Differential algebraic analysis for high order chromatic aberrations of magnetic electron lenses

One of the instrumental factors often limiting the resolution of the electron microscope is image defocussing due to changes in accelerating voltage or objective lens current. This factor is particularly important in high voltage electron microscopes both because of the higher voltages and lens currents required but also because of the inherently longer focal lengths, i.e. 6 mm in contrast to 1.5-2.2 mm for modern short focal length objectives.The usual practice in commercial electron microscopes is to design separately stabilized accelerating voltage and lens supplies. In this case chromatic aberration in the image is caused by the random and independent fluctuations of both the high voltage and objective lens current.

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New Aspects in the Design of Electron Optical Magnification Systems

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010009628x ◽

1972 ◽

Vol 30 ◽

pp. 606-607

Author(s):

Willem H.J. Andersen

Keyword(s):

Electron Microscope ◽

Imaging System ◽

Chromatic Aberration ◽

Research Tool ◽

Energy Losses ◽

Objective Lens ◽

Theoretical Limit ◽

Optical Magnification ◽

Chromatic Aberrations ◽

High Degree

Electron microscope design, and particularly the design of the imaging system, has reached a high degree of perfection. Present objective lenses perform up to their theoretical limit, while the whole imaging system, consisting of three or four lenses, provides very wide ranges of magnification and diffraction camera length with virtually no distortion of the image. Evolution of the electron microscope in to a routine research tool in which objects of steadily increasing thickness are investigated, has made it necessary for the designer to pay special attention to the chromatic aberrations of the magnification system (as distinct from the chromatic aberration of the objective lens). These chromatic aberrations cause edge un-sharpness of the image due to electrons which have suffered energy losses in the object.There exist two kinds of chromatic aberration of the magnification system; the chromatic change of magnification, characterized by the coefficient Cm, and the chromatic change of rotation given by Cp.

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

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108799 ◽

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.

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The usefulness of high index low symmetry zone axes for holz line analysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100126718 ◽

1987 ◽

Vol 45 ◽

pp. 384-385

Author(s):

C. M. Sung ◽

D. B. Williams

Keyword(s):

Lattice Parameter ◽

High Order ◽

Zone Axis ◽

High Index ◽

High Symmetry ◽

Second Phases ◽

Line Patterns ◽

Low Symmetry ◽

Line Analysis

Researchers have tended to use high symmetry zone axes (e.g. <111> <114>) for High Order Laue Zone (HOLZ) line analysis since Jones et al reported the origin of HOLZ lines and described some of their applications. But it is not always easy to find HOLZ lines from a specific high symmetry zone axis during microscope operation, especially from second phases on a scale of tens of nanometers. Therefore it would be very convenient if we can use HOLZ lines from low symmetry zone axes and simulate these patterns in order to measure lattice parameter changes through HOLZ line shifts. HOLZ patterns of high index low symmetry zone axes are shown in Fig. 1, which were obtained from pure Al at -186°C using a double tilt cooling holder. Their corresponding simulated HOLZ line patterns are shown along with ten other low symmetry orientations in Fig. 2. The simulations were based upon kinematical diffraction conditions.

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Are HOLZ lines kinematic in off-zone-axis orientation?

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100149295 ◽

1993 ◽

Vol 51 ◽

pp. 692-693

Author(s):

J. M. Zuo ◽

A. L. Weickenmeier ◽

R. Holmestad ◽

J. C. H. Spence

Keyword(s):

Structure Determination ◽

Standard Procedure ◽

High Order ◽

Zone Axis ◽

Great Promise ◽

Line Position ◽

Measured Intensity ◽

Constant Intensity ◽

Axis Orientation ◽

Diffraction Condition

The application of high order reflections in a weak diffraction condition off the zone axis center, including those in high order laue zones (HOLZ), holds great promise for structure determination using convergent beam electron diffraction (CBED). It is believed that in this case the intensities of high order reflections are kinematic or two-beam like. Hence, the measured intensity can be related to the structure factor amplitude. Then the standard procedure of structure determination in crystallography may be used for solving unknown structures. The dynamic effect on HOLZ line position and intensity in a strongly diffracting zone axis is well known. In a weak diffraction condition, the HOLZ line position may be approximated by the kinematic position, however, it is not clear whether this is also true for HOLZ intensities. The HOLZ lines, as they appear in CBED patterns, do show strong intensity variations along the line especially near the crossing of two lines, rather than constant intensity along the Bragg condition as predicted by kinematic or two beam theory.

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Toward The Simultaneous Correction of Spherical and Chromatic Aberration in Electron Optics by Means of an Electrostatic Electron Mirror

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100179786 ◽

1990 ◽

Vol 48 (1) ◽

pp. 206-207

Author(s):

Gertrude. F. Rempfer

Keyword(s):

Chromatic Aberration ◽

Transverse Magnetic ◽

Objective Lens ◽

Ion Imaging ◽

Corrected Image ◽

Electric And Magnetic Fields ◽

Chromatic Aberrations ◽

Improved Performance ◽

Electron Microscopes ◽

Image Planes

Optimum performance in electron and ion imaging instruments, such as electron microscopes and probe-forming instruments, in most cases depends on a compromise either between imaging errors due to spherical and chromatic aberrations and the diffraction error or between the imaging errors and the current in the image. These compromises result in the use of very small angular apertures. Reducing the spherical and chromatic aberration coefficients would permit the use of larger apertures with resulting improved performance, granted that other problems such as incorrect operation of the instrument or spurious disturbances do not interfere. One approach to correcting aberrations which has been investigated extensively is through the use of multipole electric and magnetic fields. Another approach involves the use of foil windows. However, a practical system for correcting spherical and chromatic aberration is not yet available.Our approach to correction of spherical and chromatic aberration makes use of an electrostatic electron mirror. Early studies of the properties of electron mirrors were done by Recknagel. More recently my colleagues and I have studied the properties of the hyperbolic electron mirror as a function of the ratio of accelerating voltage to mirror voltage. The spherical and chromatic aberration coefficients of the mirror are of opposite sign (overcorrected) from those of electron lenses (undercorrected). This important property invites one to find a way to incorporate a correcting mirror in an electron microscope. Unfortunately, the parts of the beam heading toward and away from the mirror must be separated. A transverse magnetic field can separate the beams, but in general the deflection aberrations degrade the image. The key to avoiding the detrimental effects of deflection aberrations is to have deflections take place at image planes. Our separating system is shown in Fig. 1. Deflections take place at the separating magnet and also at two additional magnetic deflectors. The uncorrected magnified image formed by the objective lens is focused in the first deflector, and relay lenses transfer the image to the separating magnet. The interface lens and the hyperbolic mirror acting in zoom fashion return the corrected image to the separating magnet, and the second set of relay lenses transfers the image to the final deflector, where the beam is deflected onto the projection axis.

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