Dynamic focussing for recording images from tilted samples in small-spot scanning with a transmission electron microscope

For three-dimensional electron microscopical structure research the specimen must be imaged in a tilted position. Specimen tilt is also often needed to achieve an optimal molecular packing orientation. The tilt with respect to the optical axis causes a defocus gradient alongside the imaged area and thus entails the following complications: (1) The phase-contrast transfer function fades for strong defocus; (2) the Fourier coefficients are split; and (3) the signal-to-noise ratio cannot be enhanced by simple averaging. An image procedure with small-spot scanning and simultaneous defocus compensation is proposed which helps to reduce these problems.     

Automated high-throughput electron tomography by pre-calibration of image shifts

Electron tomography is a versatile method for obtaining three‐dimensional (3D) images with transmission electron microscopy. The technique is suitable to investigate cell organelles and tissue sections (100–500 nm thick) with 4–20 nm resolution. 3D reconstructions are obtained by processing a series of images acquired with the samples tilted over different angles. While tilting the sample, image shifts and defocus changes of several µm can occur. The current generation of automated acquisition software detects and corrects for these changes with a procedure that incorporates switching the electron optical magnification. We developed a novel method for data collection based on the measurement of shifts prior to data acquisition, which results in a five‐fold increase in speed, enabling the acquisition of 151 images in less than 20 min. The method will enhance the quality of a tilt series by minimizing the amount of required focus‐change compensation by aligning the optical axis to the tilt axis of the specimen stage. The alignment is achieved by invoking an amount of image shift as deduced from the mathematical model describing the effect of specimen tilt. As examples for application in biological and materials sciences 3D reconstructions of a mitochondrion and a zeolite crystal are presented.     

Correction of autofocusing errors due to specimen tilt for automated electron tomography

Transmission electron microscopy images acquired under tilted‐beam conditions experience an image shift as a function of defocus settings – a fact that is exploited as a method for defocus determination in most of the automated tomography data collection systems. Although the method was shown to be highly accurate for a large variety of specimens, we point out that in its original design it can strictly only be applied to images of untilted samples. The application to tilted samples and thus in automated electron tomography is impaired mainly due to a defocus change across the images, resulting in reduced accuracy. In this communication we present a method that can be used to improve the accuracy of the basic autofocusing procedures currently used in systems for automated electron tomography.     

An autofocus method for a TEM

Autofocus and correction of astigmatism of a transmission electron microscope (TEM) based on measuring a beam-tilt-induced image displacement is proposed and its theoretical limitations are studied. Tilting the illumination beam displaces the specimen image on screen when the TEM is out of focus. This displacement has a known relationship with the defocus. Autofocusing is possible by tilting the beam, measuring the image displacement, calculating the defocus and correcting it. Correction of astigmatism is possible by measuring the defocus in different directions. The method is fast because it calculates and corrects the defocus in one step. It works with many types of specimens because it utilizes both the amplitude and phase contrast of a bright field image. The precision of this method depends on the precision of the image displacement estimation. The shifted and unshifted images differ because of shot noise, instrumentation noise, and aberrations caused by the beam tilt. An expression is derived, containing parameters of the TEM and measuring system, for the achievable precision in estimating the displacement. This expression is a tool for optimizing the automatic focussing procedure and the measuring system. It does not depend on any particular estimation method with which the displacement is calculated. Computer simulations for a TEM equipped with a Vidicon videocamera have been carried out. They show that at Scherzer defocus (86 nm) the minimum measuring time required for focussing the TEM with a precision of 5 nm is about 50 ms. The precision is less satisfactory (>30 nm) when, with the same measuring time, the TEM is far out of focus or very near focus. The precision improves proportionally to the square root of the measuring time.     

