Analytical solutions for the principal maxima in multiple slit diffraction: Effects of slit width

Optik ◽  
2020 ◽  
Vol 208 ◽  
pp. 164062 ◽  
Author(s):  
Heung-Ryoul Noh
Keyword(s):  
Analytical Solutions ◽  
Slit Width ◽  
Diffraction Effects

Effects of the slit width on the subsidiary maxima in multiple-slit diffraction: Analytical solutions

Optik ◽  
2021 ◽  
Vol 226 ◽  
pp. 166011
Author(s):  
Heung-Ryoul Noh
Keyword(s):  
Analytical Solutions ◽  
Slit Width ◽  
Subsidiary Maxima

Discovery and Measurement of Double Stars by Lunar Occultations

1965 ◽  
Vol 5 ◽  
pp. 28-37
Author(s):  
R. Edward Nather ◽  
David S. Evans
Keyword(s):  
The Moon ◽  
Double Stars ◽  
Stellar Diameters ◽  
Diffraction Effects

When a star is occulted by the dark limb of the Moon its apparent intensity drops to zero very quickly. MacMahon (1909) proposed that the time of disappearance would measure the diameter of the star, but Eddington (1909) demonstrated that diffraction effects at the lunar limb would lengthen the apparent time of disappearance to about 20 msec, and suggested that these effects would greatly limit the usefulness of the technique. MacMahon’s paper indicates that he was aware that stellar duplicity could be detected from occultation observations, but he did not amplify the point and Eddington did not comment on it. While it has been demonstrated theoretically by Williams (1939) and experimentally by Whitford (1939) and others that stellar diameters of a few arcmsec can be measured by this technique, its use for the discovery and measurement of double stars has been only incidental to other programs (O’Keefe and Anderson, 1952; Evanset al., 1954). Properly exploited, the method can contribute materially to the study of double stars.

Transmission Electron Diffraction Analysis by Computer

1970 ◽  
Vol 28 ◽  
pp. 40-41
Author(s):  
R.A. Ploc ◽  
G.H. Keech
Keyword(s):  
Electron Diffraction ◽  
Input Data ◽  
Reciprocal Lattice ◽  
Computer Programme ◽  
Transmission Electron Diffraction ◽  
Usual Procedure ◽  
Transmission Electron ◽  
Complex Shapes ◽  
Computer Input ◽  
Diffraction Effects

An unambiguous analysis of transmission electron diffraction effects requires two samplings of the reciprocal lattice (RL). However, extracting definitive information from the patterns is difficult even for a general orthorhombic case. The usual procedure has been to deduce the approximate variables controlling the formation of the patterns from qualitative observations. Our present purpose is to illustrate two applications of a computer programme written for the analysis of transmission, selected area diffraction (SAD) patterns; the studies of RL spot shapes and epitaxy.When a specimen contains fine structure the RL spots become complex shapes with extensions in one or more directions. If the number and directions of these extensions can be estimated from an SAD pattern the exact spot shape can be determined by a series of refinements of the computer input data.

Characteristic Geometry and Diffraction Contrast of Dispersed ThO2 Crystals

1969 ◽  
Vol 27 ◽  
pp. 168-169
Author(s):  
R. J. Horylev ◽  
L. E. Murr
Keyword(s):  
Dark Field ◽  
Particle Orientation ◽  
Contrast Effects ◽  
Strain Fields ◽  
Diffraction Contrast ◽  
Dispersed Particles ◽  
Field Electron Microscopy ◽  
Dark Field Electron ◽  
Particle Images ◽  
Diffraction Effects

Smith has shown by dark-field electron microscopy of extracted ThO2 particles from TD-nickel (2% ThO2) that they possess single crystal characteristics. It is generally assumed that these particle dispersions are incoherent. However, some diffraction effects associated with the particle images appeared to be similar to coherency strain fields. The present work will demonstrate conclusively that ThO2 dispersed particles in TD-nickel (2% ThO2) and TD-NiCr (2% ThO2, 20% Cr, Ni) are single crystals. Moreover, the diffraction contrast effects are extinction fringes. That is, these effects arise because of the particle orientation with respect to the electron beam and the extinction conditions for various operating reflections The particles are in fact incoherent.

