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. 2017 Apr 11;7:830. doi: 10.1038/s41598-017-00946-7

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© The Author(s) 2017

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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Principle of spatial coherence estimation on a 2D matrix array probe. (A) An ultrasound wave is focused in a random media by applying delays in emission. (B) The backscattered echoes are recorded for each element of the 2D array. The autocorrelation of the rephased signals is calculated for each pair of elements as a function of distance between elements that composed the pair. (C) Represents the theoretical coherence function for a focused emission in a random media that we would obtain with a matrix probe of N _x × N _y elements.