Atomic resolution from 500kv electron micrographs by computer image processing

1978 ◽  
Vol 36 (1) ◽  
pp. 220-221
Author(s):  
N. Uyeda ◽  
E. Kirkland ◽  
Y. Fujiyoshi ◽  
B. Siegel
Keyword(s):  
Additive Noise ◽  
Spherical Aberration ◽  
Objective Lens ◽  
Bright Field Image ◽  
Bright Field ◽  
Contrast Transfer Function ◽  
Signal Ratio ◽  
Computer Image Processing ◽  
The Fourier Transform ◽  
Image Position

We have successfully applied the method suggested by P. Schiske (1) for optimally combining several micrographs of different defocus values (Δfβ) in the presence of additive noise. If c(k) represents the Fourier transform of tne ideal, unaberrated bright field image, and jβ(k) the transform of the real micrographs obtained at different defocus values, then the filter functions Qβ(k) that reducesto a minimum, was shown (1) to be, within a common multiplicative factor,The contrast transfer function (CTF) is where λ is the electron wavelength and Cs is the spherical aberration coefficient of the objective lens. η(k) is the noise to signal ratio in reciprocal space for unit CTF.This procedure was applied to images of a tilted crystaline specimen of hexadecachloro- phtalocyanatocopper (II) taken on the Kyoto 500KV electron microscope (2).

Bright-field image contrast and resolution in STEM and CTEM

1978 ◽  
Vol 36 (1) ◽  
pp. 172-173
Author(s):  
J. M. Cowley ◽  
Andrew Y. Au
Keyword(s):  
Fourier Transforms ◽  
Spherical Aberration ◽  
Interaction Constant ◽  
Objective Lens ◽  
Bright Field Image ◽  
Two Dimensional ◽  
Phase Object ◽  
Bright Field ◽  
Heavy Atoms ◽  
Image Position

For the high resolution imaging of thin specimens, it has been shown by Cowley and Au that the bright-field image intensity may be written asHere s(r) and c(r) are the two-dimensional Fourier transforms of the imaginary and real parts of the transfer function, A(u)sinx(u) and A(u)COSX(u), where A(u) is the aperture function, x(u) is the phase factor usually writtenand u = (2sinθ)/λ is the magnitude of the two dimensional reciprocal space vector u;Δf and Cs are the defocus and spherical aberration constants of the objective lens and the * symbol indicates a convolution integral. In deriving equation (1) we have assumed the validity of the phase object approximation but not the usual weak phase object approximation (WPOA) which applies only for the weak-scattering case that σφ(r)<<l, where σ is the interaction constant (=п/λE) and ϕ(xy) is the projected potential of the object. The WPOA is known to have severely restricted validity for crystalline specimens or for specimens containing heavy atoms such as negatively stained or positively stained biological material.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Electron microscopy of biological specimens by means of an electrostatic phase plate

1972 ◽  
Vol 329 (1578) ◽  
pp. 327-359 ◽  
Keyword(s):  
Spherical Aberration ◽  
Special Property ◽  
Field Method ◽  
Objective Lens ◽  
Phase Plate ◽  
Imaging Method ◽  
Contrast Effects ◽  
Resolution Limit ◽  
Bright Field ◽  
Microscope Imaging

A new electron microscope imaging method has been developed that is especially suited to the study of thin biological materials. It involves the use of an electrostatic phase plate - a device which creates a more or less uniform difference in optical path between the un­scattered and scattered waves by means of its electric field. This phase plate functions in an analogous manner to the absorbing bright contrast phase plate of light microscopy. The contrast effects and aberrations peculiar to the method have been examined and are discussed in terms of their likely influence on the image’s representation of the object structure. Analysis of electron micrographs of some biological test specimens, whose structure is relatively well known, confirms that this representation, to a resolution of ca . 0.85 nm, is a particularly faithful one. In the analysis the resolution limit was determined by the degree of specimen preservation, and a real limit, determined by the degree of spherical aberration in the objective lens, of ca . 0.5 nm is expected. A special property of the imaging method, as distinct from the conventional bright field method, is that it emphasizes the detail within the biological material itself, but reduces the contrast from the surrounding film of stain; negative staining remains necessary only because it helps to preserve the morphology of the specimen during irradiation. Evidence is presented that this property enables the method to display information about the specimen that it would not be possible to detect with the bright field method.