The tuning of a Zernike phase plate with defocus and variable spherical aberration and its use in HRTEM imaging

With the advent of the double-hexapole aberration corrector in transmission electron microscopy the spherical aberration of the imaging system has become a tunable imaging parameter like the objective lens defocus. Now Zernike phase plates, altering the phase of the diffracted electron wave, can be approximated more perfectly than with the lens defocus alone, and the amount of phase change can be adjusted within wide limits. The tuning of the phase change allows an optimum contrast transfer in high-resolution imaging even for thick crystalline objects, thus surpassing the limits of the well-known Scherzer lamda/4 phase plate to the imaging of thin objects. The optimum values for the spherical aberration and the lens defocus are derived, and the limits and imperfections of the approximation explored. A mathematical link to the channelling approximation of high-energy electron diffraction shows how the image contrast of atomic columns can be improved systematically within wide thickness limits. Depending on the specimen thickness different combinations of spherical aberration and defocus are favourable: positive spherical aberration with an underfocus, zero spherical aberration with zero defocus, as well as negative spherical aberration with an overfocus.     

The contribution of phonon scattering to high-resolution images measured by off-axis electron holography

The contribution of electrons that have been phonon scattered to the lattice fringe amplitude and the background intensity of a high-resolution electron microscope (HREM) image is addressed experimentally through the analysis of a defocus series of energy-filtered off-axis electron holograms. It is shown that at a typical specimen thickness used for HREM imaging approximately 15% of the electrons that contribute to an energy-filtered image have been phonon scattered. At this specimen thickness, the phonon-scattered electrons contribute a lattice image of opposite contrast to the elastic lattice image. The overall lattice fringe contrast is then reduced to 70% of the value that it would have in the absence of phonon scattering. At higher specimen thickness, the behaviour is defocus-dependent, with the phonon image having lattice fringe contrast of either the same or the opposite sense to the elastic image as the defocus is varied.     

A novel method for focus assessment in atomic resolution STEM HAADF experiments

Analysis of the Fourier components of through-focal images in scanning transmission electron microscopy with a high angle annular dark field detector is used to assess illumination defocus values. The method is based on a least squares fitting of the peculiar dependence of Fourier components of the high angle annular dark field image on defocus. The validity of the method has been checked against simulations and experiments obtaining a good level of accuracy on the defocus measurement (δf=2 nm) for simulated specimen thickness up to 40 nm. The difference between simulated and experimental Fourier coefficients for large defoci can be used to estimate the specimen thickness at least up to 30 nm but with decreasing precision for larger thickness.     

Reconstruction from in-line electron holograms by digital processing

The digitized in-line electron holograms recorded in an HB-5 STEM instrument were reconstructed by computer processing in place of optical reconstruction. The important parameters of the holograms, namely the spherical aberration and defocus, can be obtained from the electron Ronchigrams. The reconstructed image shows some improvement in resolution as compared with the STEM bright field image. The main limitations appear to be mechanical vibration, drift of the specimen, the relatively small number of pixels in the images, and the uncertainties in determining the spherical aberration coefficient and defocus value.     

Correction of high-resolution data for curvature of the Ewald sphere

At sufficiently high resolution, which depends on the wavelength of the electrons, the thickness of the sample exceeds the depth of field of the microscope. At this resolution, pairs of beams scattered at symmetric angles about the incident beam are no longer related by Friedel's law; that is, the Fourier coefficients that describe their amplitudes and phases are no longer complex conjugates of each other. Under these conditions, the Fourier coefficients extracted from the image are linear combinations of independent (as opposed to Friedel related) Fourier coefficients corresponding to the three-dimensional (3-D) structure. In order to regenerate the 3-D scattering density, the Fourier coefficients corresponding to the structure have to be recovered from the Fourier coefficients of each image. The requirement for different views of the structure in order to collect a full 3-D data set remains. Computer simulations are used to determine at what resolution, voltage and specimen thickness the extracted coefficients differ significantly from the Fourier coefficients needed for the 3-D structure. This paper presents the theory that describes this situation. It reminds us that the problem can be treated by considering the curvature of the Ewald sphere or equivalently by considering that different layers within the structure are imaged with different amounts of defocus. The paper presents several methods to extract the Fourier coefficients needed for a 3-D reconstruction. The simplest of the methods is to take images with different amounts of defocus. For helical structures, however, only one image is needed.     

