MAXIMUM OF THE FACTOR OF ENCIRCLED ENERGY

1961 ◽  
Vol 39 (1) ◽  
pp. 158-188 ◽  
Author(s):  
Guy Lansraux ◽  
Germain Boivin
Keyword(s):  
Diffraction Pattern ◽  
Spherical Aberration ◽  
Asymptotic Expression ◽  
Radiant Energy ◽  
The Other ◽  
Optical Systems ◽  
Rigorous Analysis ◽  
Gauss Function ◽  
Taylor’S Series

It is recognized that the most favorable distribution of radiant energy in a diffraction pattern is that which corresponds to the best concentration around the center O. This hypothesis is expressed by an extremal condition on the factor of encircled energy E(W), that is, the ratio of the energy inside a circle of radius W and centered on the diffraction pattern, to the total energy in the same.A study of the effects of spherical aberration on this factor of encircled energy has shown that aberration always tends to decrease the factor from the value obtained with an Airy pattern. However, this factor may be increased by the use of an amplitude filter at the pupil of the optical system.In treating the case of amplitude filters one may use a rigorous analysis in terms of Taylor's series in (1−x2)p−1 or a polynomial Tn(x) of degree n−1 in terms of (1−x2).The corresponding amplitudes in the diffraction pattern are Г(W) and Гn(W); the maximum factor of encircled energy E(Wm) and En(Wm). The following convergences are established: En(Wm) → E(Wm), Tn(x) → T(x), and Гn(W) → Г(W) as n → ∞.When the interval (0, Wm) of the diffraction pattern is made to correspond to the interval (0, 1) of the pupil by means of a suitable normalization the amplitude distributions T(x) and Г(W)—with W = Wmx—are identical. Some properties are deduced from this relation; for example, the Airy pattern is the limit of Г(W) when Wm → 0; on the other hand, the Gauss function [Formula: see text] is an asymptotic expression of T(x) when Wm → ∞. In any case, the factor of encircled energy is connected to the marginal amplitude in the pupil by the relation E(Wm) = 1−T2(1).The numerical determination of E(W) given up to W = 10 and Wm = 2, 3, 4, and 5 can be extended by use of an asymptotic expression of the factor of encircled energy.Finally, a curve M(W) has been obtained, which is an envelope of the curves E(W) corresponding to various values of Wm. This gives the locus of the maximum factor of encircled energy and represents the limiting performance of optical systems.

New apodizers that arbitrarily decrease sensitivity to defocusing or to the variation of spherical aberration

1988 ◽  
Vol 66 (10) ◽  
pp. 878-882
Author(s):  
Richard Boivin
Keyword(s):  
Spherical Aberration ◽  
The Other ◽  
Optical Systems ◽  
Depth Of Focus ◽  
Rotationally Symmetric

Two families of pupil amplitude filters, or apodizers, are devised for rotationally symmetric optical systems. One type of apodizer, pertaining to systems with circular pupils, arbitrarily reduces their sensitivity to the variation of primary spherical aberration, when this is combined with defocusing to optimally compensate for the aberration. The other type of apodizer, pertaining to systems with slit pupils, arbitrarily extends their depth of focus.

Electron Diffraction Analysis of Microtwin Structures in Regrown (III) Silicon

1982 ◽  
Vol 40 ◽  
pp. 460-461
Author(s):  
P. Ling ◽  
R. Gronsky ◽  
J. Washburn
Keyword(s):  
Electron Diffraction ◽  
Ion Implantation ◽  
Diffraction Analysis ◽  
Diffraction Pattern ◽  
Direct Consequence ◽  
The Other ◽  
Electron Diffraction Analysis ◽  
Defect Microstructures ◽  
Ion Implanted

The defect microstructures of Si arising from ion implantation and subsequent regrowth for a (111) substrate have been found to be dominated by microtwins. Figure 1(a) is a typical diffraction pattern of annealed ion-implanted (111) Si showing two groups of extra diffraction spots; one at positions (m, n integers), the other at adjacent positions between <000> and <220>. The object of the present paper is to show that these extra reflections are a direct consequence of the microtwins in the material.

Determination of the lattice translation across {110} APBs in GaAs

1988 ◽  
Vol 46 ◽  
pp. 600-601
Author(s):  
D.R. Rasmussen ◽  
N.-H. Cho ◽  
C.B. Carter
Keyword(s):  
Grain Boundaries ◽  
Lower Energy ◽  
Antiphase Boundary ◽  
The Other ◽  
Boundary Structure ◽  
Interface Plane ◽  
Inversion Symmetry ◽  
High Angle ◽  
Equilibrium Distance

Domains in GaAs can exist which are related to one another by the inversion symmetry, i.e., the sites of gallium and arsenic in one domain are interchanged in the other domain. The boundary between these two different domains is known as an antiphase boundary [1], In the terminology used to describe grain boundaries, the grains on either side of this boundary can be regarded as being Σ=1-related. For the {110} interface plane, in particular, there are equal numbers of GaGa and As-As anti-site bonds across the interface. The equilibrium distance between two atoms of the same kind crossing the boundary is expected to be different from the length of normal GaAs bonds in the bulk. Therefore, the relative position of each grain on either side of an APB may be translated such that the boundary can have a lower energy situation. This translation does not affect the perfect Σ=1 coincidence site relationship. Such a lattice translation is expected for all high-angle grain boundaries as a way of relaxation of the boundary structure.

