In this study, the spin-dependent nonlinear contrast transfer in transmission electron microscopy is derived from the eikonal expansion of the Dirac equation. The transmission cross-coefficient of the standard imaging theory is amended by a spin-dependent factor, whose effect is investigated for single scattering in the object by an electrical field under polarized and unpolarized illumination, and it is illustrated with numerical results and plots for a kinetic energy of 80 keV. The resulting image displacement and image convolution increase with decreasing kinetic energy but are always smaller than a wavelength. General features of the cross-coefficient are discussed to identify favorable conditions for the measurement of the small spin effects, possibly in an unmodified instrument.

The optimum imaging of an object structure at the sub-angstrom length scale requires precise adjustment of the lens aberrations of a high-resolution instrument up to the fifth order. A least-squares optimization of defocus aberration C1, third-order spherical aberration C3, and fifth-order spherical aberration C5 yields two sets of aberration coefficients for strong phase contrast up to the information limit: one for variable C1 and C3, at fixed C5, another for variable C1, C3, and C5. An additional correction to the defocus aberration, dependent on object thickness, is described, which becomes important for the use of image simulation programs in predicting optimum high-resolution contrast from thin objects at the sub-angstrom scale. For instruments with a sub-angstrom information limit the ultimate structure resolution, the power to resolve adjacent atom columns in a crystalline object, depends on both the instrumental pointspread and an object pointspread due to finite width of the atomic column potentials. A simulation study on a simple double-column model yields a range for structure resolutions, dependent on the atomic scattering power, from 0.070 nm down to 0.059 nm, for a hypothetical 300-kV instrument with an information limit of 0.050 nm.

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.

A novel imaging mode for high-resolution transmission electron microscopy is described. It is based on the adjustment of a negative value of the spherical aberration CS of the objective lens of a transmission electron microscope equipped with a multipole aberration corrector system. Negative spherical aberration applied together with an overfocus yields high-resolution images with bright-atom contrast. Compared to all kinds of images taken in conventional transmission electron microscopes, where the then unavoidable positive spherical aberration is combined with an underfocus, the contrast is dramatically increased. This effect can only be understood on the basis of a full nonlinear imaging theory. Calculations show that the nonlinear contrast contributions diminish the image contrast relative to the linear image for a positive-CS setting whereas they reinforce the image contrast relative to the linear image for a negative-CS setting. The application of the new mode to the imaging of oxygen in SrTiO3 and YBa2Cu3O7 demonstrates the benefit to materials science investigations. It allows us to image directly, without further image processing, strongly scattering heavy-atom columns together with weakly scattering light-atom columns.