Methods for accurate and automated determination of the coefficients of the wave aberration function are compared with particular emphasis on measurements of higher order coefficients in corrected instruments. Experimental applications of aberration measurement to the determination of illumination isoplanicity and high precision local refinement of restored exit waves are also described.

The design and construction of a double-hexapole aberration corrector has made it possible to build the prototype of a spherical-aberration corrected transmission electron microscope dedicated to high-resolution imaging on the atomic scale. The corrected instrument, a Philips CM200 FEG ST, has an information limit of better than 0.13 nm, and the spherical aberration can be varied within wide limits, even to negative values. The aberration measurement and the corrector control provide instrument alignments stable enough for materials science investigations. Analysis of the contrast transfer with the possibility of tunable spherical aberration has revealed new imaging modes: high-resolution amplitude contrast, extension of the point resolution to the information limit, and enhanced image intensity modulation for negative phase contrast. In particular, through the combination of small negative spherical aberration and small overfocus, the latter mode provides the high-resolution imaging of weakly scattering atom columns, such as oxygen, in the vicinity of strongly scattering atom columns. This article reviews further lens aberration theory, the principle of aberration correction through multipole lenses, aspects for practical work, and materials science applications.

Indirect high resolution electron microscopy using one of several possible data-set geometries offers advantages over conventional high-resolution imaging in enabling the recovery of the complex wavefunction at the specimen exit plane and simultaneously eliminating the aberrations present in the objective lens. This article discusses results obtained using this method from structures formed by inorganic materials confined within the bores of carbon nanotubes. Such materials are shown to be atomically regulated due to their confinement, leading to integral layer architectures that we have termed “Feynman crystals.” These one-dimensional (1D) crystals also show a wide range of structural deviations from the bulk, including unexpected lattice distortions, and in some cases entirely new forms have been observed.

Improvements in instrumentation and image processing techniques mean that methods involving reconstruction of focal or beam-tilt series of images are now realizing the promise they have long offered. This indirect approach recovers both the phase and the modulus of the specimen exit plane wave function and can extend the interpretable resolution. However, such reconstructions require the a posteriori determination of the objective lens aberrations, including the actual beam tilt, defocus, and twofold and threefold astigmatism. In this review, we outline the theory behind exit plane wavefunction reconstruction and describe methods for the accurate and automated determination of the required coefficients of the wave aberration function. Finally, recent applications of indirect reconstruction in the structural analysis of complex oxides are presented.