The STEM transform was thus formulated as a mathematical model applicable to STEM imaging with a convergent electron beam. It was shown that it is (1) a linear convolution, (2) a generalization of the Ray transform that contains the latter as the special case where the beam convergence semi-angle α→0, and (3) self-adjoint, a result that facilitated a new iterative reconstruction algorithm for TFS based on a matched backprojection, which drastically improved the convergence rate, resulting in 60 times less iterations compared to previous methods. It also solved theoretical concerns about the convergence of the method, which was not guaranteed in the case of an unmatched projection/backprojection pair. This brings the combined tilt- and focal series one more step towards broad applicability by allowing the reconstruction of high resolution tomograms in feasible computation time.