RETRIEVAL OF OBJECT INFORMATION BY INVERSE PROBLEMS IN ELECTRON-DIFFRACTION

The imaging of crystal defects by high-resolution transmission electro n microscopy or with the help of the electron diffraction contrast tec hnique is well known and routinely used. However, a direct and phenome nological analysis of electron micrographs is mostly not possible, but requires the application of image simulation and matching techniques, The trial-and-error matching technique is the indirect solution to th e direct scattering problem applied to analyse the nature of the objec t under investigation. Alternatively, inverse problems as direct solut ions of electron scattering equations can be deduced using either an i nvertible linearized eigenvalue system or a discretized form of the di ffraction equations. This analysis is based on the knowledge of the co mplex electron wave at the exit plane of an object reconstructed for t he surrounding of single reflections by electron holography or other w ave reconstruction techniques. in principle, it enables directly the r etrieval of the local thickness and orientation of a sample as well as the refinement of potential coefficients or the determination of the atomic displacements, caused by a crystal lattice defect, relative to the atom positions of the perfect lattice. Considering especially the sample orientation as perturbation the solution is given by a generali zed and regularized Moore-Penrose inverse, where the resulting numeric al algorithms imply ill-posed inverse problems.