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.     

Contrast in confocal scanning microscopy with a finite detector

The optical properties of a general scanning microscope are determined within the framework of Fourier imaging theory. For a simple model optical system, with Gaussian lens and detector apertures, the contrast transfer function can be expressed in terms of elementary functions. The theory predicts that spatial resolution and depth discrimination vary continuously with detector aperture and that defocus phase contrast is present in transmission images obtained with a symmetric objective, collector lens confocal microscope.     

The use of histograms for transmission electron microscopy: Defocus and astigmatism correction at high resolution

A real-time method for optimizing the defocus of a conventional transmission electron microscope in the phase contrast imaging mode has been investigated using image histogram data. This method can also be used to minimize the objective lens astigmatism. It will be shown both theoretically and empirically, using a digital television frame store, that a histogram will give the largest peak when an image has a broad and flat contrast transfer function. This method has distinct advantages of speed and minimal computational requirements over obtaining the power spectrum of an image.     

Bloch wave-based calculation of imaging properties of high-resolution scanning confocal electron microscopy

An efficient, Bloch wave-based method is presented for simulation of high-resolution scanning confocal electron microscopy (SCEM) images. The latter are predicted to have coherent nature, i.e. to exhibit atomic contrast reversals depending on the lens defocus settings and sample thickness. The optimal defocus settings are suggested and the 3D imaging capabilities of SCEM are analyzed in detail. In particular, by monitoring average image intensity as a function of the probe focus depth, it should be possible to accurately measure the depth of a heavy-atom layer embedded in a light-element matrix.     

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.     

Diffracted phase and amplitude measurements by energy-filtered convergent-beam holography (CHEF)

Interference between transmitted and diffracted disks in convergent-beam electron diffraction (CBED) patterns using the CBED+EBI method proposed by Herring et al. is explored using different optical configurations on a spherical aberration corrected transmission electron microscope equipped with a biprism and imaging energy filter: the SACTEM-Toulouse. We will relate the amplitude and phase of these interference patterns, which we call convergent-beam holography (CHEF), to microscope transfer theory and the complex amplitudes of the diffracted beams. Experimental CHEF patterns recorded in the absence of aberration correction will be compared with simulations to validate the theory concerning the effect of microscope aberrations and current instabilities. Then, using aberration correction, we propose a scheme for eliminating the effect of the microscope, so that the diffracted amplitudes and phase due to dynamical scattering within the specimen can be studied. Experimental results are compared with simulations performed using the full dynamical theory. The potential for studying diffracted amplitudes and phases using CHEF analysis is discussed.     

Three‐dimensional optical transfer functions in the aberration‐corrected scanning transmission electron microscope

In the scanning transmission electron microscope, hardware aberration correctors can now correct for the positive spherical aberration of round electron lenses. These correctors make use of nonround optics such as hexapoles or octupoles, leading to the limiting aberrations often being of a nonround type. Here we explore the effect of a number of potential limiting aberrations on the imaging performance of the scanning transmission electron microscope through their resulting optical transfer functions. In particular, the response of the optical transfer function to changes in defocus are examined, given that this is the final aberration to be tuned just before image acquisition. The resulting three‐dimensional optical transfer functions also allow an assessment of the performance of a system for focal‐series experiments or optical sectioning applications.     

Transmission electron microscopy with Zernike phase plate.

The possibility of implementing a Zernike phase plate in a transmission electron microscope is investigated both theoretically and experimentally. The phase-retarding plate in the form of thin film with a hole in the center is positioned in the back-focal plane of the objective lens. The experiments show that the phase plate functions as predicted, producing a cosine-type phase contrast transfer function. Images of negatively stained horse spleen ferritin were highly improved in the contrast and the image-modulation, compared to those acquired without the phase plate. Charging and related difficulties were encountered during the phase plate experiments. In order to make the technique user-friendly a number of improvements have to be made, and are discussed in terms of the current level of technology and instrumentation.     

Astigmatic intensity equation for electron microscopy based phase retrieval

Phase retrieval, in principle, can be performed in a transmission electron microscope (TEM) using arbitrary aberrations of electron waves; provided that the aberrations are well-characterised and known. For example, the transport of intensity equation (TIE) can be used to infer the phase from a through-focus series of images. In this work an "astigmatic intensity equation" (AIE) is considered, which relates phase gradients to intensity variations caused by TEM objective lens focus and astigmatism variations. Within the paraxial approximation, it is shown that an exact solution of the AIE for the phase can be obtained using efficient Fourier transform methods. Experimental requirements for using the AIE are the measurement of a through-focus derivative and another intensity derivative, which is taken with respect to objective lens astigmatism variation. Two quasi-experimental investigations are conducted to test the validity of the solution.     

