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).     

Design of a microfabricated, two-electrode phase-contrast element suitable for electron microscopy

A miniature electrostatic element has been designed to selectively apply a 90 degrees phase shift to the unscattered beam in the back focal plane of the objective lens, in order to realize Zernike-type, in-focus phase contrast in an electron microscope. The design involves a cylindrically shaped, biased-voltage electrode, which is surrounded by a concentric grounded electrode. Electrostatic calculations have been used to determine that the fringing fields in the region of the scattered electron beams will cause a negligible phase shift as long as the ratio of electrode length to the transverse feature size is greater than 5:1. Unlike the planar, three-electrode einzel lens originally proposed by Boersch for the same purpose, this new design does not require insulating layers to separate the biased and grounded electrodes, and it can thus be produced by a very simple microfabrication process. Scanning electron microscope images confirm that mechanically robust devices with feature sizes of approximately 1 microm can be easily fabricated. Preliminary experimental images demonstrate that these devices do apply a 90 degrees phase shift between the scattered and unscattered electrons, as expected.     

Effect of a physical phase plate on contrast transfer in an aberration-corrected transmission electron microscope

In this theoretical study we analyze contrast transfer of weak-phase objects in a transmission electron microscope, which is equipped with an aberration corrector (C(s)-corrector) in the imaging lens system and a physical phase plate in the back focal plane of the objective lens. For a phase shift of pi/2 between scattered and unscattered electrons induced by a physical phase plate, the sine-type phase contrast transfer function is converted into a cosine-type function. Optimal imaging conditions could theoretically be achieved if the phase shifts caused by the objective lens defocus and lens aberrations would be equal to zero. In reality this situation is difficult to realize because of residual aberrations and varying, non-zero local defocus values, which in general result from an uneven sample surface topography. We explore the conditions--i.e. range of C(s)-values and defocus--for most favourable contrast transfer as a function of the information limit, which is only limited by the effect of partial coherence of the electron wave in C(s)-corrected transmission electron microscopes. Under high-resolution operation conditions we find that a physical phase plate improves strongly low- and medium-resolution object contrast, while improving tolerance to defocus and C(s)-variations, compared to a microscope without a phase plate.     

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.     

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.     

Imaging of soft and hard materials using a Boersch phase plate in a transmission electron microscope

Using two levels of electron beam lithography, vapor phase deposition techniques, and FIB etching, we have fabricated an electrostatic Boersch phase plate for contrast enhancement of weak phase objects in a transmission electron microscope. The phase plate has suitable dimensions for the imaging of small biological samples without compromising the high-resolution capabilities of the microscope. A micro-structured electrode allows for phase tuning of the unscattered electron beam, which enables the recording of contrast enhanced in-focus images and in-line holograms. We have demonstrated experimentally that our phase plate improves the contrast of carbon nanotubes while maintaining high-resolution imaging performance, which is demonstrated for the case of an AlGaAs heterostructure. The development opens a new way to study interfaces between soft and hard materials.     

Comparison of phase contrast transmission electron microscopy with optimized scanning transmission annular dark field imaging for protein imaging

Henderson has already shown that electron microscopy should be superior to X-ray and neutron diffraction for determining protein structure with minimum radiation damage. Since the contrast for a molecule embedded in vitreous ice is very low, it is conceivable that dark field imaging would be superior to bright field phase contrast microscopy. A detailed analysis of contrast and signal/noise for both imaging modes is presented. Annular dark field scanning transmission microscopy gives improved contrast and equivalent signal/noise to phase contrast TEM when the molecule is the same thickness as a vitreous ice embedding medium. For a constant embedding medium thickness of 200 A the contrast is equivalent to phase contrast TEM but the signal/noise is 5 times worse. Even with an efficient detector that only excludes scattering less than 5 mrad there is insufficient signal at a dose of 5 electrons/A(2) to produce an image with more than 1 electron/per pixel. For larger molecules (>100 A thick which corresponds to 420 kDa for spherical molecules) the weak phase object approximation used to analyse a phase contrast image no longer applies at 100 kV. This limit could be extended to about 200 A (about 3 MDa) if a 400 kV microscope were used.     

Upgrading a microscope with a spiral phase plate

We present the implementation of a spiral phase plate in a standard bright-field microscope to enhance the contrast of phase and amplitude samples. The method can be employed in all types of microscopy where standard phase contrast methods are applicable, for example, in bright-field transmission or reflection microscopy using an illumination source with partial spatial coherence. The spiral phase filter is placed into an accessible Fourier plane of the imaging path of the microscope. It is shown that this produces not only a strong contrast enhancement but in theory also improves the spatial resolution of the microscope for white light. A series of different set-ups for transmissive or reflective samples, including epi-illumination, are presented to demonstrate the practical range of applications of this contrasting method. A minute shift of the spiral phase plate out of the centre results in relief-like images that are similar to those obtained by differential interference contrast microscopy. A series of such relief-like images can be numerically processed to obtain quantitative phase and amplitude information of the sample.     

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.     

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.     

Enhanced contrast in electron microscopy of unstained biological material. II. Defocused contrast of large objects

A contrast minimum is observed when 88 nm diameter polystyrene latex spheres are underfocused, which is related to the wide-angle scattering peaks. Images due to scattered and non-scattered wave components are displaced due to objective-lens spherical aberration and defocus. Maximum overlap of these components produces a contrast minimum at underfocus, related to the spherical aberration of the particular lens used. Similarly, a high-contrast band at carbon-film edges arises from spherical aberration and defocus separation of non-scattered and wide-angle scattered waves. This band increases in contrast with film thickness and in width with lens defocus. These geometrical effects account for the well-known ‘blinking’ of contrast of large biological objects upon swinging through focus without an objective aperture, and for the general contrast increase of defocused large objects. Fresnel fringes account for only a narrow band of enhanced contrast at distinct edges and cannot account for contrast enhancement of large objects lacking distinct edges.     

