Inversion of dynamical electron diffraction data including absorption

A method to invert the dynamical diffraction of high-energy electrons inside a crystal, which takes into account absorption, is discussed. It is shown that, working at fixed energy, the projected potentials associated with both the elastic and the absorptive scattering can be uniquely obtained from the scattering matrix. Inversion is possible for any principal orientation of the incident beam. Model examples are given.

Three-dimensional morphometry in scanning electron microscopy: a technique for accurate dimensional and angular measurements of microstructures using stereopaired digitized images and digital image analysis.

A method for accurate dimensional and angular measurements of microstructures analysed in the scanning electron microscope is described. The method considers central and parallel projections and involves (a) digital image acquisition of stereopaired images from the scanning electron microscope's photodisplay, (b) generation of 3D-image representations, (c) setting of measuring points in the digitized stereopaired images, (d) computation of exact space coordinates (x/y/z) from the corresponding point coordinates (xL/yL; xR/yR), (e) determination of distances and angles between consecutive corresponding points using vector equations, and (f) transfer of computed data into spreadsheets of the data analysis software using dynamic data exchange with simultaneous graphical display of the frequency distribution of variables. Measurements performed on specimens with known dimensions (grid with 10 microm wide square meshes, polystyrene beads with 0.33 microm diameter) and angles (synthetic crystals of K(Al,Cr)[SO4], CuSO4.5H2O and NaCl) revealed a high accuracy in dimensional as well as angular measurements (total error 1 +/- 0.5%). In Monte Carlo experiments the overall error was found to depend strongly on the size of the measured structure relative to the size of the measurement field (field width).

Retrieval of the projected potential by inversion from the scattering matrix in electron-crystal scattering.

The retrieval of a unique crystal potential from the scattering matrix S in high-energy transmission electron diffraction is discussed. It is shown that, in general, data taken at a single orientation are not sufficient to determine all the elements of S. Additional measurements with tilted incident beam are required for the determination of the whole S matrix. An algorithm for the extraction of the crystal potential from the S matrix measured at a single energy and thickness is presented. The limiting case of thin crystals is discussed. Several examples with simulated data are considered.