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. 2022 Jun 21;12:10428. doi: 10.1038/s41598-022-14074-4

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© The Author(s) 2022

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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Experimental results. Panel (a): an example of measured intensity and phase of the scattered field for case $m = 5$ corresponding to the highest (voltage 0) and the lowest (voltage 8) scattering perturbation. All measurements are for the same propagation distance and the only adjustable parameter is the voltage applied to the heater. Panel (b): comparison between the experimental results (solid symbols, bottom axis) and the numerical calculation (solid lines, top axis) conducted for the specific scattering conditions. The experimental results were averaged over four measurements at different locations across the TPS while the numerical data was averaged over 30 realizations of the randomness. For both simulation and experiment, the vorticity was calculated over square contours around the optical axis. The equivalent extent of the phase variance was found based on the measured statistical properties of the TPS.