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. 2023 Jan 26;41(9):1307–1319. doi: 10.1038/s41587-022-01651-1

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© The Author(s) 2023

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. 1 — a–c, Schematic representations of beam illumination at objective back focal plane (BFP) and sample planes for wide-field microscopy (single-beam illumination, a), 3D SIM (three-beam illumination, b) and four-beam SIM (a mirror opposite the sample is used to back-reflect the central beam, producing four-beam interference, c). Higher magnification illumination views at right show fine axial structure in four-beam SIM pattern, absent in 3D SIM or wide-field microscopy. d, Axial cross-sectional views of 100-nm beads, as imaged in wide-field microscopy (top), 3D SIM (middle) and four-beam SIM (bottom). e, Higher magnification views of bead highlighted by colored arrowheads in d, illustrating progressive improvement in axial resolution. Insets show magnitude of OTFs (k_x/k_z plane) derived from images. f, Line profiles corresponding to bead images shown in e, taken along vertical green line in e. g, Quantification of lateral (blue) and axial (orange) FWHM for n = 102, 100 and 99 beads for wide-field microscopy, 3D SIM and four-beam SIM, respectively. See also Supplementary Table 1. Whiskers: maximum and minimum; center lines: medians; bounds of box: 75th and 25th percentiles; cross symbols: mean markers. Scale bars, 2 µm (d) and 500 nm (e); 1/200 nm⁻¹ for Fourier transform insets in e. a.u., arbitrary units.

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