Analytic derivation of optimal imaging conditions for incoherent imaging in aberration-corrected electron microscopes

The optimal lens parameters for incoherent imaging using third and fifth-order aberration-corrected electron microscopes are derived analytically. We propose simple models for the point spread function (PSF) and transfer function that give analytic formulae for the lateral resolution and depth resolution. We also derive an analytic formula for the contrast transfer function (CTF) in three dimensions and show that depth sectioning has an information limit equivalent to tomography with a missing cone of 90 degrees minus the aperture angle.     

Upper limits for the residual aberrations of a high-resolution aberration-corrected STEM

The development of correctors for electron optical systems has already brought the improvement of resolution for a low-voltage scanning electron microscope and a commercially available transmission electron microscope and is anticipated in the near future for a dedicated scanning transmission electron microscope (STEM). The resolution attainable especially of a probe-forming system at 200 kV cannot only be estimated from calculations ignoring all non-rotationally symmetric axial aberrations in an electron optical system. For a certain resolution, one would like to attain, the influence of the deviations from the ideal, aberration-free system has to be investigated. Therefore, in the following we have carried out the evaluation of the required accuracy for the compensation of the various residual aberrations in order to achieve a resolution in the sub-Angstrom regime with a probe-forming system.     

Higher-order aberration corrector for an image-forming system in a transmission electron microscope

We developed a new electron optical system with three dodecapoles to compensate for spherical aberration and six-fold astigmatism, which generally remains in a two-hexapole type corrector. In this study, we applied the corrector for image-forming system in transmission electron microscope. Compensation for higher-order aberration was demonstrated through a diffractogram tableau using a triple three-fold astigmatism field system, which was then compared with a double hexapole field system. Using this electron optical system, six-fold astigmatism was measured to be less than 0.1 mm at an acceleration voltage of 60 kV, showing that the system successfully compensated for six-fold astigmatism.     

Monte Carlo electron-trajectory simulations in bright-field and dark-field STEM: Implications for tomography of thick biological sections

A Monte Carlo electron-trajectory calculation has been implemented to assess the optimal detector configuration for scanning transmission electron microscopy (STEM) tomography of thick biological sections. By modeling specimens containing 2 and 3 at% osmium in a carbon matrix, it was found that for 1-μm-thick samples the bright-field (BF) and annular dark-field (ADF) signals give similar contrast and signal-to-noise ratio provided the ADF inner angle and BF outer angle are chosen optimally. Spatial resolution in STEM imaging of thick sections is compromised by multiple elastic scattering which results in a spread of scattering angles and thus a spread in lateral distances of the electrons leaving the bottom surface. However, the simulations reveal that a large fraction of these multiply scattered electrons are excluded from the BF detector, which results in higher spatial resolution in BF than in high-angle ADF images for objects situated towards the bottom of the sample. The calculations imply that STEM electron tomography of thick sections should be performed using a BF rather than an ADF detector. This advantage was verified by recording simultaneous BF and high-angle ADF STEM tomographic tilt series from a stained 600-nm-thick section of C. elegans. It was found that loss of spatial resolution occurred markedly at the bottom surface of the specimen in the ADF STEM but significantly less in the BF STEM tomographic reconstruction. Our results indicate that it might be feasible to use BF STEM tomography to determine the 3D structure of whole eukaryotic microorganisms prepared by freeze-substitution, embedding, and sectioning.     

Aberration‐corrected STEM for atomic‐resolution imaging and analysis

Aberration‐corrected scanning transmission electron microscopes are able to form electron beams smaller than 100 pm, which is about half the size of an average atom. Probing materials with such beams leads to atomic‐resolution images, electron energy loss and energy‐dispersive X‐ray spectra obtained from single atomic columns and even single atoms, and atomic‐resolution elemental maps. We review briefly how such electron beams came about, and show examples of applications. We also summarize recent developments that are propelling aberration‐corrected scanning transmission electron microscopes in new directions, such as complete control of geometric aberration up to fifth order, and ultra‐high‐energy resolution EELS that is allowing vibrational spectroscopy to be carried out in the electron microscope.     

