Spatial rotational alignment of identical particles in the case of (almost) coaxial projections

Knowledge of projection directions is essential to the 3D reconstruction of biological objects from electron micrographs. In the general case, mutual orientation of the particles lying randomly on a support film can be found by the geometrical method described elsewhere. In the case of coaxial projections, the geometrical method finds the rotation axis but cannot find tilting angles. We propose here a new method to solve this problem, which requires no a priori information. The method uses the first moments of plane sections of the object, and it is both simpler and more effective than the previously proposed methods [A.B. Goncharov and M.S. Gelfand, Ultramicroscopy 25 (1988) 317]. Thus we have a general solution of the stated problem. We report the results of the computer experiment and describe how the noise and deviations of the rotation axis affect the results.