Automated identification of symmetry in CBED patterns: a genetic approach

The genetic algorithm has been applied for automated identification of symmetry in CBED patterns. A normalized inner product between an original and its symmetry operated CBED patterns was found to be a good measure of similarity between them, and this inner product was used as the objective function in the genetic algorithm. A real floating number implementation of this genetic approach has been applied successfully in identifying rotation axes and mirror planes in experimental CBED patterns obtained from a single crystal of silicon. In particular a three-fold rotation axis reflecting the true three-dimensional symmetry of silicon is clearly distinguished from a six-fold rotation axis as expected from a two-dimensional crystal in the experimental <1 1 1> zone axis CBED pattern.