Fig. 1: Underlying principle of PSF engineering. | Light: Science & Applications

Fig. 1: Underlying principle of PSF engineering.

From: High-fidelity structured illumination microscopy by point-spread-function engineering

Fig. 1

a Theoretical OTFs and corresponding PSFs for wide-field fluorescence microscopy (total internal reflection fluorescence microscopy, TIRF) and directly combined SR-SIM, and the ideal OTF and corresponding PSF for SR-SIM. The downward kinks in the OTF of directly combined SR-SIM result in sidelobes in PSF, while background fluorescence signals located at the upward peaks of the OTF cause honeycomb artifacts and limit the OS capability. \(\tilde H_{{\mathrm{det}}}\left( {\mathbf{k}} \right)\) represents the actual OTF for wide-field imaging. kc represents the cut-off frequency of wide-field imaging. mex and kex represent the modulation depth and spatial frequency of the excitation pattern, respectively. b 2D OTF and corresponding PSF of directly combined SR-SIM with excitation pattern in only one orientation. c 2D OTF and corresponding PSF of directly combined SR-SIM with excitation patterns in three orientations. Green and white circles represent the diffraction limited boundaries of the wide-field and SR-SIM, respectively; blue spots represent the spatial frequencies of the excitation pattern at different orientations; cyan circles represent the circular cross-section with a radius equal to the spatial frequency of the excitation patterns. d Equivalent OTF and corresponding PSF after optimizing the directly combined OTF by HiFi-SIM. e Intensity profiles along the magenta, yellow, and cyan lines in c and d. f Intensity profiles along the blue lines in c and d. Gamma value: 0.3 for OTFs in bd

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