An accurate reconstruction algorithm for tomography experiments that involve complex probe-sample interactions

A reconstruction technique to calculate accurate tomograms of a sample, at a voxel scale, from tomographic experiments that involve probe-sample interactions of any degree of complexity is proposed. The properties of the reconstruction technique that accomplish this are outlined. The first guess to the solution is calculated directly from the reconstructed experimental projection data. To improve the accuracy of the approximate solution at every iteration, projection data are calculated by simulating the tomographic experiment, rather than by using a projection matrix. Calculating the ratio of the reconstructed experimental projection data to the reconstructed simulated projection data provides correction factors at every voxel. The approximate solution is multiplied by these correction factors. This correction formulation is identical to that used in the image-space reconstruction algorithm technique. High spatial resolution and accurate solutions are achieved by not implementing any form of smoothing. Instead, a novel technique is used to reduce the noise in the tomograms substantially. We call this reconstruction technique the discretized image-space reconstruction algorithm. This reconstruction technique provides a means to calculate the mass density and elemental composition tomograms of microscopic samples properly, utilizing the wealth of information measured in scanning transmission ion microscopy and particle-induced x-ray emission tomography experiments. To demonstrate the efficacy of this reconstruction technique, examples of scanning transmission ion microscopy tomography experiments are presented.