Determination of Energy Spread and Source Size by Optical Diffraction

1975 ◽  
Vol 33 ◽  
pp. 182-183
Author(s):  
J. Frank
Keyword(s):  
Transfer Function ◽  
Spherical Aberration ◽  
Careful Analysis ◽  
Energy Spread ◽  
Optical Diffraction ◽  
Source Distribution ◽  
Contrast Transfer Function ◽  
Spatial Frequencies ◽  
Gaussian Source ◽  
Image Position

Since the effect of energy spread and angular spread of illumination on the contrast transfer function is known from theoretical investigations, these experimental parameters can in turn be obtained by careful analysis of electron micrographs. For Gaussian energy spread (halfwidth △E), negligible voltage and current fluctuations and a Gaussian source distribution (half-width α), the coherent transfer function for monochromatic electrons appears multiplied with the envelope function(θ scattering angle, λ electron wavelength, E0 energy, △z defocus; Cc, Cs chromatic and spherical aberration constants). This causes an attenuation of the image Fourier transform at high spatial frequencies and is responsible for the fact that the visible bandlimit in optical diffraction patterns is well below the aperture limit.

On the magnetic electron lens of minimum sphrical aberration

1978 ◽  
Vol 36 (1) ◽  
pp. 24-25
Author(s):  
S. Suzuki ◽  
A. Ishikawa
Keyword(s):  
Spherical Aberration ◽  
Resolving Power ◽  
Objective Lens ◽  
Lens Design ◽  
Magnetic Lens ◽  
Initial Voltage ◽  
Path Distance ◽  
Electron Lens ◽  
Image Position ◽  
Magnetic Electron

For the development of the electron microscope, in which high resolving power is demanded, it is important to construct an electron objective lens with minimum spherical aberration.In 1943, one of the authors published the paper on the approximate calculation of the electromagnetic field to give a minimum spherical aberration and also published the papers on small spherical aberration lens design based on this calculation.We will speak a comparison between the experimental results and the numerical calculations in practical cases.The following line shows the method to get more strictly minimum spherical aberration of magnetic lens.In a space charge free electron optical system, where a pure magnetic lens is concerned, differential equation for paraxial electron path is given byU being the initial voltage applied to the electron beam and γ the path distance from the optical axis Z.

Digital Image Processing of High Resolution 500KV Micrographs

1981 ◽  
Vol 39 ◽  
pp. 234-235
Author(s):  
E.J. Kirkland ◽  
B.M. Siegel ◽  
N. Uyeda ◽  
Y. Fujiyoshi
Keyword(s):  
Phase Contrast ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Random Noise ◽  
Image Plane ◽  
Partial Coherence ◽  
Thin Specimen ◽  
The Fourier Transform ◽  
Image Position ◽  
Contrast Image

The predominate linear components of a defocus series of bright field phase contrast electron micrographs of a thin specimen may be represented in Fourier space as;(1)If there are m micrographs in the series then are m dimensional vectors, each component of which represents one micrograph. is the Fourier transform of the recorded defocus series and is the random noise content of is an mx2 matrix representing the transfer functions of the microscope (including spherical aberration, defocus, and partial coherence). is a two component vector representing the two components (real and imaginary) of the ideal unaberrated phase contrast image, is a two dimensional spatial frequency vector in the image plane.

