Chi-squared differences in Fourier space: comparing experimental with simulated images

2022 ◽  
pp. 125-128
Author(s):  
W O Saxton
Keyword(s):  
Fourier Space ◽  
Chi Squared ◽  
Simulated Images

3-D reconstruction of molecular shape from microcrystal thin sections

1983 ◽  
Vol 41 ◽  
pp. 748-749
Author(s):  
S. Cusack ◽  
J.-C. Jésior
Keyword(s):  
Three Dimensional ◽  
Molecular Shape ◽  
Biological Molecules ◽  
Fourier Space ◽  
Single Particles ◽  
Thin Sections ◽  
Standard Methods ◽  
X Ray ◽  
X Ray Crystallography ◽  
Dimensional Reconstruction

Three-dimensional reconstruction techniques using electron microscopy have been principally developed for application to 2-D arrays (i.e. monolayers) of biological molecules and symmetrical single particles (e.g. helical viruses). However many biological molecules that crystallise form multilayered microcrystals which are unsuitable for study by either the standard methods of 3-D reconstruction or, because of their size, by X-ray crystallography. The grid sectioning technique enables a number of different projections of such microcrystals to be obtained in well defined directions (e.g. parallel to crystal axes) and poses the problem of how best these projections can be used to reconstruct the packing and shape of the molecules forming the microcrystal.Given sufficient projections there may be enough information to do a crystallographic reconstruction in Fourier space. We however have considered the situation where only a limited number of projections are available, as for example in the case of catalase platelets where three orthogonal and two diagonal projections have been obtained (Fig. 1).

Faceted antiphase boundaries in GaAs grown on Ge

1987 ◽  
Vol 45 ◽  
pp. 314-315
Author(s):  
N.-H. Cho ◽  
S. McKernan ◽  
C.B. Carter ◽  
K. Wagner
Keyword(s):  
Cross Section ◽  
Atomic Resolution ◽  
Face Centered Cubic ◽  
Electrical Behavior ◽  
Sphalerite Structure ◽  
Antiphase Boundaries ◽  
Transmission Electron ◽  
Face Centered ◽  
Quality Material ◽  
Simulated Images

Interest has recently increased in the possibility of growing III-V compounds epitactically on non-polar substrates to produce device quality material. Antiphase boundaries (APBs) may then develop in the GaAs epilayer because it has sphalerite structure (face-centered cubic with a two-atom basis). This planar defect may then influence the electrical behavior of the GaAs epilayer. The orientation of APBs and their propagation into GaAs epilayers have been investigated experimentally using both flat-on and cross-section transmission electron microscope techniques. APBs parallel to (110) plane have been viewed at the atomic resolution and compared to simulated images.Antiphase boundaries were observed in GaAs epilayers grown on (001) Ge substrates. In the image shown in Fig.1, which was obtained from a flat-on sample, the (110) APB planes can be seen end-on; the faceted APB is visible because of the stacking fault-like fringes arising from a lattice translation at this interface.

The quantitative comparison of experimental and simulated diffraction contrast images

1995 ◽  
Vol 53 ◽  
pp. 102-103
Author(s):  
Stuart McKernan
Keyword(s):  
Image Processing ◽  
Personal Computer ◽  
Close Agreement ◽  
Quantitative Comparison ◽  
Image Simulation ◽  
Computing Power ◽  
Diffraction Contrast ◽  
Simulated Images ◽  
Made In

For many years the concept of quantitative diffraction contrast experiments might have consisted of the determination of dislocation Burgers vectors using a g.b = 0 criterion from several different 2-beam images. Since the advent of the personal computer revolution, the available computing power for performing image-processing and image-simulation calculations is enormous and ubiquitous. Several programs now exist to perform simulations of diffraction contrast images using various approximations. The most common approximations are the use of only 2-beams or a single systematic row to calculate the image contrast, or calculating the image using a column approximation. The increasing amount of literature showing comparisons of experimental and simulated images shows that it is possible to obtain very close agreement between the two images; although the choice of parameters used, and the assumptions made, in performing the calculation must be properly dealt with. The simulation of the images of defects in materials has, in many cases, therefore become a tractable problem.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

HRTEM simulation of interfacial structure in amorphous multilayers

1989 ◽  
Vol 47 ◽  
pp. 466-467
Author(s):  
Margaret L. Sattler ◽  
Michael A. O'Keefe
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Cross Section ◽  
High Resolution Electron Microscopy ◽  
Interfacial Structure ◽  
Multilayer Sample ◽  
Resolution Electron ◽  
Multilayered Materials ◽  
Simulated Images

Multilayered materials have been fabricated with such high perfection that individual layers having two atoms deep are possible. Characterization of the interfaces between these multilayers is achieved by high resolution electron microscopy and Figure 1a shows the cross-section of one type of multilayer. The production of such an image with atomically smooth interfaces depends upon certain factors which are not always reliable. For example, diffusion at the interface may produce complex interlayers which are important to the properties of the multilayers but which are difficult to observe. Similarly, anomalous conditions of imaging or of fabrication may occur which produce images having similar traits as the diffusion case above, e.g., imaging on a tilted/bent multilayer sample (Figure 1b) or deposition upon an unaligned substrate (Figure 1c). It is the purpose of this study to simulate the image of the perfect multilayer interface and to compare with simulated images having these anomalies.

