Accurate marker-free alignment with simultaneous geometry determination and reconstruction of tilt series in electron tomography.

An image alignment method for electron tomography is presented which is based on cross-correlation techniques and which includes a simultaneous refinement of the tilt geometry. A coarsely aligned tilt series is iteratively refined with a procedure consisting of two steps for each cycle: area matching and subsequent geometry correction. The first step, area matching, brings into register equivalent specimen regions in all images of the tilt series. It determines four parameters of a linear two-dimensional transformation, not just translation and rotation as is done during the preceding coarse alignment with conventional methods. The refinement procedure also differs from earlier methods in that the alignment references are now computed from already aligned images by reprojection of a backprojected volume. The second step, geometry correction, refines the initially inaccurate estimates of the geometrical parameters, including the direction of the tilt axis, a tilt angle offset, and the inclination of the specimen with respect to the support film or specimen holder. The correction values serve as an indicator for the progress of the refinement. For each new iteration, the correction values are used to compute an updated set of geometry parameters by a least squares fit. Model calculations show that it is essential to refine the geometrical parameters as well as the accurate alignment of the images to obtain a faithful map of the original structure.