Improved Zernike‐type phase contrast for transmission electron microscopy

Zernike phase contrast has been recognized as a means of recording high‐resolution images with high contrast using a transmission electron microscope. This imaging mode can be used to image typical phase objects such as unstained biological molecules or cryosections of biological tissue. According to the original proposal discussed in Danev and Nagayama (2001) and references therein, the Zernike phase plate applies a phase shift of π/2 to all scattered electron beams outside a given scattering angle and an image is recorded at Gaussian focus or slight underfocus (below Scherzer defocus). Alternatively, a phase shift of ‐π/2 is applied to the central beam using the Boersch phase plate. The resulting image will have an almost perfect contrast transfer function (close to 1) from a given lowest spatial frequency up to a maximum resolution determined by the wave length, the amount of defocus and the spherical aberration of the microscope. In this paper, I present theory and simulations showing that this maximum spatial frequency can be increased considerably without loss of contrast by using a Zernike or Boersch phase plate that leads to a phase shift between scattered and unscattered electrons of only π /4, and recording images at Scherzer defocus. The maximum resolution can be improved even more by imaging at extended Scherzer defocus, though at the cost of contrast loss at lower spatial frequencies.     

On the accuracy of lattice-distortion analysis directly from high-resolution transmission electron micrographs

Lattice‐distortion analysis from high‐resolution transmission electron micrographs offers a convenient and fast tool for direct measurement of strains in materials over a large area. In the present work, we have evaluated the accuracy of the strain measurement when the effects of the realistic experimental variables are explicitly taken into account by the use of image simulation techniques. These variables are focal setting and variation, local thickness and orientation of the sample, as well as misalignments of the sample and the incident beam. The evaluation reveals that consistency of image features and contrast within the micrographs is desired for the analysis to eliminate effects of the variations of local focus value and specimen thickness. After proper orientation of a crystalline specimen, the misorientation of the object will not notably influence the strain measurement even though a local bending may exist within the sample. However, the incident beam of the microscope needs to be aligned carefully as the beam misalignment may introduce a notable artefact around the interface region.     

Defocus estimation from stroboscopic cryo-electron microscopy data

Defocus estimation is an important step for improving the resolution of single particle reconstructions. It can be troublesome to estimate the defocus from low-dose cryo-electron microscopy (cryo-EM) data, particularly if there is not sufficient contrast present in the Fourier transform of the micrograph. Most existing approaches estimate the defocus from the presence of Thon rings within the power spectrum, employing image enhancement techniques to highlight these rings. In this paper, an approach to estimating the defocus from a stroboscopic image series is described. The image series is used to obtain two statistical metrics: figure of merit (FOM) and Q-factor. These metrics have been used to estimate the defoci from low-dose stroboscopic cryo-EM data consisting of a variable number of images.     

A statistical approach for intensity loss compensation of confocal microscopy images

In this paper, a probabilistic technique for compensation of intensity loss in confocal microscopy images is presented. For single-colour-labelled specimen, confocal microscopy images are modelled as a mixture of two Gaussian probability distribution functions, one representing the background and another corresponding to the foreground. Images are segmented into foreground and background by applying Expectation Maximization algorithm to the mixture. Final intensity compensation is carried out by scaling and shifting the original intensities with the help of parameters estimated for the foreground. Since foreground is separated to calculate the compensation parameters, the method is effective even when image structure changes from frame to frame. As intensity decay function is not used, complexity associated with estimation of the intensity decay function parameters is eliminated. In addition, images can be compensated out of order, as only information from the reference image is required for the compensation of any image. These properties make our method an ideal tool for intensity compensation of confocal microscopy images that suffer intensity loss due to absorption/scattering of light as well as photobleaching and the image can change structure from optical/temporal section-to-section due to changes in the depth of specimen or due to a live specimen. The proposed method was tested with a number of confocal microscopy image stacks and results are presented to demonstrate the effectiveness of the method.     

