling. We estimate that with micrographs of sufficient quality CTFFIND5 can measure sample tilt with an accuracy of 3° and sample thickness with an accuracy of 5 nm.

In scalar diffraction theory, an optical instrument can be treated as a linear system for the two limiting cases of coherent and incoherent illumination of the object, these treatments being in terms of complex amplitude and intensity, respectively. But when the illumination of the object is partially coherent, the system is no longer linear in either of these quantities and a two-stage treatment involving both quantities has been customary. Wolf has indicated the advantages of formulating diffraction theory in terms of an observable correlation function, here called the ‘coherence’, rather than in quantities such as amplitude which are not observable at optical frequencies. A Fourier theory of diffraction is developed here based on the coherence between radiation at pairs of points. As in general the coherence across a plane is a function of four spatial co-ordinates, the Fourier transforms used are in four dimensions for monochromatic light and in five for light of a finite spectral bandwidth. This diffraction theory is linear for all optical systems with illumination of any degree of coherence and leads to the concept of a ‘coherence transfer function’ to describe the performance of the instrument. In special cases, this reduces to the well-known ‘contrast transfer function' for incoherent illumination and to the transfer factors used in Hopkins’s treatment of partially coherent illumination. The theory also gives the transfer properties and the compensations required for two-beam interferometers and shows how the wave-shearing interferometer serves as an instrument for measuring coherence.

Aberration measurement using the Ronchigram contrast transfer function