Heymann, B.

Images in the electron microscope are formed by electron scattering and focusing. The spherical geometry of these processes gives rise to two coherent, conjugate spherical wave fronts, known as Ewald spheres. These spheres are associated with the two halves of the contrast transfer function (CTF), and their widths are determined by the focal gradient through the specimen. To properly correct for the CTF, each half of the CTF must be applied to an image individually and integrated into the reconstruction into the corresponding Ewald sphere. Theory indicates that this dual Ewald sphere reconstruction method should recover the maximal amount of information possible. This method was compared to the other reconstruction methods commonly used: the projection approximation (ignoring the Ewald sphere), the simple insertion and the single sideband methods. In simulated reconstructions the dual Ewald sphere method recovered the most information when the correct half of the CTF is matched to the corresponding Ewald sphere. If the wrong half is matched, the result worse than the projection approximation method. Examining reconstructions from real data indicated that the dual Ewald sphere method performs at least as well as the simple insertion method, but not as good as in simulations. The likely reason is the two-fold ambiguity in the assigned orientations of the particle images, which remains an issue to pursue in further studies. In conclusion, the dual Ewald sphere reconstruction method may offer the best way to calculate very high resolution reconstructions when the micrograph quality warrants it. Highlights The dual Ewald sphere reconstruction corrects for the two halves of the CTF. The signs of the two halves of the CTF must correspond to the focal gradient. Determining the focal gradient for individual particle images remains unresolved. Complex reconstructions indicate any real space phases are artifacts.