An electron tomography algorithm for reconstructing 3D morphology using surface tangents of projected scattering interfaces

Upon discerning the mere shape of an imaged object, as portrayed by projected perimeters, the full three-dimensional scattering density may not be of particular interest. In this situation considerable simplifications to the reconstruction problem are possible, allowing calculations based upon geometric principles. Here we describe and provide an algorithm which reconstructs the three-dimensional morphology of specimens from tilt series of images for application to electron tomography. Our algorithm uses a differential approach to infer the intersection of projected tangent lines with surfaces which define boundaries between regions of different scattering densities within and around the perimeters of specimens. Details of the algorithm implementation are given and explained using reconstruction calculations from simulations, which are built into the code. An experimental application of the algorithm to a nano-sized Aluminium tip is also presented to demonstrate practical analysis for a real specimen.Program summaryProgram title: STOMO version 1.0Catalogue identifier: AEFS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFS_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2988No. of bytes in distributed program, including test data, etc.: 191 605Distribution format: tar.gzProgramming language: C/C++Computer: PCOperating system: Windows XPRAM: Depends upon the size of experimental data as input, ranging from 200 Mb to 1.5 GbSupplementary material: Sample output files, for the test run provided, are available.Classification: 7.4, 14External routines: Dev-C++ (http://www.bloodshed.net/devcpp.html)Nature of problem: Electron tomography of specimens for which conventional back projection may fail and/or data for which there is a limited angular range. The algorithm does not solve the tomographic back-projection problem but rather reconstructs the local 3D morphology of surfaces defined by varied scattering densities.Solution method: Reconstruction using differential geometry applied to image analysis computations.Restrictions: The code has only been tested with square images and has been developed for only single-axis tilting.Running time: For high quality reconstruction, 5–15 min