High-Resolution Image Simulation of a Tilted Crystal

1990 ◽  
Vol 48 (1) ◽  
pp. 68-69
Author(s):  
C. J. D. Hetherington
Keyword(s):  
High Resolution ◽  
Crystal Thickness ◽  
Thin Specimen ◽  
Atomic Structures ◽  
Kikuchi Lines ◽  
High Resolution Images ◽  
Final Estimate ◽  
Simulated Images ◽  
Habit Planes

Most high resolution images are not directly interpretable but must be compared with simulations based on model atomic structures and appropriate imaging conditions. Typically, the only parameters that are adjusted, in addition to the structure models, are crystal thickness and microscope defocus. Small tilts of the crystal away from the exact zone axis have only rarely been considered. It is shown here that, in the analysis of an image of a silicon twin intersection, the crystal tilt could be accurately estimated and satisfactorily included in the simulations.The micrograph shown in figure 1 was taken as part of an HREM study of indentation-induced hexagonal silicon. In this instance, the intersection of two twins on different habit planes has driven the silicon into hexagonal stacking. However, in order to confirm this observation, and in order to investigate other defects in the region, it has been necessary to simulate the image taking into account the very apparent crystal tilt. The inability to orientate the specimen at the exact [110] zone was influenced by i) the buckling of the specimen caused by strains at twin intersections, ii) the absence of Kikuchi lines or a clearly visible Laue circle in the diffraction pattern of the thin specimen and iii) the avoidance of radiation damage (which had marked effects on images taken a few minutes later following attempts to realign the crystal.) The direction of the crystal tilt was estimated by observing which of the {111} planes remained close to edge-on to the beam and hence strongly imaged. Further refinement of the direction and magnitude of the tilt was done by comparing simulated images to experimental images in a through-focal series. The presence of three different orientations of the silicon lattice aided the unambiguous determination of the tilt. The final estimate of a 0.8° tilt in the 200Å thick specimen gives atomic columns a projected width of about 3Å.

On the Use of POCS for Restoring the “Missing Wedge” in Electron Tomography

1990 ◽  
Vol 48 (1) ◽  
pp. 520-521
Author(s):  
Neng-Yu Zhang ◽  
Bruce F. McEwen ◽  
Joachim Frank
Keyword(s):  
Function Space ◽  
Convex Sets ◽  
Electron Tomography ◽  
Spinal Ganglion ◽  
Fourier Space ◽  
Missing Information ◽  
Voltage Electron ◽  
High Voltage Electron Microscope ◽  
Energy Bound ◽  
Spatial Boundedness

Reconstructions of asymmetric objects computed by electron tomography are distorted due to the absence of information, usually in an angular range from 60 to 90°, which produces a “missing wedge” in Fourier space. These distortions often interfere with the interpretation of results and thus limit biological ultrastructural information which can be obtained. We have attempted to use the Method of Projections Onto Convex Sets (POCS) for restoring the missing information. In POCS, use is made of the fact that known constraints such as positivity, spatial boundedness or an upper energy bound define convex sets in function space. Enforcement of such constraints takes place by iterating a sequence of function-space projections, starting from the original reconstruction, onto the convex sets, until a function in the intersection of all sets is found. First applications of this technique in the field of electron microscopy have been promising.To test POCS on experimental data, we have artificially reduced the range of an existing projection set of a selectively stained Golgi apparatus from ±60° to ±50°, and computed the reconstruction from the reduced set (51 projections). The specimen was prepared from a bull frog spinal ganglion as described by Lindsey and Ellisman and imaged in the high-voltage electron microscope.

Risk of venous thromboembolism following surgical treatment of superficial venous incompetence

VASA ◽  
2017 ◽  
Vol 46 (6) ◽  
pp. 484-489 ◽  
Author(s):  
Tom Barker ◽  
Felicity Evison ◽  
Ruth Benson ◽  
Alok Tiwari
Keyword(s):  
Venous Thromboembolism ◽  
Varicose Vein ◽  
Lower Incidence ◽  
Varicose Veins ◽  
Secondary Data ◽  
Foam Sclerotherapy ◽  
Increased Risk ◽  
Significant Difference ◽  
Chi Squared ◽  
One Year

Abstract. Background: The invasive management of varicose veins has a known risk of post-operative deep venous thrombosis and subsequent pulmonary embolism. The aim of this study was to evaluate absolute and relative risk of venous thromboembolism (VTE) following commonly used varicose vein procedures. Patients and methods: A retrospective analysis of secondary data using Hospital Episode Statistics database was performed for all varicose vein procedures performed between 2003 and 2013 and all readmissions for VTE in the same patients within 30 days, 90 days, and one year. Comparison of the incidence of VTEs between procedures was performed using a Pearson’s Chi-squared test. Results: In total, 261,169 varicose vein procedures were performed during the period studied. There were 686 VTEs recorded at 30 days (0.26 % incidence), 884 at 90 days (0.34 % incidence), and 1,246 at one year (0.48 % incidence). The VTE incidence for different procedures was between 0.15–0.35 % at 30 days, 0.26–0.50 % at 90 days, and 0.46–0.58 % at one year. At 30 days there was a significantly lower incidence of VTEs for foam sclerotherapy compared to other procedures (p = 0.01). There was no difference in VTE incidence between procedures at 90 days (p = 0.13) or one year (p = 0.16). Conclusions: Patients undergoing varicose vein procedures have a small but appreciable increased risk of VTE compared to the general population, with the effect persisting at one year. Foam sclerotherapy had a lower incidence of VTE compared to other procedures at 30 days, but this effect did not persist at 90 days or at one year. There was no other significant difference in the incidence of VTE between open, endovenous, and foam sclerotherapy treatments.

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