Fig. 1. 3D intensity distribution^[15]. (a) Standard PSF; (b) DH-PSF

Fig. 2. Schematic of the DH-PSF system^[17]

Fig. 3. Transfer function^[10]. (a) DH-PSF using LG model light superposition; (b) high-efficiency DH-PSF initial estimation distribution; (c) high-efficiency DH-PSF distribution; (d)-(f) corresponding LG modal cloud distribution

Fig. 4. Influence of number and distribution of vortex singularities in the pupil on the PSF^[19]. (a) Left column shows the pupil phase function (phase mask) with an increasing number of vortex singularities N and constant spacing d between them, the corresponding PSF at focal plane are shown in the right column; (b) change of the phase mask (left) and PSF at focus (right) as the spacing d increasing with a constant N= 9

Fig. 5. Relationship between DH-PSF rotation and total number of the Fresnel zones in the spiral mask^[22]. (a) N=2; (b) N=6

Fig. 6. Image results^[9]. (a) Rotating PSF; (b) standard PSF; (c) reconstructed PSF; (d) reconstructed MTF

Fig. 7. Flowchart of the dual-channel complementary PSF engineering digital optical system^[11]

Fig. 8. Depth estimation and restored imaging technology^[11].(a) Scene objects recovered from cubic phase channels for image segmentation; (b) average axial distance of each car taken from the depth estimation channel after segmenting the objects within the scene

Fig. 9. Microscope image of the fabricated DH-metalens ^[18]

Fig. 10. Experimental setup and characterization of the DH-metalens^[18]. (a) Schematic of the experimental setup; (b) theoretically calculated and experimentally obtained relationship curves between the rotation angle (θ) and the imaging defocus (d) at wavelength of 750 nm; (c)-(f) rotation of DH-PSF images at different defocus positions; (g) relationship curves between θ and d at wavelengths of 730, 790, 860 nm, the insets are two DH-PSF images at a wavelength of 730 nm

Fig. 11. Design diagram of dual-aperture metasurface depth imaging system^[24]

Fig. 12. Schematic of the image acquisition setup^[25]

Fig. 13. Flowchart of the image acquisition and reconstruction^[25]

Fig. 14. Imaging results of the three-dimensional object scene^[25]. (a) Nominal image; (b) DH-PSF encoded image; (c) decoded image

Fig. 15. Schematic of the single-shot three-dimensional fluorescence microscope^[26]

Fig. 16. The conventional image and the extended depth-of-field recovered image produced by DH-PSF, the DH-PSF produces the extended depth-of-field recovered image, which is verified by the observation results of F-actin in BPAE cells^[26]. (a)(b) Images captured by using the conventional Gaussian PSF, the two images are captured at different depths (1500 nm apart); (c) raw image acquired by the DH-PSF (N=6); (d) recovered object image shown in Fig.16(c); (a1)-(d1) enlarged images of ROI1 area; (a2)-(d2) enlarged images of ROI2 area

Fig. 17. Experimental setup for three dimensional tracking of moving fluorescent particles^[13]

Fig. 18. Fluorescent microsphere tracking in three dimensions^[13]. (a) Standard PSF image; (b) DH-PSF image; (c) 3D locations of four microspheres; (d)-(f) X-Y, X-Z, and Y-Z projections of the microspheres’ 3D locations

Fig. 19. 3D tracking of a quantum dot-labeled structure in a live cell^[28]

Fig. 20. 3D trajectory of a single mRNP in a yeast cell^[29]

Fig. 21. Schematic of the DDCM system^[38]

Fig. 22. Simultaneous three-dimensional tracing of three fluorescent beads^[38]

Fig. 23. Schematic of 2π-DH-PSF system and its application in 3D trajectory^［40］. (a) Optical setup and 3D stereograms of two defocused 2π-DH-PSF combinations; (b) 3D trajectory of fluorescent microspheres in Hela cells; (c) 3D trajectory of fluorescent microspheres in saliva