Practical factors affecting the performance of a thin-film phase plate for transmission electron microscopy

A number of practical issues must be addressed when using thin carbon films as quarter-wave plates for Zernike phase-contrast electron microscopy. We describe, for example, how we meet the more stringent requirements that must be satisfied for beam alignment in this imaging mode. In addition we address the concern that one might have regarding the loss of some of the scattered electrons as they pass through such a phase plate. We show that two easily measured parameters, (1) the low-resolution image contrast produced in cryo-EM images of tobacco mosaic virus particles and (2) the fall-off of the envelope function at high resolution, can be used to quantitatively compare the data quality for Zernike phase-contrast images and for defocused bright-field images. We describe how we prepare carbon-film phase plates that are initially free of charging or other effects that degrade image quality. We emphasize, however, that even though the buildup of hydrocarbon contamination can be avoided by heating the phase plates during use, their performance nevertheless deteriorates over the time scale of days to weeks, thus requiring their frequent replacement in order to maintain optimal performance.     

Wave reconstruction in TEM using a variable phase plate

We propose a new method to use a variable phase plate in TEM which will be able to retrieve the whole image wave, even for thick objects. The method is robust and easy to implement.     

Experimental investigation of phase contrast formed by inelastically scattered electrons

Phase contrast formed by inelastically scattered electrons in a crystal has been investigated using spatially resolved EELS, which enables simultaneous observation of lattice fringes formed by electrons of various energy losses. Lattice fringes produced by low-loss electrons overlap on an elastic TEM image like Fourier images. This means that the exit wave is preserved in low-loss scattering. Similar Fourier images occur for electrons suffering core-losses in the range 50-400 eV, which indicates delocalization and spatial coherence in those core-loss scattering events. The spatial coherence of inelastically scattered electrons is estimated from the focus dependence of energy-filtered lattice fringe contrast. Spatial coherence widths shorten with increasing energy-loss, and their energy-loss dependence is similar to diffraction errors derived from the characteristic angle for inelastic scattering.     

Differential algebraic method for aberration analysis of typical electrostatic lenses

In this paper up to fifth-order geometric and third-order chromatic aberration coefficients of typical electrostatic lenses are calculated by means of the charged particle optics code, COSY INFINITY, based on the differential algebraic (DA) method. A two-tube immersion lens and a symmetric einzel lens have been chosen as two examples, whose axial potential distributions are numerically calculated by a FORTRAN program using the finite difference method. The DA results are in good agreement with those evaluated by the aberration integrals in electron optics. The DA method presented here can easily be extended to aberration analysis of other numerically computed electron lenses, including magnetic lenses.     

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.     

The simulation of high resolution images of amorphous thin films

Computer-simulated high resolution electron microscopy (HREM) images of white-noise weak phase objects show features similar to those observed in images of very thin films (2 nm) of amorphous silicon. Local patches of regular fringes arise as a result of the spatial-frequency filtering effect of the aperture and need not indicate the presence of microcrystalline regions. It is shown how drastically the appearance of a simulated amorphous image is influenced by the transfer function of the objective lens and by the objective aperture or equivalent damping of high-frequency components due to partial temporal and spatial coherence of the electron beam. Simulated images of through-focus series also show the same general appearance as for an amorphous silicon film.     

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.     

Electric charging of thin films measured using the contrast transfer function

The phase shift of electron waves due to charging of thin films is investigated using the contrast transfer properties of the microscope. We take two photos, one with film at the back focal plane and the other one without film. The phase difference between the contrast transfer functions of the two photos is evaluated using our theoretical predictions. The theoretical model is based on an analytical solution of the Laplace equation with appropriate boundary conditions. From the resulting electrostatic potential function the phase shift of electron waves is derived in a weak lens approximation. With this method, information about the radius of the electron beam and the magnitude of the electrostatic potential at the thin film is obtained. The excellent agreement between the theoretical model and experimental results is observed.     

Quantitative phase-amplitude microscopy I: optical microscopy

In this paper, the application of a new optical microscopy method (quantitative phase‐amplitude microscopy) to biological imaging is explored, and the issue of resolution and image quality is examined. The paper begins by presenting a theoretical analysis of the method using the optical transfer function formalism of Streibl (1985 ). The effect of coherence on the formation of the phase image is explored, and it is shown that the resolution of the method is not compromised over that of a conventional bright‐field image. It is shown that the signal‐to‐noise ratio of the phase recovery, however, does depend on the degree of coherence in the illumination. Streibl (1985) notes that partially coherent image formation is a non‐linear process because of the intermingling of amplitude and phase information. The work presented here shows that the quantitative phase‐amplitude microscopy method acts to linearize the image formation process, and that the phase and amplitude information is properly described using a transfer function analysis. The theoretical conclusions are tested experimentally using an optical microscope and the theoretical deductions are confirmed. Samples for microscopy influence both the phase and amplitude of the light wave and it is demonstrated that the new phase recovery method can separate the amplitude and phase information, something not possible using traditional phase microscopy. In the case of a coherent wave, knowledge of the phase and amplitude constitutes complete information that can be used to emulate other forms of microscopy. This capacity is demonstrated by recovering the phase of a sample and using the data to emulate a differential interference contrast image.