Fig. 1. Images of Fresnel transformation and reconstruction^[1] . (a) Schematic of the recording of hologram (X-ray star camera); (b) hologram recorded by the experiment (left) and reconstruction image (lower right); (c) light-path of the hologram reconstruction

Fig. 2. Schematic of incoherent holographic wave splitting mode^[4]. (a) Amplitude beam splitting by means of a birefringent double-focus lens; (b) beam splitting by diffraction on a Fresnel zone plate; (c) beam splitting by division of aperture, one half of which is covered by a lens, the other half by a plane plate for compensation of thickness; (d) beam splitting by division of aperture, which is divided into unequal portions

Fig. 3. Schematic of FINCH recorder (f=25 cm, Δλ=60 nm) ^[19]

Fig. 4. Schematic of a motionless microscopy system based on FINCH in upright fluorescence microscopes^[20]

Fig. 5. General model schematic of incoherent correlation digital holographic imaging system

Fig. 6. Schematic of recording mechanism of incoherent correlation digital holography. (a) FINCH; (b) COACH; (c) I-COACH

Fig. 7. PSH with different phase-shift values obtained by FINCH,COACH,and I-COACH system,respectively. (a) FINCH; (b) COACH; (c) I-COACH

Fig. 8. Reconstructed images of hologram of point source in FINCH. (a) Diffraction reconstruction; (b) cross-correlation correlation reconstruction; (c) cross-correlation reconstruction with phase filtering

Fig. 9. The intensity distribution curves of reconstruction images of point source in FINCH system by different reconstruction methods

Fig. 10. Reconstructed images of hologram of point source and the normalized intensity distribution curves under different recording mechanisms. (a) FINCH; (b) COACH; (c) I-COACH; (d) normalized intensity distribution curves

Fig. 11. Axial distribution of PSF in the range of 100 mm under different recording mechanisms. (a) FINCH; (b) COACH; (c) I-COACH

Fig. 12. Lateral resolution comparison of reconstructed images under different recording mechanisms. (a) FINCH; (b) COACH; (c) I-COACH; (d) normalized intensity distribution curves

Fig. 13. Resolution comparison of wide-field and α-BBO FINCH imaging of fluorescent beads^[26]. 8 μm × 8 μm zoomed selections of 110 nm fluorescent beads for resolution comparison of the same area between (a) wide-field fluorescence and (b) α-BBO-FINCH images,the full fields were 62 μm × 62 μm; (c) (d) 1 μm² zoomed images of the same randomly selected beads from Figs. 13(a) and (b), respectively,the beads in the respective parts of Figs. 13(c) and (d) are the same; (e) a histogram of full-width at half-maximum (FWHM) size distributions among the 20 beads that were measured in Figs. 13(c) and (d), showing the approximately twofold reduction in FWHM by FINCH; (f) plots depicting the average FWHM sizes of the 110 nm beads as measured by wide-field fluorescence and α-BBO-FINCH microscopy, with normalized Gaussian functions of the average width measured from the 20 selected beads

Fig. 14. The experiment results of the SRI-COACH. (a) The SNR of reconstructed image varied with CPM scattering degree and number of sparse points; (b) the visibility of reconstructed image varied with CPM scattering degree and number of sparse points; (c) ξ(σ, N) (product of visibility and signal-to-noise ratio) of reconstructed image varied with CPM scattering degree and number of sparse points; (d) resolution plate reconstruction with optimal scattering degree and number of sparse points; (e) direct imaging result

Fig. 15. Reconstructed results obtained by the diffraction propagation method and CS method, respectively. (a) The diffraction reconstructed result focused on the P1 plane; (b) the diffraction reconstructed result focused on the P2 plane; (c) the CS reconstructed result focused on the P1 plane; (d) the CS reconstructed result focused on the P2 plane

Fig. 16. Improved GS algorithms and corresponding PSH, object holograms, and reconstructed images. (a) COACH ^[41]; (b) SI-COACH ^[42]; (c) AI-COACH ^[43]

Fig. 17. Comparison of MP-NLR imaging method with non-linear and conventional imaging^[44]

Fig. 18. Comparison of reconstructed images with different reconstruction algorithms with ring sparse system response^[43]. (a) Object hologram; (b) PSH; (c) direct imaging; (d) single camera shot imaging of AI-COACH; (e) non-linear adaptive reconstruction; (f) phase filtering reconstruction

Fig. 19. Schematic of system optical path and experimental results of Fourier incoherent single channel holography (FISCH) recorder^[48]. (i) Schematic of system optical path; (ii) experimental results. (ii-a)--(ii-c) are digitally reconstructed images for z_s=30 cm from a single exposure, two, and three exposures holograms, respectively; (ii-d) is the optically reconstructed equivalent of (ii-b); (ii-e) is a two exposures hologram (shown partially to reveal details, recorded with z_s=25 cm) and (ii-f) is its digitally reconstructed image at the best plane of focus; (ii-g) and (ii-h) are optical reconstructions of (ii-e) at the best plane of focus of one of the images and its twin, respectively

Fig. 20. Results of depth-of-field extended dual channel imaging experiment with I-COACH system^[58]. (a)(b) Direct images of objects in two axial positions; (c) direct image with RQPF and DSL; (d) reconstructed image of DOFE-based modified I-COACH

Fig. 21. Comparative imaging of three different Golgi apparatus proteins in HeLa cells by wide-field and α-BBO FINCH^[26]. (a) Wide-field image; (b) reconstructed results of FINCH; (c)(d) enlarged images in the range shown in the dotted box in Figs. 21(a) and (b) respectively

Fig. 22. Computational adaptive 3D fluorescence microscopic imaging results based on FINCH of actin-labeled MCF7 breast cancer cells^[60]. (a) (b) before and (c) (d) after AO correction on different layers within the cell,(a)(c)depth is 2.75 μm, and (b)(d) depth is 6.5 μm

Fig. 23. Comparison of experimental results of confocal microscopy and confocal-FINCH (CINCH) ^[62]. (a) Confocal images of microtubules; (b) super-resolved CINCH images of microtubules; (c) plots of microtubule lateral FWHM from the images shown in Figs. 23(a) and (b)

Fig. 24. Incoherent holographic 3D color imaging results for the dice on different planes based on FINCH^[63]

Fig. 25. Incoherent off-axis Fourier color holographic imaging results based on triangular interference^[65]. (a)--(c) the hologram reconstruction images corresponding to three different color channels respectively;(d)color reconstruction image after chromatic aberration correction

Fig. 26. 3D localization of a single 0.1 μm fluorescent bead based on incoherent holography^[71]. (a) Histograms of 68 localizations in x, y, and z of one single 0.1 μm red (580/605) fluorescent bead on a coverslip, and the standard deviations of the measurements are σ_x=σ_y=5 nm and σ_z=40 nm; (b) representative image of a single bead imaged with SIDH acquired in one 50 ms frame, and the scale bar is 50 μm; (c) localizations plotted in three dimensions

Fig. 27. Phase mask acquisition for partial aperture imaging and comparison of imaging results^[74-76]. (a) Synthesis method of phase mask for PAIS system; (b) comparison of the reconstructed images of PAIS system with different annular aperture size masks and direct imaging results; (c) acquisition method of phase mask for M-PAIS system;(d) comparison of imaging results between PAIS and M-PAIS systems

Fig. 28. COACH scattering medium imaging system and imaging results^[77]

Fig. 29. Structure and experimental results of multispectral imaging system in the COACH system ^[78]