Fig. 1. Typical systems of fluorescence polarization imaging modulation method^[53] and schematic diagrams of polarization imaging space-angle characterization theory. (a) Typical system of polarized fluorescence microscopy imaging based on fluorescence anisotropy; (b) typical system of polarized fluorescence microscopy imaging based on linear dichroism; (c) intuitive diagram of real sphere harmonics; (d) constant sphere visual diagram of harmonics (left), rotationally symmetric spherical harmonics (middle), and non-rotationally symmetric spherical harmonics (right)

Fig. 2. Schematic diagrams of multifocus polarized fluorescence microscopy^[29]. (a)‒(c) Multi-focus polarized fluorescence microscope experimental device and schematic diagram; (d) using excitation light with different polarization states to excite biological samples and obtain their polarization information

Fig. 3. Schematic diagrams of confocal polarized fluorescence microscopy^[31-32]. (a) Diagram of confocal polarized fluorescence microscopy device; (b) definition of orientation distribution function and angle; (c) verification experiment on giant unilamellar vesicles; (d) improvement of confocal polarized fluorescence microscopy technology

Fig. 4. Schematic diagrams of dual-view polarized light sheet microscopy with asymmetric detection objectives^[34-35]. (a) Overview of the microscope with liquid crystal polarizers highlighted in red; (b) asymmetric detection objectives; (c) excitation from the low-NA objective along the dark-blue axis; (d) excitation from the high-NA objective is controlled with the same degrees of freedom as the low-NA objective

Fig. 5. Schematic diagrams of two-photon polarization fluorescence microscopy^[37]. (a) Schematic diagram of two-photon polarized fluorescence microscopy system; (b) schematic diagram of coordinate definition

Fig. 6. Schematic diagrams of SDOM, pSIM, and 3DOM systems^{[18,21,44,60]}. (a) Schematic diagram of SDOM system; (b) schematic diagram of pSIM system; (c) schematic diagram of DMD-3DSIM system; (d) schematic diagram of 3DOM system

Fig. 7. Principles of localization and orientation parameter estimation for single-molecule microscopy. (a) PALM excitation process^[61]; (b) PALM positioning principle^[68]; (c) different diffraction patterns caused by the right-handed spherical coordinate system and different orientation parameters^[69]

Fig. 8. Concept of the raMVR SMOLM^[43]. (a) Schematic of the raMVR microscope; (b) the raMVR pyramidal mirrors; (c) NR molecules transiently binding to DPPC SLBs containing 40% cholesterol surrounding a silica sphere, lines are oriented and colour-coded according to the measured polar angle

Fig. 9. Polarization-expanded fluorescence microscopy. (a) Schematic diagram of SPoD system ^[20]; (b) comparison of diffraction-limited fluorescence images with Richardson-Lucy deconvolution results and SPoD images; (c) schematic diagram of P-TIRF^[22]; (d) P-TIRF imaging, Ring TIRF imaging, curve fitting of fixed microtubules, and comparison of Boulanger method and P-TIRF reconstruction depth map

Fig. 10. Some biological applications. (a) COS-7 cells labeled with membrane protein dyes perpendicular to the membrane; (b) amyloid-lipid interactions; (c) super-resolution dipole imaging of septins and nucleoporins in live yeast cells