Determination of the Burgers vector of a dislocation in a Fe-Mn alloy by weak-beam image in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 330-331
Author(s):  
Y. Ishida ◽  
H. Ishida ◽  
K. Kohra ◽  
H. Ichinose
Keyword(s):  
High Order ◽  
Simulation Technique ◽  
The Other ◽  
Image Simulation ◽  
Diffraction Vector ◽  
Burgers Vector ◽  
Weak Beam ◽  
Beam Image ◽  
Edge Component

IntroductionA simple and accurate technique to determine the Burgers vector of a dislocation has become feasible with the advent of HVEM. The conventional image vanishing technique(1) using Bragg conditions with the diffraction vector perpendicular to the Burgers vector suffers from various drawbacks; The dislocation image appears even when the g.b = 0 criterion is satisfied, if the edge component of the dislocation is large. On the other hand, the image disappears for certain high order diffractions even when g.b ≠ 0. Furthermore, the determination of the magnitude of the Burgers vector is not easy with the criterion. Recent image simulation technique is free from the ambiguities but require too many parameters for the computation. The weak-beam “fringe counting” technique investigated in the present study is immune from the problems. Even the magnitude of the Burgers vector is determined from the number of the terminating thickness fringes at the exit of the dislocation in wedge shaped foil surfaces.

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.

Procedures for the Quantitative Determination of Autoprothrombin C

1962 ◽  
Vol 08 (03) ◽  
pp. 434-441 ◽  
Author(s):  
Edmond R Cole ◽  
Ewa Marciniak ◽  
Walter H Seegers
Keyword(s):  
Quantitative Determination ◽  
Plasma Sample ◽  
Quantitative Measure ◽  
The Other ◽  
Clotting Time ◽  
Bovine Plasma ◽  
Autoprothrombin C

SummaryTwo quantitative procedures for autoprothrombin C are described. In one of these purified prothrombin is used as a substrate, and the activity of autoprothrombin C can be measured even if thrombin is in the preparation. In this procedure a reaction mixture is used wherein the thrombin titer which develops in 20 minutes is proportional to the autoprothrombin C in the reaction mixture. A unit is defined as the amount which will generate 70 units of thrombin in the standardized reaction mixture. In the other method thrombin interferes with the result, because a standard bovine plasma sample is recalcified and the clotting time is noted. Autoprothrombin C shortens the clotting time, and the extent of this is a quantitative measure of autoprothrombin C activity.

Determination of Factor XIII Activity and of Factor XIII Inhibitors Using an Ammonium-Sensitive Electrode

1983 ◽  
Vol 50 (02) ◽  
pp. 563-566 ◽  
Author(s):  
P Hellstern ◽  
K Schilz ◽  
G von Blohn ◽  
E Wenzel
Keyword(s):  
Factor Xiii ◽  
Normal Subjects ◽  
The Other ◽  
Activity Measurement ◽  
Factor Xiii Deficiency ◽  
Assay Procedure ◽  
Stabilization Factor ◽  
Release Method ◽  
Sensitive Electrode

SummaryAn assay for rapid factor XIII activity measurement has been developed based on the determination of the ammonium released during fibrin stabilization. Factor XIII was activated by thrombin and calcium. Ammonium was measured by an ammonium-sensitive electrode. It was demonstrated that the assay procedure yields accurate and precise results and that factor XIII-catalyzed fibrin stabilization can be measured kinetically. The amount of ammonium released during the first 90 min of fibrin stabilization was found to be 7.8 ± 0.5 moles per mole fibrinogen, which is in agreement with the findings of other authors. In 15 normal subjects and in 15 patients suffering from diseases with suspected factor XIII deficiency there was a satisfactory correlation between the results obtained by the “ammonium-release-method”, Bohn’s method, and the immunological assay (r1 = 0.65; r2= 0.70; p<0.01). In 3 of 5 patients with paraproteinemias the values of factor XIII activity determined by the ammonium-release method were markedly lower than those estimated by the other methods. It could be shown that inhibitor mechanisms were responsible for these discrepancies.

Determination of the Number of Conserved Chromosomal Segments Between Species

Genetics ◽  
2001 ◽  
Vol 157 (3) ◽  
pp. 1387-1395 ◽  
Author(s):  
Sudhir Kumar ◽  
Sudhindra R Gadagkar ◽  
Alan Filipski ◽  
Xun Gu
Keyword(s):  
Statistical Approach ◽  
Common Ancestor ◽  
Chromosomal Rearrangements ◽  
Structural Similarity ◽  
The Other ◽  
Segment Length ◽  
Human Genomes ◽  
Genomic Divergence ◽  
Human And Mouse

AbstractGenomic divergence between species can be quantified in terms of the number of chromosomal rearrangements that have occurred in the respective genomes following their divergence from a common ancestor. These rearrangements disrupt the structural similarity between genomes, with each rearrangement producing additional, albeit shorter, conserved segments. Here we propose a simple statistical approach on the basis of the distribution of the number of markers in contiguous sets of autosomal markers (CSAMs) to estimate the number of conserved segments. CSAM identification requires information on the relative locations of orthologous markers in one genome and only the chromosome number on which each marker resides in the other genome. We propose a simple mathematical model that can account for the effect of the nonuniformity of the breakpoints and markers on the observed distribution of the number of markers in different conserved segments. Computer simulations show that the number of CSAMs increases linearly with the number of chromosomal rearrangements under a variety of conditions. Using the CSAM approach, the estimate of the number of conserved segments between human and mouse genomes is 529 ± 84, with a mean conserved segment length of 2.8 cM. This length is &lt;40% of that currently accepted for human and mouse genomes. This means that the mouse and human genomes have diverged at a rate of ∼1.15 rearrangements per million years. By contrast, mouse and rat are diverging at a rate of only ∼0.74 rearrangements per million years.

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