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. 2020 Jun 30;10:10606. doi: 10.1038/s41598-020-67590-6

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© The Author(s) 2020

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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Grid of predefined positions of the source of light S: (a) incident light from the source at position $S_{n, m}^{(1)} (i, j)$ is deflected by hogel G_ij toward observer L and forms the image of pixel $K_{n, m}^{(1)} (i, j)$ , (b) incident light from the source at position $S_{n, m}^{(- 1)} (i, j)$ is deflected by hogel G_ij turned by 180 degrees toward observer L and forms the image of pixel $K_{n, m}^{(- 1)} (i, j)$ .