Measurement of Chromatic Aberrations Using Phase Retrieval

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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Quantitative analysis by reconstruction of HREM focal series

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100171432 ◽

1994 ◽

Vol 52 ◽

pp. 740-741

Author(s):

W. Coene ◽

A. Thust ◽

M. Op de Beeck ◽

D. Van Dyck

Keyword(s):

Phase Retrieval ◽

Image Plane ◽

Initial Guess ◽

Recursive Least Squares ◽

Objective Lens ◽

Electron Wave ◽

Electron Sources ◽

Original Algorithm ◽

Coherent Field ◽

Direct Interpretation

Compared to conventional electron sources, the use of a highly coherent field-emission gun (FEG) in TEM improves the information resolution considerably. A direct interpretation of this extra information, however, is hampered since amplitude and phase of the electron wave are scrambled in a complicated way upon transfer from the specimen exit plane through the objective lens towards the image plane. In order to make the additional high-resolution information interpretable, a phase retrieval procedure is applied, which yields the aberration-corrected electron wave from a focal series of HRTEM images (Coene et al, 1992).Kirkland (1984) tackled non-linear image reconstruction using a recursive least-squares formalism in which the electron wave is modified stepwise towards the solution which optimally matches the contrast features in the experimental through-focus series. The original algorithm suffers from two major drawbacks : first, the result depends strongly on the quality of the initial guess of the first step, second, the processing time is impractically high.

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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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Limitations to the Spacing Effect

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169.52.4.257 ◽

2005 ◽

Vol 52 (4) ◽

pp. 257-263 ◽

Cited By ~ 22

Author(s):

Peter P. J. L. Verkoeijen ◽

Remy M. J. P. Rikers ◽

Henk G. Schmidt

Keyword(s):

Free Recall ◽

Phase Retrieval ◽

Incidental Learning ◽

Factor Model ◽

Recall Performance ◽

Spacing Effect ◽

Word List ◽

Intentional Learning ◽

Study Phase ◽

Learning Condition

Abstract. The spacing effect refers to the finding that memory for repeated items improves when the interrepetition interval increases. To explain the spacing effect in free-recall tasks, a two-factor model has been put forward that combines mechanisms of contextual variability and study-phase retrieval (e.g., Raaijmakers, 2003 ; Verkoeijen, Rikers, & Schmidt, 2004 ). An important, yet untested, implication of this model is that free recall of repetitions should follow an inverted u-shaped relationship with interrepetition spacing. To demonstrate the suggested relationship an experiment was conducted. Participants studied a word list, consisting of items repeated at different interrepetition intervals, either under incidental or under intentional learning instructions. Subsequently, participants received a free-recall test. The results revealed an inverted u-shaped relationship between free recall and interrepetition spacing in both the incidental-learning condition and the intentional-learning condition. Moreover, for intentionally learned repetitions, the maximum free-recall performance was located at a longer interrepetition interval than for incidentally learned repetitions. These findings are interpreted in terms of the two-factor model of spacing effects in free-recall tasks.

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