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. 2024 Aug 12;13:187. doi: 10.1038/s41377-024-01528-9

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© The Author(s) 2024

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a Schematic of the meta SHWFS. b Effect of sampling density of SHWFS in phase reconstruction. c Illustration of a sampling unit of the meta SHWFS with related lenslet parameters. The maximum allowable displacement ∆_max is set with a minimum space S to take account of the finite width of the focal spot. d Maximum allowable displacement ∆_max, localization accuracy ∆_res, and their ratio ∆_max/∆_res for different focal lengths. The ∆_max/∆_res is maximized at the focal length of 30 μm