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. 2019 Mar 15;9:4640. doi: 10.1038/s41598-019-40829-7

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© The Author(s) 2019

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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Flattop and square beam profiles as a function of the shape and size of the SFFs, and corresponding magnified views of the lower left corners. (a) Vertical phase grating. (b) Diagonal phase grating. The upper insets show the horizontal cross-sectional graphs across the centre of the beams, and right insets show the corresponding images of phase gratings. The gray scales show the phase. (c) Addition of checker and ‘ILE’ pattern with diagonal phase grating, and cross-sectional graphs across red points. (d) Original beam profile. The colour bars show signal intensity.