Optimizing phase contrast in transmission electron microscopy with an electrostatic (Boersch) phase plate

Imaging of weak amplitude and phase objects, such as unstained vitrified biological samples, by conventional transmission electron microscopy (TEM) suffers from poor object contrast since the amplitude and phase of the scattered electron wave change only very little. In phase contrast light microscopy the imaging of weak phase objects is greatly enhanced by the use of a quarter-wave phase plate, which produces high signal contrast by shifting the phase of the scattered light. An analogous quarter-wave plate for the electron microscope, designed as an electrostatic einzel lens, was proposed by Boersch in 1947 but the small dimensions of the device have impeded its realization up to now. We here present the first fabrication and application of a miniaturized electrostatic einzel lens driven as TEM quarter-wave phase plate. Phase modulation is generated by the electrostatic field confined to the inside of a microstructured ring electrode. This field affects the phase velocity of the unscattered part of the electron wave. By varying its strength the phase shift of the primary beam can be adjusted to pi/2, producing strong phase contrast independent of spatial frequency. The phase plate proves to be mechanically stable and does not impair image quality, in particular it does not reduce the high-resolution signal. The expected residual lens effect of the einzel lens is minimal. Our microlens is supported by conducting rods arranged in a threefold symmetry. This particular geometry provides optimized single-sideband signal transfer for spatial frequencies otherwise obstructed by the supporting rods.     

Theoretical aspects of image formation in the aberration-corrected electron microscope

The theoretical aspects of image formation in the transmission electron microscope (TEM) are outlined and revisited in detail by taking into account the elastic and inelastic scattering. In particular, the connection between the exit wave and the scattering amplitude is formulated for non-isoplanatic conditions. Different imaging modes are investigated by utilizing the scattering amplitude and employing the generalized optical theorem. A novel obstruction-free anamorphotic phase shifter is proposed which enables one to shift the phase of the scattered wave by an arbitrary amount over a large range of spatial frequencies. In the optimum case, the phase of the scattered wave and the introduced phase shift add up to −π/2 giving negative contrast. We obtain these optimum imaging conditions by employing an aberration-corrected electron microscope operating at voltages below the knock-on threshold for atom displacement and by shifting optimally the phase of the scattered electron wave. The optimum phase shift is achieved by adjusting appropriately the constant phase shift of the phase plate and the phase shift resulting from the defocus and the spherical aberration of the corrected objective lens. The realization of this imaging mode is the aim of the SALVE project (Sub-Å Low-Voltage Electron microscope).     

Prerequisites for a Cc/Cs-corrected ultrahigh-resolution TEM

After the introduction of a corrector to compensate for the spherical aberration of a TEM and the acceptance of this new instrumentation for high-resolution CTEM (conventional transmission electron microscope) and STEM (scanning transmission electron microscope) by the electron microscopy community, a demand for even higher resolution far below 1A has emerged. As a consequence several projects around the world have been launched to make these new instruments available and to further push the resolution limits down toward fractions of 1A. For this purpose the so-called TEAM (transmission electron aberration-corrected microscope) has been initiated and is currently under development. With the present paper we give a detailed assessment of the stability required for the base instrument and the electric stability, the manufacturing precision, and feasible semi-automatic alignment procedures for a novel C(c)/C(s)-corrector in order to achieve aberration-free imaging with an information limit of 0.5A at an acceleration voltage of 200 kV according to the goals for the first TEAM instrument. This new aberration corrector, a so-called Achroplanat, in combination with a very stable high-resolution TEM leads to an imaging device with unprecedented resolving power and imaging properties.     

Aberration-corrected microscopy for structural biology applications

This study explores the potential of a C _s-corrected transmission electron microscope for structural studies of biological samples, in particular isolated macromolecular complexes. A 300-kV transmission electron microscope, equipped with a C _s corrector was employed to record sets of images at different defocus and C _s settings. The experiments were designed to determine whether imaging with large defocus benefits from C _s correction. Defocus contrast in biological imaging has a stronger influence on image resolution than any other parameter. We find the results are in good agreement with theoretical framework, verifying that the typical imaging conditions required for biological investigations are not affected by C _s correction.     

Optimal strategies for imaging thick biological specimens: exit wavefront reconstruction and energy-filtered imaging

In transmission electron microscopy (TEM) of thick biological specimens, the relationship between the recorded image intensities and the projected specimen mass density is distorted by incoherent electron–specimen interactions and aberrations of the objective lens. It is highly desirable to develop a strategy for maximizing and extracting the coherent image component, thereby allowing the projected specimen mass density to be directly related to image intensities. For this purpose, we previously used exit wavefront reconstruction to understand the nature of image formation for thick biological specimens in conventional TEM. Because electron energy-loss filtered imaging allows the contributions of inelastically scattered electrons to be removed, it is potentially advantageous for imaging thick, biological samples. In this paper, exit wavefront reconstruction is used to quantitatively analyse the imaging properties of an energy-filtered microscope and to assess its utility for thick-section microscopy. We found that for imaging thick biological specimens (> 0.5 μm) at 200 keV, only elastically scattered electrons contribute to the coherent image component. Surprisingly little coherent transfer was seen when using energy-filtering at the most probable energy loss (in this case at the first plasmon energy-loss peak). Furthermore, the use of zero-loss filtering in combination with exit wavefront reconstruction is considerably more effective at removing the effects of multiple elastic and inelastic scattering and microscope objective lens aberrations than either technique by itself. Optimization of the zero-loss signal requires operation at intermediate to high primary voltages (> 200 keV). These results have important implications for the accurate recording of images of thick biological specimens as, for instance, in electron microscope tomography.     

