Fig. 1. Schematic of basic optical path of Ptychography

Fig. 2. Flow chart of primary iteration for single-layer Ptychography

Fig. 3. Amplitude and phase distributions of specimen reconstructed by ePIE. (a) Amplitude; (b) phase

Fig. 4. Flow chart of multi-mode Ptychography algorithm

Fig. 5. Reconstructed results of wavefront. (a)-(c) Experimental results with partially coherent X-rays^[13]. (a) is result reconstructed by single-mode Ptychography and (b)(c) are distributions of specimen and lighting probes reconstructed by 12-mode Ptychography, respectively ^[43]; (d) left-bottom inset is reconstructed results of multi-mode color imaging and top-right inset is imaging result under white

Fig. 6. Influence of translation error on reconstructed results. (a)(b) Reconstructed amplitude and phase of specimen and lighting probe with scanning errors; (c)(d) reconstructed amplitude and phase of specimen and lighting probe with accurate positions

Fig. 7. Principle of correlation matching algorithm. (a) Reconstructed amplitude of object at first position; (b) reconstructed amplitudes of object at two positions

Fig. 8. Experimental results^[14]. (a) Resolution plate reconstructed without position correction; (b) reconstructed result of correlation matching algorithm with position correction

Fig. 9. Basic schematic of annealing algorithm

Fig. 10. Imaging results of gold/graphite particles under electron beam microscopy^[15]. (a) Reconstructed result before position corrections; (b) reconstructed result after position corrections by annealing algorithm

Fig. 11. Influence of distance errors. (a) Schematic of actual optical path; (b) equivalent optical path for distance measurement with error

Fig. 12. Simulation results^[51] (unit of scale bar is 100 pixel). (a) Real distribution of specimen; (b) reconstructed result when distance is reduced by half; (c) reconstructed result after lighting probe multiplies lens factor when distance is reduced by half

Fig. 13. Schematic of super resolution. (a) Light spot recorded by facular detector with limited numerical aperture; (b) schematic of amplitude updating algorithm

Fig. 14. Experimental results of super resolution^[17]. (a)(b) Amplitude and phase distributions of pollens reconstructed by standard PIE; (c)(d) amplitude and phase distributions of pollens reconstructed by SR-PIE

Fig. 15. Results of reconstruction experiments when light spots are partially saturated^[54]. (a)-(d) Light spots with increasing saturated area from 0; (e)-(h) resolution-plate distributions reconstructed by corresponding saturated light spots in Figs. 15(a)-(d)

Fig. 16. Schematic of amplitude updating algorithm for under-sampling

Fig. 17. Experimental results. (a)-(d) Under-sampled diffraction spots and corresponding reconstructed results; (e)-(h) diffraction spots after linear interpolation for spot in Fig. 17(a) and corresponding reconstructed results; (i)-(l) diffraction spot, lighting probe, and resolution plate reconstructed by under-sampled Ptychography algorithm

Fig. 18. Experimental results with X-rays. (a)-(d) Normal sampling; (c)-(h) sampling rate decreased to 1/8; (i)-(l) sampling rate decreased to 1/16

Fig. 19. Schematic of basic optical path of 3PIE

Fig. 20. Experimental results of 3PIE stratified imaging^[16]. (a)(d) Images of different focusing slices recorded by microscope; (b)(c) amplitude reconstructed by 3PIE; (e)(f) phase reconstructed by 3PIE

Fig. 21. Basic principal of standard Ptychography. (a) Traditional position-by-position scanning mode; (b) continuous recording mode; (c) decomposition of continuous recording process into multiple independent modes

Fig. 22. Experimental results of Fly-PIE^[59]. (a)-(d) Diffraction spots recorded by continuous exposure when specimen is translated with different speeds; (e) reconstructed results with single and multiple modes; (f) reconstructed lighting probes with multiple modes

Fig. 23. Schematic of single-exposure Ptychography based on grating splitting

Fig. 24. Experimental results reconstructed by Ptychography based on grating splitting ^[19]. (a) Light spots; (b) reconstructed amplitude of specimen; (c) reconstructed phase of specimen

Fig. 25. Schematic of single-exposure Ptychography based on 4f system

Fig. 26. Experimental results with single-exposure Ptychography based on 4f system^[20]. (a) (b) Reconstructed amplitude and phase of specimen; (c) reconstructed lighting probe; (d) direct-imaging result