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. 2021 Apr 23;12:2411. doi: 10.1038/s41467-021-22692-1

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© The Author(s) 2021

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. 2 — a Coherent light source scans across the input plane of the scattering medium over time, resulting in time-varying intensity signals at the target spot on the target plane. At another spot (denoted by a triangle), the signals are uncorrelated with those at the target spot due to the random scattering of the light through the sample. These time-varying signals allow us to map the optical channels between the input and the target plane. b By injecting light into the channels that connect to the target spot, a focus pattern is formed at the target spot while other spots on the target plane receive less light on average. c, d Matrix representation of the feedback-based OCIS. c The incident optical mode sweeps through space over time, and can be represented by an identity matrix A. Its interaction with the scattering medium is represented by multiplying the intensity transmission matrix S, resulting in time-varying speckle patterns on the output. The measurement of the time-varying speckles at the target position is equivalent to taking one column of the intensity matrix B. d During display, the binarized output selects a number of rows of S as output. The integration of the selected output rows over time results in an optical focus pattern at the target position.