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. 2018 Feb 1;8:2049. doi: 10.1038/s41598-018-20530-x

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Generating projections from multi-slice reconstructions. (a) Schematic diagram showing the equivalence between the projection of a sample with discrete slices under a tilted view angle and its orthogonal projection by offsetting the slices relative to each other when the slices are infinitesimally thin. (b) Schematic diagram showing the difference between the orthogonal projection produced by multi-slice reconstruction and the ground truth projection under a tilted view angle for a sample section with certain thickness. (c) The phase projections of the sample generated from the multi-slice reconstructions at the angle of 16° by tilting the view angle by −2°, −8° and −14°.