The Ewald sphere/focus gradient does not limit the resolution of cryoEM reconstructions

In our quest to solve biomolecular structures to higher resolutions in cryoEM, care must be taken to deal with all aspects of image formation in the electron microscope. One of these is the Ewald sphere/focus gradient that derives from the scattering geometry in the microscope and its implications for recovering high resolution and handedness information. While several methods to deal with it has been proposed and implemented, there are still questions as to the correct approach. At the high acceleration voltages used for cryoEM, the traditional projection approximation that ignores the Ewald sphere breaks down around 2-3 Å and with large particles. This is likely not crucial for most biologically interesting molecules, but is required to understand detail about catalytic events, molecular orbitals, orientation of bound water molecules, etc. Through simulation I show that integration along the Ewald spheres in frequency space during reconstruction, the "simple insertion method" is adequate to reach resolutions to the Nyquist frequency. Both theory and simulations indicate that the handedness information encoded in such phases is irretrievably lost in the formation of real space images. The conclusion is that correct reconstruction along the Ewald spheres avoids the limitations of the projection approximation.