A two exposures technique of electron tomography from projections with random orientations and a quasi-Boolean angular reconstitution

The reconstruction of three-dimensional structures of macromolecular assemblies from projections with random orientation is commonly based on the detection of lines shared among couples of sinograms. This common line detection may be affected by large errors, even in simulations with noise-free data. A two exposures technique, with use of a symmetric tilt of the specimen, is proposed here. Relatively small tilt angles (±20–25°) alleviate defocus problems. The essential point of the technique is that one knows a priori the common line and the dihedral angle formed by couples of projections of the same particle. Inherent to a two exposures technique is the possibility to determine ab initio the correct handedness of the structure. The orientation of each couple with respect to a reference couple is determined by the simultaneous detection of four common lines, a task performed by a quasi-Boolean algorithm. Since multiple exposures would damage the sample, the reconstruction should be based on the first exposure, use of the second exposure being limited to the orientation process. Tests carried out with projections of asymmetric phantoms corrupted with a substantial amount of noise indicate a good algorithm performance.