A new method for the determination of the wave aberration function for high-resolution TEM.; 2. Measurement of the antisymmetric aberrations

A new method is presented for the determination of the antisymmetric coefficients of the wave aberration function from a tableau of tilted illumination images. The approach is based on measurements of the apparent defocus and two-fold astigmatism using a phase correlation function and phase contrast index calculated from a short focus series acquired at each tilt. This method is shown to be suitable for a wide range of specimens and is sufficiently accurate for exit plane wave restoration at 0.1 nm resolution. Experimental examples of this approach are provided and the method is compared to results obtained from measurements of conventional power spectra.     

High-angle annular dark-field imaging of self-assembled Ge islands on Si(0 0 1)

Low-resolution high-angle annular dark-field (HAADF) imaging is applied to the study of coherent Ge islands on a Si(0 0 1) substrate. Experimental HAADF images reveal a complicated pattern for a coherent Ge island under (0 0 1) zone axis conditions due to strain-induced interband scattering between different Bloch-wave branches. This complicated pattern varies with objective aperture size and defocus because of the effect from the depth of field. This suggests that the strain field of a coherent Ge island can be mapped out in 3 dimensions using HAADF imaging. When samples are tilted away from dynamical conditions, image contrast agrees with the predictions from atomic number variation (Z contrast). Therefore, quantitatively compositional analysis is feasible under kinematical imaging conditions when strain contrast is suppressed. Simulations using multi-beam Bloch-wave theory agree well with the experimental images on the complicated strain-induced and through-focus images.     

Effects of tilt on high-resolution ADF-STEM imaging

A study of the effects of small-angle specimen tilt on high-resolution annular dark field images was carried out for scanning transmission electron microscopes with uncorrected and aberration-corrected probes using multislice simulations. The results indicate that even in the cases of specimen tilts of the order of 1 degree a factor of 2 reduction in the contrast of the high-resolution image should be expected. The effect holds for different orientations of the crystal. Calculations also indicate that as the tilted specimen gets thicker the contrast reduction increases. Images simulated with a low-angle annular dark field detector show that tilt effects are more pronounced in this case and suggest that these low-angle detectors can be used to correct specimen tilt during scanning transmission electron microscopes operation.     

Automated microscopy for electron tomography.

Instrumentation and methodology for the automatic collection of tomographic tilt series data for the three-dimensional reconstruction of single particles is described. The system consists of a Philips EM 430 TEM, with a Gatan 673 cooled slow-scan CCD camera and a Philips C400 microscope computer control unit attached. The procedure for data collection includes direct digital recording of the images on the CCD camera and the automatic measurement and correction of (a) image shifts resulting from tilting the specimen, (b) variation of defocus and (c) the eucentric height position of the specimen. Experiments are described illustrating the possibilities and limitations of automatic data collection. Data collection at a magnification of 30k shows that the exposure time of the specimen to the beam is reduced by a factor of 10-100 compared to manual operation of the TEM.     

离焦模糊图像的维纳滤波复原研究

微操作中，显微视觉系统获取的图像通常是离焦模糊图像。离焦模糊图像的退化模型可用圆盘函数描述，利用模糊图像无方向性的二阶拉氏微分图像的自相关的负相关峰形成的环形槽的直径等于作为圆盘函数直径的2倍可以确定该函数。对模糊图像进行一次维纳滤波方法得到原图像的估计值，然后利用该初始值求得原图像及噪声的谱密度估值，进而利用这些新获得的信息构成改进的维纳滤波器对退化图像进行第二次滤波。实验表明，该方法计算量小、鉴别精度高、抗噪声能力较强，突出原图像的一些关键细节，提高了图像的复原质量。     

Spatial incoherence in phase retrieval based on focus variation

We investigate the effect of spatial incoherence on two methods of phase retrieval based on focus variation: the transport of intensity equation and iterative wave function reconstruction. Spatial incoherence provides an upper bound on the defocus step size which should be used in each case. The requirement that phase information manifests itself in sufficient variation in the defocused images provides a lower bound on the defocus step size which should be used in each case. The scaling of these upper and lower bounds with object size and imaging resolution differs in such a way that, given the spatial incoherence properties of the source, for sufficiently low resolutions neither technique can retrieve phase information. The regions of applicability of the two techniques are discussed.