Strategies for the compensation of specimen-induced spherical aberration in confocal microscopy of skin

We consider various strategies for confocal imaging of human skin which seek to reduce the effects of the specimen-induced aberrations. We calculate the spherical aberration introduced by the stratified structure of skin and show how the confocal signal is affected when attempting to image at various depths within the dermis. Using simple methods it is shown how images might be improved by compensating for the induced aberration. The methods include the use of an iris to reduce the pupil area, changing the refractive index of the immersion medium and using a lens with variable coverglass correction.     

Application of Delaunay tessellation for the characterization of solute-rich clusters in atom probe tomography

This work presents an original method for cluster selection in Atom Probe Tomography designed to be applied to large datasets. It is based on the calculation of the Delaunay tessellation generated by the distribution of atoms of a selected element. It requires a single input parameter from the user. Furthermore, no prior knowledge of the material is needed. The sensitivity of the proposed Delaunay cluster selection is demonstrated by its application on simulated APT datasets. A strong advantage of the proposed methodology is that it is reinforced by the availability of an analytical model for the distribution of Delaunay cells circumspheres, which is used to control the accuracy of the cluster selection procedure. Another advantage of the Delaunay cluster selection is the direct calculation of a sharp envelope for each identified cluster or precipitate, which leads to the more appropriate morphology of the objects as they are reconstructed in the APT dataset.     

Quantitative analysis of image contrast in phase contrast STEM for low dose imaging

This work quantitatively evaluates the contrast in phase contrast images of thin vermiculite crystals recorded by TEM and aberration-corrected bright-field STEM. Specimen movement induced by electron irradiation remains a major problem limiting the phase contrast in TEM images of radiation-sensitive specimens. While spot scanning improves the contrast, it does not eliminate the problem. One possibility is to utilise aberration-corrected scanning transmission electron microscopy (STEM) with an Ångstrom-sized probe to illuminate the sample, and thus further reduce irradiation-induced specimen movement. Vermiculite is relatively radiation insensitive in TEM to electron fluences below 100,000 e⁻/Ų and this is likely to be similar for STEM although different damage mechanisms could occur. We compare the performance of a TEM with a thermally assisted field emission electron gun (FEG) and charge coupled device (CCD) image capture to the performance of STEMs with spherical aberration correction, cold field emission electron sources and photomultiplier tube image capture at a range of electron fluences and similar illumination areas. We show that the absolute contrast of the phase contrast images obtained by aberration-corrected STEM is better than that obtained by TEM. Although the STEM contrast is higher, the efficiency of collection of electrons in bright field STEM is still much less than that in bright field TEM (where for thin samples virtually all the electrons contribute to the image), and the SNR of equivalent STEM images is three times lower. This is better than expected, probably due to the absence of a frequency dependent modulation transfer function in the STEM detection system. With optimisation of the STEM bright field collection angles, the efficiency may approach that of bright field TEM, and if reductions in beam-induced specimen movement are found, STEM could surpass the overall performance of TEM.     

Cryopreparation of mammalian tissue for X-ray microanalysis in STEM

A cryopreparation technique for studies of ultrastructure and distribution of diffusible elements in biological tissue is described. Electron microscopical contrast and characteristic X-ray spectra are found to be poor in completely frozen-hydrated ultrathin cryosections of fresh chemically untreated tissue. Both STEM contrast and detection of characteristic X-rays are enhanced by careful freeze-drying in the microscope. Although the ultrastructure is affected by ice crystals, intracellular compartments can be identified by STEM without staining and studied by X-ray microanalysis.     

Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry

Wavefront aberrations caused by the refractive index structure of the specimen are known to compromise signal intensity and three‐dimensional resolution in confocal and multiphoton microscopy. However, adaptive optics can measure and correct specimen‐induced aberrations. For the design of an adaptive optics system, information on the type and amount of the aberration is required. We have previously described an interferometric set‐up capable of measuring specimen‐induced aberrations and a method for the extraction of the Zernike mode content. In this paper we have modelled specimen‐induced aberrations caused by spherical and cylindrical objects using a ray tracing method. The Zernike mode content of the wavefronts was then extracted from the simulated wavefronts and compared with experimental results. Aberrations for a simple model of an oocyte cell consisting of two spherical regions and for a model of a well‐characterized optical fibre are calculated. This simple model gave Zernike mode data that are in good agreement with experimental results.     

