Retrieval of crystal defect structures from HREM images by simulated evolution I. Basic technique

Image interpretation of crystal defect structures by means of HREM and image simulations is performed using an advanced method of iterative digital image matching. HREM image analysis is treated as a high-dimensional numerical optimization problem. The configuration space is found to be highly multi-modal with local optima in both the sub-spaces for the structures and for the imaging parameters. Steepest descent optimization is therefore not always sufficient. The global optimization algorithm of simulated evolution by Schwefel [Numerical Optimization of Computer Models (Wiley, New York, 1981)] is tested in this first part by simulations on metal-sapphire interfaces. The capability of arriving at the globally optimal crystal structure within reasonable error bars is studied as a function of four basic quantities: (i) deviation of the initial structure model from the true solution, (ii) signal-to-noise ratio, (iii) microscope resolution, and (iv) smallest projected bond length. For each of these items a well defined limit exists which, upon crossing, leads to a failure of the technique.