Crystallographic extraction and averaging of data from small image areas

The accuracy of structure factor phases determined from electron microscope images is determined mainly by the level of statistical significance, which is limited by the low level of allowed electron exposure and by the number of identical unit cells that can be averaged. It is shown here that Fourier transforms of small image fields of purple membrane (a two-dimensional crystal consisting of bacteriorhodopsin and endogenous lipids) can be combined to provide the same quality of phases as are obtained from Fourier transforms of large image fields of the same total area. Although Fourier transforms of such small image fields are statistically significant only at lower resolution, the data from many such image fields can be averaged at the calculated positions of high-resolution reciprocal lattice points to give accurate phases. More specifically, when images of a size that can be recorded with CCD cameras are processed individually, key parameters including lattice vectors, defocus, crystal and beam tilts, and common phase origin can be accurately determined.