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. 2020 Jul 13;9:119. doi: 10.1038/s41377-020-00362-z

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© The Author(s) 2020

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. 4 — a Radially polarized light focused by an aplanatic objective (NA: 1.4). Insets: resultant intensity profiles in the transverse and longitudinal planes. b, c Line plots of the intensity in the transverse and longitudinal directions calculated using different methods. d Spiral phase plate and the phase depth distribution with the azimuthal angle. e Doughnut-shaped intensity in the focal plane. f–h Intensity distributions of different polarization components along the x, y, and z directions, respectively. i Line plots of the intensity profile of different polarization components in the focal plane. j Intensity distribution in the longitudinal plane. k–m Phase distributions of different polarization components. n, o Enlarged partial intensity distribution as labeled in (e, j), respectively. p Comparison of computation time for vector diffraction calculation in the xy-plane, yz-plane, and volumetric three dimensions