Fig. 1. System setup and principle of FPM.（a）System setup of FPM^［15］；（b）System configuration of FPM^［16］；（c~e）Imaging principle of FPM.

Fig. 2. Reconstruction flow chart of FPM^［15］

Fig. 3. Pose misalignment of LED array^［54］

Fig. 4. Effects of pose misalignments on the quality of reconstructed images^［54］.（a1~a2）Intensity and phase images of sample；（b1~b2）Reconstructed intensity and phase images when the lateral shift Δx equals to 700 μm；（c1~c2）Reconstructed intensity and phase images when the rotation angle along z-axis equals to 10°；（d1~d2）Reconstructed intensity and phase images when the tilt angle along y-axis equals to 10°；（e1~e3），（f1~f3）Curves of the pixel number difference between all ideal and true sub-spectra，RMSE between reconstructed and true intensity images of sample，RMSE between reconstructed and true phase images of sample，versus as the lateral shift Δx，rotation angle θz，and tilt angle θy.

Fig. 5. Principle of pose calibration with precision mechanical stages^［28］.（a）System configuration；（b）Calibration of the rotation and tilt misalignments；（c）Calibration of the lateral shift misalignments.

Fig. 6. Improved mechanical calibration method^［27］.（a）System configuration.（b1~b1）Calibration of the rotation misalignment；（c1~c4）Calibration of the lateral misalignments；（d）Intensity images of the aperture stop that imply the centrosymmetric characteristic of the optical system.

Fig. 7. Calibration results of SA-based search algorithms.（a）Conventional SA algorithm^［29］；（b）pcFPM method^［30］.

Fig. 8. Principle of brightfield spectral localization method^［39］.（a）Illuminating a sample with an oblique angle а；（b）Spectra of brightfield and darkfield images；（c）Pre-processing and global pose correction.

Fig. 9. Machine learning method for calibrating pose misalignment of the LED array in FPM

Fig. 10. Principle of defocusing calibration method^［53］.（a）Intensity image of sample；（b）Focused image used as reference；（c~d）Defocused images with the shift related to illumination wavevectors；（e）Shifts of the brightfield defocused images.

Fig. 11. Principle of exist pupil calibration method^［54］.（a1）Normal illumination；（a2）Oblique illumination；（b1）Captured image with normal illumination；（b2）Captured image with oblique illumination；（c）Relationship between the position of exist pupil and LED unit.

Fig. 12. Performance of exist pupil calibration method^［54］.（a）Reconstructed intensity image without pose misalignment；（b1~b3）Reconstructed intensity images with conventional FPM method under different pose misalignments；（c1~c3）Reconstructed intensity images with SC-FPM method under different pose misalignments；（d1~d3）Reconstructed intensity images with exist pupil correction method under different pose misalignments.