Resolution in Electron Tomography

Abstract

Traditionally, in computed tomography practiced in radiology, the resolution of the reconstruction is expressed in terms of the number of evenly spaced projections required for the faithful reconstruction of an object that has a given diameter (see equation (10) below).The tacit assumption is that projection data have a sufficient spectral signal-to-noise ratio (SSNR) in the whole frequency range in order to reproduce the object faithfully. In electron microscopy, the situation is dramatically different, as the electron dose limitations result in very low SSNR in the individual projections. The suppression of signal is particularly severe in high spatial frequencies, where the signal is affected by the envelope function of the microscope and the high amount of ambient noise, as well as in some low spatial frequency regions (due to the influence of the contrast transfer function (CTF) of the electron microscope). In single-particle reconstruction, a satisfactory level of the SSNR in the 3D reconstruction is achieved by including a large number of 2D projections (tens to hundreds of thousands) that are averaged during the reconstruction process. Except for rare cases (Boisset et al., 1998), the angular distribution of projections is not an issue, as the large number of molecules and the randomness of their orientations on the support grid all but guarantee uniform coverage of angular space. The concern is whether the number of projections per angular direction is sufficient to yield the desired SSNR or whether the angular distribution of projections is such that the oversampling of the 3D Fourier space achieved during the reconstruction process will yield the desired SSNR.