Fig. 1. Schemes for transport of intensity equation phase imaging^[9].(a) 4f system-based system; (b) lens-less system

Fig. 2. Reconstructed phases with transport of intensity equation method under illumination with different degrees of coherence (the larger the numerical aperture, the lower the spatial coherence of the illumination)^[26]. (a) NA=0.05; (b) NA=0.15; (c) NA=0.2; (d) NA=0.25

Fig. 3. Scheme for coherent diffraction imaging^[1]

Fig. 4. Reconstructed phases with and without mode decomposition methods under partially coherent illumination^[36]

Fig. 5. Optical setup of digital holographic microscope with partially coherent illumination^[17]

Fig. 6. Reconstructed phases with digital holographic microscopy in refocused cases (the left column is high-coherent illumination, the right column is low-coherent illumination, and the refocusing distance gradually increases from top to bottom)^[17]

Fig. 7. Scheme for self-referencing holography phase imaging^[48]

Fig. 8. Three terms in the inverse Fourier transform of the diffraction pattern versus the location of the perturbation point r048

Fig. 9. Reconstructed phases obtained by self-reference holography under partially coherent illumination, herein, (c1) and (c2) corresponds to Fig. 8(c); (b1) and (b2) corresponds to Fig. 8(b); (a1) and (a2) corresponds to Fig. 8(a)

Fig. 10. Reconstructed phases obtained by self-reference holography under specially partially coherent illumination. (a1)(a3)(b1)(b3) Amplitude and phase distribution of the direct reconstruction; (a2)(a4)(b2)(b4) amplitude and phase distribution of the illumination; (a5)(b5) actual phase distribution of the object obtained by the phase of the direct reconstruction divided by the illumination

Fig. 11. Schematic of phase reconstruction with pinhole array mask^[49]. (a) Experimental setup; (b) PAM consists of a reference pinhole at the origin (gray square) and a periodic array of the measurement pinholes with certain offset (white squares);(c) in the inverse Fourier transform of the diffraction pattern, the autocorrelation terms (gray squares) and the two interference terms (red and blue squares) are separated by the offset

Fig. 12. Reconstructed phases of different perturbation points and the final complete field of view under illumination with low degree of spatial coherence^[49]. (a-f) Reconstructed phases; (g) final complete filed of view

Fig. 13. Star-shaped mask for non-iterative focus variation phase reconstruction method^[50]

Fig. 14. Correct and complete phase reconstructions obtained with focus variation method under illumination with low degree of coherence^[50] (the first and second rows are the amplitude and phase reconstructions, respectively. The difference in each column is the selection of P, which corresponds to the four vertices of the star mask. The third row is the synthesized amplitude and phase distribution of the object, and the phase and amplitude distri

Fig. 15. Intensity and phase patterns of vortex beams with different topological charges at different distances (z)^[51]

Fig. 16. Experimental results of complex degree of coherence for partially coherent elegant Laguerre-Gaussian beam with different topological charges^[53](row 1: experimental results; row 2: simulation results)

Fig. 17. Modulus of degree of coherence of Hermite-Gaussian correlated Schell-model LG_0l beam before the focal plane^[54]

Fig. 18. Experimental setup for measuring the degree of coherence of partially coherent vortex beams at the focal plane^[55]. (a) Light path detail at BS2; (b) an example for the design of aperture and perturbation function

Fig. 19. Theoretical simulations and experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for the focused partially coherent vortex beams^[55]

Fig. 20. Experimental results of amplitude and phase distributions of spectral degree of coherence with an off-axis reference point for focused partially coherent vortex beams^[56]