Quantitative STEM mass measurement of biological macromolecules in a 300 kV TEM

For almost four decades, the scanning transmission electron microscope (STEM) has made significant contributions to structural biology by providing accurate determinations of the molecular masses of large protein assemblies that have arbitrary shapes and sizes. Nevertheless, STEM mass mapping has been implemented in very few laboratories, most of which have employed cold field‐emission gun (FEG) electron sources operating at acceleration voltages of 100 kV and lower. Here we show that a 300 kV commercial transmission electron microscope (TEM) equipped with a thermally assisted Shottky FEG can also provide accurate STEM mass measurements. Using the recently published database of elastic‐scattering cross sections from the National Institute of Standards and Technology, we show that the measured absolute mass values for tobacco mosaic virus and limpet hemocyanin didecamers agree with the known values to within better than 10%. Applying the established approach, whereby tobacco mosaic virus is added to a specimen as a calibration standard, we find that the measured molecular weight of the hemocyanin assemblies agrees with the known value to within 3%. This accuracy is achievable although only a very small fraction (∼0.002) of the incident probe current of 300 kV electrons is scattered onto the annular dark‐field STEM detector. FEG TEMs operating at intermediate voltages (200–400 kV) are becoming common tools for determining the structure of frozen hydrated protein assemblies. The ability to perform mass determination with the same instrument can provide important complementary information about the numbers of subunits comprising the protein assemblies whose structure is being studied.     

Studies of supported metal catalysts using high resolution secondary electron imaging in a STEM

An additional technique for use in the characterization of catalysts by electron microscopy is presented. High resolution secondary electron images obtained in a VG HB501 scanning transmission electron microscope have been used to study the surface topography of catalysts consisting of small metal particles on high surface area carbon supports. Surface features down to nanometre dimensions can be seen, allowing the examination of micropores in the support as well as larger pore structures. The results are compared with pore size distributions determined by gas adsorption methods, and are shown to yield valuable additional information. In addition, the method in principle allows examination of the locations of small metal catalyst particles on the support.     

KSpaceNavigator as a tool for computer-assisted sample tilting in high-resolution imaging, tomography and defect analysis

This article describes a novel software tool, the KSpaceNavigator, which combines sample stage and crystallographic coordinates in a control sphere. It also provides simulated kinematic diffraction spot patterns, Kikuchi line patterns and a unit cell view in real time, thus allowing intuitive and transparent navigation in reciprocal space. By the overlay of experimental data with the simulations and some interactive alignment algorithms, zone axis orientations of the sample can be accessed quickly and with great ease. The software can be configured to work with any double-tilt or tilt–rotation stage and overcomes nonlinearities in existing goniometers by lookup tables. A subroutine for matching the polyhedral shape of a nanoparticle assists with 3D analysis and modeling. The new possibilities are demonstrated with the case of a faceted BaTiO₃ nanoparticle, which is tilted into three low-index zone axes using the piezo-controlled TEAM stage, and with a multiply twinned tetrahedral Ge precipitate in Al, which is tilted into four equivalent zone axes using a conventional double-tilt stage. Applications to other experimental scenarios are also outlined.     

Manufacture and tests of objective zone plates for use in a scanning transmission X-ray microscope

A method of making high resolution zone plates for use as the focusing elements in soft X-ray microscopy is briefly described. Tests carried out on these zone plates indicate a first-order diffraction efficiency of ～0.3% rather than the calculated value of ～0.9%. This indicates that the zones are not positioned as accurately as expected, a conclusion also drawn from tests at optical wavelengths on electron micrographs of the zone plates. Modifications to the manufacturing method to enable zone plates with improved imaging properties to be made are described.     

Atom probe tomography investigation of assisted precipitation of secondary hardening carbides in a medium carbon martensitic steels

A medium carbon martensitic steel containing nanometer scale secondary hardening carbides and intermetallic particles is investigated by field ion microscopy and atom probe tomography. The interaction between the concomitant precipitations of both types of particles is investigated. It is shown that the presence of the intermetallic phase affects the nucleation mechanism and the spatial distribution of the secondary hardening carbides, which shifts from heterogeneous on dislocations to heterogeneous on the intermetallic particles.     

