Fig. 1. Schematic diagram of light field coherence structure engineering and applications

Fig. 2. Generation of partially coherent beams with prescribed coherence structure (a) from incoherent to partially coherent beams^[41]; (b) Coherence-modal representation (CMR), pseudo-modal representation (PMR), random-modal representation (RMR)^[76]

Fig. 3. Experimental setup for generating of partially coherent beams. (a) Experimental realization of partially coherent beams via dynamic scattering medium (rotating ground-glass disk)^[44]; (b)~(d) Experimental realization of partially coherent beams via mode superposition by using Monte Carlo^[89], and spatial light modulator (SLM) ^[90], digital micro-mirror device (DMD) ^[57]

Fig. 4. Measurement of spatial coherence structure of partially coherent beams. (a) Via Young’s interferometry with two holes^[27]; (b) Via intensity-intensity correlation^[91]; (c) Via generalized Hanbury Brown-Twiss experiment^[93]; (d) Via self-referencing holography^[96]

Fig. 5. Applications of novel coherence structures engineering of light field in beam shaping. (a) Self-splitting of a focused Hermite Gaussian correlated beam^[59]; (b) Optical cage formation with a focused Laguerre Gaussian correlated^[47]; (c) Radially polarized beam array generation^[101]; (d) Self-reconstruction of the partially coherent beams^[63] ; (e) Self-steering of a phase-engineering of the partially coherent beams^[71]; (f) Self-focusing and Self-steering of the non-uniform partially coherent beams^[50-51]

Fig. 6. Applications of novel coherence structures engineering of light field in turbulence. (a) Schematic for the propagation of light beams through turbulence atmosphere^[102]; (b) Scintillation index of multi Gaussian Schell-model beams propagation in turbulence^[105]; (c) The evolution of the intensity of the Radially polarization Gaussian Schell model (GSM) (RPPC) beam in turbulence, and the radially polarized Hermite non-uniformly correlated (RPHNUC) beams upon propagation in turbulence with different mode orders m = 0 and m = 1^[90]; (d) The on-axis scintillation of the GSM beams, PCB with vortex phase and partially coherent radially polarization (PCRP) with and without vortex phase for different transverse coherence width^[107]

Fig. 7. Applications of novel coherence structures engineering of light field in overcoming the classical Rayleigh diffraction limit. (a) Schematic diagram of the telecentric imaging system^[113]; (b) Results of the imaging of the target under the partially coherent beams with prescribed coherence structure^[113]; (c) Experimental setup for the orientation-selective sub-Rayleigh imaging with the spatial coherence lattice^[115]; (d) Experimental sub-Rayleigh imaging results of the target image under the illumination of the partially coherent beam with three kinds of spatial coherence lattice^[115]

Fig. 8. Applications of novel coherence structures engineering of light field in complex optical imaging. (a) Robust optical imaging with the special correlated partially coherent beams^[116]; (b) Moving targets tracking through scattering media via the complex spatial coherence structure^[93]; (c) The imaging of the phase object with the complex spatial coherence structure by self-reference holography^[117]; (d) The microscopic phase imaging^[118]

Fig. 9. Applications of novel coherence structures engineering of light field in optical encryption. (a) Schematic diagram of the optical encryption and decryption through the manipulation of the spatial coherence structure; (b) Results of the decryption of the original encryption image from the measured cross-spectral density function with correct decryption key; (c) The robustness of the optical imaging encryption and decryption in turbulence via the measurement of the spatial coherence structure^[128]

Fig. 10. Applications of novel coherence structures engineering of light field in the robust far-field information transmission. (a) A schematic of the principle for far-field optical image transmission with a structured random light beam^[133]; (b) Experimental setup for robust far-field imaging in free space as well as in turbulent atmosphere^[132]; (c) Results of the reconstructed image in turbulence with different strength^[132]; (d) Results for the modulus of the spatial degree of coherence in the focal plane and the corresponding results for the recovered image with the presence of the obstacle in the transmission link^[133]

Fig. 11. Applications of novel coherence structures engineering in vector light field. (a) Shaping of the far-field intensity and state of polarization^[83]; (b) Generation of the far-field arbitrary array beams^[148]; (c) An optical cage is derived around the focal region^[148]; (d) Shaping of longitudinal spectral density in the tight focusing system^[149]; (e) Recovery of the polarization state of the field hidden behind a scattering media^[94]