Aberration measurement using the Ronchigram contrast transfer function

Abstract: Contrast transfer function (CTF) is a vital function in transmission electron microscopy (TEM). It expresses to what extent amplitudes converted from the phase changes of the diffracted waves contribute to the TEM image, including the effects of lens aberrations. Simulation is very helpful to understand the application of the function thoroughly. In this work, we develop the CTFscope as a component in the Landyne software suite, to calculate the CTF with temporal and spatial dumping envelopes for conventional TEM and to extend it to various aberrations (up to fifth order) for aberration-corrected (AC)-TEM. It also includes effects on the CTF and imaging due to the objective aperture and image drift for tutorial purposes. The CTFscope has a user-friendly graphical interface for simulation, visualization, saving, and loading of the microscopy conditions and results. It can be used to explore instrumental performance information due to optical aberrations, effects on the resolution of a TEM and AC-TEM, and for teaching electron microscopy courses.

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.

IntroductionCurrently, the resolution of structural detail in conventional transmission electron microscopy (CTEM) of organic materials is limited by the electron beam damage suffered by the sample. It has recently been shown that the imaging modes now available in scanning transmission electron microscopy (STEM) provide the potential for improvements in resolution over CTEM methods. However, the effect of the sensitivity of an organic sample itself to beam damage has not been compared in STEM versus CTEM. In STEM each element of the sample area is briefly illuminated with a small diameter, high flux, scanning electron beam, whereas in CTEM the entire sample area is continuously illuminated with a large diameter, lower flux, static electron beam. Although it has been shown that the amount of sample damage in CTEM is independent of dose rate(2), the electron flux in STEM may range from 3 to 4 orders of magnitude greater than that in CTEM, with a possible influence on damage rate. Generally, the effects of beam size, high flux, and short dwell time of the scanning electron beam on sensitivity of the sample to damage in STEM are not known.

The energy filtered imaging technique has so far been carried out in a scanning transmission electron microscope (STEM) fitted with a sector type energy analyzer. The STEM has a disadvantage of low beam parallelity because it uses a convergent beam, while the conventional transmission electron microscope (CTEM) allows good phase contrast and diffraction contrast to be obtained because of the high parallelity of the beam, and allows also high resolution images to be obtained. The technique to obtain energy filtered CTEM images has thus far been carried out by a Castaing-Henry type filter or an Ω type filter. However, these filters have the disadvantage of lower energy resolution than conventional sector type energy analyzer at the present time. This paper reports energy filtered CTEM images of MgO smoke, obtained using a new scanning CTEM image technique and a high energy resolution sector type energy analyzer which can resolve bulk and surface plasmon energy.

The structure of hydrogen-induced platelets (HIPs) in silicon has been examined with conventional transmission electron microscopy (CTEM) and high-resolution transmission electron microscopy (HRTEM). Hrtem was utilized to clarify the atomic structure in which hydrogen atoms are assumed to saturate the broken bonds between adjacent (111) planes. The structural model was refined by introducing a reliability factor in real space for quantitative comparison between experimental and simulated images. Some contrast variations in HRTEM images can be well explained by allowing for atomic ledges on the (111) plane with broken bonds. Furthermore it is found from the strain contrast in a CTEM image that a considerable amount of H2 gas is contained in the open space of the HIP, which results in an internal pressure as large as 1 GPa. The formation process of Hips is discussed.

Single beam phase retrieval techniques [1-8] allow the reconstruction of the object phase information of a general volume speckle field for single beam devices such as optical microscopes. These techniques are well-suited for simple optical setups and recover the phase using the intensity recorded at a single or multiple planes. Deterministic Phase Retrieval techniques, as e.g. approaches based on the Transport of Intensity Equation [4-6] or the Contrast Transfer Function [7,8] allow recovering directly the phase of a wavefront, but are limited either to the paraxial case or impose restrictions on the phase to be estimated. Available Iterative Phase Retrieval (IPR) techniques as the Single-Beam-Multiple-Intensity-Reconstruction (SBMIR) algorithm [1-3] overcome this problem and are applicable to the non-paraxial case without imposing restrictions on the object to be investigated. However, this family of IPR techniques are subject to varying levels of performance or stagnate after few numbers of iterations. The stagnation is a result of the slow elimination of the remaining low frequency error components usually in form of a phase tilt, a bell-shaped error, or other low frequency artefacts. This problem results in a poor reconstruction for the case of slow-varying objects or the measurement of aberrations.

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)

Adult channel catfish were exposed to 0 or 15 ppm arsenic as sodium arsenate in synthetic lake water for approximately six months. After sacrifice, livers were removed and examined by conventional transmission electron microscopy, optical microscopy, scanning electron microscopy, and electron probe X-ray microanalysis. Cytoplasmic structures in the nuclei were found to contain highly concentrated deposits of iron. Thirty percent of these structures were also found to contain arsenic at a level above the minimum detectable level for the conditions of the study. The size, shape and relative position of the cytoplasmic structures were the same as the hemosiderin granules observed by conventional transmission electron microscopy. (JMT)

The effects of parenteral injection of aluminum, indium, gadolinium, or terbium in rats have been previously studied in several organs such as the liver, the kidneys, etc., but never in mammary glands. In this work, we have attempted to study the subcellular localization of these elements after their intraperitoneal administration. Their subsequent effects in the lactating mammary gland cells have also been studied. Our results using conventional transmission electron microscopy have shown that the lysosomes of the mammary glandular epithelial cells are the intracellular site of accumulation of the studied elements. Our results have also show intracellular deteriorations such as an expanded ergastoplasm and altered mitochondria after intraperitoneal injection of aluminum and indium.

It is well known that the combination of a field emission gun (FEG) and a conventional transmission electron microscope (CTEM) is extremely important for nanometer area analysis in analytical electron microscopy. However, the smaller illumination angle and reduced energy spread of FEG than those of a conventional electron gun (W hair pin filament or LaB6) give a slowly damping envelop function in phase contrast transfer function (PCTF). Thus the FEG ensures application not only to analytical microscopy but also to high resolution electron microscopy to improve the information limit.In a high voltage electron microscope (above 200 kV), high-speed vacuum pumps have to be provided below the acceleration tube to get an ultra high vacuum (UHV) around the field emission tip located at the top of the acceleration tube. However, this method is not always the best way to provide UHV because of the poor vacuum conductance caused by the electrodes inside the acceleration tube.

The aerial image contrast is a key parameter for the evaluation of the performance of optical projection systems. State-of-the-art deep ultraviolet steppers and some i-line steppers were investigated for comparison by measuring the contrast transfer function, i.e., contrast versus linewidth. Examples are shown how specific weaknesses of an imaging system like astigmatism and sensitivity from internal reflections can be quantified with this technique. For comparison the contrast transfer functions were also calculated, assuming ideal, purely diffraction limited image transfer of the optics, and with the numerical aperture and partial coherence as parameters. Interestingly none of the steppers meet the imaging performance which can be expected from theory.

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

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

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.