Diffraction effects from inclined grain boundaries in polycrystalline thin foils

1978 ◽  
Vol 36 (1) ◽  
pp. 420-421
Author(s):  
C.B. Carter ◽  
A.M. Donald ◽  
S.L. Sass
Keyword(s):  
Thin Film ◽  
Grain Boundaries ◽  
Boundary Plane ◽  
Foil Surface ◽  
Thin Foils ◽  
The Matrix ◽  
Firm Basis ◽  
Diffraction Patterns ◽  
Wave Matching ◽  
Diffraction Effects

Using thin-film gold bicrystals with the boundary plane parallel to the foil surface, it has been shown(l,2) that networks of grain boundary dislocations can act as diffraction gratings and give rise to subsidiary reflections close to the matrix reflections in electron diffraction patterns. Recently several groups of workers(3-5) have shown that inclined boundaries in polycrystalline specimens also produce extra reflections which may be due to the periodic nature of the boundaries. In general grain boundaries in polycrystalline specimens will be steeply inclined to the foil surface and additional reflections due to wave matching at the boundary(6) will also be present. The diffraction technique has the potential for providing detailed information on the structure of inclined boundaries (see, for example (5)), especially for the case where the image contains no useful information. In order to provide a firm basis for this technique, the geometry of the diffraction effects expected from inclined boundaries and the influence of these effects on the appearance of images will be examined.

Off-axis electron holography applied to the study of interfaces

1992 ◽  
Vol 50 (1) ◽  
pp. 244-245
Author(s):  
J.K. Weiss ◽  
M. Gajdardziska-Josifovska ◽  
M. R. McCartney ◽  
David J. Smith
Keyword(s):  
Electric Fields ◽  
Resolution Enhancement ◽  
Interfacial Structure ◽  
Atomic Scale ◽  
Bulk Property ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Composition And Structure ◽  
Chemical Segregation ◽  
Diffraction Effects

Interfacial structure is a controlling parameter in the behavior of many materials. Electron microscopy methods are widely used for characterizing such features as interface abruptness and chemical segregation at interfaces. The problem for high resolution microscopy is to establish optimum imaging conditions for extracting this information. We have found that off-axis electron holography can provide useful information for the study of interfaces that is not easily obtained by other techniques.Electron holography permits the recovery of both the amplitude and the phase of the image wave. Recent studies have applied the information obtained from electron holograms to characterizing magnetic and electric fields in materials and also to atomic-scale resolution enhancement. The phase of an electron wave passing through a specimen is shifted by an amount which is proportional to the product of the specimen thickness and the projected electrostatic potential (ignoring magnetic fields and diffraction effects). If atomic-scale variations are ignored, the potential in the specimen is described by the mean inner potential, a bulk property sensitive to both composition and structure. For the study of interfaces, the specimen thickness is assumed to be approximately constant across the interface, so that the phase of the image wave will give a picture of mean inner potential across the interface.

Quantitative energy-filtered tem imaging of interfaces

1996 ◽  
Vol 54 ◽  
pp. 542-543 ◽  
Author(s):  
J. Bentley ◽  
E. A. Kenik ◽  
K. Siangchaew ◽  
M. Libera
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Unit Volume ◽  
Core Loss ◽  
Mean Free Path ◽  
Slit Width ◽  
Elemental Mapping ◽  
Low Loss ◽  
Transmission Electron ◽  
Inelastic Mean Free Path

