Matching and Averaging Over Fragmented Lattices

Abstract

The limited radiation tolerance and low contrast available even from stained preparations of biological specimens mean that electron micrographs showing fine detail (below 10 nm) in such specimens are usually statistically ill-defined, i.e. “noisy”. The recovery of well-defined images from such micrographs of periodic (crystalline) specimens is a well-known technique, generally performed either by direct superposition (e.g. Markham et al., 1964) or by suitable Fourier transform filtering (e.g. De Rosier and Klug, 1972), using both optical and Computer methods (Aebi et al., 1973). In either case, the effect is to average the noisy images of many unit cells, so that the noise tends to cancel out. The fact that the specimen is periodic means that the precise position of each unit cell is known as soon as the base vectors of the lattice are established, so there is no difficulty in bringing the unit cells to be averaged into precise alignment.