The relevance of dose-fractionation in tomography of radiation-sensitive specimens

It is commonly assumed that the number of projections required for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3D reconstruction is the same as that required to obtain a single 2D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3D image can be computed from statistically insignificant projections, as long as the total dose that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3D model created from an electron micrograph. The simulations verify the basic conclusions of the theorem and extend its validity to the experimentally more realistic conditions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Individual projections in the series of fractionated-dose images could be aligned by cross-correlation because they contained significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results demonstrate that it is feasible to use single-axis tomography with soft X-ray and electron microscopy of frozen-hydrated specimens.