Quantitative elemental mapping by inner shell core-loss energy-filtered transmission electron microscopy (TEM) with a Gatan Imaging Filter (GIF) interfaced to a Philips CM30 TEM operated with a LaB6 filament at 300 kV has been applied to interfaces in a range of materials. Typically, 15s exposures, slit width Δ = 30 eV, TEM magnifications ∼2000 to 5000×, and probe currents ≥200 nA, were used. Net core-loss maps were produced by AE−r background extrapolation from two pre-edge windows. Zero-loss I0 (Δ ≈ 5 eV) and “total” intensity IT (unfiltered, no slit) images were used to produce maps of t/λ = ln(IT/I0), where λ is the total inelastic mean free path. Core-loss images were corrected for diffraction contrast by normalization with low-loss images recorded with the same slit width, and for changes in thickness by normalization with t/λ, maps. Such corrected images have intensities proportional to the concentration in atoms per unit volume. Jump-ratio images (post-edge divided by pre-edge) were also produced. Spectrum lines across planar interfaces were recorded with TEM illumination by operating the GIF in the spectroscopy mode with an area-selecting slit oriented normal to the energy-dispersion direction. Planar interfaces were oriented normal to the area-selecting slit with a specimen rotation holder.

Atomic Resolution in Crystal Aperture Stem

1990 ◽  
Vol 48 (1) ◽  
pp. 236-237
Author(s):  
J T Fourie
Keyword(s):  
Optical System ◽  
Spherical Aberration ◽  
Three Dimensional ◽  
Transmission Function ◽  
Optical Systems ◽  
Bragg Angle ◽  
Electron Optical System ◽  
Intimate Contact ◽  
Diffraction Effects ◽  
Design Aspect

The attempts at improvement of electron optical systems to date, have largely been directed towards the design aspect of magnetic lenses and towards the establishment of ideal lens combinations. In the present work the emphasis has been placed on the utilization of a unique three-dimensional crystal objective aperture within a standard electron optical system with the aim to reduce the spherical aberration without introducing diffraction effects. A brief summary of this work together with a description of results obtained recently, will be given.The concept of utilizing a crystal as aperture in an electron optical system was introduced by Fourie who employed a {111} crystal foil as a collector aperture, by mounting the sample directly on top of the foil and in intimate contact with the foil. In the present work the sample was mounted on the bottom of the foil so that the crystal would function as an objective or probe forming aperture. The transmission function of such a crystal aperture depends on the thickness, t, and the orientation of the foil. The expression for calculating the transmission function was derived by Hashimoto, Howie and Whelan on the basis of the electron equivalent of the Borrmann anomalous absorption effect in crystals. In Fig. 1 the functions for a g220 diffraction vector and t = 0.53 and 1.0 μm are shown. Here n= Θ‒ΘB, where Θ is the angle between the incident ray and the (hkl) planes, and ΘB is the Bragg angle.

A Transmission Electron Microscopical Investigation of Phase Transformations in TiNi

1980 ◽  
Vol 38 ◽  
pp. 340-341
Author(s):  
P. Moine ◽  
G. M. Michal ◽  
R. Sinclair
Keyword(s):  
Electron Microscopy ◽  
Phase Transformations ◽  
Applied Stress ◽  
Structural Changes ◽  
Microscopical Investigation ◽  
Temperature Range ◽  
Transmission Electron ◽  
Electron Microscopical ◽  
Diffraction Effects ◽  
Microscopy Images

Premartensitic effects in near equiatomic TiNi have been pointed out by several authors(1-5). These include anomalous contrast in electron microscopy images (mottling, striations, etc. ),diffraction effects(diffuse streaks, extra reflections, etc.), a resistivity peak above Ms (temperature at which a perceptible amount of martensite is formed without applied stress). However the structural changes occuring in this temperature range are not well understood. The purpose of this study is to clarify these phenomena.

Analytical solutions of the potential vorticity invertibility principle

2013 ◽  
pp. n/a-n/a ◽  
Author(s):  
Matthew T. Masarik ◽  
Wayne H. Schubert
Keyword(s):  
Analytical Solutions ◽  
Potential Vorticity
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