Defocus Series Research Articles

Discussions on the multiple‐input maximum a‐posteriori wave‐function restoration method in high‐resolution electron microscopy

The multiple-input maximum a-posteriori (MIMAP) wave-function restoration method in high-resolution electron microscopy proposed by Kirkland (1984) is further discussed. A modified MIMAP criterion that considers likely correlations between individual micrographs in a series of micrographs taken at different imaging conditions is presented. By performing wave-function restoration for a multislice method-simulated defocus series of MgO[110], the convergent properties of this modified MIMAP method are also described.

Image Restoration in Coherent Imaging System Involving Spherical Aberration

This paper describes an image restoration method based on defocus modulation processing, assuming weakly scattered objects in the coherent imaging system involving spherical aberration. The present analysis shows that the effect of the spherical aberration can be completely corrected by the image integration applied to the defocus series, if appropriate bipolar (positive and negative) weighting functions as a function of the defocus value are used in the image integration

Improved high resolution image processing of bright field electron micrographs: II. Experiment

The new methods of nonlinear image processing are applied to high resolution experimental micrographs of chlorinated copper phthalocyanine taken on the Kyoto 500 kV electron microscope. With these new methods of image processing the phase and amplitude of the specimen transmission function are reconstructed from a defocus series of conventional transmission electron micrographs (bright field). Strong scattering, partial coherence and statistical noise have been included. Both of these new methods are based on the MAP (maximum a posteriori) criterion generalized to include reconstruction from multiple input images. In a companion paper (the first part of this two-part report) the theory behind these methods was presented and in this paper it is tested on actual experimental micrographs. A significant increase in resolution has been obtained with computer image processing. The point-to-point resolution obtained here with computer image processing of 500 kV electron micrographs is of the order of 1.2–1.4 Å which represents a 30–50% increase in resolution.

Computer simulation of HREM images of network models of SiO 2 glass

The possibilities and limitations of HREM for evaluating structural details in amorphous silica were investigated by computer simulation. The calculated defocus series of HREM images for an unstrained and a linearly strained network model of vitreous SiO 2 have shown that microvoids, density fluctuations as well as strained regions can be interpretably imaged for thin specimens ( t < 5 nm).

Improved high resolution image processing of bright field electron micrographs: I. Theory

Two new improved methods of computer image reconstruction are presented. The well known MAP method of image reconstruction is generalized to include reconstruction of a single (higher resolution) image from multiple observations of the object with different imaging conditions. The resolution of the input images is assumed to be determined by the aberrations of the optical system. The first method involves an approximate form of partial coherence that allows the use of fast Fourier transforms (FFT's) to reduce the required computer time. The second method uses the more rigorous transmission cross-coefficient description of partial coherence. Although both methods have applications in both electron and light optical imaging, the discussion presented here is directed towards the reconstruction of the phase and amplitude of the specimen transmission function from a defocus series of high resolution bright field conventional transmission electron micrographs of radiation-damage-resistant specimens. This is the first of a two-part report. The theory is presented in this part and the experimental results of applying these methods to actual 500 keV micrographs will be presented in the second part of this report.

A digital processing method for structural analysis of atom clusters from high resolution electron micrographs

The electron image contrast of tungsten atom clusters changes remarkably depending on the spatial frequency, scattering factor phase, lens aberration and defocusing, but it is confirmed that the image appears in negative contrast and satisfies an anastigmatic condition when recorded under optimum focus. When based on a cluster model, the spatial frequencies can be divided into individual atom clusters by successive band pass filters. An electron micrograph taken at the optimum focus condition is selected from a defocus series of micrographs and is used for digital processing. In order to measure the exact size of the clusters, the enhancement of filtered images by their gradient images to extract edge information and the subsequent superimposition of both images are derived. Based on Fourier analysis, it is proposed that tungsten films consist of double cluster layers which correspond to a thickness consisting of 3–5 single atoms. In addition, their three-dimensional localization can be determined more precisely than by earlier computer-aided reconstruction methods. The cluster models are in good agreement with the processed data suggesting that the amorphous phase is a distinct phase and not microcrystalline.

Nonlinear high resolution image processing of conventional transmission electron micrographs: I. Theory

A new method of nonlinear computer image processing is presented and tested on theoretically simulated images. The test images were calculated with the multislice method. With this new method of image processing the phase and amplitude of the specimen transmission function may be reconstructed from a defocus series of conventional bright field transmission electron micrographs. In this paper (the first of a two-part report) this new method is found to work with simulated images and in a companion paper (the second part of this report) it is also found to work with actual experimental micrographs. In each case, a moderately significant increase in resolution has been obtained.

Nonlinear high resolution image processing of conventional transmission electron micrographs: II. Experiment

A new method of nonlinear image processing is applied to high resolution experimental micrographs of chlorinated copper phthalocyanine taken on the Kyoto 500 kV electron microscope. With this new method of image processing the phase and amplitude of the specimen transmission function are reconstructed from a defocus series of conventional transmission electron micrographs. In a companion paper (the first part of this two-part report) this method was presented and tested on theoretically simulated images and in this paper it is tested on actual experimental micrographs. In each case a moderately significant increase in resolution has been obtained with computer image processing. The point to point resolution obtained here with computer image processing of 500 kV electron micrographs is of the order of 1.2–1.4 Å.

