Fig. 1. Several typical examples of light sources with different degrees of temporal coherence and spatial coherence

Fig. 2. Representation of optical signal in time and space. (a) Optical signal is a function of time at a certain point in space; (b) optical signal is a function of space at a certain point in time

Fig. 3. Superposition of light waves with different frequencies. (a) Waves with different frequencies are coherently superimposed into one pulse wave packet; (b) waves with different frequencies are incoherently superimposed into one continuous wave (non-periodic and infinite width), and its phase and amplitude vary randomly

Fig. 4. Basic principle of Fourier transform spectrometer

Fig. 5. Michelson stellar interferometer measures the spatial coherence of a quasi-monochromatic wave field by interferometry to infer the size of the light source. (a) Optical configuration; (b) photograph of a real system

Fig. 6. Relationship between classical coherence theory and phase space optics

Fig. 7. Characterization of common signal transformations in phase space. (a) Fresnel propagation; (b) Chirp modulation (lens); (c) Fourier transform; (d) fractional Fourier transform; (e) magnifier

Fig. 8. Wigner distribution function of special signals. (a) Point source; (b) plane wave; (c) spherical wave; (d) phase slow-varying wave; (e) Gaussian signal

Fig. 9. Parameterization of the light field. (a) Seven-dimensional plenoptic function; (b) two planes parameterization of four-dimensional light field; (c) position-angular parameterization of four-dimensional light field

Fig. 10. Relationship between Wigner distribution function and light field of a smooth coherent wavefront. Phase is represented as the localized spatial frequency (instantaneous frequency) in the Wigner distribution function. Rays travel perpendicularly to the wavefront (phase normal) ^[128]. (a) Wavefront in real space; (b) Wigner distribution function in phase space; (c) light field in position-angle space

Fig. 11. Classification of phase imaging techniques

Fig. 12. Classification of the coherence measurement techniques

Fig. 13. Young’s interferometry with two holes^[22]

Fig. 14. Reversed-wavefront Young’ interferometry^[77]

Fig. 15. Distributions of nonredundant array method and experimental scheme^[78]. (a1) Superior in points on axes; (a2) central distribution of points; (a3) superior in points out of axes; (b) experimental scheme of nonredundant array method

Fig. 16. Experimental scheme of self-referencing interferometry^[80]

Fig. 17. Correspondence between Wigner distribution function and ambiguity function

Fig. 18. Basic principle of phase space tomography. (a) Vertical projection; (b) quarter rotation projection; (c) rotation by 90° projection; (d) superposition of all projections from different angles

Fig. 19. Two different transformations of WDF for phase space tomography. (a) WDF of complex signal; (b) WDF after Fresnel diffraction; (c) phase space WDF after fractional Fourier transform; (d) correspondence between Fresnel diffraction and fractional Fourier transform

Fig. 20. Optical path structure of phase space tomography^[85]

Fig. 21. Experimental device for measuring spatial coherence based on edge diffraction^[84]

Fig. 22. Direct phase space measurement. (a) Direct phase space measurement based on pinhole scanning; (b) direct phase space measurement based on microlens array

Fig. 23. Schematic of a simplistic view of coherent field and partially (spatially) coherent field. (a) A coherent field requires a 2D complex amplitude representation, the surface of the constant phase is interpreted as wavefronts with geometric light rays traveling normal to them; (b) a partially coherent field requires a 4D coherence function to accurately represent its properties such as propagation and diffraction. The “phase” (generalized phase) of a partially coherent light field is the statistical average of phases (spatial frequency, direction of propagation) at each position in space

Fig. 24. Principle of the Shack-Hartmann sensor and light field camera. (a) For coherent field, the Shack-Hartmann sensor forms a focus spot array sensor signal; (b) for partially coherent field, the Shack-Hartmann sensor forms an extended source array sensor signal; (c) for incoherent imaging, the light field camera produces a 2D sub-aperture image array

Fig. 25. Classification of light field imaging techniques

Fig. 26. Light field capture based on camera arrays. (a) Light field gantry^[126]; (b) large camera arrays^[110]; (c) micro light field acquisition acquired by the 5×5 camera array system^[189]

Fig. 27. Various light field cameras based on microlens array

Fig. 28. Computational light field imaging based on coded mask. (a) Light field acquisition of mask enhanced camera^[191]; (b) light field acquisition of compressive photography^[192]

Fig. 29. Light field imaging based on programmable aperture. (a) Programmable aperture light field camera^[104]; (b) programmable aperture light field microscope^[106]

Fig. 30. Light field representation of a slowly varying object under spatially stationary illumination^[128]

Fig. 31. Light field microscope model. (a) Traditional bright field microscope; (b) light field microscope^[111]; (c) light field microscopic model based on wave optics theory^[112]; (d) Fourier light field microscope^[113]

Fig. 32. Comparison between TIE and WOTF^[207]. (a1)(b1) Physical implications of TIE and WOTF; (a2)(b2) geometric illustrations for deriving the PGTF and WOTF; (a3)(b3) PGTF and WOTF for phase imaging under different s

Fig. 33. Direct visualization of coherent images reconstructed from coherent holograms^[209]

Fig. 34. Photon correlation holography^[213]. (a) Concept diagram of photon-dependent holography; (b) schematic diagram of intensity interferometer