Low-voltage electron microscopy of polymer and organic molecular thin films

We have demonstrated the capabilities of a novel low-voltage electron microscope (LVEM) for imaging polymer and organic molecular thin films. The LVEM can operate in transmission electron microscopy, scanning transmission electron microscopy, scanning electron microscopy, and electron diffraction modes. The microscope operates at a nominal accelerating voltage of 5 kV and fits on a tabletop. A detailed discussion of the electron-sample interaction processes is presented, and the mean free path for total electron scattering was calculated to be 15 nm for organic samples at 5 kV. The total end point dose for the destruction of crystallinity at 5 kV was estimated at 5 x 10(-4) and 3.5 x 10(-2) C/cm2 for polyethylene and pentacene, respectively. These values are significantly lower than those measured at voltages greater than 100 kV. A defocus series of colloidal gold particles allowed us to estimate the experimental contrast transfer function of the microscope. Images taken of several organic materials have shown high contrast for low atomic number elements and a resolution of 2.5 nm. The materials studied here include thin films of the organic semiconductor pentacene, triblock copolymer films, single-molecule dendrimers, electrospun polymer fibers and gold nanoparticles.     

Low-dose aberration corrected cryo-electron microscopy of organic specimens

Spherical aberration (C(s)) correction in the transmission electron microscope has enabled sub-angstrom resolution imaging of inorganic materials. To achieve similar resolution for radiation-sensitive organic materials requires the microscope to be operated under hybrid conditions: low electron dose illumination of the specimen at liquid nitrogen temperature and low defocus values. Initial images from standard inorganic and organic test specimens have indicated that under these conditions C(s)-correction can provide a significant improvement in resolution (to less than 0.16nm) for direct imaging of organic samples.     

In-focus electron microscopy of frozen-hydrated biological samples with a Boersch phase plate

We report the implementation of an electrostatic Einzel lens (Boersch) phase plate in a prototype transmission electron microscope dedicated to aberration-corrected cryo-EM. The combination of phase plate, C_s corrector and Diffraction Magnification Unit (DMU) as a new electron-optical element ensures minimal information loss due to obstruction by the phase plate and enables in-focus phase contrast imaging of large macromolecular assemblies. As no defocussing is necessary and the spherical aberration is corrected, maximal, non-oscillating phase contrast transfer can be achieved up to the information limit of the instrument. A microchip produced by a scalable micro-fabrication process has 10 phase plates, which are positioned in a conjugate, magnified diffraction plane generated by the DMU. Phase plates remained fully functional for weeks or months. The large distance between phase plate and the cryo sample permits the use of an effective anti-contaminator, resulting in ice contamination rates of <0.6 nm/h at the specimen. Maximal in-focus phase contrast was obtained by applying voltages between 80 and 700 mV to the phase plate electrode. The phase plate allows for in-focus imaging of biological objects with a signal-to-noise of 5-10 at a resolution of 2-3 nm, as demonstrated for frozen-hydrated virus particles and purple membrane at liquid-nitrogen temperature.     

High-resolution imaging with an aberration-corrected transmission electron microscope

Recently an electromagnetic hexapole system for the correction of the spherical aberration of the objective lens of a 200 kV transmission electron microscope has been constructed by Haider and coworkers. By appropriately exciting the hexapole elements it is possible to adjust specific values of the spherical aberration coefficient ranging from the value of the original uncorrected instrument over zero even to negative values. In the first part of the paper the consequences of the tunable spherical aberration are investigated. New imaging modes are available: By adjustment of an optimum value for the spherical-aberration coefficient, the point resolution of phase-contrast imaging can be extended to the information limit. Phase-contrast imaging can be improved by a reduced level of contrast delocalisation. For zero aberration contrast delocalisation does not occur. In this case high-resolution investigations are carried out under amplitude-contrast conditions, where the local image intensity of crystalline objects is controlled by electron diffraction channelling. The defocus and spherical aberration values related to the new imaging modes are given. In the second part novel applications of the instrument to semiconductor heterostructures and ceramic grain boundaries are examined.     

Enhanced contrast in electron microscopy of unstained biological material. 3. In-focus phase contrast of large objects

In-focus phase contrast electron microscopy has been investigated for the enhancement of bulk contrast (i.e. the contrast of large regions) of model biological specimens. Carbon film phase plates, of measured thickness, were introduced into the back focal plane of the objective lens. Image contrast was determined from Faraday-cage intensity measurements. A contrast enhancement was observed but was measured to be less than that obtained using a very small objective aperture. This was attributed to the smaller proportion of elastic scattering and the limited spatial frequency region over which the phase contrast transfer function was uniform. Electron beam interferometry established the ability of the phase plates to preserve the coherence of the beam traversing them. Carbon granularity, of specific dimensions, was significantly enhanced by the phase plate in accordance with the phase contrast transfer function and this enhanced granularity dominated the images of biological specimens.