Digital Image Processing of High Resolution 500KV Micrographs

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.

Linear image processing and anomalous scattering

The complete analytical image model for bright field transmission electron micrographs contains several nonlinear image components as well as several linear image components all of which are degraded by noise and an instrumental transfer function. When these small nonlinear image components are neglected it is possible, using linear processing, to recover the complete complex ideal unaberrated image from a series of micrographs taken at different defocus. The imaginary part of this ideal image is due to the so called “anomalous” part of the elastic electron-atom scattering amplitudes. In this paper the effects of neglecting the nonlinear terms are tested qualitatively and quantitatively. A theoretical phase grating calculation (including nonlinear imaging effects) of a hypothetical specimen of sixteen single atoms with varying atomic number, Z, is used to simulate a defocus series which is subsequently processed with a linear image reconstruction procedure. Quantitative agreement of the reconstructed image with the ideal unaberrated image of comparable resolution is excellent. The real part of the reconstructed image is accurate to 0.68% and the imaginary part of the reconstructed image is accurate to 3.10%. The contrast variation in the reconstructed image is found to be roughly proportional to Z0.67 for the real part of the image and roughly proportional to Z1.29 for the imaginary part of the image.

Linear image processing and anomalous scattering

The complete analytical image model for bright field transmission electron micrographs contains several nonlinear image components as well as several linear image components all of which are degraded by noise and an instrumental transfer function. When these small nonlinear image components are neglected it is possible, using linear processing, to recover the complete complex ideal unaberrated image from a series of micrographs taken at different defocus. The imaginary part of this ideal image is due to the so called “anomalous” part of the elastic electron-atom scattering amplitudes. In this paper the effects of neglecting the nonlinear terms are tested qualitatively and quantitatively. A theoretical phase grating calculation (including nonlinear imaging effects) of a hypothetical specimen of sixteen single atoms with varying atomic number, Z, is used to simulate a defocus series which is subsequently processed with a linear image reconstruction procedure. Quantitative agreement of the reconstructed image with the ideal unaberrated image of comparable resolution is excellent. The real part of the reconstructed image is accurate to 0.68% and the imaginary part of the reconstructed image is accurate to 3.10%. The contrast variation in the reconstructed image is found to be roughly proportional to Z 0.67 for the real part of the image and roughly proportional to Z 1.29 for the imaginary part of the image.

Digital reconstruction of bright field phase contrast images from high resolution electron micrographs

The theory of bright-field image formation of thin specimens in a conventional transmission electron microscope is presented. The recorded image contrast is shown to be predominantly linear in the electron atom scattering amplitudes which are in general complex (possessing phase and amplitude). A linearized image model describing multiple images of varying defocus (defocus series) is derived. Image degradation is characterized by an instrumental transfer function (including spherical aberration, defocus and partial coherence), a finite signal-to-noise ratio and a Debye--Waller temperature factor. Using the minimum mean square error criterion, a new method of image reconstruction to recover the real and imaginary parts of the ideal phase contrast image from a defocus series is derived. This new method of image reconstruction reduces to the well known Wiener filter in the appropriate limiting conditions. A defocus series of micrographs taken on the Kyoto 500 keV electron microscope using a radiation damage resistant specimen of chlorinated copper phthalocyanine is processed. The signal-to-noise ratio of this series is found to be approximately 10. A resolution of approximately 2 A is apparent in the unprocessed images. The complex image reconstructed from this defocus series shows increased resolution in the real part of the image (approximately 1.4 A) and increased heavy/light atom contrast in the imaginary part of the image.

Digital reconstruction of bright field phase contrast images from high resolution electron micrographs

The theory of bright-field image formation of thin specimens in a conventional transmission electron microscope is presented. The recorded image contrast is shown to be predominantly linear in the electron atom scattering amplitudes which are in general complex (possessing phase and amplitude). A linearized image model describing multiple images of varying defocus (defocus series) is derived. Image degradation is characterized by an instrumental transfer function (including spherical aberration, defocus and partial coherence), a finite signal-to-noise ratio and a Debye—Waller temperature factor. Using the minimum mean square error criterion, a new method of image reconstruction to recover the real and imaginary parts of the ideal phase contrast image from a defocus series is derived. This new method of image reconstruction reduces to the well known Wiener filter in the appropriate limiting conditions. A defocus series of micrographs taken on the Kyoto 500 keV electron microscope using a radiation damage resistent specimen of chlorinated copper phthalocyanine is processed. The signal-to-noise ratio of this series is found to be approximately 10. A resolution of ∼2 Å is apparent in the unprocessed images. The complex image reconstructed from this defocus series shows increased resolution in the real part of the image (∼1.4 Å) and increased heavy/light atom contrast in the imaginary part of the image.