Fig. 35. Representative optical setup for incoherent holography. (a) Optical path of modified triangular interferometer^[217]; (b) optical path of FINCH^[214]; (c) Michelson interferometer^[119]; (d) Sagnac interferometer^[215]; (e) Mach-Zehnder interferometer^[216,218]

Fig. 36. Typical imaging optical path for COACH. (a) Structure of COACH^[115]; (b) structure of I-COACH^[117]; (c) structure of LI-COACH^[116]

Fig. 37. Schematic of non-invasive scattering imaging through strong scattering layers^[237]

Fig. 38. Single frame imaging based on speckle autocorrelation through strong scattering layer^[238]. (a) Experimental setup; (b) raw camera image; (c) autocorrelation; (d) image reconstructed by an iterative phase-retrieval algorithm; (e) photograph of the experiment; (f) raw camera image; (g)--(k) Left column is calculated autocorrelation, middle column is reconstructed object; right column is image of the real object

Fig. 39. Conventional incoherent synthetic aperture structure. (a) Michelson interferometer; (b) common secondary structure; (c) multiple telescopes structure

Fig. 40. Design model of the initial generation of SPIDER imaging conceptual system. (a) Explosive view of SPIDER; (b) PIC schematics of the two physical baselines and three spectral bands; (c) arrangement of SPIDER microlens; (d) corresponding frequency-spectrum coverage

Fig. 41. Incoherent synthetic aperture technology based on FINCH^[243]

Fig. 42. RSI of visible cone-beam tomography^[79]

Fig. 43. Application of light field microscopy in bioscience.(a) Mouse with a head-mounted MiniLFM^[252]; (b) imaging Golgi-derived membrane vesicles in living COS-7 cells using HR-LFM ^[74]; (c) dynamics during neutrophil migration in mouse liver using DAOSLIMIT^[73]; (d) hunting activity of zebrafish and the neural activity of mouse brain observed by confocal light field microscope^[75]

Fig. 44. Microscopy imaging based on FINCH. (a) FINCHSCOPE schematic; (b) FINCHSCOPE fluorescence sections of pollen grains^[118]; (c) wide-field image and reconstructed FINCH image of pollen grains captured using a 20×(0.75 NA) objective^[253]; (d) comparative imaging of three different Golgi apparatus proteins in HeLa cells using wide-field (left) and FINCH(right)^[255]

Fig. 45. Light field imaging in computational photography. (a) Light field refocusing^[101]; (b) synthetic aperture imaging based on light field^[259]

Fig. 46. Computational photography refocusing based on FINCH. (a) Digital refocusing based on FINCH^[214]; (b) colorful digital holography refocusing^[260]; (c) full color holographic digital refocusing under natural light illumination^[119]

Fig. 47. X-ray characterization via phase space tomography. (a) Measured intensity distribution of the X rays as a function of lateral position and along the direction of propagation^[263]; (b) phase space density reconstructed from the data in Fig.47(a); (c)(d) measured complex degree of coherence for the beams in the two conditions ^[263]

Fig. 48. Optical beam characterization via phase space tomography. (a) 1D signal^[265]; (b) optical beams separable in Cartesian coordinates^[264]; (c) rotationally symmetric beams^[266]; (d) intensity distributions of the test beams with different degrees of coherence (first row), the Wigner distribution function of the beams exhibits hidden differences associated with their coherence state (second row)^[267]

Fig. 49. Schematic diagram of phase retrieval and factor M² calculation^[268]. (a)(b) Axial intensity images at two different longitudinal positions; (c) phase retrieval by TIE; (d) reconstructed intensity distribution at any selected plane; (e) performing a hyperbolic fit to the beam widths and calculating the M²

Fig. 50. Under different numerical apertures, the phase is recovered directly through the gravity of the light field^[128]. (a) 0.05; (b) 0.15; (c) 0.2; (d) 0.25

Fig. 51. Reconstructed phases with and without mode decomposition method under partially coherent illumination^[269]

Fig. 52. Stack imaging based on coherent mode decomposition. (a) Decoherence in scattering imaging^[270];(b) experimental scheme of Fourier stack imaging with single-mode and multi-mode multiplexing^[271]

Fig. 53. Synthetic aperture technique based on FINCH. (a)--(c) Three phase functions loaded on SLM; (d) single aperture reconstruction result; (e) synthetic multi aperture reconstruction result^[243]; (f) image obtained by the conventional imaging system; (g) reconstructed image corresponding to the hologram produced by the 360×360 FINCH system; (h) reconstructed image corresponding to the hologram produced by synthetic aperture of double lens FINCH; (i) reconstructed image corresponding to the hologram produced by the 1080×1080 FINCH system^[275]

Fig. 54. Experimental results of SPIDER imaging^[277]. (a) PIC image experimental platform; (b) iterative image reconstruction result of Fig.54(g); (c)(g) two images of the target; (d)(h) corresponding principle simulation results of target image; (e)(i) imaging results obtained by inverse Fourier transform reconstruction; (f)(j) after correcting the swing error of the turntable, the imaging results are reconstructed by inverse Fourier transform

Fig. 55. Lensless noninterference coded aperture dependent holography^[116]. (a) Two LEDs; (b) two one-dime coins

Fig. 56. Incoherent lensless imaging based on Fresnel region aperture. (a) Real time image capture and reconstruction of lens less camera^[279]; (b) binary, gray, and color images are reconstructed by Fresnel region aperture single frame lensless camera^[282]