A Calibration Method Usable in the Production of Phase Plates for High Resolution Electron Microscopy

1971 ◽  
Vol 29 ◽  
pp. 46-47
Author(s):  
F. Thon ◽  
D. Willasch
Keyword(s):  
Electron Microscopy ◽  
Frequency Spectrum ◽  
Spherical Aberration ◽  
High Resolution Electron Microscopy ◽  
Calibration Method ◽  
Objective Lens ◽  
Resolution Electron ◽  
Diffraction Angle ◽  
Phase Plates ◽  
Image Position

It is well known that phase contrast in electron microscopy is normally due to the phase shift γ introduced by defocusing and spherical aberration of the objective lens. It is given by Scherzer's formula (2) :(1)where γ is the electron wavelength, Cs the spherical aberration coefficient, θ the diffraction angle and Δz the defocus value.However, in this way, only sections out of the spatial frequency spectrum contained in the abject are transferred to the image. In order to transmit the whole frequency spectrum, it has been proposed that a phase shifting plate is inserted into the back focal plane of the objective lens.

Compensation of Lens Aberrations by Single-Sideband Holography

1972 ◽  
Vol 30 ◽  
pp. 562-563
Author(s):  
Kenneth H. Downing
Keyword(s):  
Transfer Function ◽  
Spherical Aberration ◽  
Contrast Transfer Function ◽  
Point Spread ◽  
Single Sideband ◽  
Spread Function ◽  
The Fourier Transform ◽  
A Charge ◽  
Image Defect ◽  
Wave Aberration

Single-sideband holography has been suggested as a method for extending the resolution of the electron microscope, since it produces contrast for all object spacings simultaneously and avoids the oscillations of the contrast transfer function characteristic of normal imaging. Image processing is still required to compensate for the effects of spherical aberration and defocus, which now show up in lateral shifts of image components. The method involves use of a semicircular objective aperture to stop out half of the scattered electrons. One finds, however, that a charge builds up on or around the aperture soon after it is positioned, introducing still another image defect.In order to compensate for the image defects, one needs to determine the wave aberration corresponding to the point spread function or contrast transfer function. In the case of normal (double-sideband) imaging one can determine the transfer function from measurements of the oscillations of the fourier transform of the micrograph (Fig. 1e).

High-resolution image processing of bright-field electron micrographs

1984 ◽  
Vol 42 ◽  
pp. 432-433
Author(s):  
E.J. Kirkland ◽  
B.M. Siegel ◽  
N. Uyeda ◽  
Y. Fujiyoshi
Keyword(s):  
Random Noise ◽  
Transmission Function ◽  
Image Plane ◽  
Delta Function ◽  
Bright Field Image ◽  
Bright Field ◽  
Noise Component ◽  
Dirac Delta ◽  
Recorded Image ◽  
Image Position

A general form of the analytical model of a CTEM bright field image is:(1)where G is the Fourier Transform (F.T.) of the recorded image intensity, F is the F.T. of the complex specimen transmission function, CO is a background constant, δ is the Dirac delta function, N is a random noise component, is a spatial frequency vector in the image plane, and Tμ is the transmission cross coefficient. In the special case of coherent imaging:(2)(3)

Transmission Electron Microscopy Studies of Crystal Lattice Growth in Atomic Resolution

1976 ◽  
Vol 34 ◽  
pp. 596-597
Author(s):  
H. Hashimoto ◽  
A. Kumaol ◽  
A. Ono ◽  
E. Watanabe ◽  
E. Endoh
Keyword(s):  
Spherical Aberration ◽  
Dark Field Image ◽  
Dark Field ◽  
Objective Lens ◽  
Image Method ◽  
Bright Field Image ◽  
Electron Microscopic ◽  
Single Atoms ◽  
Transmission Electron ◽  
Small Crystals

The present authors showed that the image of single atoms in Th-pyromellitate molecules and Th02 small crystals supported on graphite films could be observed in the dark field transmission electron microscopic images with tilted illumination (TDF image). The achievement of the observation of single atoms can be attributed not only to the high contrast of the dark field image but also to the two times higher resolution of the TDF image than that of the bright field image with axial illumination.Using the TDF image method, the growth process of small ThO2 crystals formed by the electron irradiation in the vacuum has been studied.Th - pyromellitate of 10-4 mol which was placed on graphite flakes was observed by JEM 100-C electron microscope with an objective lens of spherical aberration coefficient Cs = 0. 7 mm. Objective aperture and illumination tilt angles were 9 x 10-3 rad and 16 x 10-3 rad respectively .

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