Electron lenses are extremely poor: if glass lenses were as bad, we should see as well with the naked eye as with a microscope! The demonstration by Otto Scherzer in 1936 that skillful lens design could never eliminate the spherical and chromatic aberrations of rotationally symmetric electron lenses was therefore most unwelcome and the other great electron optician of those years, Walter Glaser, never ceased striving to find a loophole in Scherzer's proof. In the wartime and early post-war years, the first proposals for correcting C(s) were made and in 1947, in a second milestone paper, Scherzer listed these and other ways of correcting lenses; soon after, Dennis Gabor invented holography for the same purpose. These approaches will be briefly summarized and the work that led to the successful implementation of quadupole-octopole and sextupole correctors in the 1990 s will be analysed. In conclusion, the elegant role of image algebra in describing image formation and processing and, above all, in developing new methods will be mentioned.

Aberration correction past and present.

The spherical and chromatic aberrations of a converging electron mirror are of opposite sign from those of electron lenses. This important property makes it possible in principle to compensate the aberrations of electron lenses by means of an electron mirror and to design electron microscopes based on a corrected optics system incorporating an electron mirror. In this paper the properties of the hyperbolic electron mirror are calculated, and the conditions for simultaneous correction of spherical and chromatic aberrations are worked out for several types of electron microscopes. The hyperbolic mirror field is a rotationally symmetric potential field between two electrodes. The electrodes are shaped as equipotential surfaces of the hyperbolic field, except for an aperture on the axis of the positive electrode for entrance and exit of electrons. The effect of the aperture is to create a thin diverging aperture lens at the termination of the hyperbolic field. The properties of the mirror are calculated analytically. The problem of separating the electron beam incident on the mirror from the beam returning from the mirror without impairing the image quality is solved by means of magnetic deflecting fields located at image planes. The mirror corrections can be applied to either magnetic or electrostatic lenses. The parameters for correction of aberrations are calculated for systems using electrostatic lenses. With appropriate polarity of the accelerating voltage and the lens and mirror voltages the calculations apply to ion imaging systems as well.

A theoretical study of the hyperbolic electron mirror as a correcting element for spherical and chromatic aberration in electron optics

A technique for measuring the extremely small (<2 nm) probe sizes generated in a field emission gun analytical electron microscope is described. The technique involves scanning the fine probe across the edge of small oriented MgO cubes. A mathematical description of the intensity profiles is developed and it is shown how this relates to various definitions of the probe size. The experimentally measured probe sizes are then combined in a consistent manner with both beam broadening calculations and experimental measurements. This approach results in the first self-consistent definition of the spatial resolution of X-ray microanalysis in thin foils.

A consistent definition of probe size and spatial resolution in the analytical electron microscope

The local structure in a ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$ bulk metallic glass was examined using a spherical-aberration-corrected high resolution TEM. Fcc-Pd(Ni) type nanoclusters and local compound (phosphide)-like nanoclusters with sizes of $1--2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ embedded in a dense-randomly-packed amorphous matrix were clearly observed under an appropriate imaging condition. However, three-dimensional atom-probe elemental mapping revealed there is virtually no nanoscale compositional difference between the nanoclusters and amorphous matrix beyond the statistical error range. A very small interfacial energy between the nanophase and the matrix is able to form a metastable amorphous phase with a structural fluctuation.

Local atomic ordering and nanoscale phase separation in a Pd-Ni-P bulk metallic glass

Recently developed aberration correctors have brought significant improvements in materials characterization. In aberration-corrected scanning transmission electron microscopy (STEM), the incident probe dimensions can be refined significantly, and image resolution has already reached sub-angstrom levels in high-angle annular dark-field (HAADF) STEM imaging (Batson et al. 2002, Nellist et al. 2004). In addition, materials characterization at the atomic level can routinely be performed by electron energy-loss spectrometry (EELS) in aberration-corrected STEM (e.g. Varela et al. 2005). The aberration correction of the incident beam is also very useful for X-ray energy-dispersive spectrometry (XEDS) because the spatial resolution can be dramatically improved with the refined probe (Watanabe et al. 2006).

X-Ray Energy-Dispersive Spectrometry in Scanning Transmission Electron Microscopes

Etude de l'effet de l'aberration spherique sur un faisceau sonde avec un diametre gaussien modere de 4,4 nm. Le diametre du faisceau a ete mesure a partir du flou de l'image en champ clair du bord d'une plaque de cristal de trioxyde de molybdene pour divers semi-angles de convergence du faisceau sonde allant de 11 a 43 mrad

Effect of the Spherical Aberration on Electron Probe Size

Characteristics and effectiveness of a foil lens for correction of spherical aberration in scanning transmission electron microscopy

Reduction of the Probe Diameter through the Correction of Spherical Aberration by the Foil Lens

Improvement of an Electron Probe Profile Using the Foil Lens

Numerical Evaluations of Characteristics of the Foil Lens in Correcting the Spherical Aberration of the Objective Lens of a Conventional Transmission Electron Microscope

Takaaki Hanai

Papers

Effect of the Spherical Aberration on Electron Probe Size

Characteristics and effectiveness of a foil lens for correction of spherical aberration in scanning transmission electron microscopy

Reduction of the Probe Diameter through the Correction of Spherical Aberration by the Foil Lens

Improvement of an Electron Probe Profile Using the Foil Lens

Numerical Evaluations of Characteristics of the Foil Lens in Correcting the Spherical Aberration of the Objective Lens of a Conventional Transmission Electron Microscope