Fig. 1. Confocal rescan SIM. (a) Optical system layout. DB, dichroic beam splitter; HWP, half-wave plate; EOM, electro-optic modulator; WP, Wollaston prism; LCR, liquid crystal retarder; CL, cylindrical lens (focal length:$-25\mathrm{mm}$); DM, dichroic mirror; EM, fluorescence emission filter; GM, galvo mirror; M1 and M2, mirrors; SL, scan lens (focal length: 40 mm); TL, tube lens (focal length: 200 mm); OBJ, objective lens; L1–L8 are spherical lens with focal lengths of 50, 150, 50, 100, 40, 75, 75, and 200 mm, respectively. Inset, (left) scanning illumination line inside the area of illumination and (right) diagram representations of illumination patterns of three phases. (b) CR-SIM image reconstruction process. $I_{0\mathrm{deg}}$, $I_{120\mathrm{deg}}$, and $I_{240\mathrm{deg}}$, raw images acquired for three structured illumination pattern phases and a rescan ratio of 2; FT, two-dimensional FT; $M^{-1}$: an inverse matrix used to retrieve the baseband ($S_0$) and modulation-shifted ($S_{+p}$ and $S_{-p}$) components in the image; $I_d$, image demodulated from the three raw phase images using an optical sectioning SIM algorithm; $H_{P_0}$ and $L_{P_0}$, high-pass and low-pass filters with the same cutoff frequency of $P_0$; for conventional SR-SIM reconstruction, $S_0$, $S_{+p}$, and $S_{-p}$ are shifted to their correct positions, merged using generalized Wiener filters, and transformed into the spatial domain to obtain the SR-SIM image. For the proposed OS-SR-SIM reconstruction, the operation remains the same except that the baseband $S_0$ is corrected by merging $S_0$ with the spectrum of $I_d$ using Eq. (3). Finally, the CR-SIM image is obtained by rescan inversion with a factor of 2.

Fig. 2. Fluorescent imaging of thick-tissue phantom made of $2\text{-}\mu \mathrm{m}$ fluorescence beads. (a) Cross-sectional images acquired by WF-SIM, LSCM, and CR-SIM at the depths of 0, 250, and $500\mu \mathrm{m}$, respectively; Scale bar: $10\mu \mathrm{m}$. The plot of the (b) SBR and (c) SNR values of the fluorescent beads imaged by WF-SIM, LSCM, and CR-SIM at different depths from surface to $500\mu \mathrm{m}$.

Fig. 3. High-resolution imaging of fixed HeLa cells: (a) LSCM image of F-actin structures in a single HeLa cell using a $60\times /1.2\mathrm{NA}$ OBJ lens; (b) CR-SIM image of the same sample area; (c) comparison of the normalized intensity profiles along the yellow solid lines in (a) and (b); (d) magnified LDCM image in the region of interest (ROI) marked by the blue box in (a); (e) magnified CR-SIM image in the ROI marked by the yellow box in (b).

Fig. 4. CR-SIM imaging of Thy1-EGFP transgenic mouse brain slice. (a) Volumetric rendering of a CR-SIM image stack $138\mu \mathrm{m}$ in thickness; (b) side-by-side comparison between (left) LSCM and (right) CR-SIM images at $Z=23\mu \mathrm{m}$; (c) zoom-in view of the region enclosed in the blue square box in (b) with a side length of $2.4\mu \mathrm{m}$; (d) intensity profiles along the horizontal (blue) and vertical (green) solid lines in (c); (e) 3D rendering view of a partial volumetric scan of the tissue stack with detailed neural structural information of axons, dendrites, and spines; (f)–(h) example image slices at imaging depths of 113, 132, and $197\mu \mathrm{m}$, respectively. They are taken from another 3D stack comprising 209 layers. Scale bar, $5\mu \mathrm{m}$; (i)–(k) selected areas [enclosed in green/yellow/blue dashed boxes in (f)–(h)] magnified by a factor of 4.