The phase contrast theory describes the transfer of information from a weak-phase object to the image plane of a transmission electron microscope. For a tilted sample where the distance from the focal plane varies continuously across the field of view, the recently introduced Tilted Contrast Imaging Function (TCIF) model provides the mathematical description of this information transfer. Here we expand the TCIF model to account for astigmatism, and present several methods to generate simulated images of tilted samples and compare them to experimental results. We analyze in depth the differences between TCIF and the classical Contrast Transfer Function (CTF) model, which assumes invariant defocus, and discuss how they can affect the interpretation of experimental data. In addition, we apply the TCIF model to simulated test objects in order to explore the performance of techniques that aim to correct the artifacts introduced by the imaging function, and evaluate how well they recover the original information after optimizing the parameters. (C) 2011 Elsevier Inc. All rights reserved.