The contrast formation in high resolution TEM (HRTEM) can only be explained by the wave nature of electrons. In HRTEM a virtually planar electron wave transmits a thin specimen (thickness < 20 nm), in most cases a crystal. During transmission the incident electron wave is scattered (or diffracted in the case of a crystal) at the potentials of the atoms, and thereby the phase of the electron wave is changed. At the exit surface of the specimen the object wave is formed, which carries direct and highly resolved information on the object. The object wave is magnified in the electron microscope and during this process the wave suffers additional phase shifts due to imperfect lenses (aberrations). Finally, the image recorded on film plates or digital cameras is an interference pattern of the image wave, which itself and it contains essentially phase contrast with all the microscopic aberrations included. A single recorded image in HRTEM consists of electron intensities only - the phase of the wave and hence an important information on the object is lost.
In conventional HRTEM, image interpretation is performed by an iterative procedure by comparing numerically simulated images with images acquired at the electron microscope. The computer-simulated images are based on atomic model structures, including all imaging parameters that need to be known as precisely as possible. The resolution limit of the structure analysis is determined by the point resolution of the microscope which is the optical resolution of the objective lens.

For a few years HRTEM structure analysis has now been be performed more reliably and with better resolution by object wave reconstruction. There are different methods to retrieve the object wave, and we use the reconstruction from focus series [1,2,3]. A series of 10 to 30 images with defined focus increment is acquired from the region of interest. On the basis of the recorded image intensities, a first approximation of the exit wave is calculated by the so-called paraboloid method [4]. The object wave is then refined with a maximum-likelihood approach [5], and for that iterative procedure the comparison is made at the level of experimentally observed and calculated image intensities.

In that method the imaging process in the electron microscope is virtually inverted. The final result is the retrieved object or exit wave. The exit wave can be reconstructed from the focus series and, compared to single exposures, be interpreted up to a higher resolution that corresponds to the so-called information limit (CM3000FEG: approx. 0.12 nm). The big advantage of the object wave is that the imaging procedure in the electron microscope with all its imperfect imaging properties is eliminated, and thereby highly resolved information directly from the electron exit surface of the specimen is recovered. Further advantages are that the information is obtained in form of two images, the phase and the amplitude contrast, and these contain much less noise than the original images of the electron microscope.

We predominantly apply the reconstruction of the object wave from focus series to the structural characterisation of interfaces in real structures of solids of doped systems such as ZnO-Ga2O3 und ZnO-Fe2O3, as well as for the study of interfaces in the thin film systems produced in our group. In the latter systems it was possible to investigate in detail and finally to solve the structure on the atomic level of interfaces between sapphire and lanthanum hexaaluminate.

[1] W.O. Saxton: Object reconstruction, In Computer Techniques for Image Processing in Electron Microscopy (Ed. L. Marton), Academic Press, New York (1978) 236.
[2] D. Van Dyck, W.M.J. Coene: A new procedure for wave reconstruction in high resolution electron microscopy, Optik 77 (1987) 125.
[3] D. Van Dyck, M. Op de Beeck, W.M.J. Coene: A new approach to object wave reconstruction in electron microscopy, Optik 93 (1993) 103.
[4] M. Op de Beeck, D. Van Dyck, W.M.J. Coene: Wave function reconstruction in HRTEM: the parabola method, Ultramicroscopy 64 (1996) 167.
[5] W.M.J. Coene, A. Thust, M. Op de Beeck: Maximum-likelihood method for focus variation image reconstruction in high resolution transmission electron microscopy, Ultramicroscopy 64 (1996) 109.