Fig. 24. Schematic of the DH-PSF microscopy using light-sheet illumination^［41］

Fig. 25. DH-PSF microscopy enhanced by light sheet excitation^[41]. (a) DH-PSF obtained from light sheet fluorescence microscopy; (b) DH-PSF of epi-illumination microscopy; (c) intensity profile of the cross section for the two straight lines in Fig.25(a) and Fig.25(b); (d) three-dimensional trajectory of single fluorescent bead; (e) linear fitting of the 3D MSD of single fluorescent bead

Fig. 26. Schematic of the TILT3D system^[42]

Fig. 27. Applications of TILT3D in cell biology^[42]

Fig. 28. DH-PSF imaging system and 3D super-resolution imaging^[16]. (a) Detection path of the single-molecule DH-PSF setup; (b) typical calibration curve between angle of two lobes and axial position; (c) images of a fluorescent bead at different axial positions; (d) single molecule image of DCDHF-V-PF4-azide with high concentration in a thick PMMA sample

Fig. 29. 3D localization of a single molecule^[16]

Fig. 30. Schematic of the DH-PSF-assisted STED microscopic optical path^[68]

Fig. 31. Three dimensional imaging of a group of 100-nm diameter beads immobilized in a PDMS^[68]. (a) Confocal image; (b) corresponding STED image; (c) STED image processed by deconvolution; (d) corresponding DH images recorded at five points in Fig.31(c); (e) image of fluorescent bead at focal plane and corresponding depth map, scale bar is 500 nm

Fig. 32. Schematic of MSIMH system^[70]

Fig. 33. Imaging comparison of mitochondria in living cells by wide-field microscope and MSIMH^[70]. (a) Wide-field image of mitochondria at z= 0; (b) wide-field image of mitochondria at z=-1000 nm; (c) MSIMH 3D imaging of mitochondria at z=0

Fig. 34. Schematic of HMSIM system^[71]

Fig. 35. Flowchart of the image reconstruction process^[71]

Fig. 36. Postprocessing of each rodlike sub-image^[71]

Fig. 37. Schematic of RESCH system and RESCH fluorescent images^[72]. (a) Sketch of the RESCH optical path; (b) DH-filtered image of a 100-nm diameter fluorescent bead, the circular hole is a synthetic pinhole at the corresponding defocus

Fig. 38. Confocal and RESCH images of microtubules^[72]. (a) The first row is confocal images recorded at axial steps of 200 nm, the second row is RESCH images at corresponding position; (b) confocal image and RESCH images of another sample

Fig. 39. Schematic diagram and characterization of the MRESCH^[73]. (a) Optical configuration of MRESCH; (b) intensity distribution of the DH-PSF at different positions along z-axis; (c) relationship between the two lobe rotation angles of the DH-PSF and position along z-axis

Fig. 40. Schematic of reconstruction process of MRESCH^[73]. (a) Raw images of MRESCH; (b) double helix point with digital pinhole; (c) image reconstruction process of MRESCH

Fig. 41. saMMM setup and DH-PSF modulated through the GL phase plate^[74]

Fig. 42. Monitoring simultaneously Ca²⁺ dynamics from 113 foci on cultured expressing jRGECO1 neurons^[74]

Fig. 43. Schematic of holographic optical tweezer (HOT) and DH-PSF system and detail images. (a) Experimental setup integrated with HOT system and DH-PSF system^[79]; (b) DH-PSF distribution; (c) DH-PSF phase mask; (d) brightfield image; (e) corresponding off-axis darkfield DH-PSF image

Fig. 44. Schematic of experimental setup for two-photon polymerization with single exposure^[81]

Fig. 45. SEM images of polymerized double-helix microstructures^[81]. (a) Double-helix microstructure array; (b)(c) top and side views of single double-helix microstructure

Fig. 46. Experimental setup and conceptual design of the holograms for fabricating and detecting double-helical microstructures^[82]

Fig. 47. Diameters of double-helical microstructures to different topological charges^[82]