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. 2021 Oct 11;12:5934. doi: 10.1038/s41467-021-26228-5

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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 Vortex PSF model fitted to an experimental z-stack of one single molecule with its estimated parameters listed in each frame. All sub-image pairs are contrast stretched with the same factor for better visibility of the PSF shape and the color bars are in units of photons per pixel. The mean signal count in the frames is 25 × 10³ with a standard deviation of 4 × 10³ and a mean background of 24 counts per pixel. The mean degree of orientational constraint of this molecule is g₂ = 0.92 with standard deviation of 0.02. b Mean estimated z position as a function of the piezo z position with the shaded region representing ± one standard deviation. The average is taken from 37 single molecules of varying orientations where the piezo z is realigned in processing to account for the in-focus position not corresponding exactly with z_piezo = 0. The slope is negative due to the opposing definition of z_piezo and the sample z. c The cross-section in x−z and d y−z of a Vortex PSF, with the measurement left and fit right (pixels are stretched proportionally in z, color bar units: photons per pixel). The estimated signal photon counts were in the range 4 × 10³−50 × 10³, and the estimated background photon counts were in the range 10−40 photons per pixel. All scale bars are 500 nm.