Three-dimensional diffraction theory of microscope image formation

1952 ◽  
Vol 212 (1109) ◽  
pp. 264-274 ◽  
Keyword(s):  
Three Dimensional ◽  
Image Formation ◽  
Diffraction Theory ◽  
X Rays ◽  
Vertical Separation ◽  
Standard Methods ◽  
Microscope Image ◽  
Diffraction Of Light ◽  
Dimensional Object ◽  
Horizontal Layers

The Abbe theory of image formation for a plane object is extended to apply to the case of a three-dimensional object. The diffraction of light by such an object is treated by the standard methods applied to the diffraction of X-rays by crystals. The formation of an image of a three-dimensional periodic object is discussed, and it is shown that certain Fourier components of the structure of the object are reproduced in the image while others are left out. An expression is obtained for the minimum vertical separation between horizontal layers that can just be resolved by racking the microscope up and down; this depends on the scale of the detail in the layers.

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).

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

Measurements in 3D images

1991 ◽  
Vol 49 ◽  
pp. 408-409
Author(s):  
John C. Russ
Keyword(s):  
Three Dimensional ◽  
Image Plane ◽  
X Rays ◽  
Traditional Use ◽  
3D Images ◽  
Confocal Scanning Laser Microscope ◽  
Hard Materials ◽  
Depth Direction ◽  
Confocal Scanning ◽  
Confocal Scanning Laser

Three-dimensional (3D) images consisting of arrays of voxels can now be routinely obtained from several different types of microscopes. These include both the transmission and emission modes of the confocal scanning laser microscope (but not its most common reflection mode), the secondary ion mass spectrometer, and computed tomography using electrons, X-rays or other signals. Compared to the traditional use of serial sectioning (which includes sequential polishing of hard materials), these newer techniques eliminate difficulties of alignment of slices, and maintain uniform resolution in the depth direction. However, the resolution in the z-direction may be different from that within each image plane, which makes the voxels non-cubic and creates some difficulties for subsequent analysis.

X-ray diffraction properties of curved crystal diffractors

1992 ◽  
Vol 50 (2) ◽  
pp. 1734-1735
Author(s):  
W. Z. Chang ◽  
D. B. Wittry
Keyword(s):  
Diffraction Theory ◽  
X Rays ◽  
Diffraction Image ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Bent Crystal ◽  
Diffraction Geometry ◽  
Crystal Parameter ◽  
Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

Image formation analysis of thick biological specimens using three-dimensional power-spectra of through focus series

1994 ◽  
Vol 52 ◽  
pp. 124-125
Author(s):  
Karen F. Han
Keyword(s):  
Inelastic Scattering ◽  
Imaging Techniques ◽  
Mass Density ◽  
Relative Proportion ◽  
Three Dimensional ◽  
Power Spectra ◽  
Image Formation ◽  
Energy Filtering ◽  
Ewald Sphere ◽  
Nonlinear Imaging

The primary focus in our laboratory is the study of higher order chromatin structure using three dimensional electron microscope tomography. Three dimensional tomography involves the deconstruction of an object by combining multiple projection views of the object at different tilt angles, image intensities are not always accurate representations of the projected object mass density, due to the effects of electron-specimen interactions and microscope lens aberrations. Therefore, an understanding of the mechanism of image formation is important for interpreting the images. The image formation for thick biological specimens has been analyzed by using both energy filtering and Ewald sphere constructions. Surprisingly, there is a significant amount of coherent transfer for our thick specimens. The relative amount of coherent transfer is correlated with the relative proportion of elastically scattered electrons using electron energy loss spectoscopy and imaging techniques.Electron-specimen interactions include single and multiple, elastic and inelastic scattering. Multiple and inelastic scattering events give rise to nonlinear imaging effects which complicates the interpretation of collected images.

scholarly journals Is Micro X-ray Computer Tomography a Suitable Non-Destructive Method for the Characterisation of Dental Materials?

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1271
Author(s):  
Andreas Koenig ◽  
Leonie Schmohl ◽  
Johannes Scheffler ◽  
Florian Fuchs ◽  
Michaela Schulz-Siegmund ◽  
...  
Keyword(s):  
Flexural Strength ◽  
Computer Tomography ◽  
Mechanical Performance ◽  
Dental Materials ◽  
Three Dimensional ◽  
X Rays ◽  
Scanning Calorimetry ◽  
X Ray ◽  
Multiple Measurements ◽  
High Doses

The aim of the study was to investigate the effect of X-rays used in micro X-ray computer tomography (µXCT) on the mechanical performance and microstructure of a variety of dental materials. Standardised bending beams (2 × 2 × 25 mm3) were forwarded to irradiation with an industrial tomograph. Using three-dimensional datasets, the porosity of the materials was quantified and flexural strength was investigated prior to and after irradiation. The thermal properties of irradiated and unirradiated materials were analysed and compared by means of differential scanning calorimetry (DSC). Single µXCT measurements led to a significant decrease in flexural strength of polycarbonate with acrylnitril-butadien-styrol (PC-ABS). No significant influence in flexural strength was identified for resin-based composites (RBCs), poly(methyl methacrylate) (PMMA), and zinc phosphate cement (HAR) after a single irradiation by measurement. However, DSC results suggest that changes in the microstructure of PMMA are possible with increasing radiation doses (multiple measurements, longer measurements, higher output power from the X-ray tube). In summary, it must be assumed that X-ray radiation during µXCT measurement at high doses can lead to changes in the structure and properties of certain polymers.

Visualizing Fluid Flows With X-Rays

2007 ◽  
Author(s):  
Theodore J. Heindel ◽  
Terrence C. Jensen ◽  
Joseph N. Gray
Keyword(s):  
Computed Tomography ◽  
Flow Visualization ◽  
Three Dimensional ◽  
Fluid Flows ◽  
X Rays ◽  
Radiographic Images ◽  
Optical Access ◽  
X Ray ◽  
X Ray Computed ◽  
Density Map

There are several methods available to visualize fluid flows when one has optical access. However, when optical access is limited to near the boundaries or not available at all, alternative visualization methods are required. This paper will describe flow visualization using an X-ray system that is capable of digital X-ray radiography, digital X-ray stereography, and digital X-ray computed tomography (CT). The unique X-ray flow visualization facility will be briefly described, and then flow visualization of various systems will be shown. Radiographs provide a two-dimensional density map of a three dimensional process or object. Radiographic images of various multiphase flows will be presented. When two X-ray sources and detectors simultaneously acquire images of the same process or object from different orientations, stereographic imaging can be completed; this type of imaging will be demonstrated by trickling water through packed columns and by absorbing water in a porous medium. Finally, local time-averaged phase distributions can be determined from X-ray computed tomography (CT) imaging, and this will be shown by comparing CT images from two different gas-liquid sparged columns.

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