Sampling theory perspective on tomographic tilt increment schemes

Given a limited radiation exposure to be distributed over a discrete number of tilted projections in tomography, the optimal collection of information depends on the tilt increment scheme. Relying on principles of sampling theory, several tilt increment schemes can be compared and quantified. Following reasoning of Saxton, a revised scheme is offered in which the tilt angle increments Δθ_n are proportional to 1/cosθ_n. The revised scheme is preferable according to matrix analysis and simulations of geometrical optics. For thin specimens, applying a cosine sampling grid similar to Hoppe's scheme can improve the results. A realistic case is examined by Dr. Probe simulation of a scanning transmission electron microscope (STEM) for an atomic model adapted from the Ferritin protein molecule. Optimal reconstruction methods that are tested include the direct algebraic method, iterative reconstruction, and a new deconvolution-based weighted back-projection, which resembles the correction filter technique in signal recovery from sub-sampled data. A non-linear correction may be accounted for by iteration of the simulation with an ad-hoc atomic model.