Optimisation of mass ranging for atom probe microanalysis and application to the corrosion processes in Zr alloys

Atom probe tomography uses time-of-flight mass spectrometry to identify the chemical nature of atoms from their mass-to-charge-state ratios. Within a mass spectrum, ranges are defined so as to attribute a chemical identity to each peak. The accuracy of atom probe microanalysis relies on the definition of these ranges. Here we propose and compare several automated ranging techniques, tested against simulated mass spectra. The performance of these metrics compare favourably with a trial of users asked to manually range a simplified simulated dataset. The optimised automated ranging procedure was then used to precisely evaluate the very low iron concentration (0.003-0.018 at%) in a zirconium alloy to reveal its behaviour in the matrix during corrosion; oxygen is injected into solution and has the effect of increasing the local iron concentration near the oxide-metal interface, which in turn affects the corrosion properties of the metal substrate.     

Simulation and experimental study of the sensor emitting frequency for ultrasonic tomography system in a conducting pipe

Ultrasonic tomography techniques provide flow visualization capability, non-invasively and non-intrusively, to enhance the understanding of complex flow processes. There is limited ultrasonic research in tomography imaging systems in the tomogram analysis of fluid flow in a conducting pipe because of a high acoustic impedance mismatch, which means that very little ultrasonic energy can be transmitted through the interface. The majority of industrial pipelines are constructed from metallic composites. Therefore, the development and improvement of ultrasonic measurement methods to accommodate a stainless steel pipe are proposed in this paper. Experimental and simulation distribution studies of the ultrasonic emitting frequency in acrylic versus stainless steel pipes were studied, measured and analyzed. During the simulation, ultrasonic transducers were placed on the surface of the investigated pipe to inspect the ultrasonic sensing field. The distribution of the sound wave acoustic pressure was simulated based on the physical dimensions and parameters of the actual experimental hardware set-up. We developed ultrasonic acoustic models using the finite element method with COMSOL software, and experiments were carried out to validate the simulation results. Finally, by performing the static phantoms tests, a feasibility study of ultrasonic tomography system was presented to investigate the void fraction of liquid column inside a stainless steel pipe.     

Acoustic beam position monitor for microanalysis of particles in the 10 nm range in a TEM-SCAN system

This paper describes the principle and use of a simple equipment which makes it possible to keep the electron beam in the centre of a small particle analysed by X-ray microanalysis in a STEM system. A deviation from the correct beam position introduced by drift or other deficiencies is monitored by an audible change in a sound frequency and corrected for by a convenient manual operation.     

Modification of a TEM-goniometer specimen holder to enable beam current measurements in a (S)TEM for use in quantitative X-ray microanalysis

In order to have available a specimen holder suited to measure the beam current as is often required in quantitative electron probe X-ray microanalysis, the rod of a low background beryllium specimen holder of a transmission electron microscope was modified. The tip was electrically insulated from the mass of the microscope and connected electrically to the central contact of a BNC connector mounted on the specimen holder handle. With this modified specimen holder the current absorbed by the specimen and/or the specimen holder could be measured easily and accurately. The modified specimen holder has been used to measure the beam current stability of an analytical electron microscope under various conditions. Data were obtained for tungsten as well as lanthanum hexaboride cathodes. Small changes to other types of specimen tips made it possible to exchange these for the low background tip.     

A simple method for checking the illumination profile in a laser scanning microscope and the dependence of resolution on this profile

One of the conditions for a laser scanning microscope to reach its optimal performance is for it to operate at its full numerical aperture (NA). In most commonly used systems, the illumination intensity at the back focal plane of the objective lens is apodized. This paper presents a simple method using a photodiode for checking the actual illumination intensity profile. We show as an example the measured profiles of a laser beam when working with two high-NA immersion objectives in two different confocal systems, and also show that in theoretical studies of the point-spread function, the assumption of a flat compared with a truncated Gaussian beam profile gives rise to severe discrepancies. The measured profiles also serve as an indication of the necessity of a realignment of the optical system.