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. 2020 Apr 2;11:1645. doi: 10.1038/s41467-020-15157-4

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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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Fig. 3 — a The phasor field collected at the aperture forms a spatial frequency cube. Given the output plane, by using the RSD propagation model, we can recover the hidden wavefront at any time instance. b This space-time wave propagation method where one can reveal a spherical wavefront that moves into the hidden scene. Even though (b) only shows reconstruction at a single depth plane, our proposed method can be generalized into the three-dimensional volume as well, which leads to a four-dimensional reconstruction space-time volume.