High-resolution electron microscopy and electron tomography: resolution versus precision

The performance of high-resolution electron microscopy and electron tomography is usually discussed in terms of two-point resolution, expressing the possibility of perceiving separately two image points of an object. However, the concept resolution obtains another meaning if one uses prior knowledge about the object and the imaging procedure in the form of a parametric model describing the expectations of the observations. The unknown parameters, such as the positions of the components in an object, can be measured quantitatively by fitting this model to the observations. Due to the statistical nature of the experiment, the resulting solutions for the positions of the components and therefore for the distance between the components will never be exact. An alternative to resolution is then the precision with which the distance can be measured. In the present paper, it is shown that the precision depends on the size of the components, the distance between the components, the resolution of the instrument, and the number of electron counts. For electron tomography, it also depends on the orientation of the object with respect to the rotation axis.