Transfer of tilted sample information in transmission electron microscopy

Abstract

When a transmission electron microscope is used in imaging mode, information carried by the sample function is transformed by the optics of the instrument during the imaging process. A mathematical description of this physical process (the so-called imaging function) is a requirement for an accurate analysis and the interpretation of electron microscopy experimental data. When the sample is not imaged in tilted geometry (no defocus gradient is present across its extent), the imaging function has a well-known and extensively studied form : the Contrast Transfer Function (CTF) (Reimer, 1997). Several electron microscopy techniques, however, require the sample to be tilted to fully explore its 3-dimensional structure. Only recently a rigorous mathematical description for the imaging process under these conditions, derived from physical first principles, has been made available: the Tilted Contrast Imaging Function (TCIF) (Philippsen et al., 2006). The present work discusses in depth the nature and the characteristics of the TCIF model, expanding it to include astigmatism. A robust and efficient software implementation is presented, developed with the context of the IPLT software development framework (Philippsen et al., 2007). Computer simulations of images of tilted samples are then used to qualitatively and quantitatively analyze features of experimental images. No computationally-feasible analytical method for the inversion of the TCIF model is currently available, and its effects on experimental images are usually corrected using a number of heuristic methods that involve some approximations of the imaging parameters. Using computer simulations of tilted images, this work estimates the errors introduced by these approximations, and suggests optimal correction strategies for electron tomography and crystallography imaging conditions. Furthermore, this work describes possible approaches for the determination of the imaging parameters through the analysis of the experimental images, and for a non-analytical inversion of the effects of the TCIF model, showing preliminary results of their implementation applied to computer simulated-images.